#if defined(__unix__) && !defined(__FreeBSD__)
#define _POSIX_C_SOURCE 200809L /* required for mkdtemp */
#endif

#ifdef _MSC_VER
#define NO_THREADS 1
#define GR_INLINE
#else
#define GR_INLINE __inline__
#endif

#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#include <math.h>
#include <float.h>
#ifdef _MSC_VER
#include <BaseTsd.h>
typedef __int64 int64_t;
typedef SSIZE_T ssize_t;
#else
#include <stdint.h>
#endif
#include <signal.h>

#if !defined(VMS) && !defined(_WIN32)
#include <unistd.h>
#endif

#ifndef NO_THREADS
#include <pthread.h>
#endif

#ifdef _WIN32
#include <windows.h>
#include <wchar.h>
#define TMPDIR "C:\\Users\\%USERNAME%\\AppData\\Local\\Temp"
#define DIRDELIM "\\"
#define WIN32_LEAN_AND_MEAN 1
#else
#define TMPDIR "/tmp"
#define DIRDELIM "/"
#endif

#ifdef isnan
#define is_nan(a) isnan(a)
#else
#define is_nan(x) ((x) != (x))
#endif

#ifndef NAN
#define NAN (0.0 / 0.0)
#endif

#ifndef sign
#define sign(a) (((a) > (0) || (a) < (0)) ? ((a) / fabs(a)) : (0))
#endif

#include "gks.h"
#include "gkscore.h"
#include "gr.h"
#include "gr_version.h"
#include "text.h"
#include "spline.h"
#include "gridit.h"
#include "contour.h"
#include "contourf.h"
#include "strlib.h"
#include "stream.h"
#include "md5.h"
#include "cm.h"
#include "boundary.h"
#include "threadpool.h"

#ifndef R_OK
#define R_OK 4
#endif

#define GR_UNUSED(param) (void)param

#ifndef M_PI
#define M_PI (3.141592653589793)
#endif

#define RAYCASTING_CEIL(x) ((x > 0) ? round(x + 0.50000001) : (floor(x + 1.00000001)))
#define RAYCASTING_FLOOR(x) (round(x - 0.50000001))

typedef struct
{
  int index;
  double red, green, blue;
} color_t;

typedef struct
{
  double xmin, xmax, ymin, ymax;
} rect_t;

typedef struct
{
  double a, b, c, d;
} norm_xform;

typedef struct
{
  int scale_options;
  double xmin, xmax, ymin, ymax, zmin, zmax, a, b, c, d, e, f;
  double basex, basey, basez;
  char *basex_s, *basey_s, *basez_s;
} linear_xform;

typedef struct
{
  double zmin, zmax;
  int phi, delta;
  double a1, a2, b, c1, c2, c3, d;
} world_xform;

typedef struct
{
  double camera_pos_x, camera_pos_y, camera_pos_z;
  double up_x, up_y, up_z;
  double focus_point_x, focus_point_y, focus_point_z;
  double s_x, s_y, s_z;
  double x_axis_scale, y_axis_scale, z_axis_scale;
  int use_setspace3d;
  double setspace3d_phi, setspace3d_theta, setspace3d_fov, setspace3d_cam;
} transformation_xform;

typedef struct
{
  double left, right, bottom, top;
  double near_plane, far_plane, fov; /* only used for perspectiv */
  int projection_type;
} projection_xform;

typedef struct
{
  double xmin, xmax, ymin, ymax, zmin, zmax;
} interaction_xform;

typedef struct
{
  double x, y, z;
} point_3d;

typedef struct
{
  int sign;
  double x0, x1, y0, y1, z0, z1;
  double xmin, xmax;
  int initialize;
  double *buf, *ymin, *ymax;
} hlr_t;

typedef struct
{
  int ltype;
  double lwidth;
  int plcoli;
  int mtype;
  double mszsc;
  int pmcoli;
  int txfont, txprec;
  double chxp;
  double chsp;
  int txcoli;
  double chh;
  double chup[2];
  int txp;
  int txal[2];
  int ints;
  int styli;
  int facoli;
  int tnr;
  double wn[4], vp[4];
  int scale_options;
  double bwidth;
  int bcoli;
  int clip_tnr;
  int resize_behaviour;
  int clip_region;
  double alpha;
  double txoff[2];
} state_list;

typedef struct
{
  state_list **buf;
  size_t capacity;
  ssize_t max_non_null_id;
} state_list_vector;

typedef struct
{
  int a, b, c;
  double sp;
} triangle_with_distance;

struct ray_casting_attr
{
  int nx, ny, nz;
  int algorithm;
  double *data, *dmin_ptr, *dmax_ptr;
  double *min_val, *max_val, *pixels;
};

struct thread_attr
{
  int x_start, y_start, x_end, y_end;
};

typedef struct
{
  int border, max_threads;
  double thread_size;
  int picture_width, picture_height;
  struct ray_casting_attr *ray_casting;
  int approximative_calculation;
} volume_t;

typedef struct
{
  char *name;
  char *candidate[3];
} font_alias_t;

typedef struct text_node
{
  struct text_node *next;
  double x, y;
  char *string;
  int line_number;
  double line_width;
  int math;
  double width, height;
  double baseline[2];
} text_node_t;

typedef struct
{
  int px_width, px_height;
  const data_point3d_t *start, *end;
  kernel_f callback;
  const void **extra_data;
  double radius;
  radius_f radius_callback;
  double *pixels;
  const point3d_t *ray_dir_init;
  const point3d_t *ray_dir_x;
  const point3d_t *ray_dir_y;
  const point3d_t *ray_from_init;
  const point3d_t *ray_from_x;
  const point3d_t *ray_from_y;
  double x_factor, y_factor;
} volume_nogrid_data_struct;

struct cpubasedvolume_2pass_priv
{
  double *pixels;
};

struct hexbin_2pass_priv
{
  int *cell;
  int *cnt;
  double *xcm;
  double *ycm;
};

typedef struct
{
  double min, max;
} minmax_t;

gauss_t interp_gauss_data = {1, {1, 0, 0}, {0, 1, 0}, {0, 0, 1}};
tri_linear_t interp_tri_linear_data = {1, 1, 1};

static volume_t vt = {1, 0, 1.25, 1000, 1000, NULL, 1};

static norm_xform nx = {1, 0, 1, 0};

static linear_xform lx = {0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 10, 10, 10, "10", "10", "10"};

static world_xform wx = {0, 1, 60, 60, 0, 0, 0, 0, 0, 0, 0};

static transformation_xform tx = {0, 2, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0};

static projection_xform gpx = {-1, 1, -1, 1, 1, 0, 45, GR_PROJECTION_DEFAULT};

static interaction_xform ix = {-1, 1, -1, 1, -1, 1};

static hlr_t hlr = {1, 0, 1, 0, 1, 0, 1, 0, 1, 1, NULL, NULL, NULL};

static int predef_colors[20] = {9, 2, 0, 1, 16, 3, 15, 8, 6, 10, 11, 4, 12, 13, 14, 7, 5, 17, 18, 19};

#define MAX_SAVESTATE 16

static state_list_vector *app_context = NULL;

static state_list *ctx = NULL, *state = NULL;

static double txoff[2] = {0, 0};

#define CONTEXT_VECTOR_INCREMENT 8

static void (*previous_handler)(int);

static int autoinit = 1, double_buf = 0, state_saved = 0, def_color = 0;

static double scale_factor = 1.0;

static const char *display = NULL;

static const char *debug = NULL;

static double vxmin = 0.2, vxmax = 0.9, vymin = 0.2, vymax = 0.9;

static double cxl, cxr, cyf, cyb, czb, czt;

static int arrow_style = 0;

static double arrow_size = 1;

static int flag_printing = 0, flag_stream = 0, flag_graphics = 0;

static text_node_t *text, *head;

static int scientific_format = SCIENTIFIC_FORMAT_OPTION_E;

#define DEFAULT_FIRST_COLOR 8
#define DEFAULT_LAST_COLOR 79

static int first_color = DEFAULT_FIRST_COLOR, last_color = DEFAULT_LAST_COLOR;

#define MAX_COLOR 1256

static unsigned int rgb[MAX_COLOR], used[MAX_COLOR];

#define MAX_TICKS 500

#define check_autoinit \
  if (autoinit) initgks()

#define check_tick_marks(amin, amax, atick, axis)             \
  do                                                          \
    if ((amax - amin) / atick > MAX_TICKS)                    \
      {                                                       \
        atick = gr_tick(amin, amax);                          \
        fprintf(stderr, "auto-adjust %c tick marks\n", axis); \
      }                                                       \
  while (0)

#define nint(x) (int)((x) + 0.5)
#define round(x) (x < 0 ? ceil(x - .5) : floor(x + .5))
#define iround(x) ((int)round(x))
#define gauss(x) floor(x)
#define igauss(x) ((int)gauss(x))
#define trunc(x) (((x) > 0) ? floor(x) : ceil(x))

#define NDC 0
#define WC 1
#define MODERN_NDC 2

#define POINT_INC 2048

#define RESOLUTION_X 4096
#define BACKGROUND 0

#ifndef FLT_MAX
#define FLT_MAX 1.701411735e+38
#endif

#ifndef M_PI
#define M_PI 3.14159265358979323846
#endif

#define LEFT (1 << 0)
#define RIGHT (1 << 1)
#define FRONT (1 << 2)
#define BACK (1 << 3)
#define BOTTOM (1 << 4)
#define TOP (1 << 5)

#define XML_HEADER "<?xml version=\"1.0\" encoding=\"ISO-8859-1\"?>\n"
#define GR_HEADER "<gr>\n"
#define GR_TRAILER "</gr>\n"

typedef struct
{
  char *format;
  double width, height;
} format_t;

#ifndef max
#define max(a, b) ((a) > (b) ? (a) : (b))
#endif

#ifndef min
#define min(a, b) ((a) < (b) ? (a) : (b))
#endif

#define arc(angle) (M_PI * (angle) / 180.0)
#define deg(rad) ((rad)*180.0 / M_PI)

static unsigned char *opcode = NULL;

static double *xpath = NULL, *xpoint = NULL, *ypath = NULL, *ypoint = NULL, *zpoint = NULL;

static int npoints = 0, maxpath = 0, npath = 0;

static int *code = NULL;

/*  0 - 20    21 - 45    46 - 70    71 - 90           rot/  */
static int rep_table[16][3] = {
    /*   tilt  */
    {2, 2, 2}, {2, 2, 2}, {1, 3, 2}, {1, 3, 3}, /*  0 - 20 */
    {2, 0, 0}, {2, 0, 0}, {1, 3, 2}, {1, 3, 1}, /* 21 - 45 */
    {2, 0, 0}, {0, 0, 0}, {1, 3, 0}, {1, 3, 1}, /* 46 - 70 */
    {0, 0, 0}, {0, 0, 0}, {1, 3, 0}, {1, 3, 1}  /* 71 - 90 */
};

static int axes_rep[4][3] = {{1, 1, 1}, {1, 1, 2}, {0, 0, 0}, {0, 0, 3}};

static int angle[4] = {20, 45, 70, 90};

static format_t formats[] = {
    {"A4", 0.210, 0.297},        {"B5", 0.176, 0.250},      {"Letter", 0.216, 0.279}, {"Legal", 0.216, 0.356},
    {"Executive", 0.191, 0.254}, {"A0", 0.841, 1.189},      {"A1", 0.594, 0.841},     {"A2", 0.420, 0.594},
    {"A3", 0.297, 0.420},        {"A5", 0.148, 0.210},      {"A6", 0.105, 0.148},     {"A7", 0.074, 0.105},
    {"A8", 0.052, 0.074},        {"A9", 0.037, 0.052},      {"B0", 1.000, 1.414},     {"B1", 0.500, 0.707},
    {"B10", 0.031, 0.044},       {"B2", 0.500, 0.707},      {"B3", 0.353, 0.500},     {"B4", 0.250, 0.353},
    {"B6", 0.125, 0.176},        {"B7", 0.088, 0.125},      {"B8", 0.062, 0.088},     {"B9", 0.044, 0.062},
    {"C5E", 0.163, 0.229},       {"Comm10E", 0.105, 0.241}, {"DLE", 0.110, 0.220},    {"Folio", 0.210, 0.330},
    {"Ledger", 0.432, 0.279},    {"Tabloid", 0.279, 0.432}, {NULL, 0.000, 0.000}};

static int vertex_list[18][25] = {
    {3, -10, 80, 0, 100, 10, 80, 2, 0, 100, 0, -100, 0},
    {3, -7, 80, 0, 100, 7, 80, 2, 0, 100, 0, -100, 0},
    {6, 0, 85, -10, 80, 0, 100, 10, 80, 0, 85, 0, -100, 0},
    {-4, 0, 85, -10, 80, 0, 100, 10, 80, 2, 0, 85, 0, -100, 0},
    {6, 0, 80, -10, 80, 0, 100, 10, 80, 0, 80, 0, -100, 0},
    {-4, 0, 80, -10, 80, 0, 100, 10, 80, 2, 0, 80, 0, -100, 0},
    {6, 0, 75, -10, 80, 0, 100, 10, 80, 0, 75, 0, -100, 0},
    {-4, 0, 75, -10, 80, 0, 100, 10, 80, 2, 0, 75, 0, -100, 0},
    {3, -10, 80, 0, 100, 10, 80, 2, 0, 100, 0, -100, 3, -10, -80, 0, -100, 10, -80, 0},
    {3, -7, 80, 0, 100, 7, 80, 2, 0, 100, 0, -100, 3, -7, -80, 0, -100, 7, -80, 0},
    {10, 0, 85, -10, 80, 0, 100, 10, 80, 0, 85, 0, -85, -10, -80, 0, -100, 10, -80, 0, -85, 0},
    {-4, 0, 85, -10, 80, 0, 100, 10, 80, 2, 0, 85, 0, -85, -4, -10, -80, 0, -100, 10, -80, 0, -85, 0},
    {10, 0, 80, -10, 80, 0, 100, 10, 80, 0, 80, 0, -80, -10, -80, 0, -100, 10, -80, 0, -80, 0},
    {-4, 0, 80, -10, 80, 0, 100, 10, 80, 2, 0, 80, 0, -80, -4, -10, -80, 0, -100, 10, -80, 0, -80, 0},
    {10, 0, 75, -10, 80, 0, 100, 10, 80, 0, 75, 0, -75, -10, -80, 0, -100, 10, -80, 0, -75, 0},
    {-4, 0, 75, -10, 80, 0, 100, 10, 80, 2, 0, 75, 0, -75, -4, -10, -80, 0, -100, 10, -80, 0, -75, 0},
    {3, -10, 80, 0, 100, 10, 80, 2, -1, 98, -1, -100, 2, 1, 98, 1, -100, 0},
    {3, -10, 80, 0, 100, 10, 80, 2, -1, 98, -1, -98, 3, -10, -80, 0, -100, 10, -80, 2, 1, 98, 1, -98, 0}};

static int colormap = 0;

static int cmap[48][72] = {
    {/* COLORMAP_UNIFORM */
     0x2020df, 0x3020df, 0x4020df, 0x5020df, 0x6020df, 0x7120df, 0x8020df, 0x9120df, 0xa120df, 0xb120df, 0xc120df,
     0xd120df, 0xdf20de, 0xdf20cd, 0xdf20bd, 0xdf20ad, 0xdf209d, 0xdf208d, 0xdf207d, 0xdf206d, 0xdf205d, 0xdf204c,
     0xdf203c, 0xdf202c, 0xdf2420, 0xdf3420, 0xdf4420, 0xdf5420, 0xdf6420, 0xdf7520, 0xdf8420, 0xdf9420, 0xdfa520,
     0xdfb520, 0xdfc520, 0xdfd520, 0xd9df20, 0xc9df20, 0xb9df20, 0xa9df20, 0x99df20, 0x89df20, 0x79df20, 0x69df20,
     0x59df20, 0x49df20, 0x38df20, 0x28df20, 0x20df28, 0x20df38, 0x20df48, 0x20df58, 0x20df68, 0x20df78, 0x20df88,
     0x20df98, 0x20dfa9, 0x20dfb9, 0x20dfc9, 0x20dfd9, 0x20d6df, 0x20c6df, 0x20b5df, 0x20a5df, 0x2095df, 0x2085df,
     0x2075df, 0x2065df, 0x2055df, 0x2045df, 0x2034df, 0x2024df},

    {/* COLORMAP_TEMPERATURE */
     0x000080, 0x000090, 0x0000a0, 0x0000b1, 0x0000c1, 0x0000d1, 0x0000e1, 0x0000f2, 0x0000ff, 0x0002ff, 0x0011ff,
     0x001fff, 0x002dff, 0x003cff, 0x004aff, 0x0058ff, 0x0066ff, 0x0074ff, 0x0084ff, 0x0092ff, 0x00a0ff, 0x00afff,
     0x00bdff, 0x00cbff, 0x00daff, 0x01e7f5, 0x0df7ea, 0x19ffde, 0x25ffd2, 0x31ffc7, 0x3bffbb, 0x47ffb0, 0x53ffa4,
     0x5fff98, 0x6aff8d, 0x76ff81, 0x81ff76, 0x8dff6a, 0x98ff5f, 0xa4ff53, 0xb0ff47, 0xbbff3b, 0xc7ff31, 0xd2ff25,
     0xdeff19, 0xeaff0d, 0xf5f701, 0xffeb00, 0xffdd00, 0xffd000, 0xffc200, 0xffb500, 0xffa800, 0xff9b00, 0xff8d00,
     0xff8000, 0xff7200, 0xff6500, 0xff5800, 0xff4a00, 0xff3d00, 0xff3000, 0xff2300, 0xff1500, 0xf20800, 0xe20000,
     0xd10000, 0xc10000, 0xb10000, 0xa00000, 0x900000, 0x800000},

    {/* COLORMAP_GRAYSCALE */
     0x000000, 0x040404, 0x070707, 0x0b0b0b, 0x0e0e0e, 0x121212, 0x161616, 0x191919, 0x1d1d1d, 0x202020, 0x242424,
     0x282828, 0x2b2b2b, 0x2f2f2f, 0x323232, 0x363636, 0x393939, 0x3d3d3d, 0x414141, 0x444444, 0x484848, 0x4b4b4b,
     0x4f4f4f, 0x535353, 0x565656, 0x5a5a5a, 0x5d5d5d, 0x616161, 0x656565, 0x686868, 0x6c6c6c, 0x6f6f6f, 0x737373,
     0x777777, 0x7a7a7a, 0x7e7e7e, 0x808080, 0x848484, 0x878787, 0x8b8b8b, 0x8f8f8f, 0x929292, 0x969696, 0x999999,
     0x9d9d9d, 0xa1a1a1, 0xa4a4a4, 0xa8a8a8, 0xababab, 0xafafaf, 0xb3b3b3, 0xb6b6b6, 0xbababa, 0xbdbdbd, 0xc1c1c1,
     0xc5c5c5, 0xc8c8c8, 0xcccccc, 0xcfcfcf, 0xd3d3d3, 0xd6d6d6, 0xdadada, 0xdedede, 0xe1e1e1, 0xe5e5e5, 0xe8e8e8,
     0xececec, 0xf0f0f0, 0xf3f3f3, 0xf7f7f7, 0xfafafa, 0xfefefe},

    {/* COLORMAP_GLOWING */
     0x000000, 0x580400, 0x690700, 0x730b00, 0x7c0e00, 0x831200, 0x891600, 0x8f1900, 0x941d00, 0x982000, 0x9c2400,
     0xa02800, 0xa32b00, 0xa72f00, 0xaa3200, 0xad3601, 0xaf3901, 0xb23d01, 0xb54101, 0xb74401, 0xba4802, 0xbc4b02,
     0xbe4f02, 0xc05303, 0xc25603, 0xc45a04, 0xc65d04, 0xc86105, 0xca6506, 0xcc6807, 0xce6c08, 0xcf6f09, 0xd1730a,
     0xd2770c, 0xd47a0d, 0xd67e0f, 0xd78010, 0xd88413, 0xda8714, 0xdb8b17, 0xdd8f1a, 0xde921c, 0xdf961f, 0xe19921,
     0xe29d25, 0xe3a129, 0xe4a42c, 0xe6a830, 0xe7ab34, 0xe8af39, 0xeab33d, 0xeab643, 0xecba49, 0xedbd4e, 0xeec154,
     0xefc55a, 0xf0c861, 0xf1cc68, 0xf2cf70, 0xf3d378, 0xf4d680, 0xf5da89, 0xf6de92, 0xf7e19c, 0xf8e5a6, 0xf9e8b0,
     0xfaecbb, 0xfbf0c7, 0xfcf3d3, 0xfdf7e0, 0xfefaed, 0xfffefb},

    {/* COLORMAP_RAINBOWLIKE */
     0x800000, 0x8d0000, 0x9c0000, 0xaa0000, 0xb80000, 0xc70000, 0xd50000, 0xe40000, 0xf20000, 0xff0100, 0xff1000,
     0xff1e00, 0xff2c00, 0xff3b00, 0xff4900, 0xff5700, 0xff6600, 0xff7400, 0xff8200, 0xff9000, 0xff9e00, 0xffad00,
     0xffbb00, 0xffc900, 0xffd800, 0xffe600, 0xfff500, 0xfbff04, 0xedff12, 0xdeff21, 0xd0ff2f, 0xc2ff3d, 0xb3ff4c,
     0xa5ff5a, 0x97ff68, 0x88ff77, 0x7bff84, 0x6cff93, 0x5effa1, 0x50ffaf, 0x41ffbe, 0x33ffcc, 0x25ffda, 0x16ffe9,
     0x08fff7, 0x00f8ff, 0x00eaff, 0x00dcff, 0x00cdff, 0x00bfff, 0x00b1ff, 0x00a2ff, 0x0094ff, 0x0086ff, 0x0078ff,
     0x006aff, 0x005bff, 0x004dff, 0x003fff, 0x0030ff, 0x0022ff, 0x0014ff, 0x0005ff, 0x0000f6, 0x0000e8, 0x0000d9,
     0x0000cb, 0x0000bc, 0x0000ae, 0x0000a0, 0x000091, 0x000083},

    {/* COLORMAP_GEOLOGIC */
     0x5555ff, 0x5158f8, 0x4e5af1, 0x4a5de9, 0x475fe2, 0x4362db, 0x3f65d4, 0x3c68cd, 0x386bc6, 0x356dbe, 0x3170b7,
     0x2d73b0, 0x2a75a9, 0x2678a2, 0x237a9a, 0x1f7d93, 0x1c808c, 0x188385, 0x14867f, 0x118878, 0x0d8b70, 0x0a8d69,
     0x069062, 0x02935b, 0x039556, 0x0d985a, 0x189a5d, 0x239d61, 0x2ea065, 0x38a368, 0x43a66c, 0x4ea86f, 0x59ab73,
     0x64ae77, 0x6eb07a, 0x79b37e, 0x83b580, 0x8eb884, 0x98bb87, 0xa3be8b, 0xaec18f, 0xb9c392, 0xc4c696, 0xcec899,
     0xd9cb9d, 0xe4cea1, 0xefd0a4, 0xf9d3a8, 0xfed2a6, 0xfacd9f, 0xf6c798, 0xf3c291, 0xefbc89, 0xecb782, 0xe8b27c,
     0xe4ac75, 0xe1a76e, 0xdda267, 0xda9c5f, 0xd69758, 0xd39251, 0xcf8c4a, 0xcb8743, 0xc8823b, 0xc47c34, 0xc1772d,
     0xbd7126, 0xb96c1f, 0xb66718, 0xb26110, 0xaf5c09, 0xab5602},

    {/* COLORMAP_GREENSCALE */
     0x000000, 0x045800, 0x076900, 0x0b7300, 0x0e7c00, 0x128300, 0x168900, 0x198f00, 0x1d9400, 0x209800, 0x249c00,
     0x28a000, 0x2ba300, 0x2fa700, 0x32aa00, 0x36ad01, 0x39af01, 0x3db201, 0x41b501, 0x44b701, 0x48ba02, 0x4bbc02,
     0x4fbe02, 0x53c003, 0x56c203, 0x5ac404, 0x5dc604, 0x61c805, 0x65ca06, 0x68cc07, 0x6cce08, 0x6fcf09, 0x73d10a,
     0x77d20c, 0x7ad40d, 0x7ed60f, 0x80d710, 0x84d813, 0x87da14, 0x8bdb17, 0x8fdd1a, 0x92de1c, 0x96df1f, 0x99e121,
     0x9de225, 0xa1e329, 0xa4e42c, 0xa8e630, 0xabe734, 0xafe839, 0xb3ea3d, 0xb6ea43, 0xbaec49, 0xbded4e, 0xc1ee54,
     0xc5ef5a, 0xc8f061, 0xccf168, 0xcff270, 0xd3f378, 0xd6f480, 0xdaf589, 0xdef692, 0xe1f79c, 0xe5f8a6, 0xe8f9b0,
     0xecfabb, 0xf0fbc7, 0xf3fcd3, 0xf7fde0, 0xfafeed, 0xfefffb},

    {/* COLORMAP_CYANSCALE */
     0x000000, 0x005804, 0x006907, 0x00730b, 0x007c0e, 0x008312, 0x008916, 0x008f19, 0x00941d, 0x009820, 0x009c24,
     0x00a028, 0x00a32b, 0x00a72f, 0x00aa32, 0x01ad36, 0x01af39, 0x01b23d, 0x01b541, 0x01b744, 0x02ba48, 0x02bc4b,
     0x02be4f, 0x03c053, 0x03c256, 0x04c45a, 0x04c65d, 0x05c861, 0x06ca65, 0x07cc68, 0x08ce6c, 0x09cf6f, 0x0ad173,
     0x0cd277, 0x0dd47a, 0x0fd67e, 0x10d780, 0x13d884, 0x14da87, 0x17db8b, 0x1add8f, 0x1cde92, 0x1fdf96, 0x21e199,
     0x25e29d, 0x29e3a1, 0x2ce4a4, 0x30e6a8, 0x34e7ab, 0x39e8af, 0x3deab3, 0x43eab6, 0x49ecba, 0x4eedbd, 0x54eec1,
     0x5aefc5, 0x61f0c8, 0x68f1cc, 0x70f2cf, 0x78f3d3, 0x80f4d6, 0x89f5da, 0x92f6de, 0x9cf7e1, 0xa6f8e5, 0xb0f9e8,
     0xbbfaec, 0xc7fbf0, 0xd3fcf3, 0xe0fdf7, 0xedfefa, 0xfbfffe},

    {/* COLORMAP_BLUESCALE */
     0x000000, 0x000458, 0x000769, 0x000b73, 0x000e7c, 0x001283, 0x001689, 0x00198f, 0x001d94, 0x002098, 0x00249c,
     0x0028a0, 0x002ba3, 0x002fa7, 0x0032aa, 0x0136ad, 0x0139af, 0x013db2, 0x0141b5, 0x0144b7, 0x0248ba, 0x024bbc,
     0x024fbe, 0x0353c0, 0x0356c2, 0x045ac4, 0x045dc6, 0x0561c8, 0x0665ca, 0x0768cc, 0x086cce, 0x096fcf, 0x0a73d1,
     0x0c77d2, 0x0d7ad4, 0x0f7ed6, 0x1080d7, 0x1384d8, 0x1487da, 0x178bdb, 0x1a8fdd, 0x1c92de, 0x1f96df, 0x2199e1,
     0x259de2, 0x29a1e3, 0x2ca4e4, 0x30a8e6, 0x34abe7, 0x39afe8, 0x3db3ea, 0x43b6ea, 0x49baec, 0x4ebded, 0x54c1ee,
     0x5ac5ef, 0x61c8f0, 0x68ccf1, 0x70cff2, 0x78d3f3, 0x80d6f4, 0x89daf5, 0x92def6, 0x9ce1f7, 0xa6e5f8, 0xb0e8f9,
     0xbbecfa, 0xc7f0fb, 0xd3f3fc, 0xe0f7fd, 0xedfafe, 0xfbfeff},

    {/* COLORMAP_MAGENTASCALE */
     0x000000, 0x040058, 0x070069, 0x0b0073, 0x0e007c, 0x120083, 0x160089, 0x19008f, 0x1d0094, 0x200098, 0x24009c,
     0x2800a0, 0x2b00a3, 0x2f00a7, 0x3200aa, 0x3601ad, 0x3901af, 0x3d01b2, 0x4101b5, 0x4401b7, 0x4802ba, 0x4b02bc,
     0x4f02be, 0x5303c0, 0x5603c2, 0x5a04c4, 0x5d04c6, 0x6105c8, 0x6506ca, 0x6807cc, 0x6c08ce, 0x6f09cf, 0x730ad1,
     0x770cd2, 0x7a0dd4, 0x7e0fd6, 0x8010d7, 0x8413d8, 0x8714da, 0x8b17db, 0x8f1add, 0x921cde, 0x961fdf, 0x9921e1,
     0x9d25e2, 0xa129e3, 0xa42ce4, 0xa830e6, 0xab34e7, 0xaf39e8, 0xb33dea, 0xb643ea, 0xba49ec, 0xbd4eed, 0xc154ee,
     0xc55aef, 0xc861f0, 0xcc68f1, 0xcf70f2, 0xd378f3, 0xd680f4, 0xda89f5, 0xde92f6, 0xe19cf7, 0xe5a6f8, 0xe8b0f9,
     0xecbbfa, 0xf0c7fb, 0xf3d3fc, 0xf7e0fd, 0xfaedfe, 0xfefbff},

    {/* COLORMAP_REDSCALE */
     0x000000, 0x580004, 0x690007, 0x73000b, 0x7c000e, 0x830012, 0x890016, 0x8f0019, 0x94001d, 0x980020, 0x9c0024,
     0xa00028, 0xa3002b, 0xa7002f, 0xaa0032, 0xad0136, 0xaf0139, 0xb2013d, 0xb50141, 0xb70144, 0xba0248, 0xbc024b,
     0xbe024f, 0xc00353, 0xc20356, 0xc4045a, 0xc6045d, 0xc80561, 0xca0665, 0xcc0768, 0xce086c, 0xcf096f, 0xd10a73,
     0xd20c77, 0xd40d7a, 0xd60f7e, 0xd71080, 0xd81384, 0xda1487, 0xdb178b, 0xdd1a8f, 0xde1c92, 0xdf1f96, 0xe12199,
     0xe2259d, 0xe329a1, 0xe42ca4, 0xe630a8, 0xe734ab, 0xe839af, 0xea3db3, 0xea43b6, 0xec49ba, 0xed4ebd, 0xee54c1,
     0xef5ac5, 0xf061c8, 0xf168cc, 0xf270cf, 0xf378d3, 0xf480d6, 0xf589da, 0xf692de, 0xf79ce1, 0xf8a6e5, 0xf9b0e8,
     0xfabbec, 0xfbc7f0, 0xfcd3f3, 0xfde0f7, 0xfeedfa, 0xfffbfe},

    {/* COLORMAP_FLAME */
     0x80ffff, 0x72ffff, 0x63ffff, 0x55ffff, 0x47ffff, 0x38ffff, 0x2affff, 0x1bffff, 0x0dffff, 0x00feff, 0x00efff,
     0x00e1ff, 0x00d3ff, 0x00c4ff, 0x00b6ff, 0x00a8ff, 0x0099ff, 0x008bff, 0x007dff, 0x006fff, 0x0061ff, 0x0052ff,
     0x0044ff, 0x0036ff, 0x0027ff, 0x0019ff, 0x000aff, 0x0400fb, 0x1200ed, 0x2100de, 0x2f00d0, 0x3d00c2, 0x4c00b3,
     0x5a00a5, 0x680097, 0x770088, 0x84007b, 0x93006c, 0xa1005e, 0xaf0050, 0xbe0041, 0xcc0033, 0xda0025, 0xe90016,
     0xf70008, 0xff0700, 0xff1500, 0xff2300, 0xff3200, 0xff4000, 0xff4e00, 0xff5d00, 0xff6b00, 0xff7900, 0xff8700,
     0xff9500, 0xffa400, 0xffb200, 0xffc000, 0xffcf00, 0xffdd00, 0xffeb00, 0xfffa00, 0xffff09, 0xffff17, 0xffff26,
     0xffff34, 0xffff43, 0xffff51, 0xffff5f, 0xffff6e, 0xffff7c},

    {/* COLORMAP_BROWNSCALE */
     0x8c2600, 0x8e2a00, 0x8f2c00, 0x913000, 0x933200, 0x943500, 0x963900, 0x973b00, 0x993f00, 0x9b4100, 0x9c4500,
     0x9e4800, 0xa04b00, 0xa14e00, 0xa35100, 0xa45400, 0xa65700, 0xa85a00, 0xa95d00, 0xab6000, 0xad6300, 0xae6700,
     0xb06900, 0xb16d00, 0xb36f00, 0xb57200, 0xb67500, 0xb87800, 0xba7c00, 0xbb7e00, 0xbd8200, 0xbe8400, 0xc08800,
     0xc18b00, 0xc38e00, 0xc59100, 0xc69300, 0xc89700, 0xc99900, 0xcb9d00, 0xcda000, 0xcea300, 0xd0a600, 0xd1a900,
     0xd3ac00, 0xd5af00, 0xd6b200, 0xd8b500, 0xd9b800, 0xdbbb00, 0xddbf00, 0xdec100, 0xe0c500, 0xe1c700, 0xe3cb00,
     0xe5ce00, 0xe6d000, 0xe8d400, 0xe9d600, 0xebda00, 0xeddd00, 0xeee000, 0xf0e300, 0xf2e600, 0xf3e900, 0xf5ec00,
     0xf6ef00, 0xf8f200, 0xfaf500, 0xfbf800, 0xfdfb00, 0xfffe00},

    {/* COLORMAP_PILATUS */
     0x000008, 0x000120, 0x010239, 0x010552, 0x02096d, 0x020e86, 0x04129c, 0x0515ad, 0x0619bf, 0x071ccf, 0x0920e1,
     0x0a21f1, 0x1629fb, 0x333efb, 0x5459fb, 0x7579fb, 0x9698fc, 0xb8b9fd, 0xc1c9eb, 0xb7cdca, 0xaecfaa, 0xa4d48b,
     0x9ad66b, 0x90da4f, 0x93dd49, 0x9ce04f, 0xa5e155, 0xade45c, 0xb6e562, 0xbfe968, 0xc9ec6e, 0xd3ee71, 0xddf375,
     0xe8f67a, 0xf2f97d, 0xfcfc81, 0xfff77f, 0xfeef7a, 0xfee575, 0xfedb70, 0xfed16b, 0xfec767, 0xfec25d, 0xfdc150,
     0xfdc144, 0xfdc03a, 0xfdbf33, 0xfdbe2d, 0xf7b72b, 0xedac28, 0xe3a225, 0xda9823, 0xd18e21, 0xc7831e, 0xc7782c,
     0xcb6c4f, 0xcf6276, 0xd359a1, 0xd64fcb, 0xda49f3, 0xda53fc, 0xda60fc, 0xda70fc, 0xda7efc, 0xdb8efc, 0xdb9dfd,
     0xe1acfd, 0xe6bdfd, 0xeccdfd, 0xf3defe, 0xf8eefe, 0xffffff},

    {/* COLORMAP_AUTUMN */
     0xff0000, 0xff0400, 0xff0700, 0xff0b00, 0xff0e00, 0xff1200, 0xff1600, 0xff1900, 0xff1d00, 0xff2000, 0xff2400,
     0xff2800, 0xff2b00, 0xff2f00, 0xff3200, 0xff3600, 0xff3900, 0xff3d00, 0xff4100, 0xff4400, 0xff4800, 0xff4b00,
     0xff4f00, 0xff5300, 0xff5600, 0xff5a00, 0xff5d00, 0xff6100, 0xff6500, 0xff6800, 0xff6c00, 0xff6f00, 0xff7300,
     0xff7700, 0xff7a00, 0xff7e00, 0xff8100, 0xff8500, 0xff8800, 0xff8c00, 0xff9000, 0xff9300, 0xff9700, 0xff9a00,
     0xff9e00, 0xffa200, 0xffa500, 0xffa900, 0xffac00, 0xffb000, 0xffb400, 0xffb700, 0xffbb00, 0xffbe00, 0xffc200,
     0xffc600, 0xffc900, 0xffcd00, 0xffd000, 0xffd400, 0xffd700, 0xffdb00, 0xffdf00, 0xffe200, 0xffe600, 0xffe900,
     0xffed00, 0xfff100, 0xfff400, 0xfff800, 0xfffb00, 0xffff00},

    {/* COLORMAP_BONE */
     0x000000, 0x040305, 0x060609, 0x0a0a0d, 0x0c0c11, 0x101016, 0x12131b, 0x16161e, 0x191923, 0x1c1c27, 0x201f2c,
     0x232330, 0x262634, 0x292939, 0x2c2c3d, 0x2f2f42, 0x323246, 0x35354a, 0x39394f, 0x3c3b53, 0x3f3f58, 0x43425c,
     0x454560, 0x494965, 0x4b4b69, 0x4f4f6e, 0x515271, 0x555675, 0x575b78, 0x5b5f7b, 0x5e637e, 0x616781, 0x656c84,
     0x687088, 0x6b748b, 0x6e798e, 0x717d91, 0x748194, 0x778697, 0x7b8a9a, 0x7e8e9e, 0x8192a0, 0x8497a4, 0x879ba7,
     0x8aa0aa, 0x8ea4ae, 0x90a8b0, 0x94adb4, 0x97b1b6, 0x9ab5ba, 0x9dbabc, 0xa0bec0, 0xa4c2c3, 0xa6c6c6, 0xaccaca,
     0xb1cdcd, 0xb5d0d0, 0xbad3d3, 0xbfd6d6, 0xc4d9d9, 0xc9dcdc, 0xcee0df, 0xd3e3e3, 0xd8e6e6, 0xdde9e9, 0xe1eced,
     0xe6efef, 0xebf3f3, 0xf0f5f5, 0xf5f9f9, 0xfbfcfb, 0xffffff},

    {/* COLORMAP_COOL */
     0x00ffff, 0x04fbff, 0x07f8ff, 0x0bf4ff, 0x0ef1ff, 0x12edff, 0x16e9ff, 0x19e6ff, 0x1de2ff, 0x20dfff, 0x24dbff,
     0x28d7ff, 0x2bd4ff, 0x2fd0ff, 0x32cdff, 0x36c9ff, 0x39c6ff, 0x3dc2ff, 0x41beff, 0x44bbff, 0x48b7ff, 0x4bb4ff,
     0x4fb0ff, 0x53acff, 0x56a9ff, 0x5aa5ff, 0x5da2ff, 0x619eff, 0x659aff, 0x6897ff, 0x6c93ff, 0x6f90ff, 0x738cff,
     0x7788ff, 0x7a85ff, 0x7e81ff, 0x817eff, 0x857aff, 0x8877ff, 0x8c73ff, 0x906fff, 0x936cff, 0x9768ff, 0x9a65ff,
     0x9e61ff, 0xa25dff, 0xa55aff, 0xa956ff, 0xac53ff, 0xb04fff, 0xb44bff, 0xb748ff, 0xbb44ff, 0xbe41ff, 0xc23dff,
     0xc639ff, 0xc936ff, 0xcd32ff, 0xd02fff, 0xd42bff, 0xd728ff, 0xdb24ff, 0xdf20ff, 0xe21dff, 0xe619ff, 0xe916ff,
     0xed12ff, 0xf10eff, 0xf40bff, 0xf807ff, 0xfb04ff, 0xff00ff},

    {/* COLORMAP_COPPER */
     0x000000, 0x050302, 0x090503, 0x0e0905, 0x120b07, 0x160e09, 0x1b100b, 0x1f140c, 0x24170e, 0x281910, 0x2c1c12,
     0x301e14, 0x352215, 0x3a2517, 0x3e2719, 0x432a1b, 0x472d1c, 0x4b301e, 0x503320, 0x543522, 0x593824, 0x5e3b25,
     0x623e27, 0x664129, 0x6a432b, 0x6f462d, 0x73492e, 0x784c30, 0x7d4f32, 0x805134, 0x855436, 0x895737, 0x8e5a39,
     0x925d3b, 0x975f3d, 0x9b623f, 0xa06540, 0xa46842, 0xa96b44, 0xad6d46, 0xb27048, 0xb67349, 0xbb764b, 0xbe784d,
     0xc37b4f, 0xc87f51, 0xcc8152, 0xd18454, 0xd58656, 0xd98958, 0xdd8d5a, 0xe28f5b, 0xe7925d, 0xeb945f, 0xf09861,
     0xf49b63, 0xf89d64, 0xfda066, 0xffa267, 0xffa669, 0xffa86b, 0xffab6d, 0xffae6f, 0xffb170, 0xffb472, 0xffb674,
     0xffb976, 0xffbc78, 0xffbf79, 0xffc27b, 0xffc47d, 0xffc77f},

    {/* COLORMAP_GRAY */
     0x000000, 0x040404, 0x070707, 0x0b0b0b, 0x0e0e0e, 0x121212, 0x161616, 0x191919, 0x1d1d1d, 0x202020, 0x242424,
     0x282828, 0x2b2b2b, 0x2f2f2f, 0x323232, 0x363636, 0x393939, 0x3d3d3d, 0x414141, 0x444444, 0x484848, 0x4b4b4b,
     0x4f4f4f, 0x535353, 0x565656, 0x5a5a5a, 0x5d5d5d, 0x616161, 0x656565, 0x686868, 0x6c6c6c, 0x6f6f6f, 0x737373,
     0x777777, 0x7a7a7a, 0x7e7e7e, 0x818181, 0x858585, 0x888888, 0x8c8c8c, 0x909090, 0x939393, 0x979797, 0x9a9a9a,
     0x9e9e9e, 0xa2a2a2, 0xa5a5a5, 0xa9a9a9, 0xacacac, 0xb0b0b0, 0xb4b4b4, 0xb7b7b7, 0xbbbbbb, 0xbebebe, 0xc2c2c2,
     0xc6c6c6, 0xc9c9c9, 0xcdcdcd, 0xd0d0d0, 0xd4d4d4, 0xd7d7d7, 0xdbdbdb, 0xdfdfdf, 0xe2e2e2, 0xe6e6e6, 0xe9e9e9,
     0xededed, 0xf1f1f1, 0xf4f4f4, 0xf8f8f8, 0xfbfbfb, 0xffffff},

    {/* COLORMAP_HOT */
     0x0b0000, 0x140000, 0x1e0000, 0x270000, 0x300000, 0x3a0000, 0x430000, 0x4c0000, 0x560000, 0x600000, 0x690000,
     0x730000, 0x7b0000, 0x850000, 0x8f0000, 0x980000, 0xa10000, 0xab0000, 0xb40000, 0xbe0000, 0xc80000, 0xd00000,
     0xda0000, 0xe30000, 0xec0000, 0xf60000, 0xff0100, 0xff0a00, 0xff1400, 0xff1d00, 0xff2600, 0xff3000, 0xff3a00,
     0xff4200, 0xff4c00, 0xff5500, 0xff5f00, 0xff6900, 0xff7200, 0xff7b00, 0xff8500, 0xff8f00, 0xff9700, 0xffa100,
     0xffaa00, 0xffb400, 0xffbd00, 0xffc700, 0xffd000, 0xffda00, 0xffe300, 0xffed00, 0xfff600, 0xfffe01, 0xffff0f,
     0xffff1d, 0xffff2b, 0xffff39, 0xffff47, 0xffff56, 0xffff63, 0xffff71, 0xffff80, 0xffff8e, 0xffff9d, 0xffffaa,
     0xffffb8, 0xffffc7, 0xffffd5, 0xffffe2, 0xfffff1, 0xffffff},

    {/* COLORMAP_HSV */
     0xff0000, 0xff1600, 0xff2a00, 0xff4000, 0xff5500, 0xff6a00, 0xff7f00, 0xff9500, 0xffa900, 0xffbf00, 0xffd400,
     0xffe900, 0xfaf900, 0xeaff00, 0xd5ff00, 0xc0ff00, 0xaaff00, 0x96ff00, 0x80ff00, 0x6bff00, 0x56ff00, 0x40ff00,
     0x2bff00, 0x16ff00, 0x06ff05, 0x00ff15, 0x00ff29, 0x00ff3f, 0x00ff54, 0x00ff69, 0x00ff7e, 0x00ff94, 0x00ffa9,
     0x00ffbe, 0x00ffd4, 0x00ffe8, 0x00fffd, 0x00ebff, 0x00d6ff, 0x00c1ff, 0x00acff, 0x0096ff, 0x0081ff, 0x006cff,
     0x0057ff, 0x0041ff, 0x002cff, 0x0017ff, 0x0506ff, 0x1300ff, 0x2800ff, 0x3e00ff, 0x5300ff, 0x6800ff, 0x7e00ff,
     0x9300ff, 0xa800ff, 0xbd00ff, 0xd200ff, 0xe700ff, 0xf900fb, 0xff00ed, 0xff00d7, 0xff00c1, 0xff00ad, 0xff0097,
     0xff0082, 0xff006d, 0xff0058, 0xff0042, 0xff002e, 0xff0018},

    {/* COLORMAP_JET */
     0x000080, 0x000090, 0x0000a0, 0x0000b1, 0x0000c1, 0x0000d1, 0x0000e1, 0x0000f2, 0x0000ff, 0x0002ff, 0x0011ff,
     0x001fff, 0x002dff, 0x003cff, 0x004aff, 0x0058ff, 0x0066ff, 0x0074ff, 0x0084ff, 0x0092ff, 0x00a0ff, 0x00afff,
     0x00bdff, 0x00cbff, 0x00daff, 0x01e7f5, 0x0df7ea, 0x19ffde, 0x25ffd2, 0x31ffc7, 0x3bffbb, 0x47ffb0, 0x53ffa4,
     0x5fff98, 0x6aff8d, 0x76ff81, 0x81ff76, 0x8dff6a, 0x98ff5f, 0xa4ff53, 0xb0ff47, 0xbbff3b, 0xc7ff31, 0xd2ff25,
     0xdeff19, 0xeaff0d, 0xf5f701, 0xffeb00, 0xffdd00, 0xffd000, 0xffc200, 0xffb500, 0xffa800, 0xff9b00, 0xff8d00,
     0xff8000, 0xff7200, 0xff6500, 0xff5800, 0xff4a00, 0xff3d00, 0xff3000, 0xff2300, 0xff1500, 0xf20800, 0xe20000,
     0xd10000, 0xc10000, 0xb10000, 0xa00000, 0x900000, 0x800000},

    {/* COLORMAP_PINK */
     0x1e0000, 0x301717, 0x3d2323, 0x472b2b, 0x513131, 0x593737, 0x613d3d, 0x684141, 0x6e4646, 0x754a4a, 0x7b4e4e,
     0x805252, 0x855555, 0x8b5959, 0x905c5c, 0x956060, 0x9a6262, 0x9e6666, 0xa26969, 0xa66c6c, 0xab6f6f, 0xae7272,
     0xb37474, 0xb77777, 0xba7979, 0xbe7c7c, 0xc27e7e, 0xc38480, 0xc58982, 0xc68e85, 0xc89387, 0xc99789, 0xcb9c8c,
     0xcda18e, 0xcea590, 0xd0a992, 0xd1ad94, 0xd2b296, 0xd4b599, 0xd5b99a, 0xd7bd9c, 0xd8c09e, 0xdac4a0, 0xdbc7a2,
     0xdccba4, 0xdecfa6, 0xdfd2a7, 0xe1d6a9, 0xe2d8ab, 0xe3dcad, 0xe5e0af, 0xe6e2b0, 0xe7e6b2, 0xe8e8b4, 0xeaeab9,
     0xebebbd, 0xececc2, 0xeeeec7, 0xefefcb, 0xf0f0d0, 0xf1f1d4, 0xf3f3d8, 0xf4f4dd, 0xf5f5e1, 0xf7f7e5, 0xf8f8e8,
     0xf9f9ed, 0xfafaf1, 0xfbfbf4, 0xfdfdf8, 0xfefefb, 0xffffff},

    {/* COLORMAP_SPECTRAL */
     0x000000, 0x210027, 0x43004d, 0x650073, 0x79008a, 0x7e008f, 0x820093, 0x870098, 0x66009d, 0x4000a2, 0x1900a7,
     0x0000af, 0x0000bd, 0x0000cc, 0x0000da, 0x001bdd, 0x003cdd, 0x005edd, 0x007add, 0x0083dd, 0x008cdd, 0x0096dd,
     0x009cd3, 0x00a1c5, 0x00a6b6, 0x00aaa9, 0x00aa9f, 0x00aa95, 0x00aa8c, 0x00a771, 0x00a24b, 0x009e24, 0x009a00,
     0x00a300, 0x00ac00, 0x00b600, 0x00c000, 0x00ca00, 0x00d300, 0x00dc00, 0x00e600, 0x00f000, 0x00fa00, 0x15ff00,
     0x49ff00, 0x7eff00, 0xb3ff00, 0xc7fb00, 0xd6f600, 0xe4f100, 0xf0eb00, 0xf4e100, 0xf9d800, 0xfece00, 0xffc100,
     0xffb300, 0xffa500, 0xff9100, 0xff6500, 0xff3a00, 0xff0f00, 0xf90000, 0xef0000, 0xe50000, 0xdc0000, 0xd70000,
     0xd30000, 0xcf0000, 0xcc2020, 0xcc5959, 0xcc9393, 0xcccccc},

    {/* COLORMAP_SPRING */
     0xff00ff, 0xff04fb, 0xff07f8, 0xff0bf4, 0xff0ef1, 0xff12ed, 0xff16e9, 0xff19e6, 0xff1de2, 0xff20df, 0xff24db,
     0xff28d7, 0xff2bd4, 0xff2fd0, 0xff32cd, 0xff36c9, 0xff39c6, 0xff3dc2, 0xff41be, 0xff44bb, 0xff48b7, 0xff4bb4,
     0xff4fb0, 0xff53ac, 0xff56a9, 0xff5aa5, 0xff5da2, 0xff619e, 0xff659a, 0xff6897, 0xff6c93, 0xff6f90, 0xff738c,
     0xff7788, 0xff7a85, 0xff7e81, 0xff817e, 0xff857a, 0xff8877, 0xff8c73, 0xff906f, 0xff936c, 0xff9768, 0xff9a65,
     0xff9e61, 0xffa25d, 0xffa55a, 0xffa956, 0xffac53, 0xffb04f, 0xffb44b, 0xffb748, 0xffbb44, 0xffbe41, 0xffc23d,
     0xffc639, 0xffc936, 0xffcd32, 0xffd02f, 0xffd42b, 0xffd728, 0xffdb24, 0xffdf20, 0xffe21d, 0xffe619, 0xffe916,
     0xffed12, 0xfff10e, 0xfff40b, 0xfff807, 0xfffb04, 0xffff00},

    {/* COLORMAP_SUMMER */
     0x008066, 0x048266, 0x078366, 0x0b8566, 0x0e8766, 0x128966, 0x168b66, 0x198c66, 0x1d8e66, 0x209066, 0x249266,
     0x289366, 0x2b9566, 0x2f9766, 0x329966, 0x369b66, 0x399c66, 0x3d9e66, 0x41a066, 0x44a266, 0x48a366, 0x4ba666,
     0x4fa766, 0x53a966, 0x56ab66, 0x5aad66, 0x5dae66, 0x61b066, 0x65b266, 0x68b366, 0x6cb666, 0x6fb766, 0x73b966,
     0x77bb66, 0x7abd66, 0x7ebf66, 0x81c066, 0x85c266, 0x88c466, 0x8cc666, 0x90c866, 0x93c966, 0x97cb66, 0x9acd66,
     0x9ecf66, 0xa2d166, 0xa5d266, 0xa9d466, 0xacd666, 0xb0d866, 0xb4da66, 0xb7db66, 0xbbdd66, 0xbedf66, 0xc2e166,
     0xc6e366, 0xc9e466, 0xcde666, 0xd0e866, 0xd4ea66, 0xd7eb66, 0xdbed66, 0xdfef66, 0xe2f166, 0xe6f366, 0xe9f466,
     0xedf666, 0xf1f866, 0xf4fa66, 0xf8fc66, 0xfbfd66, 0xffff66},

    {/* COLORMAP_WINTER */
     0x0000ff, 0x0004fd, 0x0007fc, 0x000bfa, 0x000ef8, 0x0012f6, 0x0016f4, 0x0019f3, 0x001df1, 0x0020ef, 0x0024ed,
     0x0028eb, 0x002bea, 0x002fe8, 0x0032e6, 0x0036e4, 0x0039e3, 0x003de1, 0x0041df, 0x0044dd, 0x0048db, 0x004bda,
     0x004fd8, 0x0053d6, 0x0056d4, 0x005ad2, 0x005dd1, 0x0061cf, 0x0065cd, 0x0068cb, 0x006cc9, 0x006fc8, 0x0073c6,
     0x0077c3, 0x007ac2, 0x007ec0, 0x0081bf, 0x0085bd, 0x0088bb, 0x008cb9, 0x0090b7, 0x0093b6, 0x0097b3, 0x009ab2,
     0x009eb0, 0x00a2ae, 0x00a5ad, 0x00a9ab, 0x00aca9, 0x00b0a7, 0x00b4a6, 0x00b7a3, 0x00bba2, 0x00bea0, 0x00c29e,
     0x00c69c, 0x00c99b, 0x00cd99, 0x00d097, 0x00d495, 0x00d793, 0x00db92, 0x00df90, 0x00e28e, 0x00e68c, 0x00e98b,
     0x00ed89, 0x00f187, 0x00f485, 0x00f883, 0x00fb82, 0x00ff80},

    {/* COLORMAP_GIST_EARTH */
     0x000000, 0x030049, 0x050070, 0x070975, 0x091175, 0x0c1976, 0x0f2177, 0x112977, 0x133178, 0x153a78, 0x184179,
     0x1b487a, 0x1d4f7a, 0x1f567b, 0x215d7c, 0x24647c, 0x27697d, 0x296f7e, 0x2b747e, 0x2d7a7f, 0x308080, 0x31827c,
     0x338477, 0x358672, 0x37886e, 0x388a6a, 0x3a8c66, 0x3c8e61, 0x3e915c, 0x3f9258, 0x419554, 0x429650, 0x44994b,
     0x499a46, 0x509d48, 0x589f4a, 0x61a14c, 0x69a34e, 0x70a551, 0x78a652, 0x7ea853, 0x85a954, 0x8aab56, 0x90ac56,
     0x96ae58, 0x9cb059, 0xa2b15a, 0xa8b35b, 0xaeb45c, 0xb4b65d, 0xb8b55f, 0xb9b360, 0xbbaf61, 0xbcac62, 0xbea963,
     0xbfa664, 0xc1a367, 0xc5a570, 0xc9a77a, 0xcdaa82, 0xd0ad8b, 0xd5b194, 0xd9b59c, 0xddbaa6, 0xe1bfb0, 0xe5c6ba,
     0xe9cdc5, 0xedd4d0, 0xf1dcdb, 0xf5e6e5, 0xfaf0f0, 0xfdfbfb},

    {/* COLORMAP_GIST_HEAT */
     0x000000, 0x060000, 0x0b0000, 0x100000, 0x150000, 0x1b0000, 0x210000, 0x260000, 0x2c0000, 0x300000, 0x360000,
     0x3c0000, 0x410000, 0x470000, 0x4c0000, 0x510000, 0x560000, 0x5b0000, 0x610000, 0x660000, 0x6c0000, 0x720000,
     0x770000, 0x7c0000, 0x810000, 0x870000, 0x8c0000, 0x920000, 0x970000, 0x9c0000, 0xa20000, 0xa70000, 0xad0000,
     0xb20000, 0xb70000, 0xbc0000, 0xc20400, 0xc80b00, 0xcd1200, 0xd21900, 0xd82000, 0xdc2800, 0xe32f00, 0xe73600,
     0xed3d00, 0xf34400, 0xf84b00, 0xfe5300, 0xff5a00, 0xff6100, 0xff6800, 0xff6f00, 0xff7700, 0xff7e00, 0xff850b,
     0xff8c19, 0xff9328, 0xff9a36, 0xffa244, 0xffa953, 0xffb061, 0xffb76f, 0xffbe7e, 0xffc68c, 0xffcd9a, 0xffd4a9,
     0xffdbb7, 0xffe2c6, 0xffe9d4, 0xfff1e2, 0xfff8f1, 0xffffff},

    {/* COLORMAP_GIST_NCAR */
     0x000080, 0x001a5e,    0x00343c, 0x004e1b, 0x00551d, 0x003d58, 0x002594, 0x000dcf, 0x0019100, 0x004cff, 0x007eff,
     0x00b1ff, 0x00caff,    0x00daff, 0x00eaff, 0x00faf3, 0x00fedb, 0x00fcc4, 0x00faac, 0x00fa8f,  0x00fb6a, 0x00fd45,
     0x00fe1f, 0x17f8 - 01, 0x2eeb00, 0x45de00, 0x5cd000, 0x6ad800, 0x71e400, 0x78f000, 0x7ffb07,  0x8fff15, 0x9fff24,
     0xb0ff32, 0xc0ff37,    0xd1ff29, 0xe0ff1b, 0xf1ff0c, 0xfff700, 0xffee00, 0xffe500, 0xffdb00,  0xffd303, 0xffca07,
     0xffc10b, 0xffb50e,    0xff970a, 0xff7a07, 0xff5d04, 0xff4300, 0xff3200, 0xff2000, 0xff0f00,  0xff0029, 0xff0069,
     0xff00a9, 0xff00e8,    0xec09ff, 0xd416ff, 0xbb22ff, 0xa230ff, 0xb144fa, 0xc65af6, 0xdc70f2,  0xec83ef, 0xee94f1,
     0xf1a5f3, 0xf4b5f5,    0xf6c6f7, 0xf9d7fa, 0xfbe7fc, 0xfef8fe},

    {/* COLORMAP_GIST_RAINBOW */
     0xff0029, 0xff0015, 0xff0002, 0xff1100, 0xff2400, 0xff3800, 0xff4b00, 0xff5f00, 0xff7200, 0xff8600, 0xff9900,
     0xffac00, 0xffbf00, 0xffd300, 0xffe600, 0xfffa00, 0xf1ff00, 0xdeff00, 0xcaff00, 0xb7ff00, 0xa3ff00, 0x90ff00,
     0x7cff00, 0x69ff00, 0x55ff00, 0x42ff00, 0x2fff00, 0x1bff00, 0x08ff00, 0x00ff0c, 0x00ff1f, 0x00ff32, 0x00ff46,
     0x00ff58, 0x00ff6d, 0x00ff80, 0x00ff93, 0x00ffa6, 0x00ffb9, 0x00ffcc, 0x00ffe0, 0x00fff3, 0x00f7ff, 0x00e4ff,
     0x00d0ff, 0x00bdff, 0x00a9ff, 0x0096ff, 0x0082ff, 0x006fff, 0x005bff, 0x0048ff, 0x0034ff, 0x0021ff, 0x000dff,
     0x0700ff, 0x1a00ff, 0x2e00ff, 0x4100ff, 0x5500ff, 0x6800ff, 0x7b00ff, 0x8f00ff, 0xa300ff, 0xb600ff, 0xca00ff,
     0xdd00ff, 0xf100ff, 0xff00fa, 0xff00e6, 0xff00d3, 0xff00bf},

    {/* COLORMAP_GIST_STERN */
     0x000000, 0x420407, 0x83070e, 0xc50b16, 0xff0e1d, 0xeb1224, 0xd9162b, 0xc71932, 0xb51d39, 0xa32041, 0x912448,
     0x7f284f, 0x6e2b56, 0x5c2f5d, 0x4a3265, 0x38366c, 0x273973, 0x153d7a, 0x454181, 0x444488, 0x484890, 0x4b4b97,
     0x4f4f9e, 0x5353a5, 0x5656ac, 0x5a5ab4, 0x5d5dbb, 0x6161c2, 0x6565c9, 0x6868d0, 0x6c6cd7, 0x6f6fdf, 0x7373e6,
     0x7777ed, 0x7a7af4, 0x7e7efb, 0x8181f8, 0x8585e9, 0x8888d9, 0x8c8cca, 0x9090ba, 0x9393ab, 0x97979c, 0x9a9a8c,
     0x9e9e7d, 0xa2a26d, 0xa5a55e, 0xa9a94f, 0xacac40, 0xb0b031, 0xb4b422, 0xb7b712, 0xbbbb03, 0xbebe0b, 0xc2c219,
     0xc6c626, 0xc9c934, 0xcdcd41, 0xd0d04f, 0xd4d45d, 0xd7d76a, 0xdbdb77, 0xdfdf85, 0xe2e293, 0xe6e6a1, 0xe9e9ae,
     0xededbb, 0xf1f1c8, 0xf4f4d6, 0xf8f8e4, 0xfbfbf2, 0xffffff},

    {/* COLORMAP_AFMHOT */
     0x000000, 0x070000, 0x0e0000, 0x160000, 0x1d0000, 0x240000, 0x2b0000, 0x320000, 0x390000, 0x410000, 0x480000,
     0x4f0000, 0x560000, 0x5d0000, 0x650000, 0x6c0000, 0x730000, 0x7a0000, 0x810100, 0x880800, 0x901000, 0x971800,
     0x9e1f00, 0xa52600, 0xac2d00, 0xb43300, 0xbb3b00, 0xc24200, 0xc94900, 0xd05100, 0xd75900, 0xdf6000, 0xe66700,
     0xed6e00, 0xf47400, 0xfb7c00, 0xff8304, 0xff8b0b, 0xff9212, 0xff9919, 0xffa020, 0xffa628, 0xffaf2f, 0xffb536,
     0xffbd3d, 0xffc444, 0xffcc4b, 0xffd353, 0xffda5a, 0xffe161, 0xffe768, 0xffef6f, 0xfff577, 0xfffe7e, 0xffff85,
     0xffff8c, 0xffff93, 0xffff9a, 0xffffa2, 0xffffa9, 0xffffb0, 0xffffb7, 0xffffbe, 0xffffc6, 0xffffcd, 0xffffd4,
     0xffffdb, 0xffffe2, 0xffffe9, 0xfffff1, 0xfffff8, 0xffffff},

    {/* COLORMAP_BRG */
     0x0000ff, 0x0700f8, 0x0e00f1, 0x1600e9, 0x1d00e2, 0x2400db, 0x2b00d4, 0x3200cd, 0x3900c6, 0x4100be, 0x4800b7,
     0x4f00b0, 0x5600a9, 0x5d00a2, 0x65009a, 0x6c0093, 0x73008c, 0x7a0085, 0x81007e, 0x880077, 0x90006f, 0x970068,
     0x9e0061, 0xa5005a, 0xac0053, 0xb4004b, 0xbb0044, 0xc2003d, 0xc90036, 0xd0002f, 0xd70028, 0xdf0020, 0xe60019,
     0xed0012, 0xf4000b, 0xfb0004, 0xfb0400, 0xf40b00, 0xed1200, 0xe61900, 0xdf2000, 0xd72800, 0xd02f00, 0xc93600,
     0xc23d00, 0xbb4400, 0xb44b00, 0xac5300, 0xa55a00, 0x9e6100, 0x976800, 0x906f00, 0x887700, 0x817e00, 0x7a8500,
     0x738c00, 0x6c9300, 0x659a00, 0x5da200, 0x56a900, 0x4fb000, 0x48b700, 0x41be00, 0x39c600, 0x32cd00, 0x2bd400,
     0x24db00, 0x1de200, 0x16e900, 0x0ef100, 0x07f800, 0x00ff00},

    {/* COLORMAP_BWR */
     0x0000ff, 0x0707ff, 0x0e0eff, 0x1616ff, 0x1d1dff, 0x2424ff, 0x2b2bff, 0x3232ff, 0x3939ff, 0x4141ff, 0x4848ff,
     0x4f4fff, 0x5656ff, 0x5d5dff, 0x6565ff, 0x6c6cff, 0x7373ff, 0x7a7aff, 0x8181ff, 0x8888ff, 0x9090ff, 0x9797ff,
     0x9e9eff, 0xa5a5ff, 0xacacff, 0xb4b4ff, 0xbbbbff, 0xc2c2ff, 0xc9c9ff, 0xd0d0ff, 0xd7d7ff, 0xdfdfff, 0xe6e6ff,
     0xededff, 0xf4f4ff, 0xfbfbff, 0xfffbfb, 0xfff4f4, 0xffeded, 0xffe6e6, 0xffdfdf, 0xffd7d7, 0xffd0d0, 0xffc9c9,
     0xffc2c2, 0xffbbbb, 0xffb4b4, 0xffacac, 0xffa5a5, 0xff9e9e, 0xff9797, 0xff9090, 0xff8888, 0xff8181, 0xff7a7a,
     0xff7373, 0xff6c6c, 0xff6565, 0xff5d5d, 0xff5656, 0xff4f4f, 0xff4848, 0xff4141, 0xff3939, 0xff3232, 0xff2b2b,
     0xff2424, 0xff1d1d, 0xff1616, 0xff0e0e, 0xff0707, 0xff0000},

    {/* COLORMAP_COOLWARM */
     0x3b4cc0, 0x3f52c6, 0x4358cb, 0x485fd1, 0x4b65d5, 0x506bda, 0x5571df, 0x5977e3, 0x5e7de7, 0x6283ea, 0x6788ee,
     0x6b8ef1, 0x7093f3, 0x7698f6, 0x7a9df8, 0x80a3fa, 0x85a7fc, 0x89acfd, 0x8eb1fe, 0x93b5fe, 0x98b9ff, 0x9ebdff,
     0xa2c1ff, 0xa6c5fe, 0xabc8fd, 0xb1cbfc, 0xb6cdfa, 0xbad0f8, 0xbfd2f6, 0xc3d5f4, 0xc7d7f0, 0xcbd8ee, 0xcfdaea,
     0xd4dbe6, 0xd7dce3, 0xdbdcdf, 0xdedcda, 0xe2dad5, 0xe5d7d0, 0xe9d5cb, 0xecd3c5, 0xeed0c0, 0xf1cdba, 0xf2cab5,
     0xf4c6af, 0xf5c1a9, 0xf6bea4, 0xf7b99e, 0xf7b498, 0xf7b093, 0xf7ab8d, 0xf7a688, 0xf5a081, 0xf59b7c, 0xf39577,
     0xf18f71, 0xf08a6c, 0xed8367, 0xeb7c61, 0xe8765c, 0xe56f57, 0xe26952, 0xde624d, 0xda5948, 0xd65244, 0xd14a40,
     0xcd423b, 0xc93936, 0xc43032, 0xbe252e, 0xb9142b, 0xb40426},

    {/* COLORMAP_CMRMAP */
     0x000000, 0x05050e, 0x08081d, 0x0d0d2b, 0x111139, 0x161648, 0x191956, 0x1e1e65, 0x232373, 0x272681, 0x2b2688,
     0x2f268f, 0x342696, 0x38269d, 0x3c26a5, 0x4126ac, 0x4526b3, 0x4926ba, 0x4f27be, 0x5828b7, 0x602aaf, 0x692ba8,
     0x712ca1, 0x7a2e9a, 0x822f93, 0x8a318b, 0x943284, 0x9d347c, 0xa93571, 0xb43668, 0xc0385e, 0xcb3953, 0xd73b49,
     0xe33c3f, 0xed3e36, 0xf93f2b, 0xfe4424, 0xfb4b20, 0xf7521b, 0xf55917, 0xf26013, 0xef680f, 0xec6f0a, 0xea7605,
     0xe77d02, 0xe68402, 0xe68b05, 0xe69308, 0xe69a0a, 0xe6a10d, 0xe6a810, 0xe6af13, 0xe6b716, 0xe6be19, 0xe6c322,
     0xe6c62e, 0xe6cb39, 0xe6d045, 0xe6d450, 0xe6d85c, 0xe6dc68, 0xe6e172, 0xe6e57e, 0xe8e88c, 0xebeb9a, 0xededa9,
     0xf1f1b7, 0xf4f4c6, 0xf6f6d4, 0xf9f9e2, 0xfcfcf1, 0xffffff},

    {/* COLORMAP_CUBEHELIX */
     0x000000, 0x060206, 0x0b040c, 0x100713, 0x13091a, 0x160d21, 0x191128, 0x1a142f, 0x1b1936, 0x1b1e3c, 0x1a2441,
     0x192946, 0x182f49, 0x17364c, 0x163c4e, 0x15424e, 0x15484e, 0x154e4d, 0x16544b, 0x175a49, 0x1a6046, 0x1d6443,
     0x22693f, 0x276d3b, 0x2d7038, 0x347435, 0x3d7632, 0x467830, 0x50792f, 0x5a7a2f, 0x657a30, 0x707b31, 0x7b7a35,
     0x867a39, 0x907a3e, 0x9b7945, 0xa5794d, 0xae7956, 0xb6795f, 0xbe796a, 0xc47a75, 0xc97b80, 0xce7d8c, 0xd18097,
     0xd382a3, 0xd486ae, 0xd589b9, 0xd48ec3, 0xd393cc, 0xd198d4, 0xcf9edc, 0xcca4e2, 0xcaaae8, 0xc8b1ec, 0xc5b8ef,
     0xc3bef2, 0xc2c5f3, 0xc1ccf3, 0xc1d1f3, 0xc2d7f3, 0xc4ddf2, 0xc6e1f1, 0xcae6f0, 0xcdeaef, 0xd3eeef, 0xd8f1ef,
     0xdef4ef, 0xe4f7f1, 0xebf9f3, 0xf2fbf6, 0xf9fdfb, 0xffffff},

    {/* COLORMAP_GNUPLOT */
     0x000000, 0x1e0017, 0x2b002d, 0x340043, 0x3d0058, 0x44006d, 0x4a0081, 0x500094, 0x5600a6, 0x5b01b6, 0x6001c6,
     0x6501d3, 0x6901de, 0x6d02e9, 0x7102f2, 0x7502f8, 0x7a03fb, 0x7d03fe, 0x8104ff, 0x8405fe, 0x8706fa, 0x8a06f4,
     0x8e08ed, 0x9109e4, 0x940ad9, 0x970bcc, 0x9a0cbe, 0x9d0eae, 0xa0109d, 0xa3118b, 0xa61377, 0xa81563, 0xab174d,
     0xad1938, 0xb01c21, 0xb31f0b, 0xb52100, 0xb82400, 0xba2800, 0xbd2a00, 0xc02e00, 0xc23100, 0xc43500, 0xc63800,
     0xc93d00, 0xcb4100, 0xcd4500, 0xd04a00, 0xd14f00, 0xd45400, 0xd65900, 0xd85e00, 0xda6500, 0xdc6a00, 0xde7000,
     0xe17700, 0xe27d00, 0xe58400, 0xe68b00, 0xe99300, 0xea9a00, 0xeca200, 0xeeaa00, 0xf0b300, 0xf2bb00, 0xf4c400,
     0xf6cd00, 0xf8d600, 0xf9e000, 0xfbeb00, 0xfdf400, 0xffff00},

    {/* COLORMAP_GNUPLOT2 */
     0x000000, 0x00000e, 0x00001d, 0x00002b, 0x000039, 0x000048, 0x000056, 0x000065, 0x000073, 0x000081, 0x000090,
     0x00009e, 0x0000ac, 0x0000bb, 0x0000c9, 0x0000d7, 0x0000e6, 0x0000f4, 0x0300ff, 0x0e00ff, 0x1900ff, 0x2400ff,
     0x3000ff, 0x3b00ff, 0x4700ff, 0x5100ff, 0x5d00ff, 0x6800ff, 0x7300ff, 0x7e00ff, 0x8901fe, 0x9509f6, 0xa010ef,
     0xac17e8, 0xb61ee1, 0xc225da, 0xcd2dd2, 0xd834cb, 0xe33bc4, 0xee42bd, 0xfa49b6, 0xff51ae, 0xff58a7, 0xff5fa0,
     0xff6699, 0xff6d92, 0xff748b, 0xff7c83, 0xff837c, 0xff8a75, 0xff916e, 0xff9867, 0xffa05f, 0xffa758, 0xffae51,
     0xffb54a, 0xffbc43, 0xffc33c, 0xffcb34, 0xffd22d, 0xffd926, 0xffe01f, 0xffe718, 0xffef10, 0xfff609, 0xfffd02,
     0xffff1f, 0xffff4b, 0xffff78, 0xffffa5, 0xffffd2, 0xffffff},

    {/* COLORMAP_OCEAN */
     0x008000, 0x007a04, 0x007507, 0x006f0b, 0x006a0e, 0x006512, 0x005f16, 0x005a19, 0x00541d, 0x004f20, 0x004a24,
     0x004428, 0x003f2b, 0x003a2f, 0x003532, 0x002f36, 0x002a39, 0x00243d, 0x001f41, 0x001944, 0x001448, 0x000f4b,
     0x00094f, 0x000453, 0x000156, 0x00075a, 0x000d5d, 0x001261, 0x001865, 0x001d68, 0x00226c, 0x00286f, 0x002d73,
     0x003277, 0x00377a, 0x003e7e, 0x004281, 0x004885, 0x004d88, 0x00538c, 0x005890, 0x005d93, 0x006397, 0x00689a,
     0x006e9e, 0x0072a2, 0x0078a5, 0x007ea9, 0x0784ac, 0x1288b0, 0x1d8eb4, 0x2893b7, 0x3298bb, 0x3d9ebe, 0x48a3c2,
     0x53a9c6, 0x5daec9, 0x68b4cd, 0x73b9d0, 0x7ebfd4, 0x88c3d7, 0x93c9db, 0x9ecfdf, 0xa9d4e2, 0xb4dae6, 0xbedfe9,
     0xc9e4ed, 0xd4e9f1, 0xdfeef4, 0xe9f4f8, 0xf4fafb, 0xffffff},

    {/* COLORMAP_RAINBOW */
     0x8000ff, 0x790bff, 0x7217ff, 0x6a21fe, 0x632dfe, 0x5c38fd, 0x5543fd, 0x4e4dfc, 0x4758fb, 0x3f63fa, 0x386df9,
     0x3078f7, 0x2981f6, 0x228bf4, 0x1b94f3, 0x149df1, 0x0da6ef, 0x06aeed, 0x01b6eb, 0x08bfe9, 0x10c6e6, 0x18cce4,
     0x1fd3e1, 0x26d9de, 0x2ddedc, 0x33e4d9, 0x3be9d6, 0x42edd3, 0x49f2cf, 0x51f4cc, 0x59f8c9, 0x60fac6, 0x67fcc2,
     0x6efdbf, 0x74feba, 0x7cffb6, 0x83ffb3, 0x8bfeae, 0x92fdaa, 0x99fca6, 0xa0faa1, 0xa6f89d, 0xaff498, 0xb5f294,
     0xbded8f, 0xc4e98b, 0xcce486, 0xd3de81, 0xdad97c, 0xe1d377, 0xe7cc73, 0xefc66d, 0xf5bf68, 0xfeb663, 0xffae5e,
     0xffa658, 0xff9d53, 0xff944e, 0xff8b48, 0xff8143, 0xff783e, 0xff6d38, 0xff6332, 0xff582d, 0xff4d27, 0xff4322,
     0xff381c, 0xff2d17, 0xff2111, 0xff170b, 0xff0b06, 0xff0000},

    {/* COLORMAP_SEISMIC */
     0x00004d, 0x000057, 0x000061, 0x00006b, 0x000075, 0x00007f, 0x000089, 0x000093, 0x00009d, 0x0000a7, 0x0000b1,
     0x0000bb, 0x0000c5, 0x0000cf, 0x0000d9, 0x0000e4, 0x0000ed, 0x0000f7, 0x0303ff, 0x1212ff, 0x2020ff, 0x2f2fff,
     0x3d3dff, 0x4b4bff, 0x5a5aff, 0x6868ff, 0x7777ff, 0x8585ff, 0x9393ff, 0xa2a2ff, 0xb0b0ff, 0xbebeff, 0xcdcdff,
     0xdbdbff, 0xe9e9ff, 0xf8f8ff, 0xfff8f8, 0xffe9e9, 0xffdbdb, 0xffcdcd, 0xffbebe, 0xffb0b0, 0xffa2a2, 0xff9393,
     0xff8585, 0xff7777, 0xff6868, 0xff5a5a, 0xff4b4b, 0xff3d3d, 0xff2f2f, 0xff2020, 0xff1212, 0xff0303, 0xfa0000,
     0xf30000, 0xec0000, 0xe40000, 0xdd0000, 0xd60000, 0xcf0000, 0xc80000, 0xc10000, 0xb90000, 0xb20000, 0xab0000,
     0xa30000, 0x9d0000, 0x950000, 0x8e0000, 0x870000, 0x800000},

    {/* COLORMAP_TERRAIN */
     0x333399, 0x2f3da3, 0x2a46ac, 0x2450b6, 0x2059bf, 0x1b63c9, 0x176dd3, 0x1276dc, 0x0d7fe5, 0x0889ef, 0x0393f9,
     0x009cf8, 0x00a3e2, 0x00aacd, 0x00b2b7, 0x00b9a2, 0x00c08c, 0x00c777, 0x03cd66, 0x12cf69, 0x20d36d, 0x2fd56f,
     0x3dd872, 0x4bdb75, 0x5ade78, 0x68e17b, 0x77e37d, 0x85e781, 0x93ea84, 0xa2ec86, 0xb0ef89, 0xbef28c, 0xcdf58f,
     0xdbf791, 0xe9fb95, 0xf8fe98, 0xfbfa97, 0xf4f193, 0xede890, 0xe6df8b, 0xdfd687, 0xd7cc84, 0xd0c380, 0xc9ba7c,
     0xc2b178, 0xbba874, 0xb49e71, 0xac956c, 0xa58c69, 0x9e8365, 0x977a60, 0x90715d, 0x886859, 0x815e55, 0x85635c,
     0x8c6c65, 0x93756e, 0x9a7e78, 0xa28882, 0xa9918c, 0xb09a95, 0xb7a39f, 0xbeaca8, 0xc6b6b2, 0xcdbfbc, 0xd4c8c5,
     0xdbd1cf, 0xe2dad8, 0xe9e4e2, 0xf1edec, 0xf8f6f5, 0xffffff},

    {/* COLORMAP_VIRIDIS */
     0x440154, 0x46065a, 0x460b5e, 0x471164, 0x481768, 0x481b6d, 0x482070, 0x482475, 0x482979, 0x472d7b, 0x46327e,
     0x453681, 0x443a83, 0x423f85, 0x414387, 0x3f4788, 0x3e4b89, 0x3c4f8a, 0x3a538b, 0x39568c, 0x375b8d, 0x355e8d,
     0x33628d, 0x31668e, 0x30698e, 0x2e6d8e, 0x2d708e, 0x2c738e, 0x2a778e, 0x297a8e, 0x277e8e, 0x26818e, 0x25848e,
     0x24888e, 0x228b8d, 0x218f8d, 0x20928c, 0x1f958b, 0x1f988b, 0x1e9c89, 0x1fa088, 0x1fa287, 0x21a685, 0x23a983,
     0x26ad81, 0x2ab07f, 0x2eb37c, 0x34b679, 0x39b977, 0x3fbc73, 0x45c06f, 0x4cc26c, 0x54c568, 0x5bc864, 0x63cb5f,
     0x6bcd5b, 0x73d056, 0x7bd250, 0x85d44a, 0x8ed645, 0x96d83f, 0xa0da39, 0xa9dc33, 0xb3dd2c, 0xbddf26, 0xc6e020,
     0xd0e11c, 0xd9e319, 0xe3e418, 0xece51b, 0xf5e61f, 0xfde725},

    {/* COLORMAP_INFERNO */
     0x000004, 0x020109, 0x030210, 0x060419, 0x090620, 0x0d0829, 0x110a31, 0x160b39, 0x1c0c43, 0x220c4b, 0x280b53,
     0x2e0a5a, 0x340a5f, 0x3a0964, 0x410a67, 0x470b6a, 0x4d0c6b, 0x520e6d, 0x58106e, 0x5d126e, 0x64156e, 0x69166e,
     0x6f196e, 0x751a6e, 0x7a1d6d, 0x801f6c, 0x86216b, 0x8c2369, 0x912568, 0x972766, 0x9c2964, 0xa22b62, 0xa82e5f,
     0xad305c, 0xb3325a, 0xb83556, 0xbe3853, 0xc33b4f, 0xc73e4c, 0xcc4248, 0xd14644, 0xd54a41, 0xda4e3c, 0xde5237,
     0xe25734, 0xe65d2f, 0xe9612b, 0xec6726, 0xef6d22, 0xf1731d, 0xf37918, 0xf67e14, 0xf8850f, 0xf98b0b, 0xfa9207,
     0xfb9806, 0xfc9f07, 0xfca60b, 0xfcad11, 0xfcb418, 0xfbbb20, 0xfac228, 0xf9c831, 0xf8d03b, 0xf6d746, 0xf4de51,
     0xf3e55d, 0xf1eb6c, 0xf1f17a, 0xf3f689, 0xf7fa98, 0xfcffa4},

    {/* COLORMAP_PLASMA */
     0x0d0887, 0x18068b, 0x20068f, 0x280592, 0x2e0595, 0x350498, 0x3b049a, 0x41049d, 0x48039f, 0x4d02a1, 0x5302a3,
     0x5901a5, 0x5e01a6, 0x6400a7, 0x6900a8, 0x6f00a8, 0x7401a8, 0x7a02a8, 0x7f04a8, 0x8405a7, 0x8a09a5, 0x8e0ca4,
     0x9410a2, 0x99159f, 0x9d189d, 0xa21d9a, 0xa62098, 0xab2494, 0xaf2991, 0xb32c8e, 0xb7318a, 0xbb3488, 0xbf3984,
     0xc33d80, 0xc6417d, 0xca457a, 0xcc4977, 0xd04d73, 0xd35271, 0xd6556d, 0xda596a, 0xdc5d67, 0xdf6263, 0xe26561,
     0xe56a5d, 0xe76f5a, 0xe97257, 0xec7754, 0xef7b51, 0xf0804e, 0xf3844b, 0xf48948, 0xf68f44, 0xf79342, 0xf9983e,
     0xfa9d3b, 0xfba238, 0xfca735, 0xfdad33, 0xfdb22f, 0xfeb72c, 0xfebd2a, 0xfdc328, 0xfdc927, 0xfcce25, 0xfbd424,
     0xfada24, 0xf8e025, 0xf6e626, 0xf4ed27, 0xf1f327, 0xf0f921},

    {/* COLORMAP_MAGMA */
     0x000004, 0x020109, 0x030310, 0x060518, 0x08071f, 0x0c0926, 0x110b2e, 0x140e36, 0x19103e, 0x1d1148, 0x221150,
     0x281159, 0x2d1161, 0x341068, 0x390f6f, 0x400f74, 0x461078, 0x4c117a, 0x52137c, 0x57157e, 0x5d177f, 0x631a80,
     0x681c81, 0x6e1d81, 0x732081, 0x792282, 0x7f2482, 0x842681, 0x8a2981, 0x902a81, 0x952c80, 0x9b2e7f, 0xa1307e,
     0xa7317d, 0xad347c, 0xb3367a, 0xb83779, 0xbf3a77, 0xc43c75, 0xca3e72, 0xd0416f, 0xd5446d, 0xdb476a, 0xdf4b68,
     0xe44f64, 0xe95362, 0xec5860, 0xf05f5e, 0xf2645c, 0xf56b5c, 0xf7715c, 0xf9785d, 0xfa7f5e, 0xfb8660, 0xfc8c63,
     0xfd9367, 0xfd9a6a, 0xfea06e, 0xfea872, 0xfeae77, 0xfeb57b, 0xfebb81, 0xfec286, 0xfec98c, 0xfecf92, 0xfed698,
     0xfddc9e, 0xfde3a4, 0xfdeaaa, 0xfcf0b2, 0xfcf6b8, 0xfcfdbf}};

static font_alias_t font_aliases[] = {
    {"Times Roman", {"NimbusRoman-Regular.otf", "texgyretermes-regular.otf", "FreeSerif.otf"}},
    {"Times Italic", {"NimbusRoman-Italic.otf", "texgyretermes-italic.otf", "FreeSerifItalic.otf"}},
    {"Times Bold", {"NimbusRoman-Bold.otf", "texgyretermes-bold.otf", "FreeSerifBold.otf"}},
    {"Times Bold Italic", {"NimbusRoman-BoldItalic.otf", "texgyretermes-bolditalic.otf", "FreeSerifBoldItalic.otf"}},
    {"Helvetica", {"NimbusSans-Regular.otf", "texgyreheros-regular.otf", "FreeSans.otf"}},
    {"Helvetica Oblique", {"NimbusSans-Italic.otf", "texgyreheros-italic.otf", "FreeSansOblique.otf"}},
    {"Helvetica Bold", {"NimbusSans-Bold.otf", "texgyreheros-bold.otf", "FreeSansBold.otf"}},
    {"Helvetica Bold Oblique", {"NimbusSans-BoldItalic.otf", "texgyreheros-bolditalic.otf", "FreeSansBoldOblique.otf"}},
    {"Courier", {"NimbusMonoPS-Regular.otf", "texgyrecursor-regular.otf", "FreeMono.otf"}},
    {"Courier Oblique", {"NimbusMonoPS-Italic.otf", "texgyrecursor-italic.otf", "FreeMonoOblique.otf"}},
    {"Courier Bold", {"NimbusMonoPS-Bold.otf", "texgyrecursor-bold.otf", "FreeMonoBold.otf"}},
    {"Courier Bold Oblique",
     {"NimbusMonoPS-BoldItalic.otf", "texgyrecursor-bolditalic.otf", "FreeMonoBoldOblique.otf"}},
    {"Bookman Light", {"URWBookman-Light.otf", "texgyrebonum-regular.otf", NULL}},
    {"Bookman Light Italic", {"URWBookman-LightItalic.otf", "texgyrebonum-italic.otf", NULL}},
    {"Bookman Demi", {"URWBookman-Demi.otf", "texgyrebonum-bold.otf", NULL}},
    {"Bookman Demi Italic", {"URWBookman-DemiItalic.otf", "texgyrebonum-bolditalic.otf", NULL}},
    {"New Century Schoolbook Roman", {"C059-Roman.otf", "texgyreschola-regular.otf", NULL}},
    {"New Century Schoolbook Italic", {"C059-Italic.otf", "texgyreschola-italic.otf", NULL}},
    {"New Century Schoolbook Bold", {"C059-Bold.otf", "texgyreschola-bold.otf", NULL}},
    {"New Century Schoolbook Bold Italic", {"C059-BdIta.otf", "texgyreschola-bolditalic.otf", NULL}},
    {"Avantgarde Book", {"URWGothic-Book.otf", "texgyreadventor-regular.otf", NULL}},
    {"Avantgarde Book Oblique", {"URWGothic-BookOblique.otf", "texgyreadventor-italic.otf", NULL}},
    {"Avantgarde Demi", {"URWGothic-Demi.otf", "texgyreadventor-bold.otf", NULL}},
    {"Avantgarde Demi Oblique", {"URWGothic-DemiOblique.otf", "texgyreadventor-bolditalic.otf", NULL}},
    {"Palatino Roman", {"P052-Roman.otf", "texgyrepagella-regular.otf", NULL}},
    {"Palatino Italic", {"P052-Italic.otf", "texgyrepagella-italic.otf", NULL}},
    {"Palatino Bold", {"P052-Bold.otf", "texgyrepagella-bold.otf", NULL}},
    {"Palatino Bold Italic", {"P052-BoldItalic.otf", "texgyrepagella-bolditalic.otf", NULL}},
    {"Zapf Chancery Medium Italica", {"Z003-MediumItalic.otf", "texgyrechorus-mediumitalic.otf", NULL}},
    {"Zapf Dingbats", {"D050000L.otf", NULL, NULL}},
};

static int num_font_aliases = sizeof(font_aliases) / sizeof(font_aliases[0]);

static int math_font = GR_DEFAULT_MATH_FONT;

static double sizex = 0;

static int regeneration_flags = 0;

static char *titles3d[3] = {NULL, NULL, NULL};

static double titles3d_text_height = 0;

static char *xcalloc(int count, int size)
{
  char *result = (char *)calloc(count, size);
  if (!result)
    {
      fprintf(stderr, "out of virtual memory\n");
      abort();
    }
  return (result);
}

static char *xmalloc(int size)
{
  char *result = (char *)malloc(size);
  if (!result)
    {
      fprintf(stderr, "out of virtual memory\n");
      abort();
    }
  return (result);
}

static char *xrealloc(void *ptr, int size)
{
  char *result = (char *)realloc(ptr, size);
  if (!result)
    {
      fprintf(stderr, "out of virtual memory\n");
      abort();
    }
  return (result);
}

static void reallocate(int npoints)
{
  while (npoints >= maxpath) maxpath += POINT_INC;

  opcode = (unsigned char *)xrealloc(opcode, maxpath * sizeof(unsigned char));
  xpath = (double *)xrealloc(xpath, maxpath * sizeof(double));
  xpoint = (double *)xrealloc(xpoint, maxpath * sizeof(double));
  ypath = (double *)xrealloc(ypath, maxpath * sizeof(double));
  ypoint = (double *)xrealloc(ypoint, maxpath * sizeof(double));
  zpoint = (double *)xrealloc(zpoint, maxpath * sizeof(double));
  code = (int *)xrealloc(code, maxpath * sizeof(int));
}

static double blog(double base, double x)
{
  return log(x) / log(base);
}

minmax_t find_minmax(int n, double *values)
{
  int i;
  double d, min, max;
  for (i = 0; i != n && is_nan(values[i]); ++i)
    ;
  if (i == n) return (minmax_t){NAN, NAN};
  min = max = values[i];
  for (++i; i != n; ++i)
    {
      d = values[i];
      if (min > d) min = d;
      if (max < d) max = d;
    }
  return (minmax_t){min, max};
}

static double x_lin(double x)
{
  double result;

  if (GR_OPTION_X_LOG & lx.scale_options)
    {
      if (x > 0)
        result = lx.a * blog(lx.basex, x) + lx.b;
      else
        result = NAN;
    }
  else
    result = x;

  if (GR_OPTION_FLIP_X & lx.scale_options) result = lx.xmax - result + lx.xmin;

  return (result);
}

static double y_lin(double y)
{
  double result;

  if (GR_OPTION_Y_LOG & lx.scale_options)
    {
      if (y > 0)
        result = lx.c * blog(lx.basey, y) + lx.d;
      else
        result = NAN;
    }
  else
    result = y;

  if (GR_OPTION_FLIP_Y & lx.scale_options) result = lx.ymax - result + lx.ymin;

  return (result);
}

static double z_lin(double z)
{
  double result;

  if (GR_OPTION_Z_LOG & lx.scale_options)
    {
      if (z > 0)
        result = lx.e * blog(lx.basez, z) + lx.f;
      else
        result = NAN;
    }
  else
    result = z;

  if (GR_OPTION_FLIP_Z & lx.scale_options) result = lx.zmax - result + lx.zmin;

  return (result);
}

static double x_log(double x)
{
  if (GR_OPTION_FLIP_X & lx.scale_options) x = lx.xmax - x + lx.xmin;

  if (GR_OPTION_X_LOG & lx.scale_options)
    return (pow(lx.basex, (double)((x - lx.b) / lx.a)));
  else
    return (x);
}

static double y_log(double y)
{
  if (GR_OPTION_FLIP_Y & lx.scale_options) y = lx.ymax - y + lx.ymin;

  if (GR_OPTION_Y_LOG & lx.scale_options)
    return (pow(lx.basey, (double)((y - lx.d) / lx.c)));
  else
    return (y);
}

static double z_log(double z)
{
  if (GR_OPTION_FLIP_Z & lx.scale_options) z = lx.zmax - z + lx.zmin;

  if (GR_OPTION_Z_LOG & lx.scale_options)
    return (pow(lx.basez, (double)((z - lx.f) / lx.e)));
  else
    return (z);
}

static double atan_2(double x, double y)
{
  double a;

  if (y == 0)
    if (x < 0)
      a = -M_PI;
    else
      a = M_PI;
  else
    a = atan(x / y);

  return (a);
}

static void apply_world_xform(double *x, double *y, double *z)
{
  double xw, yw, zw;

  if (gpx.projection_type == GR_PROJECTION_DEFAULT)
    {
      xw = wx.a1 * *x + wx.a2 * *y + wx.b;
      yw = wx.c1 * *x + wx.c2 * *y + wx.c3 * *z + wx.d;
      zw = wx.a2 * wx.c3 * *x - wx.a1 * wx.c3 * *y - wx.c1 * wx.a2 * *z + wx.a1 * wx.c2 * *z;
    }
  else
    {
      double fov = gpx.fov * M_PI / 180; /* camera angle of perspektiv projection */
      double xaspect = (vxmax - vxmin) / (vymax - vymin);
      double yaspect = 1.0 / xaspect;
      double F[3]; /* direction between camera and focus point */
      double norm_func;
      double f[3];

      double x_val = *x * tx.x_axis_scale;
      double y_val = *y * tx.y_axis_scale;
      double z_val = *z * tx.z_axis_scale;

      if (xaspect < 1.0)
        {
          xaspect = 1.0;
        }
      else
        {
          yaspect = 1.0;
        }
      F[0] = tx.focus_point_x - tx.camera_pos_x;
      F[1] = tx.focus_point_y - tx.camera_pos_y;
      F[2] = tx.focus_point_z - tx.camera_pos_z;
      norm_func = sqrt(F[0] * F[0] + F[1] * F[1] + F[2] * F[2]);
      f[0] = F[0] / norm_func;
      f[1] = F[1] / norm_func;
      f[2] = F[2] / norm_func;

      /* transformation */
      xw = (x_val - tx.camera_pos_x) * tx.s_x + (y_val - tx.camera_pos_y) * tx.s_y + (z_val - tx.camera_pos_z) * tx.s_z;
      yw = (x_val - tx.camera_pos_x) * tx.up_x + (y_val - tx.camera_pos_y) * tx.up_y +
           (z_val - tx.camera_pos_z) * tx.up_z;
      zw = (tx.camera_pos_x - x_val) * f[0] + (tx.camera_pos_y - y_val) * f[1] + (tx.camera_pos_z - z_val) * f[2];

      if (gpx.projection_type == GR_PROJECTION_PERSPECTIVE)
        {
          /* perspective projection */
          xw = ((cos(fov / 2) / sin(fov / 2)) / xaspect * xw);
          yw = ((cos(fov / 2) / sin(fov / 2)) / yaspect * yw);
          xw /= -zw;
          yw /= -zw;
        }
      else if (gpx.projection_type == GR_PROJECTION_ORTHOGRAPHIC)
        {
          /* orthographic projection */
          xw = (xw * 2 / (gpx.right - gpx.left) / xaspect - (gpx.left + gpx.right) / (gpx.right - gpx.left));
          yw = (yw * 2 / (gpx.top - gpx.bottom) / yaspect - (gpx.bottom + gpx.top) / (gpx.top - gpx.bottom));
          zw = (zw * -2 / (gpx.far_plane - gpx.near_plane) -
                (gpx.far_plane + gpx.near_plane) / (gpx.far_plane - gpx.near_plane));
        }
    }

  *x = xw;
  *y = yw;
  *z = zw;
}

static void foreach_openws(void (*routine)(int, void *), void *arg)
{
  int state, count, n = 1, errind, ol, wkid;

  gks_inq_operating_state(&state);
  if (state >= GKS_K_WSOP)
    {
      gks_inq_open_ws(n, &errind, &ol, &wkid);
      for (count = ol; count >= 1; count--)
        {
          n = count;
          gks_inq_open_ws(n, &errind, &ol, &wkid);

          routine(wkid, arg);
        }
    }
}

static void foreach_activews(void (*routine)(int, void *), void *arg)
{
  int state, count, n = 1, errind, ol, wkid;

  gks_inq_operating_state(&state);
  if (state >= GKS_K_WSAC)
    {
      gks_inq_active_ws(n, &errind, &ol, &wkid);
      for (count = ol; count >= 1; count--)
        {
          n = count;
          gks_inq_active_ws(n, &errind, &ol, &wkid);

          routine(wkid, arg);
        }
    }
}

static void setspace(double zmin, double zmax, int rotation, int tilt)
{
  int errind, tnr;
  double wn[4], vp[4];
  double xmin = 0, xmax = 0, ymin = 0, ymax = 0, r, t, a, c;

  gks_inq_current_xformno(&errind, &tnr);
  gks_inq_xform(tnr, &errind, wn, vp);

  xmin = wn[0];
  xmax = wn[1];
  ymin = wn[2];
  ymax = wn[3];

  wx.zmin = zmin;
  wx.zmax = zmax;
  wx.phi = rotation;
  wx.delta = tilt;

  r = arc(rotation);
  wx.a1 = cos(r);
  wx.a2 = sin(r);

  a = (xmax - xmin) / (wx.a1 + wx.a2);
  wx.b = xmin;

  wx.a1 = a * wx.a1 / (xmax - xmin);
  wx.a2 = a * wx.a2 / (ymax - ymin);
  wx.b = wx.b - wx.a1 * xmin - wx.a2 * ymin;

  t = arc(tilt);
  wx.c1 = (pow(cos(r), 2.) - 1.) * tan(t / 2.);
  wx.c2 = -(pow(sin(r), 2.) - 1.) * tan(t / 2.);
  wx.c3 = cos(t);

  c = (ymax - ymin) / (wx.c2 + wx.c3 - wx.c1);
  wx.d = ymin - c * wx.c1;

  wx.c1 = c * wx.c1 / (xmax - xmin);
  wx.c2 = c * wx.c2 / (ymax - ymin);
  wx.c3 = c * wx.c3 / (zmax - zmin);
  wx.d = wx.d - wx.c1 * xmin - wx.c2 * ymin - wx.c3 * zmin;
}

static int setscale(int options)
{
  int errind, tnr;
  double wn[4], vp[4];
  double x_min, x_max, y_min, y_max, z_min, z_max;
  int result = 0;

  gks_inq_current_xformno(&errind, &tnr);
  gks_inq_xform(tnr, &errind, wn, vp);

  x_min = wn[0];
  x_max = wn[1];
  y_min = wn[2];
  y_max = wn[3];
  z_min = wx.zmin;
  z_max = wx.zmax;

  nx.a = (vp[1] - vp[0]) / (x_max - x_min);
  nx.b = vp[0] - x_min * nx.a;
  nx.c = (vp[3] - vp[2]) / (y_max - y_min);
  nx.d = vp[2] - y_min * nx.c;

  lx.scale_options = 0;

  lx.xmin = x_min;
  lx.xmax = x_max;

  if ((GR_OPTION_X_LOG | GR_OPTION_X_LOG2 | GR_OPTION_X_LN) & options)
    {
      if (x_min > 0)
        {
          if (GR_OPTION_X_LOG2 & options)
            {
              lx.basex = 2.0;
              lx.basex_s = "2";
              lx.scale_options |= GR_OPTION_X_LOG2;
            }
          else if (GR_OPTION_X_LN & options)
            {
              lx.basex = exp(1);
              lx.basex_s = "e";
              lx.scale_options |= GR_OPTION_X_LN;
            }
          else
            {
              lx.basex = 10.0;
              lx.basex_s = "10";
            }

          lx.a = (x_max - x_min) / blog(lx.basex, x_max / x_min);
          lx.b = x_min - lx.a * blog(lx.basex, x_min);
          lx.scale_options |= GR_OPTION_X_LOG;
        }
      else
        result = -1;
    }

  lx.ymin = y_min;
  lx.ymax = y_max;

  if ((GR_OPTION_Y_LOG | GR_OPTION_Y_LOG2 | GR_OPTION_Y_LN) & options)
    {
      if (y_min > 0)
        {
          if (GR_OPTION_Y_LOG2 & options)
            {
              lx.basey = 2.0;
              lx.basey_s = "2";
              lx.scale_options |= GR_OPTION_Y_LOG2;
            }
          else if (GR_OPTION_Y_LN & options)
            {
              lx.basey = exp(1);
              lx.basey_s = "e";
              lx.scale_options |= GR_OPTION_Y_LN;
            }
          else
            {
              lx.basey = 10.0;
              lx.basey_s = "10";
            }

          lx.c = (y_max - y_min) / blog(lx.basey, y_max / y_min);
          lx.d = y_min - lx.c * blog(lx.basey, y_min);
          lx.scale_options |= GR_OPTION_Y_LOG;
        }
      else
        result = -1;
    }

  setspace(z_min, z_max, wx.phi, wx.delta);

  lx.zmin = z_min;
  lx.zmax = z_max;

  if ((GR_OPTION_Z_LOG | GR_OPTION_Z_LOG2 | GR_OPTION_Z_LN) & options)
    {
      if (lx.zmin > 0)
        {
          if (GR_OPTION_Z_LOG2 & options)
            {
              lx.basez = 2.0;
              lx.basez_s = "2";
              lx.scale_options |= GR_OPTION_Z_LOG2;
            }
          else if (GR_OPTION_Z_LN & options)
            {
              lx.basez = exp(1);
              lx.basez_s = "e";
              lx.scale_options |= GR_OPTION_Z_LN;
            }
          else
            {
              lx.basez = 10.0;
              lx.basez_s = "10";
            }

          lx.e = (lx.zmax - lx.zmin) / blog(lx.basez, lx.zmax / lx.zmin);
          lx.f = lx.zmin - lx.e * blog(lx.basez, lx.zmin);
          lx.scale_options |= GR_OPTION_Z_LOG;
        }
      else
        result = -1;
    }

  if (GR_OPTION_FLIP_X & options) lx.scale_options |= GR_OPTION_FLIP_X;

  if (GR_OPTION_FLIP_Y & options) lx.scale_options |= GR_OPTION_FLIP_Y;

  if (GR_OPTION_FLIP_Z & options) lx.scale_options |= GR_OPTION_FLIP_Z;

  return result;
}

static void initialize(int state)
{
  int tnr = WC, font = 3, options = 0;
  double xmin = 0.2, xmax = 0.9, ymin = 0.2, ymax = 0.9;
  int asf[13] = {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1};
  double size = 2, height = 0.027;
  char *env;

  if (state == GKS_K_GKCL)
    {
      gks_select_xform(tnr);
      gks_set_viewport(tnr, xmin, xmax, ymin, ymax);
      gks_set_viewport(MODERN_NDC, xmin, xmax, ymin, ymax);
      gks_set_window(MODERN_NDC, -1, 1, -1, 1);

      gks_set_asf(asf);
      gks_set_pmark_size(size);
      gks_set_pmark_type(GKS_K_MARKERTYPE_ASTERISK);
      gks_set_text_fontprec(font, GKS_K_TEXT_PRECISION_STRING);
      gks_set_text_height(height);
      gks_set_text_align(GKS_K_TEXT_HALIGN_LEFT, GKS_K_TEXT_VALIGN_BASE);
    }

  autoinit = 0;
  double_buf = gks_getenv("GKS_DOUBLE_BUF") != NULL;

  env = gks_getenv("GR_SCALE_FACTOR");
  if (env != NULL)
    {
      scale_factor = atof(env);
      if (scale_factor <= 0)
        {
          fprintf(stderr, "invalid scale factor (%s) - ignored\n", env);
          scale_factor = 1.0;
        }
    }

  display = gks_getenv("GR_DISPLAY");
  if (display)
    if (*display == '\0') display = NULL;

  debug = gks_getenv("GR_DEBUG");
  flag_stream = flag_graphics || debug != NULL;

  setscale(options);

  txoff[0] = txoff[1] = 0;

  math_font = GR_DEFAULT_MATH_FONT;
}

#ifdef SIGUSR1

static void resetgks(int sig)
{
  static int exiting = 0;

  if (sig == SIGUSR1)
    {
      if (!exiting)
        {
          exiting = 1;
          gr_emergencyclosegks();

          signal(SIGUSR1, previous_handler);
          if (previous_handler != SIG_DFL) raise(SIGUSR1);

          exiting = 0;
        }
    }
}

#else

static void resetgks(void)
{
  static int exiting = 0;

  if (!exiting)
    {
      exiting = 1;
      gr_emergencyclosegks();
      exiting = 0;
    }
}

#endif


static void initgks(void)
{
  int state, errfil = 0, wkid = 1, errind, conid, wtype, color;
  double r, g, b;

  gks_inq_operating_state(&state);
  if (state == GKS_K_GKCL) gks_open_gks(errfil);

  initialize(state);

  if (state == GKS_K_GKCL || state == GKS_K_GKOP)
    {
      gks_open_ws(wkid, GKS_K_CONID_DEFAULT, GKS_K_WSTYPE_DEFAULT);
      gks_activate_ws(wkid);
    }

  gks_inq_ws_conntype(wkid, &errind, &conid, &wtype);
  if (!double_buf)
    {
      double_buf =
          wtype == 380 || wtype == 381 || wtype == 400 || wtype == 410 || wtype == 411 || wtype == 412 || wtype == 413;
    }

  if (display)
    {
      if (gr_openstream(display) == 0)
        {
          gr_writestream(XML_HEADER);
          gr_writestream(GR_HEADER);
          flag_stream = flag_graphics = 1;
        }
      else
        fprintf(stderr, "%s: open failed\n", display);
    }

  for (color = 0; color < MAX_COLOR; color++)
    {
      gks_inq_color_rep(wkid, color, GKS_K_VALUE_SET, &errind, &r, &g, &b);
      rgb[color] = ((nint(r * 255) & 0xff)) | ((nint(g * 255) & 0xff) << 8) | ((nint(b * 255) & 0xff) << 16);
      used[color] = 0;
    }

  if (gks_getenv("GKS_NO_EXIT_HANDLER") == NULL)
    {
#ifdef SIGUSR1
      previous_handler = signal(SIGUSR1, resetgks);
#else
      atexit(resetgks);
#endif
    }
}

void gr_initgr(void)
{
  if (!autoinit)
    {
      gks_init_gks();

      initialize(GKS_K_GKCL);
    }
}

int gr_debug(void)
{
  return debug != NULL;
}

void gr_opengks(void)
{
  int errfil = 0;

  gks_open_gks(errfil);

  initialize(GKS_K_GKCL);
}

void gr_closegks(void)
{
  gks_close_gks();
  autoinit = 1;
}

/*!
 * Get the current display size.
 *
 * \param[out] mwidth Display width in meters
 * \param[out] mheight Display height in meters
 * \param[out] width Display width in pixels
 * \param[out] height Display height in pixels
 *
 * Depending on the current workstation type, the current display might be
 * the primary screen (e.g. when using gksqt or GKSTerm) or a purely virtual
 * display (e.g. when using Cairo). When a high DPI screen is used as the
 * current display, width and height will be in logical pixels.
 */
void gr_inqdspsize(double *mwidth, double *mheight, int *width, int *height)
{
  int n = 1, errind, wkid, ol, conid, wtype, dcunit;

  check_autoinit;

  gks_inq_open_ws(n, &errind, &ol, &wkid);
  gks_inq_ws_conntype(wkid, &errind, &conid, &wtype);
  gks_inq_max_ds_size(wtype, &errind, &dcunit, mwidth, mheight, width, height);
}

/*!
 * Open a graphical workstation.
 *
 * \param[in] workstation_id a workstation identifier
 * \param[in] connection a connection identifier
 * \param[in] type the desired workstation type
 *
 *
 * \verbatim embed:rst:leading-asterisk
 *
 * Available workstation types:
 *
 * +-------------+------------------------------------------------------+
 * |     **Type**|**Description**                                       |
 * +-------------+------------------------------------------------------+
 * |            5|Workstation Independent Segment Storage               |
 * +-------------+------------------------------------------------------+
 * |           41|Windows GDI                                           |
 * +-------------+------------------------------------------------------+
 * |      61 - 64|PostScript (b/w, color)                               |
 * +-------------+------------------------------------------------------+
 * |     101, 102|Portable Document Format (plain, compressed)          |
 * +-------------+------------------------------------------------------+
 * |    210 - 213|X Windows                                             |
 * +-------------+------------------------------------------------------+
 * |          214|Sun Raster file (RF)                                  |
 * +-------------+------------------------------------------------------+
 * |     215, 218|Graphics Interchange Format (GIF87, GIF89)            |
 * +-------------+------------------------------------------------------+
 * |          216|Motif User Interface Language (UIL)                   |
 * +-------------+------------------------------------------------------+
 * |          320|Windows Bitmap (BMP)                                  |
 * +-------------+------------------------------------------------------+
 * |          321|JPEG image file                                       |
 * +-------------+------------------------------------------------------+
 * |          322|Portable Network Graphics file (PNG)                  |
 * +-------------+------------------------------------------------------+
 * |          323|Tagged Image File Format (TIFF)                       |
 * +-------------+------------------------------------------------------+
 * |          371|Gtk                                                   |
 * +-------------+------------------------------------------------------+
 * |          380|wxWidgets                                             |
 * +-------------+------------------------------------------------------+
 * |          381|Qt4                                                   |
 * +-------------+------------------------------------------------------+
 * |          382|Scaleable Vector Graphics (SVG)                       |
 * +-------------+------------------------------------------------------+
 * |          390|Windows Metafile                                      |
 * +-------------+------------------------------------------------------+
 * |          400|Quartz                                                |
 * +-------------+------------------------------------------------------+
 * |          410|Socket driver                                         |
 * +-------------+------------------------------------------------------+
 * |          415|0MQ driver                                            |
 * +-------------+------------------------------------------------------+
 * |          420|OpenGL                                                |
 * +-------------+------------------------------------------------------+
 *
 * \endverbatim
 */
void gr_openws(int workstation_id, char *connection, int type)
{
  if (connection)
    {
      if (!*connection) connection = NULL;
    }
  gks_open_ws(workstation_id, connection, type);
}

/*!
 * Close the specified workstation.
 *
 * \param[in] workstation_id a workstation identifier
 */
void gr_closews(int workstation_id)
{
  gks_close_ws(workstation_id);
}

/*!
 * Activate the specified workstation.
 *
 * \param[in] workstation_id a workstation identifier
 */
void gr_activatews(int workstation_id)
{
  gks_activate_ws(workstation_id);
}

/*!
 * Deactivate the specified workstation.
 *
 * \param[in] workstation_id a workstation identifier
 */
void gr_deactivatews(int workstation_id)
{
  gks_deactivate_ws(workstation_id);
}

static void configure(int workstation_id, void *dummy)
{
  GR_UNUSED(dummy);
  gks_configure_ws(workstation_id);
}

/*!
 * Configure the specified workstation.
 */
void gr_configurews(void)
{
  foreach_activews((void (*)(int, void *))configure, (void *)NULL);
}

static void clear(int workstation_id, int *clearflag)
{
  int wkid = workstation_id, state, errind, conid, wtype, wkcat;

  gks_inq_operating_state(&state);
  if (state == GKS_K_SGOP) gks_close_seg();

  gks_inq_ws_conntype(wkid, &errind, &conid, &wtype);
  gks_inq_ws_category(wtype, &errind, &wkcat);

  if (wkcat == GKS_K_WSCAT_OUTPUT || wkcat == GKS_K_WSCAT_OUTIN || wkcat == GKS_K_WSCAT_MO)
    {
      gks_clear_ws(wkid, *clearflag);
      gks_update_ws(wkid, GKS_K_POSTPONE_FLAG);
    }
}

void gr_clearws(void)
{
  int clearflag = double_buf ? GKS_K_CLEAR_CONDITIONALLY : GKS_K_CLEAR_ALWAYS;

  check_autoinit;

  foreach_activews((void (*)(int, void *))clear, (void *)&clearflag);

  if (flag_stream)
    {
      gr_writestream(GR_TRAILER);
      gr_flushstream(1);
      gr_writestream(XML_HEADER);
      gr_writestream(GR_HEADER);
    }

  def_color = 0;
}

static void update(int workstation_id, int *regenflag)
{
  int wkid = workstation_id, errind, conid, wtype, wkcat;

  gks_inq_ws_conntype(wkid, &errind, &conid, &wtype);
  gks_inq_ws_category(wtype, &errind, &wkcat);

  if (wkcat == GKS_K_WSCAT_OUTPUT || wkcat == GKS_K_WSCAT_OUTIN) gks_update_ws(wkid, *regenflag);
}

void gr_updatews(void)
{
  int regenflag = double_buf ? GKS_K_PERFORM_FLAG : GKS_K_POSTPONE_FLAG;
  regenflag |= GKS_K_WRITE_PAGE_FLAG;

  check_autoinit;

  foreach_openws((void (*)(int, void *))update, (void *)&regenflag);

  if (flag_stream)
    if (display)
      {
        gr_writestream(GR_TRAILER);
        gr_flushstream(0);
        gr_writestream(GR_HEADER);
      }
}

static void fillarea(int n, double *x, double *y)
{
  int errind, style;
  int npoints = n;
  double *px = x, *py = y;
  int i;

  check_autoinit;

  if (lx.scale_options)
    {
      if (npoints >= maxpath) reallocate(npoints);

      px = xpoint;
      py = ypoint;
      for (i = 0; i < npoints; i++)
        {
          px[i] = x_lin(x[i]);
          py[i] = y_lin(y[i]);
        }
    }

  gks_inq_fill_int_style(&errind, &style);

  if (style == GKS_K_INTSTYLE_SOLID_WITH_BORDER)
    {
      if (npoints + 1 >= maxpath) reallocate(npoints + 1);

      code[0] = 'M';
      for (i = 1; i < npoints; i++) code[i] = 'L';
      code[npoints] = 'F';

      gks_gdp(npoints, px, py, GKS_K_GDP_DRAW_PATH, npoints + 1, code);
    }
  else
    {
      gks_fillarea(npoints, px, py);
    }
}

static void print_int_array(char *name, int n, int *data)
{
  int i;

  gr_writestream(" %s=\"", name);
  for (i = 0; i < n; i++)
    {
      if (i > 0) gr_writestream(" ");
      gr_writestream("%d", data[i]);
    }
  gr_writestream("\"");
}

static void print_float_array(char *name, int n, double *data)
{
  int i;

  gr_writestream(" %s=\"", name);
  for (i = 0; i < n; i++)
    {
      if (i > 0) gr_writestream(" ");
      gr_writestream("%g", data[i]);
    }
  gr_writestream("\"");
}

static void print_vertex_array(char *name, int n, vertex_t *vertices)
{
  int i;

  gr_writestream(" %s=\"", name);
  for (i = 0; i < n; i++)
    {
      if (i > 0) gr_writestream(" ");
      gr_writestream("%g %g", vertices[i].x, vertices[i].y);
    }
  gr_writestream("\"");
}

static void print_byte_array(char *name, int n, unsigned char *data)
{
  int i;

  gr_writestream(" %s=\"", name);
  for (i = 0; i < n; i++)
    {
      if (i > 0) gr_writestream(" ");
      gr_writestream("%d", data[i]);
    }
  gr_writestream("\"");
}

static void primitive(char *name, int n, double *x, double *y)
{
  gr_writestream("<%s len=\"%d\"", name, n);
  print_float_array("x", n, x);
  print_float_array("y", n, y);
  gr_writestream("/>\n");
}

static void polyline(int n, double *x, double *y)
{
  int i, npoints;

  if (n >= maxpath) reallocate(n);

  npoints = 0;
  for (i = 0; i < n; i++)
    {
      xpoint[npoints] = x_lin(x[i]);
      ypoint[npoints] = y_lin(y[i]);
      if (is_nan(xpoint[npoints]) || is_nan(ypoint[npoints]))
        {
          if (npoints >= 2) gks_polyline(npoints, xpoint, ypoint);

          npoints = 0;
        }
      else
        npoints++;
    }

  if (npoints >= 2) gks_polyline(npoints, xpoint, ypoint);
}

/*!
 * Draw a polyline using the current line attributes, starting from the
 * first data point and ending at the last data point.
 *
 * \param[in] n The number of points
 * \param[in] x A pointer to the X coordinates
 * \param[in] y A pointer to the Y coordinates
 *
 * The values for `x` and `y` are in world coordinates. The attributes that
 * control the appearance of a polyline are linetype, linewidth and color
 * index.
 */
void gr_polyline(int n, double *x, double *y)
{
  check_autoinit;

  polyline(n, x, y);

  if (flag_stream) primitive("polyline", n, x, y);
}

static void polymarker(int n, double *x, double *y)
{
  int i, npoints;

  if (n >= maxpath) reallocate(n);

  npoints = 0;
  for (i = 0; i < n; i++)
    {
      xpoint[npoints] = x_lin(x[i]);
      ypoint[npoints] = y_lin(y[i]);
      if (is_nan(xpoint[npoints]) || is_nan(ypoint[npoints]))
        {
          if (npoints >= 1) gks_polymarker(npoints, xpoint, ypoint);

          npoints = 0;
        }
      else
        npoints++;
    }

  if (npoints != 0) gks_polymarker(npoints, xpoint, ypoint);
}

/*!
 * Draw marker symbols centered at the given data points.
 *
 * \param[in] n The number of points
 * \param[in] x A pointer to the X coordinates
 * \param[in] y A pointer to the Y coordinates
 *
 * The values for `x` and `y` are in world coordinates. The attributes that
 * control the appearance of a polymarker are marker type, marker size
 * scale factor and color index.
 */
void gr_polymarker(int n, double *x, double *y)
{
  check_autoinit;

  polymarker(n, x, y);

  if (flag_stream) primitive("polymarker", n, x, y);
}

/*!
 * Allows you to specify a polygonal shape of an area to be filled.
 *
 * \param[in] n The number of points
 * \param[in] x A pointer to the X coordinates
 * \param[in] y A pointer to the Y coordinates
 *
 * The attributes that control the appearance of fill areas are fill area
 * interior style, fill area style index and fill area color index.
 */
void gr_fillarea(int n, double *x, double *y)
{
  fillarea(n, x, y);

  if (flag_stream) primitive("fillarea", n, x, y);
}

/*!
 * Display rasterlike images in a device-independent manner. The cell array
 * function partitions a rectangle given by two corner points into DIMX X DIMY
 * cells, each of them colored individually by the corresponding color index
 * of the given cell array.
 *
 * \param[in] xmin X coordinate of the lower left point of the rectangle
 * \param[in] xmax X coordinate of the upper right point of the rectangle
 * \param[in] ymin Y coordinate of the lower left point of the rectangle
 * \param[in] ymax Y coordinate of the upper right point of the rectangle
 * \param[in] dimx X dimension of the color index array
 * \param[in] dimy Y dimension of the color index array
 * \param[in] scol number of leading columns in the color index array
 * \param[in] srow number of leading rows in the color index array
 * \param[in] ncol total number of columns in the color index array
 * \param[in] nrow total number of rows in the color index array
 * \param[in] color color index array
 *
 * The values for `xmin`, `xmax`, `ymin` and `ymax` are in world coordinates.
 */
void gr_cellarray(double xmin, double xmax, double ymin, double ymax, int dimx, int dimy, int scol, int srow, int ncol,
                  int nrow, int *color)
{
  check_autoinit;

  gks_cellarray(x_lin(xmin), y_lin(ymax), x_lin(xmax), y_lin(ymin), dimx, dimy, scol, srow, ncol, nrow, color);

  if (flag_stream)
    {
      gr_writestream("<cellarray xmin=\"%g\" xmax=\"%g\" ymin=\"%g\" ymax=\"%g\" "
                     "dimx=\"%d\" dimy=\"%d\" scol=\"%d\" srow=\"%d\" "
                     "ncol=\"%d\" nrow=\"%d\"",
                     xmin, xmax, ymin, ymax, dimx, dimy, scol, srow, ncol, nrow);
      print_int_array("color", dimx * dimy, color);
      gr_writestream("/>\n");
    }
}

/*!
 * Display a two dimensional color index array with nonuniform cell sizes.
 *
 * \param[in] x ascending X coordinates of the cell edges in world coordinates
 * \param[in] y ascending Y coordinates of the cell edges in world coordinates
 * \param[in] dimx (possibly negated) X dimension of the color index array
 * \param[in] dimy (possibly negated) Y dimension of the color index array
 * \param[in] scol 1-based starting column of color index and x array
 * \param[in] srow 1-based starting row of color index and y array
 * \param[in] ncol number of columns displayed
 * \param[in] nrow number of rows displayed
 * \param[in] color color index array
 *
 * These memory accesses must be valid:
 * - `x[scol-1]` through `x[scol+ncol-2+clamp(dimx,0,1)]`
 * - `y[scol-1]` through `y[scol+ncol-2+clamp(dimy,0,1)]`
 * - `color[scol-1+(srow-1)*ncol]` through `color[scol+ncol-2+(srow+nrow-2)*ncol]`
 *
 * If `dimx`/`dimy` is positive, `x`/`y` must contain `dimx+1`/`dimy+1` elements.
 * The elements are the coordinates of the cell-edges, where the i-th and i+1-th
 * elements are the edges of the i-th cell in X/Y direction.
 *
 * If `dimx`/`dimy` is negative, `x`/`y` must contain `-dimx`/`-dimy` elements.
 * The elements are the coordinates of the cell-centers, where the i-th element
 * is the center of the i-th cell in X/Y direction. The inner edges are placed
 * halfway (in world coordinates) between the surrounding centers. The outer
 * edges will be placed at the coordinates given by the first and last element
 * respectively. However, they will still be considered centers for interpolating
 * the edge-positions, which means the first and last cells will be half the size.
 * Hence, -1 cannot be used as a dimension parameter, because the size of the only
 * cell would be impossible to determine.
 *
 * Assume you have a `dimx` by `dimy` color index array.
 * To draw all cells of the color index array using edges use:
 *
 *      gr_nonuniformcellarray(x, y, dimx, dimy, 1, 1, dimx, dimy, color)
 *
 * To draw all cells of the color index array using centers use:
 *
 *      gr_nonuniformcellarray(x, y, -dimx, -dimy, 1, 1, dimx, dimy, color)
 *
 * `scol` and `srow` can be used to specify a (1-based) starting column and row
 * in the `color`, `x` and `y` array. `dimx` and `dimy` specify the actual dimension of the
 * arrays in the memory whereof `ncol` and `nrow` values are displayed.
 */
void gr_nonuniformcellarray(double *x, double *y, int dimx, int dimy, int scol, int srow, int ncol, int nrow,
                            int *color)
{
  int img_data_x, img_data_y, color_x_ind, color_y_ind, color_ind, edges_x = 1, edges_y = 1,
                                                                   size = (int)(2000 * scale_factor), scale_options;
  int *img_data;
  double x_pos, y_pos, x_size, y_size, *x_orig = x, *y_orig = y;
  double xmin, xmax, ymin, ymax;

  if (dimx < 0)
    {
      dimx = -dimx;
      edges_x = 0;
    }
  if (dimy < 0)
    {
      dimy = -dimy;
      edges_y = 0;
    }

  if (scol < 1 || srow < 1 || scol + ncol - 1 > dimx || srow + nrow - 1 > dimy || (!edges_x && ncol < 2) ||
      (!edges_y && nrow < 2))
    {
      fprintf(stderr, "Dimensions of color index array are invalid.\n");
      return;
    }

  check_autoinit;

  scol--;
  srow--;
  nrow += srow;
  ncol += scol;

  x = (double *)gks_malloc(sizeof(double) * (ncol + 1));
  y = (double *)gks_malloc(sizeof(double) * (nrow + 1));

  if (!edges_x)
    {
      x[scol] = x_orig[scol];
      for (color_x_ind = scol + 1; color_x_ind < ncol; color_x_ind++)
        {
          x[color_x_ind] = 0.5 * (x_orig[color_x_ind] + x_orig[color_x_ind - 1]);
        }
      x[ncol] = x_orig[ncol - 1];
    }
  else
    {
      memcpy(x, x_orig, sizeof(double) * (ncol + 1));
    }
  xmin = x[scol];
  xmax = x[ncol];

  if (lx.scale_options & (GR_OPTION_X_LOG | GR_OPTION_X_LOG2 | GR_OPTION_X_LN))
    {
      for (color_x_ind = scol; color_x_ind <= ncol; color_x_ind++)
        {
          x[color_x_ind] = blog(lx.basex, x[color_x_ind]);
        }
    }

  if (!edges_y)
    {
      y[srow] = y_orig[srow];
      for (color_y_ind = srow + 1; color_y_ind < nrow; color_y_ind++)
        {
          y[color_y_ind] = 0.5 * (y_orig[color_y_ind] + y_orig[color_y_ind - 1]);
        }
      y[nrow] = y_orig[nrow - 1];
    }
  else
    {
      memcpy(y, y_orig, sizeof(double) * (nrow + 1));
    }
  ymin = y[nrow];
  ymax = y[srow];

  if (lx.scale_options & (GR_OPTION_Y_LOG | GR_OPTION_Y_LOG2 | GR_OPTION_Y_LN))
    {
      for (color_y_ind = srow; color_y_ind <= nrow; color_y_ind++)
        {
          y[color_y_ind] = blog(lx.basey, y[color_y_ind]);
        }
    }

  for (color_x_ind = scol; color_x_ind < ncol; color_x_ind++)
    {
      if (x[color_x_ind] > x[color_x_ind + 1])
        {
          if (!edges_x)
            {
              gks_free(x);
            }
          if (!edges_y)
            {
              gks_free(y);
            }
          fprintf(stderr, "x points not sorted in ascending order\n");
          return;
        }
    }

  for (color_y_ind = srow; color_y_ind < nrow; color_y_ind++)
    {
      if (y[color_y_ind] > y[color_y_ind + 1])
        {
          if (!edges_x)
            {
              gks_free(x);
            }
          if (!edges_y)
            {
              gks_free(y);
            }
          fprintf(stderr, "y points not sorted in ascending order\n");
          return;
        }
    }

  x_size = x[ncol] - x[scol];
  y_size = y[nrow] - y[srow];
  img_data = (int *)xmalloc(size * size * sizeof(int));

  color_y_ind = srow;
  for (img_data_y = 0; img_data_y < size; img_data_y++)
    {
      y_pos = y[srow] + img_data_y * y_size / size;
      while (color_y_ind < nrow && y[color_y_ind + 1] <= y_pos)
        {
          color_y_ind++;
        }
      color_x_ind = scol;
      for (img_data_x = 0; img_data_x < size; img_data_x++)
        {
          x_pos = x[scol] + img_data_x * x_size / size;
          while (color_x_ind < ncol && x[color_x_ind + 1] <= x_pos)
            {
              color_x_ind++;
            }
          color_ind = color[color_y_ind * dimx + color_x_ind];
          if (color_ind >= 0 && color_ind < MAX_COLOR)
            {
              img_data[img_data_y * size + img_data_x] = (255 << 24) + rgb[color_ind];
            }
          else
            {
              /* invalid color indices in input data result in transparent pixel */
              img_data[img_data_y * size + img_data_x] = 0;
            }
        }
    }

  scale_options = lx.scale_options;
  if (scale_options & GR_OPTION_FLIP_X)
    {
      double tmp = xmin;
      xmin = xmax;
      xmax = tmp;
    }
  if (scale_options & GR_OPTION_FLIP_Y)
    {
      double tmp = ymin;
      ymin = ymax;
      ymax = tmp;
    }
  lx.scale_options = 0;
  gr_drawimage(xmin, xmax, ymin, ymax, size, size, img_data, 0);
  free(img_data);
  lx.scale_options = scale_options;

  gks_free(x);
  gks_free(y);
}

/*!
 * Display a two dimensional color index array mapped to a disk using polar
 * coordinates.
 *
 * \param[in] x_org X coordinate of the disk center in world coordinates
 * \param[in] y_org Y coordinate of the disk center in world coordinates
 * \param[in] phimin start angle of the disk sector in degrees
 * \param[in] phimax end angle of the disk sector in degrees
 * \param[in] rmin inner radius of the punctured disk in world coordinates
 * \param[in] rmax outer radius of the disk in world coordinates
 * \param[in] dimphi Phi (X) dimension of the color index array
 * \param[in] dimr R (Y) dimension of the color index array
 * \param[in] scol number of leading columns in the color index array
 * \param[in] srow number of leading rows in the color index array
 * \param[in] ncol total number of columns in the color index array
 * \param[in] nrow total number of rows in the color index array
 * \param[in] color color index array
 *
 * The two dimensional color index array is mapped to the resulting image by
 * interpreting the X-axis of the array as the angle and the Y-axis as the radius.
 * The center point of the resulting disk is located at `x_org`, `y_org` and the
 * radius of the disk is `rmax`.
 *
 * To draw a contiguous array as a complete disk use:
 *
 *     gr_polarcellarray(x_org, y_org, 0, 360, 0, rmax, dimphi, dimr, 1, 1, dimphi, dimr, color)
 *
 * The additional parameters to the function can be used to further control the
 * mapping from polar to cartesian coordinates.
 *
 * If `rmin` is greater than 0 the input data is mapped to a punctured disk (or
 * annulus) with an inner radius of `rmin` and an outer radius `rmax`. If `rmin`
 * is greater than `rmax` the Y-axis of the array is reversed.
 *
 * The parameter `phimin` and `phimax` can be used to map the data to a sector
 * of the (punctured) disk starting at `phimin` and ending at `phimax`. If
 * `phimin` is greater than `phimax` the X-axis is reversed. The visible sector
 * is the one starting in mathematically positive direction (counterclockwise)
 * at the smaller angle and ending at the larger angle. An example of the four
 * possible options can be found below:
 *
 * \verbatim embed:rst:leading-asterisk
 *
 * +-----------+-----------+---------------------------------------------------+
 * |**phimin** |**phimax** |**Result**                                         |
 * +-----------+-----------+---------------------------------------------------+
 * |90         |270        |Left half visible, mapped counterclockwise         |
 * +-----------+-----------+---------------------------------------------------+
 * |270        |90         |Left half visible, mapped clockwise                |
 * +-----------+-----------+---------------------------------------------------+
 * |-90        |90         |Right half visible, mapped counterclockwise        |
 * +-----------+-----------+---------------------------------------------------+
 * |90         |-90        |Right half visible, mapped clockwise               |
 * +-----------+-----------+---------------------------------------------------+
 *
 * \endverbatim
 *
 * `scol` and `srow` can be used to specify a (1-based) starting column and row
 * in the `color` array. `ncol` and `nrow` specify the actual dimension of the
 * array in the memory whereof `dimphi` and `dimr` values are mapped to the disk.
 *
 */
void gr_polarcellarray(double x_org, double y_org, double phimin, double phimax, double rmin, double rmax, int dimphi,
                       int dimr, int scol, int srow, int ncol, int nrow, int *color)
{
  int x, y, color_ind, r_ind, phi_ind, phi_reverse, phi_wrapped_reverse, r_reverse, size = (int)(2000 * scale_factor);
  int *img_data;
  double r, phi, tmp, center = size / 2.;

  phimin = arc(phimin);
  phimax = arc(phimax);

  if (!(scol >= 1 && srow >= 1 && scol + ncol - 1 <= dimphi && srow + nrow - 1 <= dimr))
    {
      fprintf(stderr, "Dimensions of color index array are invalid.\n");
      return;
    }

  if (phimin == phimax)
    {
      fprintf(stderr, "Invalid angles specified.\n");
      return;
    }

  if (rmin == rmax || rmin < 0 || rmax < 0)
    {
      fprintf(stderr, "Invalid radii specified.\n");
      return;
    }

  check_autoinit;

  if ((r_reverse = rmin > rmax))
    {
      tmp = rmin;
      rmin = rmax;
      rmax = tmp;
    }

  phi_reverse = phimin > phimax;

  /* Wrap phimin and phimax to [0, 2Pi] */
  phimin -= floor(phimin / M_PI / 2) * 2 * M_PI;
  phimax -= floor(phimax / M_PI / 2) * 2 * M_PI;

  if (fabs(phimin - phimax) < 1e-8) /* Avoid empty images when drawing a full circle */
    {
      if (!phi_reverse)
        {
          phimax += 2 * M_PI;
        }
      else
        {
          phimin += 2 * M_PI;
        }
    }

  if ((phi_wrapped_reverse = phimin > phimax))
    {
      tmp = phimin;
      phimin = phimax;
      phimax = tmp;
    }

  if (phi_reverse != phi_wrapped_reverse) /* Drawing in negative direction */
    {
      phimin += 2 * M_PI;
    }

  img_data = (int *)xmalloc(size * size * sizeof(int));

  for (y = 0; y < size; y++)
    {
      for (x = 0; x < size; x++)
        {
          double px = (x - center) / center;
          double py = (y - center) / center;
          r = sqrt(px * px + py * py);
          phi = atan2(py, px);
          if (phi < min(phimin, phimax))
            {
              phi += 2 * M_PI;
            }

          /* map phi from [phimin, phimax] to [0, 1] */
          phi = (phi - phimin) / (phimax - phimin);

          if (r * rmax < rmin || r >= 1 || phi < 0 || phi > 1)
            {
              img_data[y * size + x] = 0;
              continue;
            }
          r = (r * rmax - rmin) / (rmax - rmin);
          r_ind = (int)(r * dimr);
          phi_ind = (int)(phi * dimphi) % dimphi;
          if (r_reverse)
            {
              r_ind = dimr - r_ind - 1;
            }
          if (phi_wrapped_reverse)
            {
              phi_ind = dimphi - phi_ind - 1;
            }
          img_data[y * size + x] = color[(r_ind + srow - 1) * ncol + phi_ind + scol - 1];
          color_ind = color[(r_ind + srow - 1) * ncol + phi_ind + scol - 1];
          if (color_ind >= 0 && color_ind < MAX_COLOR)
            {
              img_data[y * size + x] = (255 << 24) + rgb[color_ind];
            }
          else
            {
              /* invalid color indices in input data result in transparent pixel */
              img_data[y * size + x] = 0;
            }
        }
    }

  gr_drawimage(x_org - rmax, x_org + rmax, y_org + rmax, y_org - rmax, size, size, img_data, 0);
  free(img_data);
}

/*!
 * Display a two dimensional color index array mapped to a disk using polar
 * coordinates with nonuniform cell sizes.
 *
 * \param[in] x_org X coordinate of the disk center in world coordinates
 * \param[in] y_org Y coordinate of the disk center in world coordinates
 * \param[in] phi sorted array with the angles of the disk sectors in degrees
 * \param[in] r sorted array with the radii of the cells in world coordinates
 * \param[in] dimphi (possibly negated) Phi/X dimension of the color index array
 * \param[in] dimr (possibly negated) R/Y dimension of the color index array
 * \param[in] scol 1-based starting index of the angles and rows of the color index array
 * \param[in] srow 1-based starting index of the radii and columns of the color index array
 * \param[in] ncol number of angles/columns displayed
 * \param[in] nrow number of radii/rows displayed
 * \param[in] color color index array
 *
 * The mapping of the polar coordinates and the drawing is performed simialr to `gr_polarcellarray`
 * with the difference that the individual cell sizes are specified allowing nonuniform sized cells.
 *
 * These memory accesses must be valid:
 * - `phi[scol-1]` through `phi[scol+ncol-2+clamp(dimphi,0,1)]`
 * - `r[srow-1]` through `r[srow+nrow-2+clamp(dimr,0,1)]`
 * - `color[scol-1+(srow-1)*ncol]` through `color[scol+ncol-2+(srow+nrow-2)*ncol]``
 *
 * If `dimphi`/`dimr` is positive, `phi`/`r` must contain `dimphi+1`/`dimr+1` elements.
 * The elements are used to calculate the cell-edges, where the i-th and i+1-th
 * elements are used for the edges of the i-th cell in Phi/R direction.
 *
 * If `dimphi`/`dimr` is negative, `phi`/`r` must contain `-dimphi`/`-dimr` elements.
 * The elements are used to calculate the cell-centers, where the i-th element is used
 * for the center of the i-th cell in Phi/R direction. The inner edges are placed
 * halfway (in world coordinates) between the surrounding centers. The outer edges
 * will be placed at the coordinates calculated for the center of the first and last
 * cell respectively. However, they will still be considered centers for interpolating
 * the edge-positions, which means the first and last cells will be half the size.
 * Hence, -1 cannot be used as a dimension parameter, because the size of the only
 * cell would be impossible to determine.
 *
 * Assume you have a `dimphi` by `dimr` color index array.
 * To draw all cells of the color index array using edges use:
 *
 *      gr_nonuniformpolarcellarray(x_org, y_org, phi, r, dimphi, dimr, 1, 1, dimphi, dimr, color)
 *
 * To draw all cells of the color index array using centers use:
 *
 *      gr_nonuniformpolarcellarray(x_org, y_org, phi, r, -dimphi, -dimr, 1, 1, dimphi, dimr, color)
 *
 * `scol` and `srow` can be used to specify a (1-based) starting column and row
 * in the `color`, `phi` and `r` array. `dimr` and `dimphi` specify the actual dimension of the
 * arrays in the memory whereof `ncol` and `nrow` values are displayed.
 *
 */
void gr_nonuniformpolarcellarray(double x_org, double y_org, double *phi, double *r, int dimphi, int dimr, int scol,
                                 int srow, int ncol, int nrow, int *color)
{
  int x, y, color_ind, r_ind, phi_ind, phi_reverse, r_reverse, start, end, edges_phi = 1, edges_r = 1,
                                                                           size = (int)(2000 * scale_factor);
  int *img_data;
  double cur_r, cur_phi, tmp, phimin, phimax, rmin, rmax, center = size / 2.;
  double *r_sorted, *phi_sorted;
  if (dimphi < 0)
    {
      edges_phi = 0;
      dimphi = -dimphi;
      ncol--;
    }
  if (dimr < 0)
    {
      edges_r = 0;
      dimr = -dimr;
      nrow--;
    }

  if (scol < 1 || srow < 1 || scol + ncol - 1 > dimphi || srow + nrow - 1 > dimr || (!edges_phi && ncol < 1) ||
      (!edges_r && nrow < 1))
    {
      fprintf(stderr, "Dimensions of color index array are invalid.\n");
      return;
    }

  phimin = phi[scol - 1];
  phimax = phi[ncol];

  rmin = r[srow - 1];
  rmax = r[nrow];

  if (phimin == phimax)
    {
      fprintf(stderr, "Invalid angles specified.\n");
      return;
    }

  if (rmin == rmax || rmin < 0 || rmax < 0)
    {
      fprintf(stderr, "Invalid radii specified.\n");
      return;
    }

  check_autoinit;

  if ((r_reverse = rmin > rmax))
    {
      tmp = rmin;
      rmin = rmax;
      rmax = tmp;
    }
  if (!edges_r)
    {
      r_sorted = (double *)gks_malloc(sizeof(double) * (nrow - srow + 3));
    }
  else
    {
      r_sorted = (double *)gks_malloc(sizeof(double) * (nrow - srow + 2));
    }
  for (y = 0; y < nrow - srow + 2; y++)
    {
      if (r_reverse)
        {
          if (!edges_r && y)
            {
              r_sorted[y] = 0.5 * (r[nrow - y] + r[nrow - y + 1]);
            }
          else
            {
              r_sorted[y] = r[nrow - y];
            }
        }
      else
        {
          if (!edges_r && y)
            {
              r_sorted[y] = 0.5 * (r[srow - 1 + y] + r[srow - 2 + y]);
            }
          else
            {
              r_sorted[y] = r[srow - 1 + y];
            }
        }
      if (y && r_sorted[y] < r_sorted[y - 1])
        {
          fprintf(stderr, "radii not sorted.\n");
          gks_free(r_sorted);
          return;
        }
    }
  if (!edges_r)
    {
      if (r_reverse)
        {
          r_sorted[nrow - srow + 2] = r[srow - 1];
        }
      else
        {
          r_sorted[nrow - srow + 2] = r[nrow];
        }
      nrow++;
    }

  if ((phi_reverse = phimin > phimax))
    {
      tmp = phimin;
      phimin = phimax;
      phimax = tmp;
    }
  if (!edges_phi)
    {
      phi_sorted = (double *)gks_malloc(sizeof(double) * (ncol - scol + 3));
    }
  else
    {
      phi_sorted = (double *)gks_malloc(sizeof(double) * (ncol - scol + 2));
    }
  for (x = 0; x < ncol - scol + 2; x++)
    {
      if (phi_reverse)
        {
          if (!edges_phi && x)
            {
              phi_sorted[x] = 0.5 * (phi[ncol - x] + phi[ncol - x + 1]);
            }
          else
            {
              phi_sorted[x] = phi[ncol - x];
            }
        }
      else
        {
          if (!edges_phi && x)
            {
              phi_sorted[x] = 0.5 * (phi[scol - 1 + x] + phi[scol - 2 + x]);
            }
          else
            {
              phi_sorted[x] = phi[scol - 1 + x];
            }
        }
      phi_sorted[x] = phi_sorted[x] - phimax + 360;
      if (x && phi_sorted[x] < phi_sorted[x - 1])
        {
          fprintf(stderr, "angles not sorted.\n");
          gks_free(r_sorted);
          gks_free(phi_sorted);
          return;
        }
    }
  if (!edges_phi)
    {
      if (phi_reverse)
        {
          phi_sorted[ncol - scol + 2] = phi[scol - 1] - phimax + 360;
        }
      else
        {
          phi_sorted[ncol - scol + 2] = phi[ncol] - phimax + 360;
        }
      ncol++;
    }

  phimin = fmod(phimin, 360);
  phimax = fmod(phimax, 360);

  img_data = (int *)gks_malloc(size * size * sizeof(int));

  for (y = 0; y < size; y++)
    {
      for (x = 0; x < size; x++)
        {
          double px = (x - center) / center * rmax;
          double py = (y - center) / center * rmax;

          cur_r = sqrt(px * px + py * py);
          if (r_reverse)
            {
              cur_r = rmax - cur_r + rmin;
            }

          if (phi_reverse)
            {
              cur_phi = fmod(-fmod(atan2(py, px) * 180 / M_PI + 360, 360) + phimin + 2 * 360, 360);
            }
          else
            {
              cur_phi = fmod(fmod(atan2(py, px) * 180 / M_PI + 360, 360) + 2 * 360 - phimax, 360);
            }

          start = 0;
          end = nrow - srow + 1;
          if (cur_r < r_sorted[start] || cur_r >= r_sorted[end])
            {
              img_data[y * size + x] = 0;
              continue;
            }

          while (start != end)
            {
              int m = ((start + end) / 2);
              if (cur_r >= r_sorted[m + 1])
                {
                  start = m + 1;
                }
              else if (r_sorted[m] > cur_r)
                {
                  end = m;
                }
              else
                {
                  start = end = m;
                }
            }
          r_ind = start;

          start = 0;
          end = ncol - scol + 1;
          if (cur_phi < phi_sorted[start] || cur_phi >= phi_sorted[end])
            {
              img_data[y * size + x] = 0;
              continue;
            }
          while (start != end)
            {
              int m = ((start + end) / 2);
              if (cur_phi >= phi_sorted[m + 1])
                {
                  start = m + 1;
                }
              else if (phi_sorted[m] > cur_phi)
                {
                  end = m;
                }
              else
                {
                  start = end = m;
                }
            }
          phi_ind = start;

          color_ind = color[(r_ind + srow - 1) * ncol + phi_ind + scol - 1];
          if (color_ind >= 0 && color_ind < MAX_COLOR)
            {
              img_data[y * size + x] = (255 << 24) + rgb[color_ind];
            }
          else
            {
              /* invalid color indices in input data result in transparent pixel */
              img_data[y * size + x] = 0;
            }
        }
    }

  gks_free(r_sorted);
  gks_free(phi_sorted);
  gr_drawimage(x_org - rmax, x_org + rmax, y_org + rmax, y_org - rmax, size, size, img_data, 0);
  gks_free(img_data);
}

void gr_gdp(int n, double *x, double *y, int primid, int ldr, int *datrec)
{
  int npoints = n;
  double *px = x, *py = y;
  int i;

  check_autoinit;

  if (lx.scale_options)
    {
      if (npoints >= maxpath) reallocate(npoints);

      px = xpoint;
      py = ypoint;
      for (i = 0; i < npoints; i++)
        {
          px[i] = x_lin(x[i]);
          py[i] = y_lin(y[i]);
        }
    }

  gks_gdp(npoints, px, py, primid, ldr, datrec);

  if (flag_stream)
    {
      gr_writestream("<gdp len=\"%d\"", n);
      print_float_array("x", n, x);
      print_float_array("y", n, y);
      gr_writestream(" primid=\"%d\" ldr=\"%d\"", primid, ldr);
      print_int_array("datrec", ldr, datrec);
      gr_writestream("/>\n");
    }
}

/*!
 * Generate a cubic spline-fit, starting from the first data point and
 * ending at the last data point.
 *
 * \param[in] n The number of points
 * \param[in] px A pointer to the X coordinates
 * \param[in] py A pointer to the Y coordinates
 * \param[in] m The number of points in the polygon to be drawn (m > n)
 * \param[in] method The smoothing method
 *
 * The values for `x` and `y` are in world coordinates. The attributes that
 * control the appearance of a spline-fit are linetype, linewidth and color
 * index.
 *
 * If `method` is > 0, then a generalized cross-validated smoothing spline is calculated.
 * If `method` is 0, then an interpolating natural cubic spline is calculated.
 * If `method` is < -1, then a cubic B-spline is calculated.
 */
void gr_spline(int n, double *px, double *py, int m, int method)
{
  int err = 0, i, j;
  double *t, *s;
  double *sx, *sy, *x, *f, *df, *y, *c, *wk, *se, var, d;
  int ic, job, ier;

  if (n <= 2)
    {
      fprintf(stderr, "invalid number of points\n");
      return;
    }
  else if (n >= m)
    {
      fprintf(stderr, "invalid number of domain values\n");
      return;
    }

  check_autoinit;

  t = (double *)xmalloc(sizeof(double) * m);
  s = (double *)xmalloc(sizeof(double) * m);
  sx = (double *)xmalloc(sizeof(double) * m);
  sy = (double *)xmalloc(sizeof(double) * m);
  x = (double *)xmalloc(sizeof(double) * n);
  f = (double *)xmalloc(sizeof(double) * n);
  df = (double *)xmalloc(sizeof(double) * n);
  y = (double *)xmalloc(sizeof(double) * n);
  c = (double *)xmalloc(sizeof(double) * 3 * (n - 1));
  se = (double *)xmalloc(sizeof(double) * n);
  wk = (double *)xmalloc(sizeof(double) * 7 * (n + 2));

  for (i = 0; i < n; i++)
    {
      x[i] = (double)((x_lin(px[i]) - lx.xmin) / (lx.xmax - lx.xmin));
      f[i] = (double)((y_lin(py[i]) - lx.ymin) / (lx.ymax - lx.ymin));
      df[i] = 1;
    }

  if (method >= -1)
    {
      for (i = 1; i < n; i++)
        if (px[i - 1] >= px[i])
          {
            fprintf(stderr, "points not sorted in ascending order\n");
            err = 1;
          }

      if (!err)
        {
          sx[0] = x[0];
          for (j = 1; j < m - 1; j++) sx[j] = x[0] + j * (x[n - 1] - x[0]) / (m - 1);
          sx[m - 1] = x[n - 1];

          job = 0;
          ic = n - 1;
          var = (double)method;

          cubgcv(x, f, df, &n, y, c, &ic, &var, &job, se, wk, &ier);

          if (ier == 0)
            {
              for (j = 0; j < m; j++)
                {
                  i = 0;
                  while ((i < ic) && (x[i] <= sx[j])) i++;
                  if (x[i] > sx[j]) i--;
                  if (i < 0)
                    i = 0;
                  else if (i >= ic)
                    i = ic - 1;
                  d = sx[j] - x[i];

                  s[j] = (double)(((c[i + 2 * ic] * d + c[i + ic]) * d + c[i]) * d + y[i]);
                }
            }
          else
            {
              fprintf(stderr, "invalid argument to math library\n");
              err = 1;
            }
        }
    }
  else
    {
      b_spline(n, x, f, m, sx, sy);

      for (j = 0; j < m; j++) s[j] = (double)sy[j];
    }

  if (!err)
    {
      for (j = 0; j < m; j++)
        {
          t[j] = x_log((double)(lx.xmin + sx[j] * (lx.xmax - lx.xmin)));
          s[j] = y_log((double)(lx.ymin + s[j] * (lx.ymax - lx.ymin)));
        }
      polyline(m, t, s);
    }

  free(wk);
  free(se);
  free(c);
  free(y);
  free(df);
  free(f);
  free(x);
  free(sy);
  free(sx);
  free(s);
  free(t);

  if (flag_stream)
    {
      gr_writestream("<spline len=\"%d\"", n);
      print_float_array("x", n, px);
      print_float_array("y", n, py);
      gr_writestream(" m=\"%d\" method=\"%d\"/>\n", m, method);
    }
}

/*!
 * Interpolate data from arbitrary points at points on a rectangular grid.
 *
 * \param[in] nd The number of input points
 * \param[in] xd A pointer to the X coordinates of the input points
 * \param[in] yd A pointer to the Y coordinates of the input points
 * \param[in] zd A pointer to the values of the points
 * \param[in] nx The number of points in X direction for the output grid
 * \param[in] ny The number of points in Y direction for the output grid
 * \param[out] x A pointer to the points in X direction for the output grid
 * \param[out] y A pointer to the points in Y direction for the output grid
 * \param[out] z A pointer to the interpolated values on the nx x ny grid points
 */
void gr_gridit(int nd, double *xd, double *yd, double *zd, int nx, int ny, double *x, double *y, double *z)
{
  int i, md, ncp;
  minmax_t xminmax, yminmax;
  double xmin, ymin, xmax, ymax;
  int *iwk;
  double *wk;

  if (nd < 5)
    {
      fprintf(stderr, "invalid number of domain values\n");
      return;
    }
  else if (nx < 1 || ny < 1)
    {
      fprintf(stderr, "invalid number of points\n");
      return;
    }

  check_autoinit;

  /* CALCULATION OF MIN/MAX VALUES */
  xminmax = find_minmax(nd, xd);
  yminmax = find_minmax(nd, yd);
  xmin = xminmax.min;
  xmax = xminmax.max;
  ymin = yminmax.min;
  ymax = yminmax.max;
  if (is_nan(xmin) || is_nan(ymin))
    {
      fprintf(stderr, "all coordinates are NAN\n");
      return;
    }

  /* DETERMINE GRID POINTS INSIDE THE DATA AREA */
  for (i = 0; i < nx; ++i)
    {
      x[i] = xmin + i / (double)(nx - 1) * (xmax - xmin);
    }
  for (i = 0; i < ny; ++i)
    {
      y[i] = ymin + i / (double)(ny - 1) * (ymax - ymin);
    }

  /* CALL THE SMOOTH SURFACE FIT ROUTINE */
  md = 1;
  ncp = 4;
  iwk = (int *)xcalloc(31 * nd + nx * ny, sizeof(int));
  wk = (double *)xcalloc(6 * (nd + 1), sizeof(double));

  idsfft(&md, &ncp, &nd, xd, yd, zd, &nx, &ny, x, y, z, iwk, wk);

  free(wk);
  free(iwk);
}

/*!
 * Specify the line style for polylines.
 *
 * \param[in] type The polyline line style
 *
 *
 * \verbatim embed:rst:leading-asterisk
 *
 * The available line types are:
 *
 * +---------------------------+----+---------------------------------------------------+
 * |LINETYPE_SOLID             |   1|Solid line                                         |
 * +---------------------------+----+---------------------------------------------------+
 * |LINETYPE_DASHED            |   2|Dashed line                                        |
 * +---------------------------+----+---------------------------------------------------+
 * |LINETYPE_DOTTED            |   3|Dotted line                                        |
 * +---------------------------+----+---------------------------------------------------+
 * |LINETYPE_DASHED_DOTTED     |   4|Dashed-dotted line                                 |
 * +---------------------------+----+---------------------------------------------------+
 * |LINETYPE_DASH_2_DOT        |  -1|Sequence of one dash followed by two dots          |
 * +---------------------------+----+---------------------------------------------------+
 * |LINETYPE_DASH_3_DOT        |  -2|Sequence of one dash followed by three dots        |
 * +---------------------------+----+---------------------------------------------------+
 * |LINETYPE_LONG_DASH         |  -3|Sequence of long dashes                            |
 * +---------------------------+----+---------------------------------------------------+
 * |LINETYPE_LONG_SHORT_DASH   |  -4|Sequence of a long dash followed by a short dash   |
 * +---------------------------+----+---------------------------------------------------+
 * |LINETYPE_SPACED_DASH       |  -5|Sequence of dashes double spaced                   |
 * +---------------------------+----+---------------------------------------------------+
 * |LINETYPE_SPACED_DOT        |  -6|Sequence of dots double spaced                     |
 * +---------------------------+----+---------------------------------------------------+
 * |LINETYPE_DOUBLE_DOT        |  -7|Sequence of pairs of dots                          |
 * +---------------------------+----+---------------------------------------------------+
 * |LINETYPE_TRIPLE_DOT        |  -8|Sequence of groups of three dots                   |
 * +---------------------------+----+---------------------------------------------------+
 *
 * \endverbatim
 */
void gr_setlinetype(int type)
{
  check_autoinit;

  gks_set_pline_linetype(type);
  if (ctx) ctx->ltype = type;

  if (flag_stream) gr_writestream("<setlinetype type=\"%d\"/>\n", type);
}

void gr_inqlinetype(int *ltype)
{
  int errind;

  check_autoinit;

  gks_inq_pline_linetype(&errind, ltype);
}

/*!
 * Define the line width of subsequent polyline output primitives.
 *
 * \param[in] width The polyline line width scale factor
 *
 * The line width is calculated as the nominal line width generated
 * on the workstation multiplied by the line width scale factor.
 * This value is mapped by the workstation to the nearest available line width.
 * The default line width is 1.0, or 1 times the line width generated on the
 * graphics device.
 */
void gr_setlinewidth(double width)
{
  check_autoinit;

  gks_set_pline_linewidth(width);
  if (ctx) ctx->lwidth = width;

  if (flag_stream) gr_writestream("<setlinewidth width=\"%g\"/>\n", width);
}

void gr_inqlinewidth(double *width)
{
  int errind;

  check_autoinit;

  gks_inq_pline_linewidth(&errind, width);
}

/*!
 * Define the color of subsequent polyline output primitives.
 *
 * \param[in] color The polyline color index (COLOR < 1256)
 */
void gr_setlinecolorind(int color)
{
  check_autoinit;

  gks_set_pline_color_index(color);
  if (ctx) ctx->plcoli = color;

  if (flag_stream) gr_writestream("<setlinecolorind color=\"%d\"/>\n", color);
}

void gr_inqlinecolorind(int *coli)
{
  int errind;

  check_autoinit;

  gks_inq_pline_color_index(&errind, coli);
}

/*!
 * Specifiy the marker type for polymarkers.
 *
 * \param[in] type The polymarker marker type
 *
 * \verbatim embed:rst:leading-asterisk
 *
 * The available marker types are:
 *
 * +-----------------------------+-----+------------------------------------------------+
 * |MARKERTYPE_DOT               |    1|Smallest displayable dot                        |
 * +-----------------------------+-----+------------------------------------------------+
 * |MARKERTYPE_PLUS              |    2|Plus sign                                       |
 * +-----------------------------+-----+------------------------------------------------+
 * |MARKERTYPE_ASTERISK          |    3|Asterisk                                        |
 * +-----------------------------+-----+------------------------------------------------+
 * |MARKERTYPE_CIRCLE            |    4|Hollow circle                                   |
 * +-----------------------------+-----+------------------------------------------------+
 * |MARKERTYPE_DIAGONAL_CROSS    |    5|Diagonal cross                                  |
 * +-----------------------------+-----+------------------------------------------------+
 * |MARKERTYPE_SOLID_CIRCLE      |   -1|Filled circle                                   |
 * +-----------------------------+-----+------------------------------------------------+
 * |MARKERTYPE_TRIANGLE_UP       |   -2|Hollow triangle pointing upward                 |
 * +-----------------------------+-----+------------------------------------------------+
 * |MARKERTYPE_SOLID_TRI_UP      |   -3|Filled triangle pointing upward                 |
 * +-----------------------------+-----+------------------------------------------------+
 * |MARKERTYPE_TRIANGLE_DOWN     |   -4|Hollow triangle pointing downward               |
 * +-----------------------------+-----+------------------------------------------------+
 * |MARKERTYPE_SOLID_TRI_DOWN    |   -5|Filled triangle pointing downward               |
 * +-----------------------------+-----+------------------------------------------------+
 * |MARKERTYPE_SQUARE            |   -6|Hollow square                                   |
 * +-----------------------------+-----+------------------------------------------------+
 * |MARKERTYPE_SOLID_SQUARE      |   -7|Filled square                                   |
 * +-----------------------------+-----+------------------------------------------------+
 * |MARKERTYPE_BOWTIE            |   -8|Hollow bowtie                                   |
 * +-----------------------------+-----+------------------------------------------------+
 * |MARKERTYPE_SOLID_BOWTIE      |   -9|Filled bowtie                                   |
 * +-----------------------------+-----+------------------------------------------------+
 * |MARKERTYPE_HGLASS            |  -10|Hollow hourglass                                |
 * +-----------------------------+-----+------------------------------------------------+
 * |MARKERTYPE_SOLID_HGLASS      |  -11|Filled hourglass                                |
 * +-----------------------------+-----+------------------------------------------------+
 * |MARKERTYPE_DIAMOND           |  -12|Hollow diamond                                  |
 * +-----------------------------+-----+------------------------------------------------+
 * |MARKERTYPE_SOLID_DIAMOND     |  -13|Filled Diamond                                  |
 * +-----------------------------+-----+------------------------------------------------+
 * |MARKERTYPE_STAR              |  -14|Hollow star                                     |
 * +-----------------------------+-----+------------------------------------------------+
 * |MARKERTYPE_SOLID_STAR        |  -15|Filled Star                                     |
 * +-----------------------------+-----+------------------------------------------------+
 * |MARKERTYPE_TRI_UP_DOWN       |  -16|Hollow triangles pointing up and down overlaid  |
 * +-----------------------------+-----+------------------------------------------------+
 * |MARKERTYPE_SOLID_TRI_RIGHT   |  -17|Filled triangle point right                     |
 * +-----------------------------+-----+------------------------------------------------+
 * |MARKERTYPE_SOLID_TRI_LEFT    |  -18|Filled triangle pointing left                   |
 * +-----------------------------+-----+------------------------------------------------+
 * |MARKERTYPE_HOLLOW PLUS       |  -19|Hollow plus sign                                |
 * +-----------------------------+-----+------------------------------------------------+
 * |MARKERTYPE_SOLID PLUS        |  -20|Solid plus sign                                 |
 * +-----------------------------+-----+------------------------------------------------+
 * |MARKERTYPE_PENTAGON          |  -21|Pentagon                                        |
 * +-----------------------------+-----+------------------------------------------------+
 * |MARKERTYPE_HEXAGON           |  -22|Hexagon                                         |
 * +-----------------------------+-----+------------------------------------------------+
 * |MARKERTYPE_HEPTAGON          |  -23|Heptagon                                        |
 * +-----------------------------+-----+------------------------------------------------+
 * |MARKERTYPE_OCTAGON           |  -24|Octagon                                         |
 * +-----------------------------+-----+------------------------------------------------+
 * |MARKERTYPE_STAR_4            |  -25|4-pointed star                                  |
 * +-----------------------------+-----+------------------------------------------------+
 * |MARKERTYPE_STAR_5            |  -26|5-pointed star (pentagram)                      |
 * +-----------------------------+-----+------------------------------------------------+
 * |MARKERTYPE_STAR_6            |  -27|6-pointed star (hexagram)                       |
 * +-----------------------------+-----+------------------------------------------------+
 * |MARKERTYPE_STAR_7            |  -28|7-pointed star (heptagram)                      |
 * +-----------------------------+-----+------------------------------------------------+
 * |MARKERTYPE_STAR_8            |  -29|8-pointed star (octagram)                       |
 * +-----------------------------+-----+------------------------------------------------+
 * |MARKERTYPE_VLINE             |  -30|verical line                                    |
 * +-----------------------------+-----+------------------------------------------------+
 * |MARKERTYPE_HLINE             |  -31|horizontal line                                 |
 * +-----------------------------+-----+------------------------------------------------+
 * |MARKERTYPE_OMARK             |  -32|o-mark                                          |
 * +-----------------------------+-----+------------------------------------------------+
 * \endverbatim
 *
 * Polymarkers appear centered over their specified coordinates.
 */
void gr_setmarkertype(int type)
{
  check_autoinit;

  gks_set_pmark_type(type);
  if (ctx) ctx->mtype = type;

  if (flag_stream) gr_writestream("<setmarkertype type=\"%d\"/>\n", type);
}

void gr_inqmarkertype(int *mtype)
{
  int errind;

  check_autoinit;

  gks_inq_pmark_type(&errind, mtype);
}

/*!
 * Specify the marker size for polymarkers.
 *
 * \param[in] size Scale factor applied to the nominal marker size
 *
 * The polymarker size is calculated as the nominal size generated on the graphics device
 * multiplied by the marker size scale factor.
 */
void gr_setmarkersize(double size)
{
  check_autoinit;

  gks_set_pmark_size(size);
  if (ctx) ctx->mszsc = size;

  if (flag_stream) gr_writestream("<setmarkersize size=\"%g\"/>\n", size);
}

/*!
 *
 * Inquire the marker size for polymarkers.
 *
 * \param[out] size Scale factor applied to the nominal marker size
 *
 */
void gr_inqmarkersize(double *size)
{
  int errind;

  check_autoinit;

  gks_inq_pmark_size(&errind, size);
}

/*!
 * Define the color of subsequent polymarker output primitives.
 *
 * \param[in] color The polymarker color index (COLOR < 1256)
 */
void gr_setmarkercolorind(int color)
{
  check_autoinit;

  gks_set_pmark_color_index(color);
  if (ctx) ctx->pmcoli = color;

  if (flag_stream) gr_writestream("<setmarkercolorind color=\"%d\"/>\n", color);
}

void gr_inqmarkercolorind(int *coli)
{
  int errind;

  check_autoinit;

  gks_inq_pmark_color_index(&errind, coli);
}

/*!
 * Specify the text font and precision for subsequent text output primitives.
 *
 * \param[in] font Text font (see tables)
 * \param[in] precision Text precision (see table below)
 *
 * \verbatim embed:rst:leading-asterisk
 *
 * The available text fonts are:
 *
 * +--------------------------------------+-----+
 * |FONT_TIMES_ROMAN                      |  101|
 * +--------------------------------------+-----+
 * |FONT_TIMES_ITALIC                     |  102|
 * +--------------------------------------+-----+
 * |FONT_TIMES_BOLD                       |  103|
 * +--------------------------------------+-----+
 * |FONT_TIMES_BOLDITALIC                 |  104|
 * +--------------------------------------+-----+
 * |FONT_HELVETICA                        |  105|
 * +--------------------------------------+-----+
 * |FONT_HELVETICA_OBLIQUE                |  106|
 * +--------------------------------------+-----+
 * |FONT_HELVETICA_BOLD                   |  107|
 * +--------------------------------------+-----+
 * |FONT_HELVETICA_BOLDOBLIQUE            |  108|
 * +--------------------------------------+-----+
 * |FONT_COURIER                          |  109|
 * +--------------------------------------+-----+
 * |FONT_COURIER_OBLIQUE                  |  110|
 * +--------------------------------------+-----+
 * |FONT_COURIER_BOLD                     |  111|
 * +--------------------------------------+-----+
 * |FONT_COURIER_BOLDOBLIQUE              |  112|
 * +--------------------------------------+-----+
 * |FONT_SYMBOL                           |  113|
 * +--------------------------------------+-----+
 * |FONT_BOOKMAN_LIGHT                    |  114|
 * +--------------------------------------+-----+
 * |FONT_BOOKMAN_LIGHTITALIC              |  115|
 * +--------------------------------------+-----+
 * |FONT_BOOKMAN_DEMI                     |  116|
 * +--------------------------------------+-----+
 * |FONT_BOOKMAN_DEMIITALIC               |  117|
 * +--------------------------------------+-----+
 * |FONT_NEWCENTURYSCHLBK_ROMAN           |  118|
 * +--------------------------------------+-----+
 * |FONT_NEWCENTURYSCHLBK_ITALIC          |  119|
 * +--------------------------------------+-----+
 * |FONT_NEWCENTURYSCHLBK_BOLD            |  120|
 * +--------------------------------------+-----+
 * |FONT_NEWCENTURYSCHLBK_BOLDITALIC      |  121|
 * +--------------------------------------+-----+
 * |FONT_AVANTGARDE_BOOK                  |  122|
 * +--------------------------------------+-----+
 * |FONT_AVANTGARDE_BOOKOBLIQUE           |  123|
 * +--------------------------------------+-----+
 * |FONT_AVANTGARDE_DEMI                  |  124|
 * +--------------------------------------+-----+
 * |FONT_AVANTGARDE_DEMIOBLIQUE           |  125|
 * +--------------------------------------+-----+
 * |FONT_PALATINO_ROMAN                   |  126|
 * +--------------------------------------+-----+
 * |FONT_PALATINO_ITALIC                  |  127|
 * +--------------------------------------+-----+
 * |FONT_PALATINO_BOLD                    |  128|
 * +--------------------------------------+-----+
 * |FONT_PALATINO_BOLDITALIC              |  129|
 * +--------------------------------------+-----+
 * |FONT_ZAPFCHANCERY_MEDIUMITALIC        |  130|
 * +--------------------------------------+-----+
 * |FONT_ZAPFDINGBATS                     |  131|
 * +--------------------------------------+-----+
 * |FONT_COMPUTERMODERN                   |  232|
 * +--------------------------------------+-----+
 * |FONT_DEJAVUSANS                       |  233|
 * +--------------------------------------+-----+
 * |FONT_STIXTWOMATH                      |  234|
 * +--------------------------------------+-----+
 *
 * The available text precisions are:
 *
 * +---------------------------+---+--------------------------------------+
 * |TEXT_PRECISION_STRING      |  0|String precision (higher quality)     |
 * +---------------------------+---+--------------------------------------+
 * |TEXT_PRECISION_CHAR        |  1|Character precision (medium quality)  |
 * +---------------------------+---+--------------------------------------+
 * |TEXT_PRECISION_STROKE      |  2|Stroke precision (lower quality)      |
 * +---------------------------+---+--------------------------------------+
 * |TEXT_PRECISION_OUTLINE     |  3|Outline precision (highest quality)   |
 * +---------------------------+---+--------------------------------------+
 *
 * \endverbatim
 *
 * The appearance of a font depends on the text precision value specified.
 * STRING, CHARACTER, STROKE or OUTLINE precision allows for a greater or
 * lesser realization of the text primitives, for efficiency. STRING is the
 * default precision for GR and produces the high quality output using either
 * native font rendering or FreeType. OUTLINE uses the GR path rendering
 * functions to draw individual glyphs and produces the highest quality
 * output.
 */
void gr_settextfontprec(int font, int precision)
{
  check_autoinit;

  gks_set_text_fontprec(font, precision);
  if (ctx)
    {
      ctx->txfont = font;
      ctx->txprec = precision;
    }

  if (flag_stream) gr_writestream("<settextfontprec font=\"%d\" precision=\"%d\"/>\n", font, precision);
}

static int loadfont(char *name)
{
  int i, j, font;

  for (i = 0; i < num_font_aliases; i++)
    {
      if (strcmp(name, font_aliases[i].name) == 0)
        {
          for (j = 0; j < 3; j++)
            {
              if (font_aliases[i].candidate[j] != NULL)
                {
                  font = gks_ft_load_user_font(font_aliases[i].candidate[j], 1);
                  if (font > 0)
                    {
                      return font;
                      break;
                    }
                }
            }
        }
    }
  return -1;
}

/*!
 * Load a font file from a given filename.
 *
 * \param[in] filename The absolute filename of the font
 * \param[out] font The font index to use with gr_settextfontprec
 *
 * This function loads a font from a given filename and assigns a font index to it. To use the loaded font call
 * `gr_settextfontprec` using the resulting font index and precision 3.
 *
 *      int font;
 *      gr_loadfont(filename, &font);
 *      gr_settextfontprec(font, 3);
 *
 * The filename can either be an absolute path or a filename like `Arial.ttf`. Font files are searched in the
 * directories specified by the `GKS_FONT_DIRS` environment variable and the operating systems default font locations.
 *
 * As the font file is internally loaded using FreeType, it is required that FreeType support is compiled
 * in and FreeType has to support the given file type. On error the font index is set to -1.
 *
 */
void gr_loadfont(char *filename, int *font)
{
  check_autoinit;

  if (strchr(filename, '.') == NULL)
    {
      *font = loadfont(filename);
      if (*font == -1) fprintf(stderr, "could not find font %s\n", filename);
    }
  else
    {
      *font = gks_ft_load_user_font(filename, 0);
    }
  if (*font > 0)
    {
      if (flag_stream) gr_writestream("<loadfont filename=\"%s\"/>\n", filename);
    }
}

/*!
 * Set the current character expansion factor (width to height ratio).
 *
 * \param[in] factor Text expansion factor applied to the nominal text
 *                   width-to-height ratio
 *
 * This function defines the width of subsequent text output primitives. The
 * expansion factor alters the width of the generated characters, but not their
 * height. The default text expansion factor is 1, or one times the normal
 * width-to-height ratio of the text.
 */
void gr_setcharexpan(double factor)
{
  check_autoinit;

  gks_set_text_expfac(factor);
  if (ctx) ctx->chxp = factor;

  if (flag_stream) gr_writestream("<setcharexpan factor=\"%g\"/>\n", factor);
}

void gr_setcharspace(double spacing)
{
  check_autoinit;

  gks_set_text_spacing(spacing);
  if (ctx) ctx->chsp = spacing;

  if (flag_stream) gr_writestream("<setcharspace spacingr=\"%g\"/>\n", spacing);
}

/*!
 * Set the current text color index.
 *
 * \param[in] color The text color index (COLOR < 1256)
 *
 * This function defines the color of subsequent text output primitives. GR uses
 * the default foreground color (black=1) for the default text color index.
 */
void gr_settextcolorind(int color)
{
  check_autoinit;

  gks_set_text_color_index(color);
  if (ctx) ctx->txcoli = color;

  if (flag_stream) gr_writestream("<settextcolorind color=\"%d\"/>\n", color);
}

/*!
 * Gets the current text color index.
 *
 * \param[out] color The text color index (COLOR < 1256)
 *
 * This function gets the color of text output primitives.
 */
void gr_inqtextcolorind(int *color)
{
  int errind;
  gks_inq_text_color_index(&errind, color);
}

/*!
 * Set the current character height.
 *
 * \param[in] height Text height value
 *
 * This function defines the height of subsequent text output primitives. Text
 * height is defined as a percentage of the default window. GR uses the default
 * text height of 0.027 (2.7% of the height of the default window).
 */
void gr_setcharheight(double height)
{
  check_autoinit;

  gks_set_text_height(height);
  if (ctx) ctx->chh = height;

  if (flag_stream) gr_writestream("<setcharheight height=\"%g\"/>\n", height);
}

void gr_setwscharheight(double chh, double height)
{
  gr_setcharheight(gks_inq_ws_text_height(chh, height));
}

/*!
 * Gets the current character height..
 *
 * \param[out] height Text height value
 *
 * This function gets the height of text output primitives. Text height is
 * defined as a percentage of the default window. GR uses the default text
 * height of 0.027 (2.7% of the height of the default window).
 */
void gr_inqcharheight(double *height)
{
  int errind;
  gks_inq_text_height(&errind, height);
}

/*!
 * Set the current character text angle up vector.
 *
 * \param[in] ux X coordinate of the text up vector
 * \param[in] uy Y coordinate of the text up vector
 *
 * This function defines the vertical rotation of subsequent text output primitives.
 The text up vector is initially set to (0, 1), horizontal to the baseline.
 */
void gr_setcharup(double ux, double uy)
{
  check_autoinit;

  gks_set_text_upvec(ux, uy);
  if (ctx)
    {
      ctx->chup[0] = ux;
      ctx->chup[1] = uy;
    }

  if (flag_stream) gr_writestream("<setcharup x=\"%g\" y=\"%g\"/>\n", ux, uy);
}

/*!
 * Define the current direction in which subsequent text will be drawn.
 *
 * \param[in] path Text path (see table)
 *
 * \verbatim embed:rst:leading-asterisk
 *
 * +----------------------+---+---------------+
 * |TEXT_PATH_RIGHT       |  0|left-to-right  |
 * +----------------------+---+---------------+
 * |TEXT_PATH_LEFT        |  1|right-to-left  |
 * +----------------------+---+---------------+
 * |TEXT_PATH_UP          |  2|downside-up    |
 * +----------------------+---+---------------+
 * |TEXT_PATH_DOWN        |  3|upside-down    |
 * +----------------------+---+---------------+
 *
 * \endverbatim
 */
void gr_settextpath(int path)
{
  check_autoinit;

  gks_set_text_path(path);
  if (ctx) ctx->txp = path;

  if (flag_stream) gr_writestream("<settextpath path=\"%d\"/>\n", path);
}

/*!
 * Set the current horizontal and vertical alignment for text.
 *
 * \param[in] horizontal Horizontal text alignment (see the table)
 * \param[in] vertical Vertical text alignment (see the table)
 *
 * \verbatim embed:rst:leading-asterisk
 *
 * +-------------------------+---+----------------+
 * |TEXT_HALIGN_NORMAL       |  0|                |
 * +-------------------------+---+----------------+
 * |TEXT_HALIGN_LEFT         |  1|Left justify    |
 * +-------------------------+---+----------------+
 * |TEXT_HALIGN_CENTER       |  2|Center justify  |
 * +-------------------------+---+----------------+
 * |TEXT_HALIGN_RIGHT        |  3|Right justify   |
 * +-------------------------+---+----------------+
 *
 * +-------------------------+---+------------------------------------------------+
 * |TEXT_VALIGN_NORMAL       |  0|                                                |
 * +-------------------------+---+------------------------------------------------+
 * |TEXT_VALIGN_TOP          |  1|Align with the top of the characters            |
 * +-------------------------+---+------------------------------------------------+
 * |TEXT_VALIGN_CAP          |  2|Aligned with the cap of the characters          |
 * +-------------------------+---+------------------------------------------------+
 * |TEXT_VALIGN_HALF         |  3|Aligned with the half line of the characters    |
 * +-------------------------+---+------------------------------------------------+
 * |TEXT_VALIGN_BASE         |  4|Aligned with the base line of the characters    |
 * +-------------------------+---+------------------------------------------------+
 * |TEXT_VALIGN_BOTTOM       |  5|Aligned with the bottom line of the characters  |
 * +-------------------------+---+------------------------------------------------+
 *
 * \endverbatim
 *
 * This function specifies how the characters in a text primitive will be
 * aligned in horizontal and vertical space. The default text alignment
 * indicates horizontal left alignment and vertical baseline alignment.
 */
void gr_settextalign(int horizontal, int vertical)
{
  check_autoinit;

  gks_set_text_align(horizontal, vertical);
  if (ctx)
    {
      ctx->txal[0] = horizontal;
      ctx->txal[1] = vertical;
    }

  if (flag_stream) gr_writestream("<settextalign halign=\"%d\" valign=\"%d\"/>\n", horizontal, vertical);
}

/*!
 * Set the fill area interior style to be used for fill areas.
 *
 * \param[in] style The style of fill to be used
 *
 * \verbatim embed:rst:leading-asterisk
 *
 * +------------------+---+-------------------------------------------------------------------------------------------+
 * |HOLLOW            |  0|No filling. Just draw the bounding polyline                                                |
 * +------------------+---+-------------------------------------------------------------------------------------------+
 * |SOLID             |  1|Fill the interior of the polygon using the fill color index                                |
 * +------------------+---+-------------------------------------------------------------------------------------------+
 * |PATTERN           |  2|Fill the interior of the polygon using the style index as a pattern index                  |
 * +------------------+---+-------------------------------------------------------------------------------------------+
 * |HATCH             |  3|Fill the interior of the polygon using the style index as a cross-hatched style            |
 * +------------------+---+-------------------------------------------------------------------------------------------+
 * |SOLID_WITH_BORDER |  4|Fill the interior of the polygon using the fill color index and draw the bounding polyline |
 * +------------------+---+-------------------------------------------------------------------------------------------+
 * \endverbatim
 *
 * This function defines the interior style  for subsequent fill area output
 * primitives. The default interior style is HOLLOW.
 */
void gr_setfillintstyle(int style)
{
  check_autoinit;

  gks_set_fill_int_style(style);
  if (ctx) ctx->ints = style;

  if (flag_stream) gr_writestream("<setfillintstyle intstyle=\"%d\"/>\n", style);
}

/*!
 * Set the fill area interior style to be used for fill areas.
 *
 * \param[out] style The currently set fill style
 *
 * This function gets the currently set fill style.
 */
void gr_inqfillintstyle(int *style)
{
  int errind;

  check_autoinit;

  gks_inq_fill_int_style(&errind, style);
}

/*!
 * Set the fill area interior style to be used for fill areas.
 *
 * \param[in] index The fill style index to be used
 *
 * This function specifies an index when PATTERN fill or HATCH fill is
 * requested by the gr_setfillintstyle function. If the interior style is set
 * to PATTERN, the fill style index points to a device-independent pattern
 * table. If interior style is set to HATCH the fill style index indicates
 * different hatch styles. If HOLLOW or SOLID is specified for the interior
 * style, the fill style index is unused.
 */
void gr_setfillstyle(int index)
{
  check_autoinit;

  gks_set_fill_style_index(index);
  if (ctx) ctx->styli = index;

  if (flag_stream) gr_writestream("<setfillstyle style=\"%d\"/>\n", index);
}

/*!
 * Get the fill area interior style to be used for fill areas.
 *
 * \param[out] index The currently set fill style color index
 *
 * This function gets the color index for PATTERN and HATCH fills.
 */
void gr_inqfillstyle(int *index)
{
  int errind;

  check_autoinit;

  gks_inq_fill_style_index(&errind, index);
}

/*!
 * Sets the current fill area color index.
 *
 * \param[in] color The fill area color index (COLOR < 1256)
 *
 * This function defines the color of subsequent fill area output primitives.
 * GR uses the default foreground color (black=1) for the default fill area
 * color index.
 */
void gr_setfillcolorind(int color)
{
  check_autoinit;

  gks_set_fill_color_index(color);
  if (ctx) ctx->facoli = color;

  if (flag_stream) gr_writestream("<setfillcolorind color=\"%d\"/>\n", color);
}

/*!
 * Gets the current fill area color index.
 *
 * \param[out] color The fill area color index (COLOR < 1256)
 *
 * This function gets the color of fill area output primitives.
 */
void gr_inqfillcolorind(int *color)
{
  int errind;

  check_autoinit;

  gks_inq_fill_color_index(&errind, color);
}

void gr_setresizebehaviour(int flag)
{
  check_autoinit;

  gks_set_resize_behaviour(flag);
  if (ctx) ctx->resize_behaviour = flag;

  if (flag_stream) gr_writestream("<setresizebehaviour=\"%d\"/>\n", flag);
}

void gr_inqresizebehaviour(int *flag)
{
  check_autoinit;

  gks_inq_resize_behaviour(flag);
}

static void setcolor(int workstation_id, color_t *color)
{
  int wkid = workstation_id;

  gks_set_color_rep(wkid, color->index, color->red, color->green, color->blue);
}

static void setcolorrep(int index, double red, double green, double blue)
{
  color_t color;

  color.index = index;
  color.red = red;
  color.green = green;
  color.blue = blue;

  if (index >= 0 && index < MAX_COLOR)
    rgb[index] = ((nint(red * 255) & 0xff)) | ((nint(green * 255) & 0xff) << 8) | ((nint(blue * 255) & 0xff) << 16);

  foreach_activews((void (*)(int, void *))setcolor, (void *)&color);
}

/*!
 * Redefine an existing color index representation by specifying an RGB color
 * triplet.
 *
 * \param[in] index Color index in the range 0 to 1256
 * \param[in] red Red intensity in the range 0.0 to 1.0
 * \param[in] green Green intensity in the range 0.0 to 1.0
 * \param[in] blue Blue intensity in the range 0.0 to 1.0
 */
void gr_setcolorrep(int index, double red, double green, double blue)
{
  check_autoinit;

  setcolorrep(index, red, green, blue);

  if (flag_stream)
    gr_writestream("<setcolorrep index=\"%d\" red=\"%g\" green=\"%g\" blue=\"%g\"/>\n", index, red, green, blue);
}

/*!
 * Set the type of transformation to be used for subsequent GR output
 * primitives.
 *
 * \param[in] options Scale specification (see table)
 *
 * \verbatim embed:rst:leading-asterisk
 *
 * +------------------+--------------------+
 * |GR_OPTION_X_LOG   |Logarithmic X-axis  |
 * +------------------+--------------------+
 * |GR_OPTION_Y_LOG   |Logarithmic Y-axis  |
 * +------------------+--------------------+
 * |GR_OPTION_Z_LOG   |Logarithmic Z-axis  |
 * +------------------+--------------------+
 * |GR_OPTION_FLIP_X  |Flip X-axis         |
 * +------------------+--------------------+
 * |GR_OPTION_FLIP_Y  |Flip Y-axis         |
 * +------------------+--------------------+
 * |GR_OPTION_FLIP_Z  |Flip Z-axis         |
 * +------------------+--------------------+
 * |GR_OPTION_X_LOG2  |log2 scaled X-axis  |
 * +------------------+--------------------+
 * |GR_OPTION_Y_LOG2  |log2 scaled Y-axis  |
 * +------------------+--------------------+
 * |GR_OPTION_Z_LOG2  |log2 scaled Z-axis  |
 * +------------------+--------------------+
 * |GR_OPTION_X_LN    |ln scaled X-axis    |
 * +------------------+--------------------+
 * |GR_OPTION_Y_LN    |ln scaled Y-axis    |
 * +------------------+--------------------+
 * |GR_OPTION_Z_LN    |ln scaled Z-axis    |
 * +------------------+--------------------+
 *
 * \endverbatim
 *
 * This function defines the current transformation according to the given scale
 * specification which may be or'ed together using any of the above options. GR
 * uses these options for all subsequent output primitives until another value
 * is provided. The scale options are used to transform points from an abstract
 * logarithmic or semi-logarithmic coordinate system, which may be flipped along
 * each axis, into the world coordinate system.
 *
 * \note When applying a logarithmic transformation to a specific axis, the
 * system assumes that the axes limits are greater than zero.
 */
int gr_setscale(int options)
{
  int result = 0;

  check_autoinit;

  result = setscale(options);
  if (ctx) ctx->scale_options = options;

  if (flag_stream) gr_writestream("<setscale scale=\"%d\"/>\n", options);

  return result;
}

void gr_inqscale(int *options)
{
  check_autoinit;

  *options = lx.scale_options;
}

/*!
 * Establishes a window, or rectangular subspace, of world coordinates to be
 * plotted. If you desire log scaling or mirror-imaging of axes, use the
 * gr_setscale function.
 *
 * \param[in] xmin The left horizontal coordinate of the window (xmin < xmax).
 * \param[in] xmax The right horizontal coordinate of the window (xmin < xmax).
 * \param[in] ymin The bottom vertical coordinate of the window (ymin < ymax).
 * \param[in] ymax The top vertical coordinate of the window (ymin < ymax).
 *
 * This function defines the rectangular portion of the World Coordinate space
 * (WC) to be associated with the specified normalization transformation. The
 * WC window and the Normalized Device Coordinates (NDC) viewport define the
 * normalization transformation through which all output primitives are mapped.
 * The WC window is mapped onto the rectangular NDC viewport which is, in turn,
 * mapped onto the display surface of the open and active workstation, in device
 * coordinates. By default, GR uses the range [0,1] x [0,1], in world
 * coordinates, as the normalization transformation window.
 */
void gr_setwindow(double xmin, double xmax, double ymin, double ymax)
{
  int tnr = WC;

  check_autoinit;

  gks_set_window(tnr, xmin, xmax, ymin, ymax);
  gks_set_window(MODERN_NDC, -1, 1, -1, 1);
  if (ctx)
    {
      ctx->wn[0] = xmin;
      ctx->wn[1] = xmax;
      ctx->wn[2] = ymin;
      ctx->wn[3] = ymax;
    }
  setscale(lx.scale_options);

  if (flag_stream)
    gr_writestream("<setwindow xmin=\"%g\" xmax=\"%g\" ymin=\"%g\" ymax=\"%g\"/>\n", xmin, xmax, ymin, ymax);
}

void gr_inqwindow(double *xmin, double *xmax, double *ymin, double *ymax)
{
  check_autoinit;

  *xmin = lx.xmin;
  *xmax = lx.xmax;
  *ymin = lx.ymin;
  *ymax = lx.ymax;
}

/*
 * Return the three dimensional window.
 */
void gr_inqwindow3d(double *xmin, double *xmax, double *ymin, double *ymax, double *zmin, double *zmax)
{

  check_autoinit;

  *xmin = ix.xmin;
  *xmax = ix.xmax;
  *ymin = ix.ymin;
  *ymax = ix.ymax;
  *zmin = ix.zmin;
  *zmax = ix.zmax;
}

/*!
 * Establishes a rectangular subspace of normalized device coordinates.
 *
 * \param[in] xmin The left horizontal coordinate of the viewport
 *                 (0 <= xmin < xmax).
 * \param[in] xmax The right horizontal coordinate of the viewport
 *                 (xmin < xmax <= 1).
 * \param[in] ymin The bottom vertical coordinate of the viewport
 *                 (0 <= ymin < ymax).
 * \param[in] ymax The top vertical coordinate of the viewport
 *                 (ymin < ymax <= 1).
 *
 * This function defines the rectangular portion of the Normalized Device
 * Coordinate (NDC) space to be associated with the specified normalization
 * transformation. The NDC viewport and World Coordinate (WC) window define
 * the normalization transformation through which all output primitives pass.
 * The WC window is mapped onto the rectangular NDC viewport which is, in turn,
 * mapped onto the display surface of the open and active workstation, in device
 * coordinates.
 */
void gr_setviewport(double xmin, double xmax, double ymin, double ymax)
{
  int tnr = WC;

  check_autoinit;

  gks_set_viewport(tnr, xmin, xmax, ymin, ymax);
  gks_set_viewport(MODERN_NDC, xmin, xmax, ymin, ymax);
  if (ctx)
    {
      ctx->vp[0] = xmin;
      ctx->vp[1] = xmax;
      ctx->vp[2] = ymin;
      ctx->vp[3] = ymax;
    }
  setscale(lx.scale_options);

  vxmin = xmin;
  vxmax = xmax;
  vymin = ymin;
  vymax = ymax;

  if (flag_stream)
    gr_writestream("<setviewport xmin=\"%g\" xmax=\"%g\" ymin=\"%g\" ymax=\"%g\"/>\n", xmin, xmax, ymin, ymax);
}

void gr_inqviewport(double *xmin, double *xmax, double *ymin, double *ymax)
{
  check_autoinit;

  *xmin = vxmin;
  *xmax = vxmax;
  *ymin = vymin;
  *ymax = vymax;
}

/*!
 * Select a predefined transformation from world coordinates to normalized
 * device coordinates.
 *
 * \param[in] transform A normalization transformation number.
 *
 * \verbatim embed:rst:leading-asterisk
 *
 * +------+----------------------------------------------------------------------------------------------------+
 * |     0|Selects the identity transformation in which both the window and viewport have the range of 0 to 1  |
 * +------+----------------------------------------------------------------------------------------------------+
 * |  >= 1|Selects a normalization transformation as defined by `setwindow` and `setviewport`                  |
 * +------+----------------------------------------------------------------------------------------------------+
 *
 * \endverbatim
 */
void gr_selntran(int transform)
{
  check_autoinit;

  gks_select_xform(transform);

  if (flag_stream) gr_writestream("<selntran transform=\"%d\"/>\n", transform);
}

/*!
 * Set the clipping indicator.
 *
 * \param[in] indicator An indicator specifying whether clipping is on or off.
 *
 * \verbatim embed:rst:leading-asterisk
 *
 * +----+---------------------------------------------------------------+
 * |   0|Clipping is off. Data outside of the window will be drawn.     |
 * +----+---------------------------------------------------------------+
 * |   1|Clipping is on. Data outside of the window will not be drawn.  |
 * +----+---------------------------------------------------------------+
 *
 * \endverbatim
 *
 * This function enables or disables clipping of the image drawn in the current
 * window. Clipping is defined as the removal of those portions of the graph
 * that lie outside of the defined viewport. If clipping is on, GR does not
 * draw generated output primitives past the viewport boundaries. If clipping
 * is off, primitives may exceed the viewport boundaries, and they will be
 * drawn to the edge of the workstation window. By default, clipping is on.
 */
void gr_setclip(int indicator)
{
  check_autoinit;

  gks_set_clipping(indicator);

  if (flag_stream) gr_writestream("<setclip indicator=\"%d\"/>\n", indicator);
}

static void wswindow(int workstation_id, rect_t *rect)
{
  int wkid = workstation_id;

  gks_set_ws_window(wkid, rect->xmin, rect->xmax, rect->ymin, rect->ymax);
}

/*!
 * Set the area of the NDC viewport that is to be drawn in the workstation
 * window.
 *
 * \param[in] xmin The left horizontal coordinate of the workstation window
 *                 (0 <= xmin < xmax).
 * \param[in] xmax The right horizontal coordinate of the workstation window
 *                 (xmin < xmax <= 1).
 * \param[in] ymin The bottom vertical coordinate of the workstation window
 *                 (0 <= ymin < ymax).
 * \param[in] ymax The top vertical coordinate of the workstation window
 *                 (ymin < ymax <= 1).
 *
 * This function defines the rectangular area of the Normalized Device
 * Coordinate space to be output to the device. By default, the workstation
 * transformation will map the range [0,1] x [0,1] in NDC onto the largest
 * square on the workstation's display surface. The aspect ratio of the
 * workstation window is maintained at 1 to 1.
 */
void gr_setwswindow(double xmin, double xmax, double ymin, double ymax)
{
  rect_t rect;

  rect.xmin = xmin;
  rect.xmax = xmax;
  rect.ymin = ymin;
  rect.ymax = ymax;

  check_autoinit;

  foreach_activews((void (*)(int, void *))wswindow, (void *)&rect);

  if (flag_stream)
    gr_writestream("<setwswindow xmin=\"%g\" xmax=\"%g\" ymin=\"%g\" ymax=\"%g\"/>\n", xmin, xmax, ymin, ymax);
}

static void wsviewport(int workstation_id, rect_t *rect)
{
  int wkid = workstation_id;

  gks_set_ws_viewport(wkid, rect->xmin, rect->xmax, rect->ymin, rect->ymax);
}

/*!
 * Define the size of the workstation graphics window in meters.
 *
 * \param[in] xmin The left horizontal coordinate of the workstation window.
 * \param[in] xmax The right horizontal coordinate of the workstation window.
 * \param[in] ymin The bottom vertical coordinate of the workstation window.
 * \param[in] ymax The top vertical coordinate of the workstation window.
 *
 * This function places a workstation window on the display of the specified
 * size in meters. This command allows the workstation window to be accurately
 * sized for a display or hardcopy device, and is often useful for sizing
 * graphs for desktop publishing applications.
 */
void gr_setwsviewport(double xmin, double xmax, double ymin, double ymax)
{
  rect_t rect;

  rect.xmin = xmin;
  rect.xmax = xmax;
  rect.ymin = ymin;
  rect.ymax = ymax;

  check_autoinit;

  foreach_activews((void (*)(int, void *))wsviewport, (void *)&rect);

  sizex = xmax - xmin;

  if (flag_stream)
    gr_writestream("<setwsviewport xmin=\"%g\" xmax=\"%g\" ymin=\"%g\" ymax=\"%g\"/>\n", xmin, xmax, ymin, ymax);
}

void gr_createseg(int segment)
{
  check_autoinit;

  gks_create_seg(segment);
}

static void copyseg(int workstation_id, int *segment)
{
  int wkid = workstation_id, errind, conid, wtype, wkcat;

  gks_inq_ws_conntype(wkid, &errind, &conid, &wtype);
  gks_inq_ws_category(wtype, &errind, &wkcat);

  if (wkcat == GKS_K_WSCAT_OUTPUT || wkcat == GKS_K_WSCAT_OUTIN)
    {
      gks_copy_seg_to_ws(wkid, *segment);
      gks_update_ws(wkid, GKS_K_POSTPONE_FLAG);
    }
}

void gr_copysegws(int segment)
{
  int segn = segment;

  check_autoinit;

  foreach_activews((void (*)(int, void *))copyseg, (void *)&segn);
}

static void redrawseg(int workstation_id, void *foo)
{
  int wkid = workstation_id;
  GR_UNUSED(foo);

  gks_redraw_seg_on_ws(wkid);
}

void gr_redrawsegws(void)
{
  check_autoinit;

  foreach_activews((void (*)(int, void *))redrawseg, (void *)NULL);
}

void gr_setsegtran(int segment, double fx, double fy, double transx, double transy, double phi, double scalex,
                   double scaley)
{
  int segn = segment;
  double mat[3][2];

  check_autoinit;

  gks_eval_xform_matrix(fx, fy, transx, transy, phi, scalex, scaley, GKS_K_COORDINATES_NDC, mat);
  gks_set_seg_xform(segn, mat);
}

void gr_closeseg(void)
{
  check_autoinit;

  gks_close_seg();
}

void gr_samplelocator(double *x, double *y, int *state)
{
  int wkid = 1, errind;

  check_autoinit;

  gks_sample_locator(wkid, &errind, x, y, state);
}

void gr_emergencyclosegks(void)
{
  gks_emergency_close();
  autoinit = 1;
}

static void updatews(int wkid, void *foo)
{
  int errind, conid, wtype, wkcat;
  GR_UNUSED(foo);

  gks_inq_ws_conntype(wkid, &errind, &conid, &wtype);
  gks_inq_ws_category(wtype, &errind, &wkcat);

  if (wkcat == GKS_K_WSCAT_OUTPUT || wkcat == GKS_K_WSCAT_OUTIN)
    {
      gks_update_ws(wkid, GKS_K_WRITE_PAGE_FLAG);
    }
}

void gr_updategks(void)
{
  foreach_openws(updatews, NULL);
}

/*!
 * Set the abstract Z-space used for mapping three-dimensional output primitives
 * into the current world coordinate space.
 *
 * \param[in] zmin Minimum value for the Z-axis.
 * \param[in] zmax Maximum value for the Z-axis.
 * \param[in] rotation Angle for the rotation of the X axis, in degrees.
 * \param[in] tilt Viewing angle of the Z axis, in degrees.
 *
 * This function establishes the limits of an abstract Z-axis and defines the
 * angles for rotation and for the viewing angle (tilt) of a simulated
 * three-dimensional graph, used for mapping corresponding output primitives
 * into the current window. These settings are used for all subsequent
 * three-dimensional output primitives until other values are specified. Angles
 * of rotation and viewing angle must be specified between 0 and 90 degrees.
 */
int gr_setspace(double zmin, double zmax, int rotation, int tilt)
{
  if (zmin < zmax)
    {
      if (rotation < 0 || rotation > 90 || tilt < 0 || tilt > 90) return -1;
    }
  else
    return -1;

  check_autoinit;

  setspace(zmin, zmax, rotation, tilt);

  if (flag_stream)
    gr_writestream("<setspace zmin=\"%g\" zmax=\"%g\" rotation=\"%d\" tilt=\"%d\"/>\n", zmin, zmax, rotation, tilt);

  return 0;
}

/*!
 * Set the projection type with this flag.
 *
 * \param[in] flag projection type
 *
 * The available options are:
 *
 * \verbatim embed:rst:leading-asterisk
 *
 * +---------------------------+---+--------------+
 * |GR_PROJECTION_DEFAULT      |  0|default       |
 * +---------------------------+---+--------------+
 * |GR_PROJECTION_ORTHOGRAPHIC |  1|orthographic  |
 * +---------------------------+---+--------------+
 * |GR_PROJECTION_PERSPECTIVE  |  2|perspective   |
 * +---------------------------+---+--------------+
 *
 * \endverbatim
 *
 */
void gr_setprojectiontype(int flag)
{
  check_autoinit;

  if (flag == GR_PROJECTION_DEFAULT || flag == GR_PROJECTION_ORTHOGRAPHIC || flag == GR_PROJECTION_PERSPECTIVE)
    {
      gpx.projection_type = flag;

      if (flag_stream) gr_writestream("<setprojectiontype flag=\"%i\"/>\n", flag);
    }
  else
    {
      fprintf(stderr, "Invalid projection flag. Possible options are GR_PROJECTION_DEFAULT, GR_PROJECTION_ORTHOGRAPHIC "
                      "and GR_PROJECTION_PERSPECTIV\n");
    }
}

/*!
 * Return the projection type.
 */
void gr_inqprojectiontype(int *projection_type)
{
  check_autoinit;

  *projection_type = gpx.projection_type;
}

void settransformationparameters(double camera_pos_x, double camera_pos_y, double camera_pos_z, double up_x,
                                 double up_y, double up_z, double focus_point_x, double focus_point_y,
                                 double focus_point_z)
{
  int i;
  double F[3], f[3], up[3], s_deri[3], s[3], u[3], u_deri[3];
  double norm_func, norm_up, s_norm, norm_u;

  tx.camera_pos_x = camera_pos_x;
  tx.camera_pos_y = camera_pos_y;
  tx.camera_pos_z = camera_pos_z;

  tx.focus_point_x = focus_point_x;
  tx.focus_point_y = focus_point_y;
  tx.focus_point_z = focus_point_z;

  F[0] = tx.focus_point_x - tx.camera_pos_x; /* direction between camera and focus point */
  F[1] = tx.focus_point_y - tx.camera_pos_y;
  F[2] = tx.focus_point_z - tx.camera_pos_z;
  norm_func = sqrt(F[0] * F[0] + F[1] * F[1] + F[2] * F[2]);
  f[0] = F[0] / norm_func;
  f[1] = F[1] / norm_func;
  f[2] = F[2] / norm_func;
  norm_up = sqrt(up_x * up_x + up_y * up_y + up_z * up_z);
  up[0] = up_x / norm_up;
  up[1] = up_y / norm_up;
  up[2] = up_z / norm_up;
  for (i = 0; i < 3; i++) /*  f cross up */
    {
      s_deri[i] = f[(i + 1) % 3] * up[(i + 2) % 3] - up[(i + 1) % 3] * f[(i + 2) % 3];
    }
  s_norm = sqrt(s_deri[0] * s_deri[0] + s_deri[1] * s_deri[1] + s_deri[2] * s_deri[2]);
  s[0] = s_deri[0] / s_norm;
  s[1] = s_deri[1] / s_norm;
  s[2] = s_deri[2] / s_norm;
  for (i = 0; i < 3; i++) /* s cross f */
    {
      u_deri[i] = s[(i + 1) % 3] * f[(i + 2) % 3] - f[(i + 1) % 3] * s[(i + 2) % 3];
    }
  norm_u = sqrt(u_deri[0] * u_deri[0] + u_deri[1] * u_deri[1] + u_deri[2] * u_deri[2]);
  u[0] = u_deri[0] / norm_u;
  u[1] = u_deri[1] / norm_u;
  u[2] = u_deri[2] / norm_u;

  tx.up_x = u[0];
  tx.up_y = u[1];
  tx.up_z = u[2];
  tx.s_x = s[0];
  tx.s_y = s[1];
  tx.s_z = s[2];

  /* Undo possible axis scaling */
  tx.x_axis_scale = 1;
  tx.y_axis_scale = 1;
  tx.z_axis_scale = 1;

  tx.use_setspace3d = 0;
}

/*!
 * Method to set the camera position, the upward facing direction and the focus point of the shown
 * volume
 *
 * \param camera_pos_x x component of the cameraposition in world coordinates
 * \param camera_pos_y y component of the cameraposition in world coordinates
 * \param camera_pos_z z component of the cameraposition in world coordinates
 * \param up_x x component of the up vector
 * \param up_y y component of the up vector
 * \param up_z z component of the up vector
 * \param focus_point_x x component of focus-point inside volume
 * \param focus_point_y y component of focus-point inside volume
 * \param focus_point_z z component of focus-point inside volume
 *
 */
void gr_settransformationparameters(double camera_pos_x, double camera_pos_y, double camera_pos_z, double up_x,
                                    double up_y, double up_z, double focus_point_x, double focus_point_y,
                                    double focus_point_z)
{
  check_autoinit;

  settransformationparameters(camera_pos_x, camera_pos_y, camera_pos_z, up_x, up_y, up_z, focus_point_x, focus_point_y,
                              focus_point_z);

  if (flag_stream)
    gr_writestream("<settransformationparameters camera_pos_x=\"%g\" camera_pos_y=\"%g\" camera_pos_z=\"%g\" "
                   "up_x=\"%g\" up_y=\"%g\" "
                   "up_z=\"%g\" focus_point_x=\"%g\" focus_point_y=\"%g\" focus_point_z=\"%g\"/>\n",
                   camera_pos_x, camera_pos_y, camera_pos_z, up_x, up_y, up_z, focus_point_x, focus_point_y,
                   focus_point_z);
}

static void setperspectiveprojection(double near_plane, double far_plane, double fov)
{
  gpx.near_plane = near_plane;
  gpx.far_plane = far_plane;

  if (0 < fov && fov < 180)
    {
      gpx.fov = fov;
    }
  else
    {
      fprintf(stderr, "The value for the fov parameter is not between 0 and 180 degree\n");
    }

  gpx.projection_type = GR_PROJECTION_PERSPECTIVE;
}

/*!
 * Set the far and near clipping plane for perspective projection and the vertical field ov view
 *
 * \param near_plane distance to near clipping plane
 * \param far_plane distance to far clipping plane
 * \param fov vertical field of view, input must be between 0 and 180 degrees
 *
 * Switches projection type to perspective
 */
void gr_setperspectiveprojection(double near_plane, double far_plane, double fov)
{
  check_autoinit;

  setperspectiveprojection(near_plane, far_plane, fov);

  if (flag_stream)
    gr_writestream("<setperspectiveprojection near_plane=\"%g\" far_plane=\"%g\" fov=\"%g\"/>\n", near_plane, far_plane,
                   fov);
}

static void setorthographicprojection(double left, double right, double bottom, double top, double near_plane,
                                      double far_plane)
{
  gpx.left = left;
  gpx.right = right;
  gpx.bottom = bottom;
  gpx.top = top;
  gpx.near_plane = near_plane;
  gpx.far_plane = far_plane;

  gpx.projection_type = GR_PROJECTION_ORTHOGRAPHIC;
}

/*!
 * Set parameters for orthographic transformation
 *
 * \param left xmin of the volume in worldcoordinates
 * \param right xmax of volume in worldcoordinates
 * \param bottom ymin of volume in worldcoordinates
 * \param top ymax of volume in worldcoordinates
 * \param near_plane distance to near clipping plane
 * \param far_plane distance to far clipping plane
 *
 * Switches projection type to orthographic
 */
void gr_setorthographicprojection(double left, double right, double bottom, double top, double near_plane,
                                  double far_plane)
{
  check_autoinit;

  setorthographicprojection(left, right, bottom, top, near_plane, far_plane);

  if (flag_stream)
    gr_writestream("<setorthographicprojection left=\"%g\" right=\"%g\" bottom=\"%g\" top=\"%g\" near_plane=\"%g\" "
                   "far_plane=\"%g\"/>\n",
                   left, right, bottom, top, near_plane, far_plane);
}

/*!
 * Return the camera position, up vector and focus point.
 */
void gr_inqtransformationparameters(double *camera_pos_x, double *camera_pos_y, double *camera_pos_z, double *up_x,
                                    double *up_y, double *up_z, double *focus_point_x, double *focus_point_y,
                                    double *focus_point_z)
{

  check_autoinit;

  *camera_pos_x = tx.camera_pos_x;
  *camera_pos_y = tx.camera_pos_y;
  *camera_pos_z = tx.camera_pos_z;

  *up_x = tx.up_x;
  *up_y = tx.up_y;
  *up_z = tx.up_z;

  *focus_point_x = tx.focus_point_x;
  *focus_point_y = tx.focus_point_y;
  *focus_point_z = tx.focus_point_z;
}

/*!
 *  Return the parameters for the orthographic projection.
 */
void gr_inqorthographicprojection(double *left, double *right, double *bottom, double *top, double *near_plane,
                                  double *far_plane)
{

  check_autoinit;

  *left = gpx.left;
  *right = gpx.right;
  *bottom = gpx.bottom;
  *top = gpx.top;
  *near_plane = gpx.near_plane;
  *far_plane = gpx.far_plane;
}

/*!
 *  Return the parameters for the perspective projection.
 */
void gr_inqperspectiveprojection(double *near_plane, double *far_plane, double *fov)
{

  check_autoinit;

  *near_plane = gpx.near_plane;
  *far_plane = gpx.far_plane;
  *fov = gpx.fov;
}

void gr_inqspace(double *zmin, double *zmax, int *rotation, int *tilt)
{
  check_autoinit;

  *zmin = wx.zmin;
  *zmax = wx.zmax;
  *rotation = wx.phi;
  *tilt = wx.delta;
}

double intpart(double x)
{
  double ipart;
  modf(x, &ipart);
  return ipart;
}

static double pred(double x)
{
  double ipart;
  ipart = intpart(x);
  if (x == ipart)
    return ipart - 1;
  else
    return gauss(x);
}

#define ipred(x) ((int64_t)pred(x))

double succ(double x)
{
  double ipart;
  ipart = intpart(x);
  if (x == ipart)
    return ipart;
  else
    return gauss(x) + 1;
}

#define isucc(x) ((int64_t)succ(x))

static double fract(double x)
{
  double _intpart;
  return modf(x, &_intpart);
}

static void end_pline(void)
{
  if (npoints >= 2)
    {
      gks_polyline(npoints, xpoint, ypoint);
      npoints = 0;
    }
}

static void pline(double x, double y)
{
  if (npoints >= maxpath) reallocate(npoints);

  xpoint[npoints] = x_lin(x);
  ypoint[npoints] = y_lin(y);
  npoints++;
}

static void start_pline(double x, double y)
{
  end_pline();

  npoints = 0;
  pline(x, y);
}

static void end_pline3d(void)
{
  int errind, tnr;
  int modern_projection_type;

  if (npoints >= 2)
    {
      modern_projection_type =
          gpx.projection_type == GR_PROJECTION_PERSPECTIVE || gpx.projection_type == GR_PROJECTION_ORTHOGRAPHIC;
      if (modern_projection_type)
        {
          gks_inq_current_xformno(&errind, &tnr);
          gks_select_xform(MODERN_NDC);
        }

      gks_polyline(npoints, xpoint, ypoint);
      npoints = 0;

      if (modern_projection_type) gks_select_xform(tnr);
    }
}

static void pline3d(double x, double y, double z)
{
  if (npoints >= maxpath) reallocate(npoints);

  xpoint[npoints] = x_lin(x);
  ypoint[npoints] = y_lin(y);
  zpoint[npoints] = z_lin(z);

  apply_world_xform(xpoint + npoints, ypoint + npoints, zpoint + npoints);

  npoints++;
}

static void start_pline3d(double x, double y, double z)
{
  end_pline3d();

  npoints = 0;
  pline3d(x, y, z);
}

/*!
 * Draw a text at position `x`, `y` using the current text attributes. Strings
 * can be defined to create basic mathematical expressions and Greek letters.
 *
 * \param[in] x The X coordinate of starting position of the text string
 * \param[in] y The Y coordinate of starting position of the text string
 * \param[in] string The text to be drawn
 *
 * The values for X and Y are in normalized device coordinates.
 * The attributes that control the appearance of text are text font and
 * precision, character expansion factor, character spacing, text color index,
 * character height, character up vector, text path and text alignment.
 *
 * The character string is interpreted to be a simple mathematical formula.
 * The following notations apply:
 *
 * Subscripts and superscripts: These are indicated by carets ('^') and
 * underscores ('_'). If the sub/superscript contains more than one character,
 * it must be enclosed in curly braces ('{}').
 *
 * Fractions are typeset with A '/' B, where A stands for the numerator and B
 * for the denominator.
 *
 * To include a Greek letter you must specify the corresponding keyword after a
 * backslash ('\') character. The text translator produces uppercase or
 * lowercase Greek letters depending on the case of the keyword.

 * \verbatim embed:rst:leading-asterisk
 *
 * +----------------------------------+--------+
 * |Letter                            |Keyword |
 * +----------------------------------+--------+
 * |:math:`A`      :math:`\alpha`     |alpha   |
 * +----------------------------------+--------+
 * |:math:`B` :math:`\beta`           |beta    |
 * +----------------------------------+--------+
 * |:math:`\Gamma` :math:`\gamma`     |gamma   |
 * +----------------------------------+--------+
 * |:math:`\Delta` :math:`\delta`     |delta   |
 * +----------------------------------+--------+
 * |:math:`E` :math:`\epsilon`        |epsilon |
 * +----------------------------------+--------+
 * |:math:`Z` :math:`\zeta`           |zeta    |
 * +----------------------------------+--------+
 * |:math:`H` :math:`\eta`            |eta     |
 * +----------------------------------+--------+
 * |:math:`\Theta` :math:`\theta`     |theta   |
 * +----------------------------------+--------+
 * |:math:`I` :math:`\iota`           |iota    |
 * +----------------------------------+--------+
 * |:math:`K` :math:`\kappa`          |kappa   |
 * +----------------------------------+--------+
 * |:math:`\Lambda` :math:`\lambda`   |lambda  |
 * +----------------------------------+--------+
 * |:math:`M` :math:`\mu`             |mu      |
 * +----------------------------------+--------+
 * |:math:`N` :math:`\nu`             |v       |
 * +----------------------------------+--------+
 * |:math:`\Xi` :math:`\xi`           |xi      |
 * +----------------------------------+--------+
 * |:math:`O` :math:`o`               |omicron |
 * +----------------------------------+--------+
 * |:math:`\Pi` :math:`\pi`           |pi      |
 * +----------------------------------+--------+
 * |:math:`P` :math:`\rho`            |rho     |
 * +----------------------------------+--------+
 * |:math:`\Sigma` :math:`\sigma`     |sigma   |
 * +----------------------------------+--------+
 * |:math:`T` :math:`\tau`            |tau     |
 * +----------------------------------+--------+
 * |:math:`\Upsilon` :math:`\upsilon` |upsilon |
 * +----------------------------------+--------+
 * |:math:`\Phi` :math:`\phi`         |phi     |
 * +----------------------------------+--------+
 * |:math:`X` :math:`\chi`            |chi     |
 * +----------------------------------+--------+
 * |:math:`\Psi` :math:`\psi`         |psi     |
 * +----------------------------------+--------+
 * |:math:`\Omega` :math:`\omega`     |omega   |
 * +----------------------------------+--------+
 *
 * \endverbatim
 *
 * For more sophisticated mathematical formulas, you should use the gr_mathtex
 * function.
 *
 * Note: 'v' is a replacement for 'nu' which would conflict with '\n' (newline)
 */
int gr_textext(double x, double y, char *string)
{
  int errind, tnr, result;

  check_autoinit;

  gks_inq_current_xformno(&errind, &tnr);
  if (tnr != NDC) gks_select_xform(NDC);

  result = gr_textex(x, y, string, 0, NULL, NULL);

  if (tnr != NDC) gks_select_xform(tnr);

  if (flag_stream) gr_writestream("<textext x=\"%g\" y=\"%g\" text=\"%s\"/>\n", x, y, string);

  return result;
}

void gr_inqtextext(double x, double y, char *string, double *tbx, double *tby)
{
  int errind, tnr;
  int i;

  check_autoinit;

  gks_inq_current_xformno(&errind, &tnr);
  if (tnr != NDC) gks_select_xform(NDC);

  gr_textex(x, y, string, 1, tbx, tby);

  if (tnr != NDC)
    {
      gks_select_xform(tnr);

      for (i = 0; i < 4; i++)
        {
          tbx[i] = (tbx[i] - nx.b) / nx.a;
          tby[i] = (tby[i] - nx.d) / nx.c;
          if (lx.scale_options)
            {
              tbx[i] = x_log(tbx[i]);
              tby[i] = y_log(tby[i]);
            }
        }
    }
}


/*!
 * Specify the format to be used when scientific notation is used.
 *
 * \param[in] format_option Scientific format
 *
 *
 * \verbatim embed:rst:leading-asterisk
 *
 * The available options are:
 *
 * +----------------------------------+---+
 * |SCIENTIFIC_FORMAT_OPTION_E        |  1|
 * +----------------------------------+---+
 * |SCIENTIFIC_FORMAT_OPTION_TEXTEX   |  2|
 * +----------------------------------+---+
 * |SCIENTIFIC_FORMAT_OPTION_MATHTEX  |  3|
 * +----------------------------------+---+
 *
 * \endverbatim
 */
void gr_setscientificformat(int format_option)
{
  check_autoinit;

  if (format_option >= SCIENTIFIC_FORMAT_OPTION_E && format_option <= SCIENTIFIC_FORMAT_OPTION_MATHTEX)
    {
      scientific_format = format_option;
    }

  if (flag_stream) gr_writestream("<setscientificformat option=>\n", format_option);
}

static void text2dlbl(double x, double y, char *chars, double value, void (*fp)(double, double, const char *, double))
{
  int errind, tnr;

  if (lx.scale_options)
    {
      x = x_lin(x);
      y = y_lin(y);
    }

  gks_inq_current_xformno(&errind, &tnr);
  if (tnr != NDC)
    {
      x = nx.a * x + nx.b;
      y = nx.c * y + nx.d;
      gks_select_xform(NDC);
    }

  if (fp == NULL)
    {
      if (scientific_format == SCIENTIFIC_FORMAT_OPTION_MATHTEX)
        {
          gr_mathtex(x, y, chars);
        }
      else
        {
          gr_textex(x, y, chars, 0, NULL, NULL);
        }
    }
  else
    fp(x, y, chars, value);

  if (tnr != NDC) gks_select_xform(tnr);
}

static void text2d(double x, double y, char *chars)
{
  /* 42. dummy value will not be interpreted until last argument fp != NULL */
  text2dlbl(x, y, chars, 42., NULL);
}

static char *replace_minus_sign(char *string)
{
  int errind, font, prec, encoding, n = 0;
  char *s = string, *out;

  gks_inq_text_fontprec(&errind, &font, &prec);
  gks_inq_encoding(&encoding);
  if (prec != GKS_K_TEXT_PRECISION_OUTLINE || encoding != ENCODING_UTF8) return s;

  out = xmalloc(256);

  while (*s && n < 255)
    {
      if (*s == '-')
        {
          out[n++] = (char)0xe2;
          out[n++] = (char)0x88;
          out[n++] = (char)0x92;
        }
      else
        out[n++] = *s;
      s++;
    }
  out[n] = '\0';

  strcpy(string, out);
  free(out);

  return string;
}

char *gr_ftoa(char *string, double value, format_reference_t *reference)
{
  char *s;

  s = str_ftoa(string, value, (str_format_reference_t *)reference, scientific_format);

  return replace_minus_sign(s);
}

void gr_getformat(format_reference_t *result, double origin, double min_value, double max_value, double tick_width,
                  int major)
{
  str_get_format_reference((str_format_reference_t *)result, origin, min_value, max_value, tick_width, major);
}

/*!
 * Create axes in the current workspace and supply a custom function for changing
 * the behaviour of the tick labels.
 *
 * Similar to gr_axes() but allows more fine-grained control over tick labels
 * and text positioning by supplying callback functions. Within the callback
 * function you can use normal GR text primitives for performing any manipulations
 * on the label text.
 *
 * \param[in] x_tick The interval between minor tick marks on the X axis.
 * \param[in] y_tick The interval between minor tick marks on the Y axis.
 * \param[in] x_org The world coordinate of the origin (point of intersection)
 *                  of the X axis.
 * \param[in] y_org The world coordinate of the origin (point of intersection)
 *                  of the Y axis.
 * \param[in] major_x Unitless integer value specifying the number of minor tick
 *                    intervals between major tick marks on the X axis. Values
 *                    of 0 or 1 imply no minor ticks. Negative values specify no
 *                    labels will be drawn for the associated axis.
 * \param[in] major_y Unitless integer value specifying the number of minor tick
 *                    intervals between major tick marks on the Y axis. Values
 *                    of 0 or 1 imply no minor ticks. Negative values specify no
 *                    labels will be drawn for the associated axis.
 * \param[in] tick_size The length of minor tick marks specified in a normalized
 *                      device coordinate unit. Major tick marks are twice as
 *                      long as minor tick marks. A negative value reverses the
 *                      tick marks on the axes from inward facing to outward
 *                      facing (or vice versa).
 * \param[in] fpx Function pointer to a function that returns a label for a given
 *                tick on the X axis. The callback function should have the following arguments:
 *                \param[in] x NDC of the label in X direction.
 *                \param[in] y NDC of the label in Y direction.
 *                \param[in] svalue Internal string representation of the text
 *                                  drawn by GR at (x,y).
 *                \param[in] value Floating point representation of the label drawn
 *                                 at (x,y).
 * \param[in] fpy Exactly same as the fpx above, but for the the Y axis.
 *
 * See gr_axes() for more details on drawing axes.
 */
void gr_axeslbl(double x_tick, double y_tick, double x_org, double y_org, int major_x, int major_y, double tick_size,
                void (*fpx)(double, double, const char *, double), void (*fpy)(double, double, const char *, double))
{
  int errind, tnr;
  int ltype, halign, valign, clsw;
  double chux, chuy;

  double clrt[4], wn[4], vp[4];
  double x_min, x_max, y_min, y_max, feps;

  double tick, minor_tick, major_tick, x_label, y_label, x0, y0, xi, yi;
  int64_t i;
  int decade, exponent;
  char string[256];

  format_reference_t format_reference;

  if (x_tick < 0 || y_tick < 0)
    {
      fprintf(stderr, "invalid interval length for major tick-marks\n");
      return;
    }
  else if (tick_size == 0)
    {
      fprintf(stderr, "invalid tick-size\n");
      return;
    }

  check_autoinit;

  /* inquire current normalization transformation */

  gks_inq_current_xformno(&errind, &tnr);
  gks_inq_xform(tnr, &errind, wn, vp);

  x_min = wn[0];
  x_max = wn[1];
  y_min = wn[2];
  y_max = wn[3];

  if (x_min > x_org || x_org > x_max || y_min > y_org || y_org > y_max)
    {
      fprintf(stderr, "origin outside current window\n");
      return;
    }

  /* save linetype, text alignment, character-up vector and
     clipping indicator */

  gks_inq_pline_linetype(&errind, &ltype);
  gks_inq_text_align(&errind, &halign, &valign);
  gks_inq_text_upvec(&errind, &chux, &chuy);
  gks_inq_clip(&errind, &clsw, clrt);

  gks_set_pline_linetype(GKS_K_LINETYPE_SOLID);
  gks_set_text_upvec(0, 1);
  gks_set_clipping(GKS_K_NOCLIP);

  if (y_tick != 0)
    {
      tick = tick_size * (x_max - x_min) / (vp[1] - vp[0]);

      minor_tick = x_log(x_lin(x_org) + tick);
      major_tick = x_log(x_lin(x_org) + 2. * tick);
      x_label = x_log(x_lin(x_org) + 3. * tick);

      /* set text alignment */

      if (x_lin(x_org) <= (x_lin(x_min) + x_lin(x_max)) / 2.)
        {
          gks_set_text_align(GKS_K_TEXT_HALIGN_RIGHT, GKS_K_TEXT_VALIGN_HALF);

          if (tick > 0) x_label = x_log(x_lin(x_org) - tick);
        }
      else
        {
          gks_set_text_align(GKS_K_TEXT_HALIGN_LEFT, GKS_K_TEXT_VALIGN_HALF);

          if (tick < 0) x_label = x_log(x_lin(x_org) - tick);
        }

      if (GR_OPTION_Y_LOG & lx.scale_options)
        {
          y0 = pow(lx.basey, gauss(blog(lx.basey, y_min)));

          i = ipred(y_min / y0);
          yi = y0 + i * y0;
          decade = igauss(blog(lx.basey, y_min / y_org));

          /* draw Y-axis */

          while (yi <= y_max)
            {
              xi = minor_tick;
              if (i == 0)
                {
                  if (major_y > 0)
                    if (decade % major_y == 0)
                      {
                        xi = major_tick;
                        if (yi != y_org || x_min == x_org || x_max == x_org)
                          {
                            if (y_tick > 1)
                              {
                                exponent = iround(blog(lx.basey, yi));
                                snprintf(string, 256, "%s^{%d}", lx.basey_s, exponent);
                                text2dlbl(x_label, yi, replace_minus_sign(string), yi, fpy);
                              }
                            else
                              text2dlbl(x_label, yi, gr_ftoa(string, yi, NULL), yi, fpy);
                          }
                      }
                }

              if (i == 0 || abs(major_y) == 1)
                {
                  start_pline(x_org, yi);
                  pline(xi, yi);
                  end_pline();
                }

              if (i == 9 || lx.basey < 10)
                {
                  y0 = y0 * lx.basey;
                  i = 0;
                  decade++;
                }
              else
                i++;

              yi = y0 + i * y0;
            }
        }
      else
        {
          feps = FEPS * (y_max - y_min);

          check_tick_marks(y_min, y_max, y_tick, 'Y');

          i = isucc(y_min / y_tick);
          yi = i * y_tick;

          /* draw Y-axis */

          gr_getformat(&format_reference, y_org, yi, y_max, y_tick, major_y);

          while (yi <= y_max + feps)
            {
              if (major_y != 0)
                {
                  if (i % major_y == 0)
                    {
                      xi = major_tick;
                      if (yi != y_org || x_min == x_org || x_max == x_org)
                        {
                          if (major_y > 0) text2dlbl(x_label, yi, gr_ftoa(string, yi, &format_reference), yi, fpy);
                        }
                    }
                  else
                    xi = minor_tick;
                }
              else
                xi = major_tick;

              start_pline(x_org, yi);
              pline(xi, yi);
              end_pline();

              i++;
              yi = i * y_tick;
            }
        }

      start_pline(x_org, y_min);
      pline(x_org, y_max);
      end_pline();
    }

  if (x_tick != 0)
    {
      tick = tick_size * (y_max - y_min) / (vp[3] - vp[2]);

      minor_tick = y_log(y_lin(y_org) + tick);
      major_tick = y_log(y_lin(y_org) + 2. * tick);
      y_label = y_log(y_lin(y_org) + 3. * tick);

      /* set text alignment */

      if (y_lin(y_org) <= (y_lin(y_min) + y_lin(y_max)) / 2.)
        {
          gks_set_text_align(GKS_K_TEXT_HALIGN_CENTER, GKS_K_TEXT_VALIGN_TOP);

          if (tick > 0) y_label = y_log(y_lin(y_org) - tick);
        }
      else
        {
          gks_set_text_align(GKS_K_TEXT_HALIGN_CENTER, GKS_K_TEXT_VALIGN_BOTTOM);

          if (tick < 0) y_label = y_log(y_lin(y_org) - tick);
        }

      if (GR_OPTION_X_LOG & lx.scale_options)
        {
          x0 = pow(lx.basex, gauss(blog(lx.basex, x_min)));

          i = ipred(x_min / x0);
          xi = x0 + i * x0;
          decade = igauss(blog(lx.basex, x_min / x_org));

          /* draw X-axis */

          while (xi <= x_max)
            {
              yi = minor_tick;
              if (i == 0)
                {
                  if (major_x > 0)
                    if (decade % major_x == 0)
                      {
                        yi = major_tick;
                        if (xi != x_org || y_org == y_min || y_org == y_max)
                          {
                            if (x_tick > 1)
                              {
                                exponent = iround(blog(lx.basex, xi));
                                snprintf(string, 256, "%s^{%d}", lx.basex_s, exponent);
                                text2dlbl(xi, y_label, replace_minus_sign(string), xi, fpx);
                              }
                            else
                              text2dlbl(xi, y_label, gr_ftoa(string, xi, NULL), xi, fpx);
                          }
                      }
                }

              if (i == 0 || abs(major_x) == 1)
                {
                  start_pline(xi, y_org);
                  pline(xi, yi);
                  end_pline();
                }

              if (i == 9 || lx.basex < 10)
                {
                  x0 = x0 * lx.basex;
                  i = 0;
                  decade++;
                }
              else
                i++;

              xi = x0 + i * x0;
            }
        }
      else
        {
          feps = FEPS * (x_max - x_min);

          check_tick_marks(x_min, x_max, x_tick, 'X');

          i = isucc(x_min / x_tick);
          xi = i * x_tick;

          gr_getformat(&format_reference, x_org, xi, x_max, x_tick, major_x);

          /* draw X-axis */

          while (xi <= x_max + feps)
            {
              if (major_x != 0)
                {
                  if (i % major_x == 0)
                    {
                      yi = major_tick;
                      if (xi != x_org || y_org == y_min || y_org == y_max)
                        {
                          if (major_x > 0) text2dlbl(xi, y_label, gr_ftoa(string, xi, &format_reference), xi, fpx);
                        }
                    }
                  else
                    yi = minor_tick;
                }
              else
                yi = major_tick;

              start_pline(xi, y_org);
              pline(xi, yi);
              end_pline();

              i++;
              xi = i * x_tick;
            }
        }

      start_pline(x_min, y_org);
      pline(x_max, y_org);
      end_pline();
    }

  /* restore linetype, text alignment, character-up vector
     and clipping indicator */

  gks_set_pline_linetype(ltype);
  gks_set_text_align(halign, valign);
  gks_set_text_upvec(chux, chuy);
  gks_set_clipping(clsw);

  if (flag_stream)
    gr_writestream("<axes xtick=\"%g\" ytick=\"%g\" xorg=\"%g\" yorg=\"%g\" "
                   "majorx=\"%d\" majory=\"%d\" ticksize=\"%g\"/>\n",
                   x_tick, y_tick, x_org, y_org, major_x, major_y, tick_size);
}

/*!
 * Draw X and Y coordinate axes with linearly and/or logarithmically spaced
 * tick marks.
 *
 * \param[in] x_tick The interval between minor tick marks on the X axis.
 * \param[in] y_tick The interval between minor tick marks on the Y axis.
 * \param[in] x_org The world coordinate of the origin (point of intersection)
 *                  of the X axis.
 * \param[in] y_org The world coordinate of the origin (point of intersection)
 *                  of the Y axis.
 * \param[in] major_x Unitless integer value specifying the number of minor tick
 *                    intervals between major tick marks on the X axis. Values
 *                    of 0 or 1 imply no minor ticks. Negative values specify no
 *                    labels will be drawn for the associated axis.
 * \param[in] major_y Unitless integer value specifying the number of minor tick
 *                    intervals between major tick marks on the Y axis. Values
 *                    of 0 or 1 imply no minor ticks. Negative values specify no
 *                    labels will be drawn for the associated axis.
 * \param[in] tick_size The length of minor tick marks specified in a normalized
 *                      device coordinate unit. Major tick marks are twice as
 *                      long as minor tick marks. A negative value reverses the
 *                      tick marks on the axes from inward facing to outward
 *                      facing (or vice versa).
 *
 * Tick marks are positioned along each axis so that major tick marks fall on
 * the axes origin (whether visible or not). Major tick marks are labeled with
 * the corresponding data values. Axes are drawn according to the scale of the
 * window. Axes and tick marks are drawn using solid lines; line color and width
 * can be modified using the gr_setlinetype and gr_setlinewidth functions. Axes
 * are drawn according to the linear or logarithmic transformation established
 * by the gr_setscale function.
 */
void gr_axes(double x_tick, double y_tick, double x_org, double y_org, int major_x, int major_y, double tick_size)
{
  gr_axeslbl(x_tick, y_tick, x_org, y_org, major_x, major_y, tick_size, NULL, NULL);
}

void gr_axis(char which, axis_t *axis)
{
  int errind, tnr;
  double wn[4], vp[4];
  double x_min, x_max, y_min, y_max;
  int scale_option = 0, base, decade, exponent;
  double tick, epsilon;
  int64_t i;
  int j, k;
  double a, a0, tbx[4], tby[4];
  char *s;
  format_reference_t formatReference;

  check_autoinit;

  /* inquire current normalization transformation */

  gks_inq_current_xformno(&errind, &tnr);
  gks_inq_xform(tnr, &errind, wn, vp);

  x_min = wn[0];
  x_max = wn[1];
  y_min = wn[2];
  y_max = wn[3];

  if (is_nan(axis->tick_size)) axis->tick_size = 0.0075;

  if (which == 'X')
    {
      scale_option = GR_OPTION_X_LOG;
      base = lx.basex;
      if (is_nan(axis->min)) axis->min = x_min;
      if (is_nan(axis->max)) axis->max = x_max;
      if (is_nan(axis->org)) axis->org = x_min;
      if (is_nan(axis->position)) axis->position = y_min;
      if (is_nan(axis->label_position))
        {
          tick = axis->tick_size * (wn[3] - wn[2]) / (vp[3] - vp[2]);
          axis->label_position = y_log(y_lin(axis->position) + 3 * tick);
          if (y_lin(axis->position) <= 0.5 * (y_lin(wn[2] + y_lin(wn[3]))))
            {
              if (tick > 0) axis->label_position = y_log(y_lin(axis->position) - tick);
            }
          else
            {
              if (tick < 0) axis->label_position = y_log(y_lin(axis->position) - tick);
            }
        }
    }
  else if (which == 'Y')
    {
      scale_option = GR_OPTION_Y_LOG;
      base = lx.basey;
      if (is_nan(axis->min)) axis->min = y_min;
      if (is_nan(axis->max)) axis->max = y_max;
      if (is_nan(axis->org)) axis->org = y_min;
      if (is_nan(axis->position)) axis->position = x_min;
      if (is_nan(axis->label_position))
        {
          tick = axis->tick_size * (wn[1] - wn[0]) / (vp[1] - vp[0]);
          axis->label_position = x_log(x_lin(axis->position) + 3 * tick);
          if (x_lin(axis->position) <= 0.5 * (x_lin(wn[0] + x_lin(wn[1]))))
            {
              if (tick > 0) axis->label_position = x_log(x_lin(axis->position) - tick);
            }
          else
            {
              if (tick < 0) axis->label_position = x_log(x_lin(axis->position) - tick);
            }
        }
    }

  if (scale_option & lx.scale_options)
    {
      axis->num_tick_labels = igauss(blog(base, axis->max / axis->min)) + 2;
      axis->tick_labels = (tick_label_t *)xcalloc(axis->num_tick_labels, sizeof(tick_label_t));
      axis->num_ticks = (axis->num_tick_labels + 1) * base;
      axis->ticks = (tick_t *)xcalloc(axis->num_ticks, sizeof(tick_t));
      a0 = pow(base, gauss(blog(base, axis->min)));
      i = ipred(axis->min / a0);
      a = a0 + i * a0;
      decade = igauss(blog(base, axis->min / axis->org));
      j = k = 0;
      while (a <= axis->max)
        {
          axis->ticks[j].value = a;
          axis->ticks[j++].is_major = (i == 0);
          if (i == 0)
            {
              if (axis->major_count > 0)
                {
                  if (decade % axis->major_count == 0)
                    {
                      exponent = iround(blog(base, a));
                      s = (char *)xcalloc(256, sizeof(char));
                      snprintf(s, 256, "%d^{%d}", base, exponent);
                      axis->tick_labels[k].tick = a;
                      axis->tick_labels[k].label = replace_minus_sign(s);
                      gr_inqtext(0, 0, axis->tick_labels[k].label, tbx, tby);
                      axis->tick_labels[k].width = tbx[2] - tbx[0];
                      k++;
                    }
                }
            }
          if (i == 9 || base < 10)
            {
              a0 = a0 * base;
              i = 0;
              if (j > 0) j--;
              decade++;
            }
          else
            {
              i++;
            }
          a = a0 + i * a0;
        }
      axis->num_ticks = j;
      axis->num_tick_labels = k;
    }
  else
    {
      if (is_nan(axis->tick)) axis->tick = gr_tick(axis->min, axis->max) / 5;
      axis->num_ticks = (int)((axis->max - axis->min) / axis->tick + 0.5) + 1;
      axis->ticks = (tick_t *)xcalloc(axis->num_ticks, sizeof(tick_t));
      if (axis->major_count > 0)
        {
          axis->num_tick_labels = (int)(axis->num_ticks / axis->major_count + 0.5) + 1;
          axis->tick_labels = (tick_label_t *)xcalloc(axis->num_tick_labels, sizeof(tick_label_t));
        }
      else
        {
          axis->num_tick_labels = 0;
          axis->tick_labels = NULL;
        }

      epsilon = FEPS * (axis->max - axis->min);

      i = isucc(axis->min / axis->tick);
      a = i * axis->tick;
      j = k = 0;
      while (a <= axis->max + epsilon)
        {
          axis->ticks[j].value = a;
          if (axis->major_count > 0)
            {
              axis->ticks[j++].is_major = (i % axis->major_count == 0);
              gr_getformat(&formatReference, axis->min, a, axis->max, axis->tick, axis->major_count);
              if (i % axis->major_count == 0)
                {
                  s = (char *)xcalloc(256, sizeof(char));
                  gr_ftoa(s, a, &formatReference);
                  axis->tick_labels[k].tick = a;
                  axis->tick_labels[k].label = replace_minus_sign(s);
                  gr_inqtext(0, 0, axis->tick_labels[k].label, tbx, tby);
                  axis->tick_labels[k].width = tbx[2] - tbx[0];
                  k++;
                }
            }
          else
            {
              axis->ticks[j++].is_major = 1;
            }
          i++;
          a = i * axis->tick;
        }
      axis->num_ticks = j;
      axis->num_tick_labels = k;
    }

  if (axis->num_ticks > 0)
    {
      axis->ticks = (tick_t *)xrealloc(axis->ticks, axis->num_ticks * sizeof(tick_t));
    }
  if (axis->num_tick_labels > 0)
    {
      axis->tick_labels = (tick_label_t *)xrealloc(axis->tick_labels, axis->num_tick_labels * sizeof(tick_label_t));
    }
}

static void draw_axis(char which, axis_t *axis, int pass)
{
  int errind, tnr, halign, valign;
  double wn[4], vp[4];
  double tick, minor_tick, major_tick;
  int i;

  check_autoinit;

  /* inquire current normalization transformation */

  gks_inq_current_xformno(&errind, &tnr);
  gks_inq_xform(tnr, &errind, wn, vp);

  if (which == 'X')
    {
      tick = axis->tick_size * (wn[3] - wn[2]) / (vp[3] - vp[2]);
      minor_tick = y_log(y_lin(axis->position) + tick);
      major_tick = y_log(y_lin(axis->position) + 2 * tick);
    }
  else
    {
      tick = axis->tick_size * (wn[1] - wn[0]) / (vp[1] - vp[0]);
      minor_tick = x_log(x_lin(axis->position) + tick);
      major_tick = x_log(x_lin(axis->position) + 2 * tick);
    }

  if (pass == 0 || pass == 1)
    {
      if (axis->tick_size != 0)
        {
          for (i = 0; i < axis->num_ticks; i++)
            {
              if (pass != axis->ticks[i].is_major)
                {
                  tick = axis->ticks[i].is_major ? major_tick : minor_tick;
                  if (which == 'X')
                    {
                      pline(axis->ticks[i].value, axis->position);
                      pline(axis->ticks[i].value, tick);
                      end_pline();
                    }
                  else
                    {
                      pline(axis->position, axis->ticks[i].value);
                      pline(tick, axis->ticks[i].value);
                      end_pline();
                    }
                }
            }
        }
    }
  else if (pass == 2)
    {
      if (axis->draw_axis_line)
        {
          if (which == 'X')
            {
              start_pline(axis->min, axis->position);
              pline(axis->max, axis->position);
              end_pline();
            }
          else
            {
              start_pline(axis->position, axis->min);
              pline(axis->position, axis->max);
              end_pline();
            }
        }
    }
  else if (pass == 3)
    {
      if (axis->major_count > 0)
        {
          if (axis->num_tick_labels > 0)
            {
              /* save text alignment */
              gks_inq_text_align(&errind, &halign, &valign);

              if (which == 'X')
                {
                  if (axis->position <= wn[2])
                    gks_set_text_align(GKS_K_TEXT_HALIGN_CENTER, GKS_K_TEXT_VALIGN_TOP);
                  else
                    gks_set_text_align(GKS_K_TEXT_HALIGN_CENTER, GKS_K_TEXT_VALIGN_BOTTOM);
                }
              else
                {
                  if (axis->position <= wn[0])
                    gks_set_text_align(GKS_K_TEXT_HALIGN_RIGHT, GKS_K_TEXT_VALIGN_HALF);
                  else
                    gks_set_text_align(GKS_K_TEXT_HALIGN_LEFT, GKS_K_TEXT_VALIGN_HALF);
                }
              for (i = 0; i < axis->num_tick_labels; i++)
                {
                  if (which == 'X')
                    text2d(axis->tick_labels[i].tick, axis->label_position, axis->tick_labels[i].label);
                  else
                    text2d(axis->label_position, axis->tick_labels[i].tick, axis->tick_labels[i].label);
                }

              /* restore text alignment */
              gks_set_text_align(halign, valign);
            }
        }
    }
}

void gr_drawaxis(char which, axis_t *axis)
{
  int errind, tnr, ltype, clsw, halign, valign;
  double wn[4], vp[4], clrt[4];
  int i, pass;

  check_autoinit;

  /* inquire current normalization transformation */

  gks_inq_current_xformno(&errind, &tnr);
  gks_inq_xform(tnr, &errind, wn, vp);

  /* save linetype and clipping indicator */

  gks_inq_pline_linetype(&errind, &ltype);
  gks_inq_clip(&errind, &clsw, clrt);

  gks_set_pline_linetype(GKS_K_LINETYPE_SOLID);
  gks_set_clipping(GKS_K_NOCLIP);

  for (pass = 0; pass <= 3; pass++)
    {
      draw_axis(which, axis, pass);
    }

  /* restore linetype and clipping indicator */

  gks_set_pline_linetype(ltype);
  gks_set_clipping(clsw);
}

static void draw_axis_grid(char which, axis_t *axis, int pass)
{
  int errind, tnr, color;
  double wn[4], vp[4], width;
  int i;

  /* inquire current normalization transformation */

  gks_inq_current_xformno(&errind, &tnr);
  gks_inq_xform(tnr, &errind, wn, vp);

  /* save line width and line color */

  gks_inq_pline_linewidth(&errind, &width);
  gks_inq_pline_color_index(&errind, &color);

  gks_inq_pline_color_index(&errind, &color);

  for (i = 0; i < axis->num_ticks; i++)
    {
      if (axis->ticks[i].is_major == pass)
        {
          if (color != 0)
            gks_set_pline_color_index(axis->ticks[i].is_major ? 88 : 90);
          else
            gks_set_pline_linewidth(axis->ticks[i].is_major ? 2.0 : 1.0);

          if (which == 'X')
            {
              pline(axis->ticks[i].value, wn[2]);
              pline(axis->ticks[i].value, wn[3]);
              end_pline();
            }
          else
            {
              pline(wn[0], axis->ticks[i].value);
              pline(wn[1], axis->ticks[i].value);
              end_pline();
            }
        }
    }

  /* restore line width and line color */

  gks_set_pline_linewidth(width);
  gks_set_pline_color_index(color);
}

void gr_drawaxes(axis_t *x_axis, axis_t *y_axis, int options)
{
  int errind, tnr, ltype, clsw;
  double wn[4], vp[4], clrt[4];
  double tick, minor_tick, major_tick;
  int pass;
  axis_t axis;

  check_autoinit;

  /* inquire current normalization transformation */

  gks_inq_current_xformno(&errind, &tnr);
  gks_inq_xform(tnr, &errind, wn, vp);

  /* save linetype and clipping indicator */

  gks_inq_pline_linetype(&errind, &ltype);
  gks_inq_clip(&errind, &clsw, clrt);

  gks_set_pline_linetype(GKS_K_LINETYPE_SOLID);
  gks_set_clipping(GKS_K_NOCLIP);

  if ((options & GR_AXES_WITH_GRID) != 0)
    {
      for (pass = 0; pass <= 1; pass++)
        {
          if (y_axis != NULL) draw_axis_grid('Y', y_axis, pass);
          if (x_axis != NULL) draw_axis_grid('X', x_axis, pass);
        }
    }

  for (pass = 0; pass <= 3; pass++)
    {
      if ((options & GR_AXES_TWIN_AXES) != 0)
        {
          if (y_axis != NULL)
            {
              memcpy(&axis, y_axis, sizeof(axis_t));
              y_axis->position = wn[1];
              if (lx.scale_options & GR_OPTION_FLIP_X) y_axis->position = wn[0];
              y_axis->tick_size = -y_axis->tick_size;
              y_axis->major_count = -y_axis->major_count;
              draw_axis('Y', y_axis, pass);
              memcpy(y_axis, &axis, sizeof(axis_t));
            }
        }
      if ((options & GR_AXES_SIMPLE_AXES) != 0)
        {
          if (y_axis != NULL) draw_axis('Y', y_axis, pass);
        }

      if ((options & GR_AXES_TWIN_AXES) != 0)
        {
          if (x_axis != NULL)
            {
              memcpy(&axis, x_axis, sizeof(axis_t));
              x_axis->position = wn[3];
              if (lx.scale_options & GR_OPTION_FLIP_Y) x_axis->position = wn[2];
              x_axis->tick_size = -x_axis->tick_size;
              x_axis->major_count = -x_axis->major_count;
              draw_axis('X', x_axis, pass);
              memcpy(x_axis, &axis, sizeof(axis_t));
            }
        }
      if ((options & GR_AXES_SIMPLE_AXES) != 0)
        {
          if (x_axis != NULL) draw_axis('X', x_axis, pass);
        }
    }

  /* restore linetype and clipping indicator */

  gks_set_pline_linetype(ltype);
  gks_set_clipping(clsw);
}

void gr_freeaxis(axis_t *axis)
{
  int i;
  if (axis != NULL)
    {
      if (axis->tick_labels != NULL)
        {
          for (i = 0; i < axis->num_tick_labels; i++)
            {
              free(axis->tick_labels[i].label);
            }
          free(axis->tick_labels);
        }
      if (axis->ticks != NULL)
        {
          free(axis->ticks);
        }
    }
}

static void grid_line(double x0, double y0, double x1, double y1, int color, int major)
{
  if (color != 0)
    gks_set_pline_color_index(major ? 88 : 90);
  else
    gks_set_pline_linewidth(major ? 2.0 : 1.0);

  start_pline(x0, y0);
  pline(x1, y1);
  end_pline();
}

/*!
 * Draw a linear and/or logarithmic grid.
 *
 * \param[in] x_tick The length in world coordinates of the interval between
 *                   minor grid lines in X direction.
 * \param[in] y_tick The length in world coordinates of the interval between
 *                   minor grid lines in Y direction.
 * \param[in] x_org The world coordinate of the origin (point of intersection)
 *                  of the X axis.
 * \param[in] y_org The world coordinate of the origin (point of intersection)
 *                  of the Y axis.
 * \param[in] major_x Unitless integer value specifying the number of minor
 *                    grid lines between major grid lines on the X axis. Values
 *                    of 0 or 1 imply no grid lines.
 * \param[in] major_y Unitless integer value specifying the number of minor
 *                    grid lines between major grid lines on the Y axis. Values
 *                    of 0 or 1 imply no grid lines.
 *
 * Major grid lines correspond to the axes origin and major tick marks whether
 * visible or not. Minor grid lines are drawn at points equal to minor tick
 * marks. Major grid lines are drawn using black lines and minor grid lines are
 * drawn using gray lines.
 */
void gr_grid(double x_tick, double y_tick, double x_org, double y_org, int major_x, int major_y)
{
  int errind, tnr;
  int ltype, color, clsw, major;
  double width;

  double clrt[4], wn[4], vp[4];
  double x_min, x_max, y_min, y_max, feps;

  double x0, y0, xi, yi;
  int64_t i;
  int pass;

  if (x_tick < 0 || y_tick < 0)
    {
      fprintf(stderr, "invalid interval length for major tick-marks\n");
      return;
    }

  check_autoinit;

  /* inquire current normalization transformation */

  gks_inq_current_xformno(&errind, &tnr);
  gks_inq_xform(tnr, &errind, wn, vp);

  x_min = wn[0];
  x_max = wn[1];
  y_min = wn[2];
  y_max = wn[3];

  /* save linetype, line width, line color and clipping indicator */

  gks_inq_pline_linetype(&errind, &ltype);
  gks_inq_pline_linewidth(&errind, &width);
  gks_inq_pline_color_index(&errind, &color);
  gks_inq_clip(&errind, &clsw, clrt);

  gks_set_pline_linetype(GKS_K_LINETYPE_SOLID);
  gks_set_clipping(GKS_K_NOCLIP);

  for (pass = 0; pass <= 1; pass++)
    {
      if (y_tick != 0)
        {
          if (GR_OPTION_Y_LOG & lx.scale_options)
            {
              y0 = pow(lx.basey, gauss(blog(lx.basey, y_min)));

              i = ipred(y_min / y0);
              yi = y0 + i * y0;

              /* draw horizontal grid lines */

              while (yi <= y_max)
                {
                  if (i == 0 || major_y == 1)
                    {
                      major = i == 0 ? 1 : 0;
                      if (yi != y_min)
                        {
                          if (pass == major) grid_line(x_min, yi, x_max, yi, color, major);
                        }
                    }

                  if (i == 9 || lx.basey < 10)
                    {
                      y0 = y0 * lx.basey;
                      i = 0;
                    }
                  else
                    i++;

                  yi = y0 + i * y0;
                }
            }
          else
            {
              feps = FEPS * (y_max - y_min);

              check_tick_marks(y_min, y_max, y_tick, 'Y');

              i = isucc((y_min - y_org) / y_tick);
              yi = y_org + i * y_tick;

              /* draw horizontal grid lines */

              while (yi <= y_max + feps)
                {
                  if (major_y > 0)
                    major = (i % major_y == 0 && major_y > 1) ? 1 : 0;
                  else
                    major = 0;

                  if (pass == major) grid_line(x_min, yi, x_max, yi, color, major);

                  i++;
                  yi = y_org + i * y_tick;
                }
            }
        }

      if (x_tick != 0)
        {
          if (GR_OPTION_X_LOG & lx.scale_options)
            {
              x0 = pow(lx.basex, gauss(blog(lx.basex, x_min)));

              i = ipred(x_min / x0);
              xi = x0 + i * x0;

              /* draw vertical grid lines */

              while (xi <= x_max)
                {
                  if (i == 0 || major_x == 1)
                    {
                      major = i == 0 ? 1 : 0;
                      if (xi != x_min)
                        {
                          if (pass == major) grid_line(xi, y_min, xi, y_max, color, major);
                        }
                    }

                  if (i == 9 || lx.basex < 10)
                    {
                      x0 = x0 * lx.basex;
                      i = 0;
                    }
                  else
                    i++;

                  xi = x0 + i * x0;
                }
            }
          else
            {
              feps = FEPS * (x_max - x_min);

              check_tick_marks(x_min, x_max, x_tick, 'X');

              i = isucc((x_min - x_org) / x_tick);
              xi = x_org + i * x_tick;

              /* draw vertical grid lines */

              while (xi <= x_max + feps)
                {
                  if (major_x > 0)
                    major = (i % major_x == 0 && major_x > 1) ? 1 : 0;
                  else
                    major = 0;

                  if (pass == major) grid_line(xi, y_min, xi, y_max, color, major);

                  i++;
                  xi = x_org + i * x_tick;
                }
            }
        }
    }

  /* restore linetype, line width, line color and clipping indicator */

  gks_set_pline_linetype(ltype);
  gks_set_pline_linewidth(width);
  gks_set_pline_color_index(color);
  gks_set_clipping(clsw);

  if (flag_stream)
    gr_writestream("<grid xtick=\"%g\" ytick=\"%g\" xorg=\"%g\" yorg=\"%g\" "
                   "majorx=\"%d\" majory=\"%d\"/>\n",
                   x_tick, y_tick, x_org, y_org, major_x, major_y);
}

static void grid_line3d(double x0, double y0, double z0, double x1, double y1, double z1, int color, int major)
{
  if (color != 0)
    gks_set_pline_color_index(major ? 88 : 90);
  else
    gks_set_pline_linewidth(major ? 2.0 : 1.0);

  start_pline3d(x0, y0, z0);
  pline3d(x1, y1, z1);
  end_pline3d();
}

/*!
 * Draw a linear and/or logarithmic grid.
 *
 * \param[in] x_tick The length in world coordinates of the interval between
 *                   minor grid lines in X direction.
 * \param[in] y_tick The length in world coordinates of the interval between
 *                   minor grid lines in Y direction.
 * \param[in] z_tick The length in world coordinates of the interval between
 *                   minor grid lines in Z direction.
 * \param[in] x_org The world coordinate of the origin (point of intersection)
 *                  of the X axis.
 * \param[in] y_org The world coordinate of the origin (point of intersection)
 *                  of the Y axis.
 * \param[in] z_org The world coordinate of the origin (point of intersection)
 *                  of the Z axis.
 * \param[in] major_x Unitless integer value specifying the number of minor
 *                    grid lines between major grid lines on the X axis. Values
 *                    of 0 or 1 imply no grid lines.
 * \param[in] major_y Unitless integer value specifying the number of minor
 *                    grid lines between major grid lines on the Y axis. Values
 *                    of 0 or 1 imply no grid lines.
 * \param[in] major_z Unitless integer value specifying the number of minor
 *                    grid lines between major grid lines on the Z axis. Values
 *                    of 0 or 1 imply no grid lines.
 *
 * Major grid lines correspond to the axes origin and major tick marks whether
 * visible or not. Minor grid lines are drawn at points equal to minor tick
 * marks. Major grid lines are drawn using black lines and minor grid lines are
 * drawn using gray lines.
 */
void gr_grid3d(double x_tick, double y_tick, double z_tick, double x_org, double y_org, double z_org, int major_x,
               int major_y, int major_z)
{
  int errind, tnr;
  double clrt[4], wn[4], vp[4];
  int modern_projection_type;

  int ltype, color, clsw, major;
  double width;

  double x_min = 0, x_max = 0, y_min = 0, y_max = 0, z_min = 0, z_max = 0;

  double x0, y0, z0, xi, yi, zi;

  int i;

  if (x_tick < 0 || y_tick < 0 || z_tick < 0)
    {
      fprintf(stderr, "invalid interval length for major tick-marks\n");
      return;
    }

  check_autoinit;

  setscale(lx.scale_options);

  /* inquire current normalization transformation */

  gks_inq_current_xformno(&errind, &tnr);
  gks_inq_xform(tnr, &errind, wn, vp);

  modern_projection_type =
      gpx.projection_type == GR_PROJECTION_PERSPECTIVE || gpx.projection_type == GR_PROJECTION_ORTHOGRAPHIC;

  if (modern_projection_type)
    {
      lx.xmin = ix.xmin;
      lx.xmax = ix.xmax;
      lx.ymin = ix.ymin;
      lx.ymax = ix.ymax;
      lx.zmin = ix.zmin;
      lx.zmax = ix.zmax;

      x_min = ix.xmin;
      x_max = ix.xmax;
      y_min = ix.ymin;
      y_max = ix.ymax;
      z_min = ix.zmin;
      z_max = ix.zmax;
    }
  else
    {
      x_min = wn[0];
      x_max = wn[1];
      y_min = wn[2];
      y_max = wn[3];
      z_min = wx.zmin;
      z_max = wx.zmax;
    }

  /* save linetype, line width, line color and clipping indicator */

  gks_inq_pline_linetype(&errind, &ltype);
  gks_inq_pline_linewidth(&errind, &width);
  gks_inq_pline_color_index(&errind, &color);
  gks_inq_clip(&errind, &clsw, clrt);

  gks_set_pline_linetype(GKS_K_LINETYPE_SOLID);
  gks_set_clipping(GKS_K_NOCLIP);

  if (z_tick != 0)
    {
      if (GR_OPTION_Z_LOG & lx.scale_options)
        {
          z0 = pow(lx.basez, gauss(blog(lx.basez, z_min)));

          i = ipred(z_min / z0);
          zi = z0 + i * z0;

          /* draw horizontal grid lines */

          while (zi <= z_max)
            {
              if (i == 0 || major_z == 1)
                {
                  major = i == 0;
                  if (fabs(zi - z_min) > FEPS * zi)
                    {
                      grid_line3d(x_org, y_min, zi, x_org, y_max, zi, color, major);
                      grid_line3d(x_min, y_org, zi, x_max, y_org, zi, color, major);
                    }
                }

              if (i == 9 || lx.basez < 10)
                {
                  z0 = z0 * lx.basez;
                  i = 0;
                }
              else
                i++;

              zi = z0 + i * z0;
            }
        }
      else
        {
          check_tick_marks(z_min, z_max, z_tick, 'Z');

          i = 0;
          z0 = succ(z_min / z_tick) * z_tick;
          zi = z0;

          /* draw horizontal grid lines */

          while (zi <= z_max)
            {
              if (major_z > 0)
                major = i % major_z == 0 && major_z > 1;
              else
                major = 0;

              if (fabs(zi - z_min) > FEPS * zi)
                {
                  grid_line3d(x_org, y_min, zi, x_org, y_max, zi, color, major);
                  grid_line3d(x_min, y_org, zi, x_max, y_org, zi, color, major);
                }

              i++;
              zi = z0 + i * z_tick;
            }
        }
    }

  if (y_tick != 0)
    {
      if (GR_OPTION_Y_LOG & lx.scale_options)
        {
          y0 = pow(lx.basey, gauss(blog(lx.basey, y_min)));

          i = ipred(y_min / y0);
          yi = y0 + i * y0;

          /* draw horizontal grid lines */

          while (yi <= y_max)
            {
              if (i == 0 || major_y == 1)
                {
                  major = i == 0;
                  if (fabs(yi - y_min) > FEPS * yi)
                    {
                      grid_line3d(x_min, yi, z_org, x_max, yi, z_org, color, major);
                      grid_line3d(x_org, yi, z_min, x_org, yi, z_max, color, major);
                    }
                }

              if (i == 9 || lx.basey < 10)
                {
                  y0 = y0 * lx.basey;
                  i = 0;
                }
              else
                i++;

              yi = y0 + i * y0;
            }
        }
      else
        {
          check_tick_marks(y_min, y_max, y_tick, 'Y');

          i = 0;
          y0 = succ(y_min / y_tick) * y_tick;
          yi = y0;

          /* draw horizontal grid lines */

          while (yi <= y_max)
            {
              if (major_y > 0)
                major = i % major_y == 0 && major_y > 1;
              else
                major = 0;

              if (fabs(yi - y_min) > FEPS * yi)
                {
                  grid_line3d(x_min, yi, z_org, x_max, yi, z_org, color, major);
                  grid_line3d(x_org, yi, z_min, x_org, yi, z_max, color, major);
                }

              i++;
              yi = y0 + i * y_tick;
            }
        }
    }

  if (x_tick != 0)
    {
      if (GR_OPTION_X_LOG & lx.scale_options)
        {
          x0 = pow(lx.basex, gauss(blog(lx.basex, x_min)));

          i = ipred(x_min / x0);
          xi = x0 + i * x0;

          /* draw vertical grid lines */

          while (xi <= x_max)
            {
              if (i == 0 || major_x == 1)
                {
                  major = i == 0;
                  if (fabs(xi - x_min) > FEPS * xi)
                    {
                      grid_line3d(xi, y_min, z_org, xi, y_max, z_org, color, major);
                      grid_line3d(xi, y_org, z_min, xi, y_org, z_max, color, major);
                    }
                }

              if (i == 9 || lx.basex < 10)
                {
                  x0 = x0 * lx.basex;
                  i = 0;
                }
              else
                i++;

              xi = x0 + i * x0;
            }
        }
      else
        {
          check_tick_marks(x_min, x_max, x_tick, 'X');

          i = 0;
          x0 = succ(x_min / x_tick) * x_tick;
          xi = x0;

          /* draw vertical grid lines */

          while (xi <= x_max)
            {
              if (major_x > 0)
                major = i % major_x == 0 && major_x > 1;
              else
                major = 0;

              if (fabs(xi - x_min) > FEPS * xi)
                {
                  grid_line3d(xi, y_min, z_org, xi, y_max, z_org, color, major);
                  grid_line3d(xi, y_org, z_min, xi, y_org, z_max, color, major);
                }

              i++;
              xi = x0 + i * x_tick;
            }
        }
    }

  /* restore linetype, line width, line color and clipping indicator */

  gks_set_pline_linetype(ltype);
  gks_set_pline_linewidth(width);
  gks_set_pline_color_index(color);
  gks_set_clipping(clsw);

  if (flag_stream)
    gr_writestream("<grid3d xtick=\"%g\" ytick=\"%g\" ztick=\"%g\" "
                   "xorg=\"%g\" yorg=\"%g\" zorg=\"%g\" "
                   "majorx=\"%d\" majory=\"%d\" majorz=\"%d\"/>\n",
                   x_tick, y_tick, z_tick, x_org, y_org, z_org, major_x, major_y, major_z);
}

/*!
 * Draw a standard vertical error bar graph.
 *
 * \param[in] n The number of points
 * \param[in] px A pointer to the X coordinates
 * \param[in] py A pointer to the Y coordinates
 * \param[in] e1 A pointer to the absolute values of the lower error bar data
 * \param[in] e2 A pointer to the absolute values of the upper error bar data
 */
void gr_verrorbars(int n, double *px, double *py, double *e1, double *e2)
{
  int errind, i;
  double tick, x, x1, x2, y1, y2, marker_size;

  if (n < 1)
    {
      fprintf(stderr, "invalid number of points\n");
      return;
    }

  check_autoinit;

  gks_inq_pmark_size(&errind, &marker_size);

  for (i = 0; i < n; i++)
    {
      tick = marker_size * 0.0075 * (lx.xmax - lx.xmin);

      x = px[i];
      x1 = x_log(x_lin(x) - tick);
      x2 = x_log(x_lin(x) + tick);
      y1 = e1[i];
      y2 = e2[i];

      start_pline(x1, y1);
      pline(x2, y1);
      end_pline();

      start_pline(x, y1);
      pline(x, y2);
      end_pline();

      start_pline(x1, y2);
      pline(x2, y2);
      end_pline();
    }

  polymarker(n, px, py);

  if (flag_stream)
    {
      gr_writestream("<verrorbars len=\"%d\"", n);
      print_float_array("x", n, px);
      print_float_array("y", n, py);
      print_float_array("e1", n, e1);
      print_float_array("e2", n, e2);
      gr_writestream("/>\n");
    }
}

/*!
 * Draw a standard horizontal error bar graph.
 *
 * \param[in] n The number of points
 * \param[in] px A pointer to the X coordinates
 * \param[in] py A pointer to the Y coordinates
 * \param[in] e1 A pointer to the absolute values of the lower error bar data
 * \param[in] e2 A pointer to the absolute values of the upper error bar data
 */
void gr_herrorbars(int n, double *px, double *py, double *e1, double *e2)
{
  int errind, i;
  double tick, y, x1, x2, y1, y2, marker_size;

  if (n < 1)
    {
      fprintf(stderr, "invalid number of points\n");
      return;
    }

  check_autoinit;

  gks_inq_pmark_size(&errind, &marker_size);

  for (i = 0; i < n; i++)
    {
      tick = marker_size * 0.0075 * (lx.ymax - lx.ymin);

      y = py[i];
      y1 = y_log(y_lin(y) - tick);
      y2 = y_log(y_lin(y) + tick);
      x1 = e1[i];
      x2 = e2[i];

      start_pline(x1, y1);
      pline(x1, y2);
      end_pline();

      start_pline(x1, y);
      pline(x2, y);
      end_pline();

      start_pline(x2, y1);
      pline(x2, y2);
      end_pline();
    }

  polymarker(n, px, py);

  if (flag_stream)
    {
      gr_writestream("<herrorbars len=\"%d\"", n);
      print_float_array("x", n, px);
      print_float_array("y", n, py);
      print_float_array("e1", n, e1);
      print_float_array("e2", n, e2);
      gr_writestream("/>\n");
    }
}

static void clip_code(double x, double y, double z, int *c)
{
  *c = 0;
  if (x < cxl)
    *c = LEFT;
  else if (x > cxr)
    *c = RIGHT;
  if (y < cyf)
    *c = *c | FRONT;
  else if (y > cyb)
    *c = *c | BACK;
  if (z < czb)
    *c = *c | BOTTOM;
  else if (z > czt)
    *c = *c | TOP;
}

static void clip3d(double *x0, double *x1, double *y0, double *y1, double *z0, double *z1, int *visible)
{
  int c, c0, c1;
  double x = 0, y = 0, z = 0;

  clip_code(*x0, *y0, *z0, &c0);
  clip_code(*x1, *y1, *z1, &c1);

  *visible = 0;

  while (c0 | c1)
    {
      if (c0 & c1) return;
      c = c0 ? c0 : c1;

      if (c & LEFT)
        {
          x = cxl;
          y = *y0 + (*y1 - *y0) * (cxl - *x0) / (*x1 - *x0);
          z = *z0 + (*z1 - *z0) * (cxl - *x0) / (*x1 - *x0);
        }
      else if (c & RIGHT)
        {
          x = cxr;
          y = *y0 + (*y1 - *y0) * (cxr - *x0) / (*x1 - *x0);
          z = *z0 + (*z1 - *z0) * (cxr - *x0) / (*x1 - *x0);
        }
      else if (c & FRONT)
        {
          x = *x0 + (*x1 - *x0) * (cyf - *y0) / (*y1 - *y0);
          y = cyf;
          z = *z0 + (*z1 - *z0) * (cyf - *y0) / (*y1 - *y0);
        }
      else if (c & BACK)
        {
          x = *x0 + (*x1 - *x0) * (cyb - *y0) / (*y1 - *y0);
          y = cyb;
          z = *z0 + (*z1 - *z0) * (cyb - *y0) / (*y1 - *y0);
        }
      else if (c & BOTTOM)
        {
          x = *x0 + (*x1 - *x0) * (czb - *z0) / (*z1 - *z0);
          y = *y0 + (*y1 - *y0) * (czb - *z0) / (*z1 - *z0);
          z = czb;
        }
      else if (c & TOP)
        {
          x = *x0 + (*x1 - *x0) * (czt - *z0) / (*z1 - *z0);
          y = *y0 + (*y1 - *y0) * (czt - *z0) / (*z1 - *z0);
          z = czt;
        }
      if (c == c0)
        {
          *x0 = x;
          *y0 = y;
          *z0 = z;
          clip_code(x, y, z, &c0);
        }
      else
        {
          *x1 = x;
          *y1 = y;
          *z1 = z;
          clip_code(x, y, z, &c1);
        }
    }

  /* if we reach here, the line from (x0, y0, z0) to (x1, y1, z1) is visible */

  *visible = 1;
}

static void clip3d_for_surface(double *x0, double *x1, double *y0, double *y1, double *z0, double *z1)
{
  int l, border;
  for (border = 0; border < 6; border++)
    {
      for (l = 0; l < 4; l++)
        {
          double d0, d1, s;
          double inter_x, inter_y, inter_z;
          if (border == 0)
            {
              d0 = *x0 - cxl;
              d1 = *x1 - cxl;
            }
          else if (border == 1)
            {
              d1 = *x0 - cxr;
              d0 = *x1 - cxr;
            }
          else if (border == 2)
            {
              d0 = *y0 - cyf;
              d1 = *y1 - cyf;
            }
          else if (border == 3)
            {
              d1 = *y0 - cyb;
              d0 = *y1 - cyb;
            }
          else if (border == 4)
            {
              d0 = *z0 - czb;
              d1 = *z1 - czb;
            }
          else
            {
              d1 = *z0 - czt;
              d0 = *z1 - czt;
            }
          if ((d0 <= 0 && d1 <= 0) || (d1 >= 0 && d0 >= 0))
            {
              continue;
            }

          s = d0 / (d0 - d1);
          if (border == 1 || border == 3 || border == 5) s = 1 - s;

          inter_x = *x0 + s * (*x1 - *x0);
          inter_y = *y0 + s * (*y1 - *y0);
          inter_z = *z0 + s * (*z1 - *z0);

          if (d0 < 0)
            {
              *x0 = inter_x;
              *y0 = inter_y;
              *z0 = inter_z;
            }
          else
            {
              *x1 = inter_x;
              *y1 = inter_y;
              *z1 = inter_z;
            }
        }
    }
}

/*!
 * Draw a 3D curve using the current line attributes, starting from the
 * first data point and ending at the last data point.
 *
 * \param[in] n The number of points
 * \param[in] px A pointer to the X coordinates
 * \param[in] py A pointer to the Y coordinates
 * \param[in] pz A pointer to the Z coordinates
 *
 * The values for x, y and z are in world coordinates. The attributes that
 * control the appearance of a polyline are linetype, linewidth and color
 * index.
 */
void gr_polyline3d(int n, double *px, double *py, double *pz)
{
  int errind, clsw, i, tnr;
  double clrt[4], wn[4], vp[4];
  int modern_projection_type;

  double x, y, z, x0, y0, z0, x1, y1, z1;
  int clip = 1, visible = 1;

  check_autoinit;

  setscale(lx.scale_options);

  /* inquire current normalization transformation */

  gks_inq_current_xformno(&errind, &tnr);
  gks_inq_xform(tnr, &errind, wn, vp);

  gks_inq_clip(&errind, &clsw, clrt);

  modern_projection_type =
      gpx.projection_type == GR_PROJECTION_PERSPECTIVE || gpx.projection_type == GR_PROJECTION_ORTHOGRAPHIC;

  if (modern_projection_type)
    {
      lx.xmin = ix.xmin;
      lx.xmax = ix.xmax;
      lx.ymin = ix.ymin;
      lx.ymax = ix.ymax;
      lx.zmin = ix.zmin;
      lx.zmax = ix.zmax;
    }

  if (clsw == GKS_K_CLIP)
    {
      if (modern_projection_type)
        {
          cxl = ix.xmin;
          cxr = ix.xmax;
          cyf = ix.ymin;
          cyb = ix.ymax;
          czb = ix.zmin;
          czt = ix.zmax;
        }
      else
        {
          cxl = lx.xmin;
          cxr = lx.xmax;
          cyf = lx.ymin;
          cyb = lx.ymax;
          czb = lx.zmin;
          czt = lx.zmax;
        }
    }
  else
    {
      visible = 1;
    }

  x0 = px[0];
  y0 = py[0];
  z0 = pz[0];

  for (i = 1; i < n; i++)
    {
      x1 = px[i];
      y1 = py[i];
      z1 = pz[i];
      if (is_nan(x1) || is_nan(y1) || is_nan(z1)) continue;
      if (is_nan(x0) || is_nan(y0) || is_nan(z0))
        {
          x0 = x1;
          y0 = y1;
          z0 = z1;
          continue;
        }

      x = x1;
      y = y1;
      z = z1;
      if (clsw == GKS_K_CLIP)
        {
          clip3d(&x0, &x1, &y0, &y1, &z0, &z1, &visible);
        }
      if (visible)
        {
          if (clip)
            {
              start_pline3d(x0, y0, z0);
              clip = 0;
            }
          pline3d(x1, y1, z1);
        }

      clip = !visible || x != x1 || y != y1 || z != z1;
      x0 = x;
      y0 = y;
      z0 = z;
    }

  end_pline3d();

  if (flag_stream)
    {
      gr_writestream("<polyline3d len=\"%d\"", n);
      print_float_array("x", n, px);
      print_float_array("y", n, py);
      print_float_array("z", n, pz);
      gr_writestream("/>\n");
    }
}

static int cmp(const void *a, const void *b)
{
  const point_3d *pa = (const point_3d *)a;
  const point_3d *pb = (const point_3d *)b;
  double x, y, da, db;

  x = (GR_OPTION_FLIP_X & lx.scale_options) ? lx.xmin : lx.xmax;
  y = (GR_OPTION_FLIP_Y & lx.scale_options) ? lx.ymin : lx.ymax;

  da = sqrt(pow(x - pa->x, 2) + pow(y - pa->y, 2));
  db = sqrt(pow(x - pb->x, 2) + pow(y - pb->y, 2));

  return db - da;
}

/*!
 * Draw marker symbols centered at the given 3D data points.
 *
 * \param[in] n The number of points
 * \param[in] px A pointer to the X coordinates
 * \param[in] py A pointer to the Y coordinates
 * \param[in] pz A pointer to the Z coordinates
 *
 * The values for x, y and z are in world coordinates. The attributes
 * that control the appearance of a polymarker are marker type, marker size
 * scale factor and color index.
 */
void gr_polymarker3d(int n, double *px, double *py, double *pz)
{
  int errind, clsw, i, tnr;
  double clrt[4], wn[4], vp[4];
  int modern_projection_type;

  double x, y, z;
  point_3d *point;
  int m, visible;

  check_autoinit;

  setscale(lx.scale_options);

  /* inquire current normalization transformation */

  gks_inq_current_xformno(&errind, &tnr);
  gks_inq_xform(tnr, &errind, wn, vp);

  gks_inq_clip(&errind, &clsw, clrt);

  modern_projection_type =
      gpx.projection_type == GR_PROJECTION_PERSPECTIVE || gpx.projection_type == GR_PROJECTION_ORTHOGRAPHIC;

  if (modern_projection_type)
    {
      lx.xmin = ix.xmin;
      lx.xmax = ix.xmax;
      lx.ymin = ix.ymin;
      lx.ymax = ix.ymax;
      lx.zmin = ix.zmin;
      lx.zmax = ix.zmax;
    }

  m = 0;
  point = (point_3d *)xmalloc(n * sizeof(point_3d));

  for (i = 0; i < n; i++)
    {
      x = px[i];
      y = py[i];
      z = pz[i];

      if (clsw == GKS_K_CLIP)
        {
          if (modern_projection_type)
            {
              visible = x >= ix.xmin && x <= ix.xmax && y >= ix.ymin && y <= ix.ymax && z >= ix.zmin && z <= ix.zmax;
            }
          else
            {
              visible = x >= lx.xmin && x <= lx.xmax && y >= lx.ymin && y <= lx.ymax && z >= lx.zmin && z <= lx.zmax;
            }
        }
      else
        {
          visible = 1;
        }
      if (visible)
        {
          x = x_lin(x);
          y = y_lin(y);
          z = z_lin(z);

          apply_world_xform(&x, &y, &z);

          point[m].x = x;
          point[m].y = y;
          point[m].z = z;
          m++;
        }
    }

  qsort(point, m, sizeof(point_3d), cmp);

  if (m >= maxpath) reallocate(m);

  for (i = 0; i < m; i++)
    {
      xpoint[i] = point[i].x;
      ypoint[i] = point[i].y;
      zpoint[i] = point[i].z;
    }

  if (m > 0)
    {
      int errind, tnr, modern_projection_type;

      modern_projection_type =
          gpx.projection_type == GR_PROJECTION_PERSPECTIVE || gpx.projection_type == GR_PROJECTION_ORTHOGRAPHIC;
      if (modern_projection_type)
        {
          gks_inq_current_xformno(&errind, &tnr);
          gks_select_xform(MODERN_NDC);
        }

      gks_polymarker(m, xpoint, ypoint);
      npoints = 0;

      if (modern_projection_type) gks_select_xform(tnr);
    }

  if (flag_stream)
    {
      gr_writestream("<polymarker3d len=\"%d\"", n);
      print_float_array("x", n, px);
      print_float_array("y", n, py);
      print_float_array("z", n, pz);
      gr_writestream("/>\n");
    }
}

static double text3d_get_height(void)
{
  int errind, tnr;
  double focus_point_x, focus_point_y, focus_point_z, focus_up_x, focus_up_y, focus_up_z;
  int scale_save = lx.scale_options;

  gks_inq_current_xformno(&errind, &tnr);
  gks_select_xform(MODERN_NDC);

  /* Calculate char height */
  focus_point_x = tx.focus_point_x / tx.x_axis_scale;
  focus_point_y = tx.focus_point_y / tx.y_axis_scale;
  focus_point_z = tx.focus_point_z / tx.z_axis_scale;
  focus_up_x = focus_point_x + tx.up_x / tx.x_axis_scale;
  focus_up_y = focus_point_y + tx.up_y / tx.y_axis_scale;
  focus_up_z = focus_point_z + tx.up_z / tx.z_axis_scale;

  gr_wc3towc(&focus_point_x, &focus_point_y, &focus_point_z);
  gr_wc3towc(&focus_up_x, &focus_up_y, &focus_up_z);

  lx.scale_options = 0;
  gks_WC_to_NDC(MODERN_NDC, &focus_point_x, &focus_point_y);
  gks_WC_to_NDC(MODERN_NDC, &focus_up_x, &focus_up_y);
  lx.scale_options = scale_save;

  gks_select_xform(tnr);

  return sqrt(pow(focus_point_x - focus_up_x, 2) + pow(focus_point_y - focus_up_y, 2)) /
         (min((vxmax - vxmin), (vymax - vymin)));
}

static void text3d(double x, double y, double z, char *chars, int axis)
{
  double p_x, p_y, p_z;
  int errind, tnr;
  double scaleFactors[3];

  check_autoinit;

  p_x = x_lin(x);
  p_y = y_lin(y);
  p_z = z_lin(z);

  if (axis == 0)
    {
      apply_world_xform(&p_x, &p_y, &p_z);

      gks_inq_current_xformno(&errind, &tnr);
      if (tnr != NDC)
        {
          p_x = nx.a * p_x + nx.b;
          p_y = nx.c * p_y + nx.d;
          gks_select_xform(NDC);
        }

      if (scientific_format == SCIENTIFIC_FORMAT_OPTION_MATHTEX)
        {
          gr_mathtex(p_x, p_y, chars);
        }
      else
        {
          gr_textex(p_x, p_y, chars, 0, NULL, NULL);
        }

      if (tnr != NDC) gks_select_xform(tnr);
    }
  else if (scientific_format == SCIENTIFIC_FORMAT_OPTION_MATHTEX)
    {
      gr_mathtex3d(p_x, p_y, p_z, chars, axis);
    }
  else
    {
      gks_inq_current_xformno(&errind, &tnr);
      gks_select_xform(MODERN_NDC);

      scaleFactors[0] = tx.x_axis_scale;
      scaleFactors[1] = tx.y_axis_scale;
      scaleFactors[2] = tx.z_axis_scale;
      gks_ft_text3d(p_x, p_y, p_z, chars, axis, gks_state(), text3d_get_height(), scaleFactors, gks_ft_gdp, gr_wc3towc);

      gks_select_xform(tnr);
    }
}

void gr_text3d(double x, double y, double z, char *chars, int axis)
{
  int errind, tnr;
  double scaleFactors[3];

  check_autoinit;

  gks_inq_current_xformno(&errind, &tnr);
  gks_select_xform(MODERN_NDC);

  x = x_lin(x);
  y = y_lin(y);
  z = z_lin(z);

  scaleFactors[0] = tx.x_axis_scale;
  scaleFactors[1] = tx.y_axis_scale;
  scaleFactors[2] = tx.z_axis_scale;
  gks_ft_text3d(x, y, z, chars, axis, gks_state(), text3d_get_height(), scaleFactors, gks_ft_gdp, gr_wc3towc);

  gks_select_xform(tnr);

  if (flag_stream)
    gr_writestream("<text3d x=\"%g\" y=\"%g\" z=\"%g\" text=\"%s\" axis=\"%d\"/>\n", x, y, z, chars, axis);
}

/*!
 * Allows you to get the 2d coordinates and transformed coordinates of a text as if displayed by gr_text3d
 *
 * \param[in] x The base X coordinate
 * \param[in] y The base Y coordinate
 * \param[in] z The base z coordinate
 * \param[in] chars The string to draw
 * \param[in] axis In which direction the text is drawn (1: YX-plane, 2: XY plane, 3: YZ plane, 4: XZ plane)
 * \param[in] tbx A double array of 16 elements to write x-coordinates to
 * \param[in] tby A double array of 16 elements to write y-coordinates to
 *
 * The first 8 coordinates are pre-transformation coordinates, while the last 8 coordinates are transformed coordinates
 * The first 4 coordinates each are the corners of the bounding box, including ascender and descender space, while the
 * last 4 coordinates are without ascenders and descenders.
 */
void gr_inqtext3d(double x, double y, double z, char *chars, int axis, double *tbx, double *tby)
{
  int errind, tnr;
  double scaleFactors[3];

  check_autoinit;

  gks_inq_current_xformno(&errind, &tnr);
  gks_select_xform(MODERN_NDC);

  x = x_lin(x);
  y = y_lin(y);
  z = z_lin(z);

  scaleFactors[0] = tx.x_axis_scale;
  scaleFactors[1] = tx.y_axis_scale;
  scaleFactors[2] = tx.z_axis_scale;
  gks_ft_inq_text3d_extent(x, y, z, chars, axis, gks_state(), text3d_get_height(), scaleFactors, gks_ft_gdp, gr_wc3towc,
                           tbx, tby);

  gks_select_xform(tnr);
}

static void axes3d_get_params(int axis, int *tick_axis, double x_org, double y_org, double z_org, int *text_axis)
{
  /* This function calculates (and sets) the axis of ticks, upvec, valign and axis of text for gr_axes3d.
   * axis: when the axis currently drawn is x = 0, y = 1 or z = 2
   * tick_axis: the preferable axis to draw ticks on
   * x_org, y_org, z_org: the origin of the coordinate system. Used to determine where to rotate text.
   * text_axis: same as tick_axis
   */
  int plane, direction, rotate_text, flip_text;
  double fx, fy, fz, xi, yi, zi;
  double x_min, x_max, y_min, y_max, z_min, z_max;
  double cam_x, cam_y, cam_z, up_x, up_y, up_z, nor_x, nor_y, nor_z, angle;
  double bBoxX[16], bBoxY[16];
  double bBoxSpace, bBoxSpace2;

  int axes[3] = {/* plane (xy, xz, yz) */
                 2, 4, 3};
  int upvecs[4][2] = {
      {0, 1},  /* x pos or y pos if plane = xz */
      {-1, 0}, /* y pos if plane = xy or z pos */
      {0, -1}, /* x neg or y neg if plane = xz */
      {1, 0}   /* y neg if plane = xy or z neg */
  };
  if (axis < 0 || axis > 2)
    {
      fprintf(stderr, "Axis should be between 0 and 2\n");
      return;
    }
  /* Reset options for consistent gr_inqtext3d values */
  gks_set_text_upvec(0, 1);
  gks_set_text_align(GKS_K_TEXT_HALIGN_CENTER, GKS_K_TEXT_VALIGN_HALF);
  gr_inqwindow3d(&x_min, &x_max, &y_min, &y_max, &z_min, &z_max);
  fx = tx.camera_pos_x - tx.focus_point_x;
  fy = tx.camera_pos_y - tx.focus_point_y;
  fz = tx.camera_pos_z - tx.focus_point_z;
  cam_x = tx.camera_pos_x / tx.x_axis_scale;
  cam_y = tx.camera_pos_y / tx.y_axis_scale;
  cam_z = tx.camera_pos_z / tx.z_axis_scale;
  xi = (x_max + x_min) / 2;
  yi = (y_max + y_min) / 2;
  zi = (z_max + z_min) / 2;

  if (lx.scale_options & GR_OPTION_FLIP_X)
    {
      x_org = -x_org + x_min + x_max;
    }
  if (lx.scale_options & GR_OPTION_FLIP_Y)
    {
      y_org = -y_org + y_min + y_max;
    }
  if (lx.scale_options & GR_OPTION_FLIP_Z)
    {
      z_org = -z_org + z_min + z_max;
    }

  if (axis == 0)
    {
      gr_inqtext3d(xi, y_org, z_org, "A", axes[1], bBoxX, bBoxY);
      bBoxSpace =
          fabs((bBoxX[10] - bBoxX[8]) * (bBoxY[11] - bBoxY[9]) + (bBoxX[11] - bBoxX[9]) * (bBoxY[8] - bBoxY[10]));

      gr_inqtext3d(xi, y_org, z_org, "A", axes[0], bBoxX, bBoxY);
      bBoxSpace2 =
          fabs((bBoxX[10] - bBoxX[8]) * (bBoxY[11] - bBoxY[9]) + (bBoxX[11] - bBoxX[9]) * (bBoxY[8] - bBoxY[10]));

      plane = bBoxSpace2 > bBoxSpace ? 0 : 1; /* 0: xy-plane, 1: xz-plane */
      *tick_axis = plane == 0 ? 1 : 2;
      direction = (!plane && fz <= -fabs(fy)) || (plane && fy > fabs(fz)); /* 1: positive, 0: negative */

      if (plane == 1)
        {
          direction = (zi < z_org); /* align the text and ticks to the 'outside' */
        }
      else
        {
          direction = (yi < y_org);
        }
      rotate_text = (fx < 0) ^ !direction;
      direction = 1 + 2 * !direction; /* always in y or z-direction */
    }
  else if (axis == 1)
    {
      gr_inqtext3d(x_org, yi, z_org, "A", axes[2], bBoxX, bBoxY);
      bBoxSpace =
          fabs((bBoxX[10] - bBoxX[8]) * (bBoxY[11] - bBoxY[9]) + (bBoxX[11] - bBoxX[9]) * (bBoxY[8] - bBoxY[10]));

      gr_inqtext3d(x_org, yi, z_org, "A", axes[0], bBoxX, bBoxY);
      bBoxSpace2 =
          fabs((bBoxX[10] - bBoxX[8]) * (bBoxY[11] - bBoxY[9]) + (bBoxX[11] - bBoxX[9]) * (bBoxY[8] - bBoxY[10]));

      plane = bBoxSpace2 > bBoxSpace ? 0 : 2; /* 2: yz-plane, 0: xy-plane */
      *tick_axis = plane == 0 ? 0 : 2;
      direction = (2 == plane && fx <= -fabs(fz)) || (!plane && fz > fabs(fx)); /* 1: positive, 0: negative */
      if (plane == 0)
        {
          direction = (xi < x_org); /* align the text and ticks to the 'outside' */
          rotate_text = (fy < 0) ^ direction;
        }
      else
        {
          direction = (zi < z_org);
          rotate_text = (fy < 0) ^ !direction;
        }
      direction = (plane == 2) + 2 * !direction; /* always in x or z-direction */
    }
  else /* z-axis */
    {
      gr_inqtext3d(x_org, y_org, zi, "A", axes[2], bBoxX, bBoxY);
      bBoxSpace =
          fabs((bBoxX[10] - bBoxX[8]) * (bBoxY[11] - bBoxY[9]) + (bBoxX[11] - bBoxX[9]) * (bBoxY[8] - bBoxY[10]));

      gr_inqtext3d(x_org, y_org, zi, "A", axes[1], bBoxX, bBoxY);
      bBoxSpace2 =
          fabs((bBoxX[10] - bBoxX[8]) * (bBoxY[11] - bBoxY[9]) + (bBoxX[11] - bBoxX[9]) * (bBoxY[8] - bBoxY[10]));

      plane = bBoxSpace2 > bBoxSpace ? 1 : 2; /* 1: xz-plane, 2: yz-plane */
      *tick_axis = plane == 1 ? 0 : 1;
      direction = (1 == plane && fy <= -fabs(fx)) || (2 == plane && fx > fabs(fy)); /* 1: positive, 0: negative */

      if (plane == 1)
        {
          direction = (xi < x_org); /* align the text and ticks to the 'outside' */
        }
      else
        {
          direction = (yi < y_org);
        }
      rotate_text = (tx.up_z > 0) ^ direction;

      direction = 2 * !direction; /* always in x or y-direction */
    }
  /* now: direction is the direction (0 for negative, 1 for positive) of either the ticks, or if the ticks are on the */
  /* other plane, the direction facing outwards. */
  if (rotate_text)
    {
      direction = (direction + 2) % 4; /* rotate text by 180 degrees */
    }
  *text_axis = axes[plane];
  if (gpx.projection_type == GR_PROJECTION_ORTHOGRAPHIC)
    {
      if (plane == 0)
        {
          cam_x = upvecs[direction][1] * tx.x_axis_scale;
          cam_y = -upvecs[direction][0] * tx.y_axis_scale;
          cam_z = 0;
          up_x = upvecs[direction][0] * tx.x_axis_scale;
          up_y = upvecs[direction][1] * tx.y_axis_scale;
          up_z = 0;
        }
      else if (plane == 1)
        {
          cam_x = upvecs[direction][1] * tx.x_axis_scale;
          cam_y = 0;
          cam_z = -upvecs[direction][0] * tx.z_axis_scale;
          up_x = upvecs[direction][0] * tx.x_axis_scale;
          up_y = 0;
          up_z = upvecs[direction][1] * tx.z_axis_scale;
        }
      else
        {
          cam_x = 0;
          cam_y = upvecs[direction][1] * tx.y_axis_scale;
          cam_z = -upvecs[direction][0] * tx.z_axis_scale;
          up_x = 0;
          up_y = upvecs[direction][0] * tx.y_axis_scale;
          up_z = upvecs[direction][1] * tx.z_axis_scale;
        }

      nor_x = cam_y * up_z - cam_z * up_y;
      nor_y = cam_z * up_x - cam_x * up_z;
      nor_z = cam_x * up_y - cam_y * up_x;

      angle = nor_x * fx + nor_y * fy + nor_z * fz;
      flip_text = angle < 0;
    }
  else
    {
      /* if the camera is on the opposite side of the text, flip/mirror it. */
      flip_text = (plane == 0 && cam_z < z_org) || (plane == 1 && cam_y > y_org) || (plane == 2 && cam_x < x_org);
    }

  if (rotate_text ^ flip_text)
    {
      gks_set_text_align(GKS_K_TEXT_HALIGN_RIGHT, GKS_K_TEXT_VALIGN_HALF);
    }
  else
    {
      gks_set_text_align(GKS_K_TEXT_HALIGN_LEFT, GKS_K_TEXT_VALIGN_HALF);
    }
  if (flip_text)
    {
      *text_axis *= -1;
    }

  gks_set_text_upvec(upvecs[direction][0], upvecs[direction][1]);
}

/*!
 * Draw X, Y and Z coordinate axes with linearly and/or logarithmically
 * spaced tick marks.
 *
 * \param[in] x_tick The length in world coordinates of the interval between
 *                   minor grid lines in X direction.
 * \param[in] y_tick The length in world coordinates of the interval between
 *                   minor grid lines in Y direction.
 * \param[in] z_tick The length in world coordinates of the interval between
 *                   minor grid lines in Z direction.
 * \param[in] x_org The world coordinate of the origin (point of intersection)
 *                  of the X axis.
 * \param[in] y_org The world coordinate of the origin (point of intersection)
 *                  of the Y axis.
 * \param[in] z_org The world coordinate of the origin (point of intersection)
 *                  of the Z axis.
 * \param[in] major_x Unitless integer value specifying the number of minor
 *                    grid lines between major grid lines on the X axis. Values
 *                    of 0 or 1 imply no grid lines.
 * \param[in] major_y Unitless integer value specifying the number of minor
 *                    grid lines between major grid lines on the Y axis. Values
 *                    of 0 or 1 imply no grid lines.
 * \param[in] major_z Unitless integer value specifying the number of minor
 *                    grid lines between major grid lines on the Z axis. Values
 *                    of 0 or 1 imply no grid lines.
 * \param[in] tick_size The length of minor tick marks specified in a normalized
 *                      device coordinate unit. Major tick marks are twice as
 *                      long as minor tick marks. A negative value reverses the
 *                      tick marks on the axes from inward facing to outward
 *                      facing (or vice versa).
 *
 * Tick marks are positioned along each axis so that major tick marks fall on
 * the axes origin (whether visible or not). Major tick marks are labeled with
 * the corresponding data values. Axes are drawn according to the scale of the
 * window. Axes and tick marks are drawn using solid lines; line color and width
 * can be modified using the gr_setlinetype and gr_setlinewidth functions. Axes
 * are drawn according to the linear or logarithmic transformation established
 * by the gr_setscale function.
 */
void gr_axes3d(double x_tick, double y_tick, double z_tick, double x_org, double y_org, double z_org, int major_x,
               int major_y, int major_z, double tick_size)
{
  int errind, tnr;
  double clrt[4], wn[4], vp[4];
  int modern_projection_type;

  int ltype, halign, valign, font, prec, clsw, axis, tick_axis;
  double chux, chuy, slant, chh;

  double x_min = 0, x_max = 0, y_min = 0, y_max = 0, z_min = 0, z_max = 0;

  double r, alpha, beta;
  double a[2], c[2], text_slant[4];
  int *anglep, which_rep, rep;

  double tick;
  double x_minor_tick, x_major_tick, x_label, x_title;
  double y_minor_tick, y_major_tick, y_label, y_title;
  double z_minor_tick, z_major_tick, z_label, z_title;
  double x0, y0, z0, xi, yi, zi;
  int64_t i;
  int decade, exponent;
  char string[256];

  format_reference_t format_reference;

  if (x_tick < 0 || y_tick < 0 || z_tick < 0)
    {
      fprintf(stderr, "invalid interval length for major tick-marks\n");
      return;
    }
  else if (tick_size == 0)
    {
      fprintf(stderr, "invalid tick-size\n");
      return;
    }

  check_autoinit;

  setscale(lx.scale_options);

  /* inquire current normalization transformation */

  gks_inq_current_xformno(&errind, &tnr);
  gks_inq_xform(tnr, &errind, wn, vp);

  modern_projection_type =
      gpx.projection_type == GR_PROJECTION_PERSPECTIVE || gpx.projection_type == GR_PROJECTION_ORTHOGRAPHIC;

  if (modern_projection_type)
    {
      lx.xmin = ix.xmin;
      lx.xmax = ix.xmax;
      lx.ymin = ix.ymin;
      lx.ymax = ix.ymax;
      lx.zmin = ix.zmin;
      lx.zmax = ix.zmax;

      x_min = ix.xmin;
      x_max = ix.xmax;
      y_min = ix.ymin;
      y_max = ix.ymax;
      z_min = ix.zmin;
      z_max = ix.zmax;
    }
  else
    {
      x_min = wn[0];
      x_max = wn[1];
      y_min = wn[2];
      y_max = wn[3];
      z_min = wx.zmin;
      z_max = wx.zmax;
    }

  if (x_min > x_org || x_org > x_max || y_min > y_org || y_org > y_max || z_min > z_org || z_org > z_max)
    {
      fprintf(stderr, "origin outside current window\n");
      return;
    }

  r = (x_max - x_min) / (y_max - y_min) * (vp[3] - vp[2]) / (vp[1] - vp[0]);

  alpha = atan_2(r * wx.c1, wx.a1);
  a[0] = -sin(alpha);
  c[0] = cos(alpha);
  alpha = deg(alpha);

  beta = atan_2(r * wx.c2, wx.a2);
  a[1] = -sin(beta);
  c[1] = cos(beta);
  beta = deg(beta);

  text_slant[0] = alpha;
  text_slant[1] = beta;
  text_slant[2] = -(90.0 + alpha - beta);
  text_slant[3] = 90.0 + alpha - beta;

  /* save linetype, text alignment, text font, text slant,
     character-up vector and clipping indicator */

  gks_inq_pline_linetype(&errind, &ltype);
  gks_inq_text_align(&errind, &halign, &valign);
  gks_inq_text_fontprec(&errind, &font, &prec);
  gks_inq_text_slant(&errind, &slant);
  gks_inq_text_upvec(&errind, &chux, &chuy);
  gks_inq_text_height(&errind, &chh);
  gks_inq_clip(&errind, &clsw, clrt);

  gks_set_pline_linetype(GKS_K_LINETYPE_SOLID);
  gks_set_text_fontprec(font, GKS_K_TEXT_PRECISION_STROKE);
  gks_set_clipping(GKS_K_NOCLIP);

  which_rep = 0;
  anglep = angle;
  while (wx.delta > *anglep++) which_rep++;
  anglep = angle;
  while (wx.phi > *anglep++) which_rep += 4;
  if (z_tick != 0)
    {
      if (modern_projection_type)
        tick = tick_size / tx.y_axis_scale / text3d_get_height();
      else
        tick = tick_size * (y_max - y_min) / (vp[3] - vp[2]);

      y_minor_tick = y_log(y_lin(y_org) + tick);
      y_major_tick = y_log(y_lin(y_org) + 2. * tick);
      y_label = y_log(y_lin(y_org) + 3. * tick);
      y_title = y_log(y_lin(y_org) + 10. * tick);

      /* set text alignment */

      if (y_lin(y_org) <= (y_lin(y_min) + y_lin(y_max)) / 2.)
        {
          gks_set_text_align(GKS_K_TEXT_HALIGN_RIGHT, GKS_K_TEXT_VALIGN_HALF);
          if (tick > 0)
            {
              y_label = y_log(y_lin(y_org) - tick);
              y_title = y_log(y_lin(y_org) - 10. * tick);
            }
        }
      else
        {
          gks_set_text_align(GKS_K_TEXT_HALIGN_LEFT, GKS_K_TEXT_VALIGN_HALF);
          if (tick < 0)
            {
              y_label = y_log(y_lin(y_org) - tick);
              y_title = y_log(y_lin(y_org) - 10. * tick);
            }
        }


      if (!modern_projection_type)
        {
          rep = rep_table[which_rep][2];

          gks_set_text_upvec(a[axes_rep[rep][0]], c[axes_rep[rep][1]]);
          gks_set_text_slant(text_slant[axes_rep[rep][2]]);
          tick_axis = 1;
        }
      else
        {
          tick = tick_size / tx.x_axis_scale / text3d_get_height();

          x_minor_tick = x_log(x_lin(x_org) + tick);
          x_major_tick = x_log(x_lin(x_org) + 2. * tick);
          x_label = x_log(x_lin(x_org) + 3. * tick);
          x_title = x_log(x_lin(x_org) + 10. * tick);

          if (x_lin(x_org) <= (x_lin(x_min) + x_lin(x_max)) / 2.)
            {
              if (tick > 0)
                {
                  x_label = x_log(x_lin(x_org) - tick);
                  x_title = x_log(x_lin(x_org) - 10. * tick);
                }
            }
          else
            {
              if (tick < 0)
                {
                  x_label = x_log(x_lin(x_org) - tick);
                  x_title = x_log(x_lin(x_org) - 10. * tick);
                }
            }
          axes3d_get_params(2, &tick_axis, x_org, y_org, z_org, &axis);
        }

      if (tick_axis != 1)
        {
          y_title = y_label = y_major_tick = y_minor_tick = y_org;
        }
      if (tick_axis != 0)
        {
          x_title = x_label = x_major_tick = x_minor_tick = x_org;
        }

      if (GR_OPTION_Z_LOG & lx.scale_options)
        {
          z0 = pow(lx.basez, gauss(blog(lx.basez, z_min)));

          i = ipred(z_min / z0);
          zi = z0 + i * z0;
          decade = igauss(blog(lx.basez, z_min / z_org));

          /* draw Z-axis */

          start_pline3d(x_org, y_org, z_min);

          while (zi <= z_max)
            {
              pline3d(x_org, y_org, zi);

              xi = x_minor_tick;
              yi = y_minor_tick;
              if (i == 0)
                {
                  if (major_z > 0 && zi != z_org)
                    if (decade % major_z == 0)
                      {
                        xi = x_major_tick;
                        yi = y_major_tick;
                        if (z_tick > 1 && scientific_format == SCIENTIFIC_FORMAT_OPTION_MATHTEX)
                          {
                            exponent = iround(blog(lx.basez, zi));
                            snprintf(string, 256, "%s^{%d}", lx.basez_s, exponent);
                            text3d(x_label, y_label, zi, replace_minus_sign(string), modern_projection_type ? axis : 0);
                          }
                        else
                          text3d(x_label, y_label, zi, gr_ftoa(string, zi, NULL), modern_projection_type ? axis : 0);
                      }
                }

              if (i == 0 || abs(major_z) == 1)
                {
                  pline3d(xi, yi, zi);
                  pline3d(x_org, y_org, zi);
                }

              if (i == 9 || lx.basez < 10)
                {
                  z0 = z0 * lx.basez;
                  i = 0;
                  decade++;
                }
              else
                i++;

              zi = z0 + i * z0;
            }

          pline3d(x_org, y_org, z_max);

          end_pline3d();
        }
      else
        {
          check_tick_marks(z_min, z_max, z_tick, 'Z');

          i = isucc(z_min / z_tick);
          zi = i * z_tick;

          gr_getformat(&format_reference, z_org, zi, z_max, z_tick, major_z);

          /* draw Z-axis */

          start_pline3d(x_org, y_org, z_min);


          while (zi <= z_max)
            {
              pline3d(x_org, y_org, zi);

              if (major_z == 0 || i % major_z == 0)
                {
                  xi = x_major_tick;
                  yi = y_major_tick;
                  if ((zi != z_org) && (major_z > 0))
                    text3d(x_label, y_label, zi, gr_ftoa(string, zi, &format_reference),
                           modern_projection_type ? axis : 0);
                }
              else
                {
                  xi = x_minor_tick;
                  yi = y_minor_tick;
                }

              pline3d(xi, yi, zi);
              pline3d(x_org, y_org, zi);

              i++;
              zi = i * z_tick;
            }

          if (zi > z_max) pline3d(x_org, y_org, z_max);

          end_pline3d();
        }

      if (titles3d[2] != NULL)
        {
          gks_inq_text_upvec(&errind, &xi, &yi);
          gks_set_text_align(GKS_K_TEXT_HALIGN_CENTER, GKS_K_TEXT_VALIGN_TOP);
          gks_set_text_height(titles3d_text_height);
          if (tick_axis == 0 && x_lin(x_org) <= (x_lin(x_min) + x_lin(x_max)) / 2. ||
              tick_axis == 1 && y_lin(y_org) <= (y_lin(y_min) + y_lin(y_max)) / 2.)
            {
              gks_set_text_upvec(1, 0);
            }
          else
            {
              gks_set_text_upvec(-1, 0);
            }
          text3d(x_title, y_title, z_log(0.5 * (z_lin(z_min) + z_lin(z_max))), titles3d[2],
                 modern_projection_type ? axis : 0);
          gks_set_text_height(chh);
        }
    }

  if (y_tick != 0)
    {
      if (modern_projection_type)
        tick = tick_size / tx.x_axis_scale / text3d_get_height();
      else
        tick = tick_size * (x_max - x_min) / (vp[1] - vp[0]);

      x_minor_tick = x_log(x_lin(x_org) + tick);
      x_major_tick = x_log(x_lin(x_org) + 2. * tick);
      x_label = x_log(x_lin(x_org) + 3. * tick);
      x_title = x_log(x_lin(x_org) + 10. * tick);

      /* set text alignment */

      if (x_lin(x_org) <= (x_lin(x_min) + x_lin(x_max)) / 2.)
        {
          gks_set_text_align(GKS_K_TEXT_HALIGN_RIGHT, GKS_K_TEXT_VALIGN_HALF);
          if (tick > 0)
            {
              x_label = x_log(x_lin(x_org) - tick);
              x_title = x_log(x_lin(x_org) - 10. * tick);
            }
        }
      else
        {
          gks_set_text_align(GKS_K_TEXT_HALIGN_LEFT, GKS_K_TEXT_VALIGN_HALF);
          if (tick < 0)
            {
              x_label = x_log(x_lin(x_org) - tick);
              x_title = x_log(x_lin(x_org) - 10. * tick);
            }
        }

      if (!modern_projection_type)
        {
          rep = rep_table[which_rep][1];
          if (rep == 0) gks_set_text_align(GKS_K_TEXT_HALIGN_CENTER, GKS_K_TEXT_VALIGN_TOP);

          gks_set_text_upvec(a[axes_rep[rep][0]], c[axes_rep[rep][1]]);
          gks_set_text_slant(text_slant[axes_rep[rep][2]]);
          tick_axis = 0;
        }
      else
        {
          tick = tick_size / tx.z_axis_scale / text3d_get_height();

          z_minor_tick = z_log(z_lin(z_org) + tick);
          z_major_tick = z_log(z_lin(z_org) + 2. * tick);
          z_label = z_log(z_lin(z_org) + 3. * tick);
          z_title = z_log(z_lin(z_org) + 10. * tick);

          if (z_lin(z_org) <= (z_lin(z_min) + z_lin(z_max)) / 2.)
            {
              if (tick > 0)
                {
                  z_label = z_log(z_lin(z_org) - tick);
                  z_title = z_log(z_lin(z_org) - 10. * tick);
                }
            }
          else
            {
              if (tick < 0)
                {
                  z_label = z_log(z_lin(z_org) - tick);
                  z_title = z_log(z_lin(z_org) - 10. * tick);
                }
            }

          axes3d_get_params(1, &tick_axis, x_org, y_org, z_org, &axis);
        }

      if (tick_axis != 0)
        {
          x_title = x_label = x_major_tick = x_minor_tick = x_org;
        }
      if (tick_axis != 2)
        {
          z_title = z_label = z_major_tick = z_minor_tick = z_org;
        }

      if (GR_OPTION_Y_LOG & lx.scale_options)
        {
          y0 = pow(lx.basey, gauss(blog(lx.basey, y_min)));

          i = ipred(y_min / y0);
          yi = y0 + i * y0;
          decade = igauss(blog(lx.basey, y_min / y_org));

          /* draw Y-axis */

          start_pline3d(x_org, y_min, z_org);

          while (yi <= y_max)
            {
              pline3d(x_org, yi, z_org);

              xi = x_minor_tick;
              zi = z_minor_tick;
              if (i == 0)
                {
                  if (major_y > 0 && yi != y_org)
                    if (decade % major_y == 0)
                      {
                        xi = x_major_tick;
                        zi = z_major_tick;
                        if (y_tick > 1 && scientific_format == SCIENTIFIC_FORMAT_OPTION_MATHTEX)
                          {
                            exponent = iround(blog(lx.basey, yi));
                            snprintf(string, 256, "%s^{%d}", lx.basey_s, exponent);
                            text3d(x_label, yi, z_label, replace_minus_sign(string), modern_projection_type ? axis : 0);
                          }
                        else
                          text3d(x_label, yi, z_label, gr_ftoa(string, yi, NULL), modern_projection_type ? axis : 0);
                      }
                }

              if (i == 0 || abs(major_y) == 1)
                {
                  pline3d(xi, yi, zi);
                  pline3d(x_org, yi, z_org);
                }

              if (i == 9 || lx.basey < 10)
                {
                  y0 = y0 * lx.basey;
                  i = 0;
                  decade++;
                }
              else
                i++;

              yi = y0 + i * y0;
            }

          pline3d(x_org, y_max, z_org);

          end_pline3d();
        }
      else
        {
          check_tick_marks(y_min, y_max, y_tick, 'Y');

          i = isucc(y_min / y_tick);
          yi = i * y_tick;

          gr_getformat(&format_reference, y_org, yi, y_max, y_tick, major_y);

          /* draw Y-axis */

          start_pline3d(x_org, y_min, z_org);

          while (yi <= y_max)
            {
              pline3d(x_org, yi, z_org);

              if (major_y == 0 || i % major_y == 0)
                {
                  xi = x_major_tick;
                  zi = z_major_tick;
                  if ((yi != y_org) && (major_y > 0))
                    text3d(x_label, yi, z_label, gr_ftoa(string, yi, &format_reference),
                           modern_projection_type ? axis : 0);
                }
              else
                {
                  xi = x_minor_tick;
                  zi = z_minor_tick;
                }

              pline3d(xi, yi, zi);
              pline3d(x_org, yi, z_org);

              i++;
              yi = i * y_tick;
            }

          if (yi > y_max) pline3d(x_org, y_max, z_org);

          end_pline3d();
        }

      if (titles3d[1] != NULL)
        {
          gks_inq_text_upvec(&errind, &xi, &yi);
          gks_set_text_align(GKS_K_TEXT_HALIGN_CENTER, GKS_K_TEXT_VALIGN_TOP);
          gks_set_text_height(titles3d_text_height);
          if (tick_axis == 2 && z_lin(z_org) <= (z_lin(z_min) + z_lin(z_max)) / 2.)
            {
              gks_set_text_upvec(0, 1);
            }
          else if (tick_axis == 2)
            {
              gks_set_text_upvec(0, -1);
            }
          else if (tick_axis == 0 && x_lin(x_org) <= (x_lin(x_min) + x_lin(x_max)) / 2.)
            {
              gks_set_text_upvec(1, 0);
            }
          else
            {
              gks_set_text_upvec(-1, 0);
            }
          text3d(x_title, y_log(0.5 * (y_lin(y_min) + y_lin(y_max))), z_title, titles3d[1],
                 modern_projection_type ? axis : 0);
          gks_set_text_height(chh);
        }
    }

  if (x_tick != 0)
    {
      if (modern_projection_type)
        tick = tick_size / tx.y_axis_scale / text3d_get_height();
      else
        tick = tick_size * (y_max - y_min) / (vp[3] - vp[2]);

      y_minor_tick = y_log(y_lin(y_org) + tick);
      y_major_tick = y_log(y_lin(y_org) + 2. * tick);
      y_label = y_log(y_lin(y_org) + 3. * tick);
      y_title = y_log(y_lin(y_org) + 10. * tick);

      /* set text alignment */

      if (y_lin(y_org) <= (y_lin(y_min) + y_lin(y_max)) / 2.)
        {
          gks_set_text_align(GKS_K_TEXT_HALIGN_RIGHT, GKS_K_TEXT_VALIGN_HALF);
          if (tick > 0)
            {
              y_label = y_log(y_lin(y_org) - tick);
              y_title = y_log(y_lin(y_org) - 10. * tick);
            }
        }
      else
        {
          gks_set_text_align(GKS_K_TEXT_HALIGN_LEFT, GKS_K_TEXT_VALIGN_HALF);
          if (tick < 0)
            {
              y_label = y_log(y_lin(y_org) - tick);
              y_title = y_log(y_lin(y_org) - 10. * tick);
            }
        }

      if (!modern_projection_type)
        {
          rep = rep_table[which_rep][0];
          if (rep == 2) gks_set_text_align(GKS_K_TEXT_HALIGN_CENTER, GKS_K_TEXT_VALIGN_TOP);

          gks_set_text_upvec(a[axes_rep[rep][0]], c[axes_rep[rep][1]]);
          gks_set_text_slant(text_slant[axes_rep[rep][2]]);
          tick_axis = 1;
        }
      else
        {
          tick = tick_size / tx.z_axis_scale / text3d_get_height();

          z_minor_tick = z_log(z_lin(z_org) + tick);
          z_major_tick = z_log(z_lin(z_org) + 2. * tick);
          z_label = z_log(z_lin(z_org) + 3. * tick);
          z_title = z_log(z_lin(z_org) + 10. * tick);

          if (z_lin(z_org) <= (z_lin(z_min) + z_lin(z_max)) / 2.)
            {
              if (tick > 0)
                {
                  z_label = z_log(z_lin(z_org) - tick);
                  z_title = z_log(z_lin(z_org) - 10. * tick);
                }
            }
          else
            {
              if (tick < 0)
                {
                  z_label = z_log(z_lin(z_org) - tick);
                  z_title = z_log(z_lin(z_org) - 10. * tick);
                }
            }

          axes3d_get_params(0, &tick_axis, x_org, y_org, z_org, &axis);
        }

      if (tick_axis != 1)
        {
          y_title = y_label = y_major_tick = y_minor_tick = y_org;
        }
      if (tick_axis != 2)
        {
          z_title = z_label = z_major_tick = z_minor_tick = z_org;
        }

      if (GR_OPTION_X_LOG & lx.scale_options)
        {
          x0 = pow(lx.basex, gauss(blog(lx.basex, x_min)));

          i = ipred(x_min / x0);
          xi = x0 + i * x0;
          decade = igauss(blog(lx.basex, x_min / x_org));

          /* draw X-axis */

          start_pline3d(x_min, y_org, z_org);

          while (xi <= x_max)
            {
              pline3d(xi, y_org, z_org);

              yi = y_minor_tick;
              zi = z_minor_tick;
              if (i == 0)
                {
                  if (major_x > 0 && xi != x_org)
                    if (decade % major_x == 0)
                      {
                        yi = y_major_tick;
                        zi = z_major_tick;
                        if (x_tick > 1 && scientific_format == SCIENTIFIC_FORMAT_OPTION_MATHTEX)
                          {
                            exponent = iround(blog(lx.basex, xi));
                            snprintf(string, 256, "%s^{%d}", lx.basex_s, exponent);
                            text3d(xi, y_label, z_label, replace_minus_sign(string), modern_projection_type ? axis : 0);
                          }
                        else
                          text3d(xi, y_label, z_label, gr_ftoa(string, xi, NULL), modern_projection_type ? axis : 0);
                      }
                }

              if (i == 0 || abs(major_x) == 1)
                {
                  pline3d(xi, yi, zi);
                  pline3d(xi, y_org, z_org);
                }

              if (i == 9 || lx.basex < 10)
                {
                  x0 = x0 * lx.basex;
                  i = 0;
                  decade++;
                }
              else
                i++;

              xi = x0 + i * x0;
            }

          pline3d(x_max, y_org, z_org);

          end_pline3d();
        }
      else
        {
          check_tick_marks(x_min, x_max, x_tick, 'X');

          i = isucc(x_min / x_tick);
          xi = i * x_tick;

          gr_getformat(&format_reference, x_org, xi, x_max, x_tick, major_x);

          /* draw X-axis */

          start_pline3d(x_min, y_org, z_org);

          while (xi <= x_max)
            {
              pline3d(xi, y_org, z_org);

              if (major_x == 0 || i % major_x == 0)
                {
                  yi = y_major_tick;
                  zi = z_major_tick;
                  if ((xi != x_org) && (major_x > 0))
                    text3d(xi, y_label, z_label, gr_ftoa(string, xi, &format_reference),
                           modern_projection_type ? axis : 0);
                }
              else
                {
                  yi = y_minor_tick;
                  zi = z_minor_tick;
                }

              pline3d(xi, yi, zi);
              pline3d(xi, y_org, z_org);

              i++;
              xi = i * x_tick;
            }

          if (xi > x_max) pline3d(x_max, y_org, z_org);

          end_pline3d();
        }

      if (titles3d[0] != NULL)
        {
          gks_inq_text_upvec(&errind, &xi, &yi);
          gks_set_text_align(GKS_K_TEXT_HALIGN_CENTER, GKS_K_TEXT_VALIGN_TOP);
          gks_set_text_height(titles3d_text_height);
          if (tick_axis == 1 && y_lin(y_org) <= (y_lin(y_min) + y_lin(y_max)) / 2. ||
              tick_axis == 2 && z_lin(z_org) <= (z_lin(z_min) + z_lin(z_max)) / 2.)
            {
              gks_set_text_upvec(0, 1);
            }
          else
            {
              gks_set_text_upvec(0, -1);
            }
          text3d(x_log(0.5 * (x_lin(x_min) + x_lin(x_max))), y_title, z_title, titles3d[0],
                 modern_projection_type ? axis : 0);
          gks_set_text_height(chh);
        }
    }

  /* restore linetype, text alignment, text font, text slant,
     character-up vector and clipping indicator */

  gks_set_pline_linetype(ltype);
  gks_set_text_align(halign, valign);
  gks_set_text_fontprec(font, prec);
  gks_set_text_slant(slant);
  gks_set_text_upvec(chux, chuy);
  gks_set_clipping(clsw);

  if (flag_stream)
    gr_writestream("<axes3d xtick=\"%g\" ytick=\"%g\" ztick=\"%g\" "
                   "xorg=\"%g\" yorg=\"%g\" zorg=\"%g\" "
                   "majorx=\"%d\" majory=\"%d\" majorz=\"%d\" ticksize=\"%g\"/>\n",
                   x_tick, y_tick, z_tick, x_org, y_org, z_org, major_x, major_y, major_z, tick_size);
}

/*!
 * Display axis titles just outside of their respective axes.
 *
 * \param[in] x_title The text to be displayed on the X axis
 * \param[in] y_title The text to be displayed on the Y axis
 * \param[in] z_title The text to be displayed on the Z axis
 */
void gr_titles3d(char *x_title, char *y_title, char *z_title)
{
  int errind, tnr;
  double clrt[4], wn[4], vp[4];
  int modern_projection_type;

  int halign, valign, clsw, font, prec;
  double chux, chuy;

  double x_min, x_max, y_min, y_max, z_min, z_max;
  double x_rel, y_rel, z_rel, x, y, z;

  double r, t, alpha, beta;
  double a[2], c[2];

  double slant, text_slant[4];
  int *anglep, which_rep, rep;

  double x_2d, y_2d, x_2d_max, y_2d_max;
  double x_angle, y_angle;
  double x_mid_x, x_mid_y, y_mid_x, y_mid_y;
  double a1, a2, c1, c2, c3, aa, cc;
  double xr, yr, zr;

  int flip_x, flip_y, flip_z;

  check_autoinit;

  setscale(lx.scale_options);

  /* inquire current normalization transformation */

  gks_inq_current_xformno(&errind, &tnr);
  gks_inq_xform(tnr, &errind, wn, vp);

  modern_projection_type =
      gpx.projection_type == GR_PROJECTION_PERSPECTIVE || gpx.projection_type == GR_PROJECTION_ORTHOGRAPHIC;

  if (modern_projection_type)
    {
      lx.xmin = ix.xmin;
      lx.xmax = ix.xmax;
      lx.ymin = ix.ymin;
      lx.ymax = ix.ymax;
      lx.zmin = ix.zmin;
      lx.zmax = ix.zmax;

      x_min = ix.xmin;
      x_max = ix.xmax;
      y_min = ix.ymin;
      y_max = ix.ymax;
      z_min = ix.zmin;
      z_max = ix.zmax;

      if (*x_title)
        {
          gks_set_text_align(GKS_K_TEXT_HALIGN_CENTER, GKS_K_TEXT_VALIGN_TOP);
          x = x_log(0.5 * (x_lin(x_min) + x_lin(x_max)));
          y = y_log(y_lin(y_min) - 0.2 * (y_lin(y_max) - y_lin(y_min)));
          z = z_min;
          text3d(x, y, z, x_title, 2);
        }

      if (*y_title)
        {
          gks_set_text_align(GKS_K_TEXT_HALIGN_CENTER, GKS_K_TEXT_VALIGN_TOP);
          x = x_log(x_lin(x_max) + 0.2 * (x_lin(x_max) - x_lin(x_min)));
          y = y_log(0.5 * (y_lin(y_min) + y_lin(y_max)));
          z = z_min;
          text3d(x, y, z, y_title, 1);
        }

      if (*z_title)
        {
          gks_set_text_align(GKS_K_TEXT_HALIGN_LEFT, GKS_K_TEXT_VALIGN_BOTTOM);
          x = x_min;
          y = y_min;
          z = z_max;
          text3d(x, y, z, z_title, 3);
        }
    }
  else if (wx.phi != 0 || wx.delta != 90)
    {
      x_min = wn[0];
      x_max = wn[1];
      y_min = wn[2];
      y_max = wn[3];
      z_min = wx.zmin;
      z_max = wx.zmax;

      r = (x_max - x_min) / (y_max - y_min) * (vp[3] - vp[2]) / (vp[1] - vp[0]);

      alpha = atan_2(r * wx.c1, wx.a1);
      a[0] = -sin(alpha);
      c[0] = cos(alpha);
      alpha = deg(alpha);

      beta = atan_2(r * wx.c2, wx.a2);
      a[1] = -sin(beta);
      c[1] = cos(beta);
      beta = deg(beta);

      text_slant[0] = alpha;
      text_slant[1] = beta;
      text_slant[2] = -(90.0 + alpha - beta);
      text_slant[3] = 90.0 + alpha - beta;

      /* save text alignment, text font, text slant,
         character-up vector and clipping indicator */

      gks_inq_text_align(&errind, &halign, &valign);
      gks_inq_text_fontprec(&errind, &font, &prec);
      gks_inq_text_slant(&errind, &slant);
      gks_inq_text_upvec(&errind, &chux, &chuy);
      gks_inq_clip(&errind, &clsw, clrt);

      gks_set_pline_linetype(GKS_K_LINETYPE_SOLID);
      gks_set_text_fontprec(font, GKS_K_TEXT_PRECISION_STROKE);
      gks_set_clipping(GKS_K_NOCLIP);

      which_rep = 0;
      anglep = angle;
      while (wx.delta > *anglep++) which_rep++;
      anglep = angle;
      while (wx.phi > *anglep++) which_rep += 4;

      r = arc(wx.phi);
      a1 = cos(r);
      a2 = sin(r);
      aa = a1 + a2;
      a1 = a1 / aa;
      a2 = a2 / aa;

      t = arc(wx.delta);
      c1 = (pow(cos(r), 2.) - 1) * tan(t / 2.);
      c2 = -(pow(sin(r), 2.) - 1) * tan(t / 2.);
      c3 = cos(t);
      cc = (c2 + c3 - c1);
      c1 = c1 / cc;
      c2 = c2 / cc;
      c3 = c3 / cc;

      a1 = fabs(a1) * (vp[1] - vp[0]);
      a2 = fabs(a2) * (vp[1] - vp[0]);
      c1 = fabs(c1) * (vp[3] - vp[2]);
      c2 = fabs(c2) * (vp[3] - vp[2]);
      c3 = fabs(c3) * (vp[3] - vp[2]);

      x_mid_x = vp[0] + a1 / 2.;
      x_mid_y = vp[2] + c1 / 2.;
      y_mid_x = 1 - vp[1] + a2 / 2.;
      y_mid_y = vp[2] + c2 / 2.;

      x_2d_max = sqrt(y_mid_x * y_mid_x + y_mid_y * y_mid_y);
      y_2d_max = sqrt(x_mid_x * x_mid_x + x_mid_y * x_mid_y);

      x_angle = atan_2(a1, c1);
      x_2d = y_mid_y / cos(x_angle);

      if (x_2d > x_2d_max)
        {
          x_angle = M_PI / 2. - x_angle;
          x_2d = y_mid_x / cos(x_angle);
        }

      xr = x_2d / (2 * sqrt(pow(c1, 2.) + pow(a1, 2.)));

      y_angle = atan_2(c2, a2);
      y_2d = x_mid_x / cos(y_angle);

      if (y_2d > y_2d_max)
        {
          y_angle = M_PI / 2. - y_angle;
          y_2d = x_mid_y / cos(y_angle);
        }

      if (wx.phi + wx.delta != 0)
        yr = y_2d / (2 * sqrt(pow(c2, 2.) + pow(a2, 2.)));
      else
        yr = 0;

      x_rel = xr * (x_lin(x_max) - x_lin(x_min));
      y_rel = yr * (y_lin(y_max) - y_lin(y_min));

      flip_x = GR_OPTION_FLIP_X & lx.scale_options;
      flip_y = GR_OPTION_FLIP_Y & lx.scale_options;
      flip_z = GR_OPTION_FLIP_Z & lx.scale_options;

      if (*x_title)
        {
          rep = rep_table[which_rep][1];

          x = x_log(0.5 * (x_lin(x_min) + x_lin(x_max)));
          if (rep == 0)
            {
              gks_set_text_align(GKS_K_TEXT_HALIGN_CENTER, GKS_K_TEXT_VALIGN_TOP);

              rep = rep_table[which_rep][0];

              if (flip_y)
                y = y_max;
              else
                y = y_min;

              zr = x_mid_y / (2 * c3);
              z_rel = zr * (z_lin(z_max) - z_lin(z_min));

              if (flip_z)
                z = z_log(z_lin(z_max) + z_rel);
              else
                z = z_log(z_lin(z_min) - z_rel);
            }
          else
            {
              if (flip_y)
                y = y_log(y_lin(y_max) + y_rel);
              else
                y = y_log(y_lin(y_min) - y_rel);

              if (flip_z)
                z = z_max;
              else
                z = z_min;

              gks_set_text_align(GKS_K_TEXT_HALIGN_CENTER, GKS_K_TEXT_VALIGN_HALF);
            }

          gks_set_text_upvec(a[axes_rep[rep][0]], c[axes_rep[rep][1]]);
          gks_set_text_slant(text_slant[axes_rep[rep][2]]);

          text3d(x, y, z, x_title, 0);
        }

      if (*y_title)
        {
          rep = rep_table[which_rep][0];

          y = y_log(0.5 * (y_lin(y_min) + y_lin(y_max)));
          if (rep == 2)
            {
              gks_set_text_align(GKS_K_TEXT_HALIGN_CENTER, GKS_K_TEXT_VALIGN_TOP);

              rep = rep_table[which_rep][1];

              if (flip_x)
                x = x_min;
              else
                x = x_max;

              zr = y_mid_y / (2 * c3);
              z_rel = zr * (z_lin(z_max) - z_lin(z_min));

              if (flip_z)
                z = z_log(z_lin(z_max) + z_rel);
              else
                z = z_log(z_lin(z_min) - z_rel);
            }
          else
            {
              if (flip_x)
                x = x_log(x_lin(x_min) - x_rel);
              else
                x = x_log(x_lin(x_max) + x_rel);

              if (flip_z)
                z = z_max;
              else
                z = z_min;

              gks_set_text_align(GKS_K_TEXT_HALIGN_CENTER, GKS_K_TEXT_VALIGN_HALF);
            }

          gks_set_text_upvec(a[axes_rep[rep][0]], c[axes_rep[rep][1]]);
          gks_set_text_slant(text_slant[axes_rep[rep][2]]);

          text3d(x, y, z, y_title, 0);
        }

      if (*z_title)
        {
          rep = rep_table[which_rep][2];

          gks_set_text_upvec(a[axes_rep[rep][0]], c[axes_rep[rep][1]]);
          gks_set_text_slant(text_slant[axes_rep[rep][2]]);

          if (flip_x)
            x = x_max;
          else
            x = x_min;

          if (flip_y)
            y = y_max;
          else
            y = y_min;

          zr = (1 - (c1 + c3 + vp[2])) / (2 * c3);
          z_rel = zr * (z_lin(z_max) - z_lin(z_min));

          if (flip_z)
            z = z_log(z_lin(z_min) - 0.5 * z_rel);
          else
            z = z_log(z_lin(z_max) + 0.5 * z_rel);

          gks_set_text_align(GKS_K_TEXT_HALIGN_CENTER, GKS_K_TEXT_VALIGN_BASE);

          text3d(x, y, z, z_title, 0);
        }

      /* restore text alignment, text font, text slant,
         character-up vector and clipping indicator */

      gks_set_text_align(halign, valign);
      gks_set_text_fontprec(font, prec);
      gks_set_text_slant(slant);
      gks_set_text_upvec(chux, chuy);
      gks_set_clipping(clsw);
    }
  else
    {
      /* save text alignment and character-up vector */

      gks_inq_text_align(&errind, &halign, &valign);
      gks_inq_text_upvec(&errind, &chux, &chuy);

      if (*x_title)
        {
          gks_set_text_align(GKS_K_TEXT_HALIGN_CENTER, GKS_K_TEXT_VALIGN_BASE);
          gks_set_text_upvec(0.0, 1.0);

          x = 0.5 * (vp[0] + vp[1]);
          y = vp[2] * 0.2 * (vp[3] - vp[2]);
          gr_ndctowc(&x, &y);

          text2d(x, y, x_title);
        }

      if (*y_title)
        {
          gks_set_text_align(GKS_K_TEXT_HALIGN_CENTER, GKS_K_TEXT_VALIGN_TOP);
          gks_set_text_upvec(-1.0, 0.0);

          x = vp[0] * 0.1 * (vp[1] - vp[0]);
          y = 0.5 * (vp[2] + vp[3]);
          gr_ndctowc(&x, &y);

          text2d(x, y, y_title);
        }

      if (*z_title)
        {
          gks_set_text_align(GKS_K_TEXT_HALIGN_CENTER, GKS_K_TEXT_VALIGN_BASE);
          gks_set_text_upvec(0.0, 1.0);

          x = 0.5 * (vp[0] + vp[1]);
          y = vp[3] + 0.05 * (vp[3] - vp[2]);
          gr_ndctowc(&x, &y);

          text2d(x, y, z_title);
        }

      /* restore text alignment and character-up vector */

      gks_set_text_align(halign, valign);
      gks_set_text_upvec(chux, chuy);
    }

  if (flag_stream) gr_writestream("<titles3d xtitle=\"%s\" ytitle=\"%s\" ztitle=\"%s\"/>\n", x_title, y_title, z_title);
}

/*!
 * Set axis titles to display when gr_axes3d is called, similar to gr_titles3d.
 *
 * \param[in] x_title The text to be displayed on the X axis
 * \param[in] y_title The text to be displayed on the Y axis
 * \param[in] z_title The text to be displayed on the Z axis
 */
void gr_settitles3d(char *x_title, char *y_title, char *z_title)
{
  int errind;

  check_autoinit;

  if (titles3d[0] != NULL)
    {
      free(titles3d[0]);
      titles3d[0] = NULL;
    }
  if (titles3d[1] != NULL)
    {
      free(titles3d[1]);
      titles3d[1] = NULL;
    }
  if (titles3d[2] != NULL)
    {
      free(titles3d[2]);
      titles3d[2] = NULL;
    }

  if (x_title != NULL)
    {
      if (*x_title) titles3d[0] = strdup(x_title);
    }
  if (y_title != NULL)
    {
      if (*y_title) titles3d[1] = strdup(y_title);
    }
  if (z_title != NULL)
    {
      if (*z_title) titles3d[2] = strdup(z_title);
    }

  gks_inq_text_height(&errind, &titles3d_text_height);

  if (flag_stream)
    gr_writestream("<settitles3d xtitle=\"%s\" ytitle=\"%s\" ztitle=\"%s\"/>\n", x_title, y_title, z_title);
}

static void init_hlr(void)
{
  int sign, i, j, x1, x2;
  double *hide, a, b, m = 0;
  double x[3], y[3], z[3], yj;
  double eps;

  eps = (lx.ymax - lx.ymin) * 1E-5;

  for (i = 0; i <= RESOLUTION_X; i++)
    {
      hlr.ymin[i] = -FLT_MAX;
      hlr.ymax[i] = FLT_MAX;
    }

  for (sign = -1; sign <= 1; sign += 2)
    {
      if (sign == 1)
        {
          hide = hlr.ymin;
          x[0] = hlr.x0;
          y[0] = hlr.y0;
          z[0] = hlr.z0;
          x[1] = hlr.x1;
          y[1] = hlr.y0;
          z[1] = hlr.z0;
          x[2] = hlr.x1;
          y[2] = hlr.y1;
          z[2] = hlr.z0;
        }
      else
        {
          hide = hlr.ymax;
          x[0] = hlr.x0;
          y[0] = hlr.y0;
          z[0] = hlr.z1;
          x[1] = hlr.x0;
          y[1] = hlr.y1;
          z[1] = hlr.z1;
          x[2] = hlr.x1;
          y[2] = hlr.y1;
          z[2] = hlr.z1;
        }

      for (i = 0; i < 3; i++) apply_world_xform(x + i, y + i, z + i);

      if (hlr.xmax != hlr.xmin)
        {
          a = RESOLUTION_X / (hlr.xmax - hlr.xmin);
          b = -(hlr.xmin * a);
        }
      else
        {
          a = 1;
          b = 0;
        }

      x1 = nint(a * x[0] + b);
      if (x1 < 0) x1 = 0;
      x2 = x1;

      for (i = 1; i < 3; i++)
        {
          x1 = x2;
          x2 = nint(a * x[i] + b);

          if (x1 <= x2)
            {
              if (x1 != x2) m = (y[i] - y[i - 1]) / (x2 - x1);

              x1 = max(x1, 0);
              x2 = min(x2, RESOLUTION_X);

              for (j = x1; j <= x2; j++)
                {
                  if (x1 != x2)
                    yj = y[i - 1] + m * (j - x1);
                  else
                    yj = y[i];

                  hide[j] = yj - sign * eps;
                }
            }
        }
    }
}

static void pline_hlr(int n, double *x, double *y, double *z)
{
  int i, j, x1, x2;
  int visible, draw;
  double *hide, a, b, c, m = 0;

  int saved_scale_options;
  double xj, yj;

  int errind, clsw;
  double clrt[4];

  gks_inq_clip(&errind, &clsw, clrt);

  if (hlr.buf == NULL)
    {
      hlr.buf = (double *)xmalloc(sizeof(double) * (RESOLUTION_X + 1) * 2);
      hlr.ymin = hlr.buf;
      hlr.ymax = hlr.buf + RESOLUTION_X + 1;
    }

  if (hlr.sign == 1)
    hide = hlr.ymin;
  else
    hide = hlr.ymax;

  for (i = 0; i < n; i++) apply_world_xform(x + i, y + i, z + i);

  draw = !hlr.initialize || hlr.sign > 0;
  visible = 0;

  saved_scale_options = lx.scale_options;
  lx.scale_options = 0;

  if (hlr.xmax != hlr.xmin)
    {
      a = RESOLUTION_X / (hlr.xmax - hlr.xmin);
      b = -(hlr.xmin * a);
    }
  else
    {
      a = 1;
      b = 0;
    }
  c = 1.0 / a;

  x1 = nint(a * x[0] + b);
  if (x1 < 0) x1 = 0;
  x2 = x1;

  if (hlr.initialize)
    {
      init_hlr();

      if (hlr.ymin[x1] <= y[0] && y[0] <= hlr.ymax[x1])
        {
          hide[x1] = y[0];

          if (draw) start_pline(x[0], y[0]);

          visible = 1;
        }
    }

  for (i = 1; i < n; i++)
    {
      x1 = x2;
      x2 = nint(a * x[i] + b);

      if (x1 < x2)
        {
          if (x1 != x2) m = (y[i] - y[i - 1]) / (x2 - x1);

          x1 = max(x1, 0);
          x2 = min(x2, RESOLUTION_X);

          for (j = x1; j <= x2; j++)
            {
              if (x1 != x2)
                yj = y[i - 1] + m * (j - x1);
              else
                yj = y[i];

              if (hlr.ymin[j] <= yj && yj <= hlr.ymax[j])
                {
                  if (!visible)
                    {
                      if (draw)
                        {
                          xj = c * j + hlr.xmin;

                          start_pline(xj, yj);
                        }

                      visible = 1;
                    }
                }
              else
                {
                  if (visible)
                    {
                      if (draw)
                        {
                          xj = c * j + hlr.xmin;

                          pline(xj, yj);
                          end_pline();
                        }

                      visible = 0;
                    }
                }

              if ((yj - hide[j]) * hlr.sign > 0) hide[j] = yj;
            }

          if (visible && draw) pline(x[i], y[i]);
        }

      else if (x1 == x2)
        {
          if (draw)
            {
              j = x1;
              xj = c * j + hlr.xmin;
              yj = y[i];

              if ((yj - hide[j]) * hlr.sign > 0)
                {
                  if (clsw == GKS_K_CLIP && (hide[j] == hlr.ymin[j] || hide[j] == hlr.ymax[j]))
                    {
                      if (hlr.ymin[j] <= yj && yj <= hlr.ymax[j]) start_pline(xj, yj);
                    }
                  else
                    {
                      start_pline(xj, hide[j]);
                      pline(xj, yj);
                    }
                  end_pline();

                  visible = 1;
                  hide[j] = yj;
                }
              else
                visible = 0;
            }
        }
    }

  if (visible && draw) end_pline();

  lx.scale_options = saved_scale_options;
}

static void glint(int dinp, int *inp, int doutp, int *outp)
{
  int i, j, k, n;
  double ratio, delta;

  n = (doutp + 1) / dinp;
  ratio = 1.0 / n;

  j = (n + 1) / 2;
  for (k = 0; k < j; k++) outp[k] = inp[0];

  for (i = 0; i < dinp - 1; i++)
    {
      delta = ratio * (inp[i + 1] - inp[i]);
      for (k = 1; k <= n; k++) outp[j++] = inp[i] + (int)(k * delta + 0.5);
    }

  for (k = j; k < doutp; k++) outp[k] = inp[dinp - 1];
}

static void pixel(double xmin, double xmax, double ymin, double ymax, int dx, int dy, int *colia, int w, int h,
                  int *pixmap, int dwk, int *wk1, int *wk2)
{
  int i, j, ix, nx;
  int sx = 1, sy = 1;
  GR_UNUSED(dwk);

  if ((w + 1) % dx != 0 || (h + 1) % dy != 0)
    {
      fprintf(stderr, "improper input parameter values\n");
      return;
    }

  ix = 0;
  nx = (w + 1) / dx;

  for (i = 0; i < dx; i++)
    {
      for (j = 0; j < dy; j++) wk1[j] = colia[i + j * dx];

      glint(dy, wk1, h, wk2);
      for (j = 0; j < h; j++) pixmap[ix + j * w] = wk2[j];

      ix += nx;
    }

  for (j = 0; j < h; j++)
    {
      ix = 0;
      for (i = 0; i < dx; i++)
        {
          wk1[i] = pixmap[ix + j * w];
          ix += nx;
        }

      glint(dx, wk1, w, wk2);
      for (i = 0; i < w; i++) pixmap[i + j * w] = wk2[i];
    }

  gks_cellarray(xmin, ymin, xmax, ymax, w, h, sx, sy, w, h, pixmap);
}

static void get_intensity(double *fx, double *fy, double *fz, double *light_source, double *intensity)
{
  int k;
  double max_x, max_y, max_z, min_x, min_y, min_z, norm_1, norm_2;
  double center[4], normal[4], negated[4], oddnormal[4], negated_norm[4];

  min_x = max_x = fx[0];
  min_y = max_y = fy[0];
  min_z = max_z = fz[0];

  for (k = 1; k < 4; k++)
    {
      if (fx[k] > max_x)
        max_x = fx[k];
      else if (fx[k] < min_x)
        min_x = fx[k];
      if (fy[k] > max_y)
        max_y = fy[k];
      else if (fy[k] < min_y)
        min_y = fy[k];
      if (fz[k] > max_z)
        max_z = fz[k];
      else if (fz[k] < min_z)
        min_z = fz[k];
    }

  center[0] = (max_x + min_x) / 2;
  center[1] = (max_y + min_y) / 2;
  center[2] = (max_z + min_z) / 2;

  for (k = 0; k < 3; k++) negated[k] = light_source[k] - center[k];

  norm_1 = (double)sqrt(negated[0] * negated[0] + negated[1] * negated[1] + negated[2] * negated[2]);

  for (k = 0; k < 3; k++) negated_norm[k] = negated[k] / norm_1;

  normal[0] = ((fy[1] - fy[0]) * (fz[2] - fz[0]) - (fz[1] - fz[0]) * (fy[2] - fy[0])) +
              ((fy[2] - fy[1]) * (fz[3] - fz[1]) - (fz[2] - fz[1]) * (fy[3] - fy[1]));
  normal[1] = ((fz[1] - fz[0]) * (fx[2] - fx[0]) - (fx[1] - fx[0]) * (fz[2] - fz[0])) +
              ((fz[2] - fz[1]) * (fx[3] - fx[1]) - (fx[2] - fx[1]) * (fz[3] - fz[1]));
  normal[2] = ((fx[1] - fx[0]) * (fy[2] - fy[0]) - (fy[1] - fy[0]) * (fx[2] - fx[0])) +
              ((fx[2] - fx[1]) * (fy[3] - fy[1]) - (fy[2] - fy[1]) * (fx[3] - fx[1]));
  normal[3] = 1;

  norm_2 = (double)sqrt(normal[0] * normal[0] + normal[1] * normal[1] + normal[2] * normal[2]);

  for (k = 0; k < 3; k++) oddnormal[k] = normal[k] / norm_2;

  *intensity =
      (oddnormal[0] * negated_norm[0] + oddnormal[1] * negated_norm[1] + oddnormal[2] * negated_norm[2]) * 0.8 + 0.2;
}

/*!
 * Draw a three-dimensional surface plot for the given data points.
 *
 * \param[in] nx The number of points along the X axis
 * \param[in] ny The number of points along the Y axis
 * \param[in] px A pointer to the X coordinates
 * \param[in] py A pointer to the Y coordinates
 * \param[in] pz A pointer to the Z coordinates
 * \param[in] option Surface display option (see table)
 *
 * x and y define a grid. z is a singly dimensioned array containing at least
 * nx * ny data points. z describes the surface height at each point on the
 * grid. Data is ordered as shown in the following table:
 *
 * \verbatim embed:rst:leading-asterisk
 *
 * +------------------+--+--------------------------------------------------------------+
 * |LINES             | 0|Use X Y polylines to denote the surface                       |
 * +------------------+--+--------------------------------------------------------------+
 * |MESH              | 1|Use a wire grid to denote the surface                         |
 * +------------------+--+--------------------------------------------------------------+
 * |FILLED_MESH       | 2|Applies an opaque grid to the surface                         |
 * +------------------+--+--------------------------------------------------------------+
 * |Z_SHADED_MESH     | 3|Applies Z-value shading to the surface                        |
 * +------------------+--+--------------------------------------------------------------+
 * |COLORED_MESH      | 4|Applies a colored grid to the surface                         |
 * +------------------+--+--------------------------------------------------------------+
 * |CELL_ARRAY        | 5|Applies a grid of individually-colored cells to the surface   |
 * +------------------+--+--------------------------------------------------------------+
 * |SHADED_MESH       | 6|Applies light source shading to the 3-D surface               |
 * +------------------+--+--------------------------------------------------------------+
 *
 * To see option 2 correctly change linecolorind or fillcolorind. Both default values are black.
 * \endverbatim
 */
void gr_surface(int nx, int ny, double *px, double *py, double *pz, int option)
{
  int errind, ltype, coli, int_style, tnr, clsw;
  int modern_projection_type;

  int i, ii, j, jj, k;
  int color;
  double color_min, color_max;

  double *xn, *yn, *zn, *x, *y, *z;
  double *clipx, *clipy, *clipz;
  double facex[4], facey[4], facez[4], clrt[4], vp[4], wn[4], intensity = 0, meanz;
  double a, b, c, d, e, f;

  double ymin, ymax, zmin, zmax;
  int visible;

  int flip_x, flip_y, flip_z;
  int np;

  int *colia, w, h, *ca, dwk, *wk1, *wk2;

  static double light_source[3] = {0.5, -1, 2};

  if ((nx <= 0) || (ny <= 0))
    {
      fprintf(stderr, "invalid number of points\n");
      return;
    }

  /* be sure that points ordinates are sorted in ascending order */

  for (i = 1; i < nx; i++)
    if (px[i - 1] >= px[i])
      {
        fprintf(stderr, "points not sorted in ascending order\n");
        return;
      }

  for (j = 1; j < ny; j++)
    if (py[j - 1] >= py[j])
      {
        fprintf(stderr, "points not sorted in ascending order\n");
        return;
      }

  check_autoinit;

  setscale(lx.scale_options);

  /* inquire current normalization transformation and clipping indicator */

  gks_inq_current_xformno(&errind, &tnr);
  gks_inq_xform(tnr, &errind, wn, vp);
  gks_inq_clip(&errind, &clsw, clrt);

  modern_projection_type =
      gpx.projection_type == GR_PROJECTION_PERSPECTIVE || gpx.projection_type == GR_PROJECTION_ORTHOGRAPHIC;

  if (modern_projection_type)
    {
      lx.xmin = ix.xmin;
      lx.xmax = ix.xmax;
      lx.ymin = ix.ymin;
      lx.ymax = ix.ymax;
      lx.zmin = ix.zmin;
      lx.zmax = ix.zmax;
    }

#define Z(x, y) pz[(x) + nx * (y)]

  a = 1.0 / (lx.xmax - lx.xmin);
  b = -(lx.xmin * a);
  c = 1.0 / (lx.ymax - lx.ymin);
  d = -(lx.ymin * c);
  e = 1.0 / (wx.zmax - wx.zmin);
  f = -(wx.zmin * e);

  /* save linetype, fill area interior style and color
     index */

  gks_inq_pline_linetype(&errind, &ltype);
  gks_inq_fill_int_style(&errind, &int_style);
  gks_inq_fill_color_index(&errind, &coli);

  k = sizeof(double) * (nx + ny) * 3;
  xn = (double *)xmalloc(k);
  yn = (double *)xmalloc(k);
  zn = (double *)xmalloc(k);
  x = (double *)xmalloc(nx * sizeof(double));
  y = (double *)xmalloc(ny * sizeof(double));
  z = (double *)xmalloc(nx * ny * sizeof(double));
  if (clsw == GKS_K_CLIP)
    {
      clipx = (double *)xmalloc(k);
      clipy = (double *)xmalloc(k);
      clipz = (double *)xmalloc(k);
    }

  flip_x = GR_OPTION_FLIP_X & lx.scale_options;
  if ((gpx.projection_type == GR_PROJECTION_PERSPECTIVE || gpx.projection_type == GR_PROJECTION_ORTHOGRAPHIC) &&
      tx.camera_pos_x < tx.focus_point_x)
    {
      flip_x = 1;
    }

  for (i = 0; i < nx; i++) x[i] = x_lin(px[flip_x ? nx - 1 - i : i]);

  flip_y = GR_OPTION_FLIP_Y & lx.scale_options;
  if ((gpx.projection_type == GR_PROJECTION_PERSPECTIVE || gpx.projection_type == GR_PROJECTION_ORTHOGRAPHIC) &&
      tx.camera_pos_y > tx.focus_point_y)
    {
      flip_y = 1;
    }
  for (j = 0; j < ny; j++) y[j] = y_lin(py[flip_y ? ny - 1 - j : j]);

  k = 0;
  for (j = 0; j < ny; j++)
    {
      jj = flip_y ? ny - j - 1 : j;
      for (i = 0; i < nx; i++)
        {
          ii = flip_x ? nx - i - 1 : i;
          z[k++] = z_lin(Z(ii, jj));
        }
    }

#undef Z

  hlr.x0 = x[0];
  hlr.x1 = x[nx - 1];
  hlr.y0 = y[0];
  hlr.y1 = y[ny - 1];
  hlr.z0 = wx.zmin;
  hlr.z1 = wx.zmax;

  hlr.xmin = x[0];
  hlr.xmax = x[nx - 1];
  ymin = y[0];
  ymax = y[ny - 1];
  zmin = wx.zmin;
  zmax = wx.zmax;

  color_min = zmin;
  color_max = zmax;

  apply_world_xform(&hlr.xmin, &ymin, &zmin);
  apply_world_xform(&hlr.xmax, &ymax, &zmax);

  flip_z = GR_OPTION_FLIP_Z & lx.scale_options;
  gks_set_pline_linetype(flip_z ? GKS_K_LINETYPE_DOTTED : GKS_K_LINETYPE_SOLID);
  if ((gpx.projection_type == GR_PROJECTION_PERSPECTIVE || gpx.projection_type == GR_PROJECTION_ORTHOGRAPHIC) &&
      tx.camera_pos_z < tx.focus_point_z)
    {
      flip_z = 1;
    }

#define Z(x, y) z[(x) + nx * (y)]

  hlr.sign = -1;

  if (clsw == GKS_K_CLIP)
    {
      if (modern_projection_type)
        {
          cxl = ix.xmin;
          cxr = ix.xmax;
          cyf = ix.ymin;
          cyb = ix.ymax;
          czb = ix.zmin;
          czt = ix.zmax;
        }
      else
        {
          cxl = hlr.x0;
          cxr = hlr.x1;
          cyf = hlr.y0;
          cyb = hlr.y1;
          czb = hlr.z0;
          czt = hlr.z1;
        }
      for (i = 0; i < nx * ny; i++)
        {
          color_min = min(color_min, z[i]);
          color_max = max(color_max, z[i]);
        }
    }

  do
    {
      hlr.sign = -hlr.sign;

      switch (option)
        {

        case GR_OPTION_LINES:
          {
            j = 0;
            hlr.initialize = 1;

            while (j < ny)
              {
                k = 0;

                if (j > 0)
                  {
                    xn[k] = x[0];
                    yn[k] = y[j - 1];
                    zn[k] = Z(0, j - 1);
                    k++;
                  }

                for (i = 0; i < nx; i++)
                  {
                    xn[k] = x[i];
                    yn[k] = y[j];
                    zn[k] = Z(i, j);
                    k++;
                  }

                if (j == 0)

                  for (i = 1; i < ny; i++)
                    {
                      xn[k] = x[nx - 1];
                      yn[k] = y[i];
                      zn[k] = Z(nx - 1, i);
                      k++;
                    }

                if (clsw == GKS_K_CLIP)
                  {
                    int cnt = 0;

                    for (i = 0; i < k - 1; i++)
                      {
                        clip3d(&xn[i], &xn[i + 1], &yn[i], &yn[i + 1], &zn[i], &zn[i + 1], &visible);
                        if (visible == 1)
                          {
                            clipx[cnt] = xn[i];
                            clipy[cnt] = yn[i];
                            clipz[cnt] = zn[i];
                            cnt += 1;
                            if (i == k - 2)
                              {
                                clipx[cnt] = xn[i + 1];
                                clipy[cnt] = yn[i + 1];
                                clipz[cnt] = zn[i + 1];
                                cnt += 1;
                              }
                          }
                      }
                    pline_hlr(cnt, clipx, clipy, clipz);
                  }
                else
                  {
                    pline_hlr(k, xn, yn, zn);
                  }

                hlr.initialize = 0;
                j++;
              }

            break;
          }

        case GR_OPTION_MESH:
          {
            k = 0;

            for (i = 0; i < nx; i++)
              {
                xn[k] = x[i];
                yn[k] = y[0];
                zn[k] = Z(i, 0);
                k++;
              }

            for (j = 1; j < ny; j++)
              {
                xn[k] = x[nx - 1];
                yn[k] = y[j];
                zn[k] = Z(nx - 1, j);
                k++;
              }

            hlr.initialize = 1;

            if (clsw == GKS_K_CLIP)
              {
                int cnt = 0;

                for (i = 0; i < k - 1; i++)
                  {
                    clip3d(&xn[i], &xn[i + 1], &yn[i], &yn[i + 1], &zn[i], &zn[i + 1], &visible);
                    if (visible == 1)
                      {
                        clipx[cnt] = xn[i];
                        clipy[cnt] = yn[i];
                        clipz[cnt] = zn[i];
                        cnt += 1;
                        if (i == k - 2)
                          {
                            clipx[cnt] = xn[i + 1];
                            clipy[cnt] = yn[i + 1];
                            clipz[cnt] = zn[i + 1];
                            cnt += 1;
                          }
                      }
                  }
                pline_hlr(cnt, clipx, clipy, clipz);
              }
            else
              {
                pline_hlr(k, xn, yn, zn);
              }

            i = nx - 1;

            while (i > 0)
              {
                hlr.initialize = 0;

                for (j = 1; j < ny; j++)
                  {
                    xn[0] = x[i - 1];
                    yn[0] = y[j - 1];
                    zn[0] = Z(i - 1, j - 1);

                    xn[1] = x[i - 1];
                    yn[1] = y[j];
                    zn[1] = Z(i - 1, j);

                    xn[2] = x[i];
                    yn[2] = y[j];
                    zn[2] = Z(i, j);

                    if (clsw == GKS_K_CLIP)
                      {
                        int cnt = 0, l;

                        for (l = 0; l < 2; l++)
                          {
                            clip3d(&xn[l], &xn[l + 1], &yn[l], &yn[l + 1], &zn[l], &zn[l + 1], &visible);
                            if (visible == 1)
                              {
                                if (cnt == 0)
                                  {
                                    clipx[cnt] = xn[l];
                                    clipy[cnt] = yn[l];
                                    clipz[cnt] = zn[l];
                                    clipx[cnt + 1] = xn[l + 1];
                                    clipy[cnt + 1] = yn[l + 1];
                                    clipz[cnt + 1] = zn[l + 1];
                                    cnt += 2;
                                  }
                                else
                                  {
                                    clipx[cnt] = xn[l + 1];
                                    clipy[cnt] = yn[l + 1];
                                    clipz[cnt] = zn[l + 1];
                                    cnt += 1;
                                  }
                              }
                          }
                        pline_hlr(cnt, clipx, clipy, clipz);
                      }
                    else
                      {
                        pline_hlr(3, xn, yn, zn);
                      }
                  }

                i--;
              }

            break;
          }

        case GR_OPTION_FILLED_MESH:
        case GR_OPTION_Z_SHADED_MESH:
        case GR_OPTION_COLORED_MESH:
        case GR_OPTION_SHADED_MESH:
          {
            j = ny - 1;

            gks_set_fill_int_style(GKS_K_INTSTYLE_SOLID);

            while (j > 0)
              {
                for (i = 1; i < nx; i++)
                  {

                    if (clsw == GKS_K_CLIP && ((flip_x == 0 && x[i - 1] < cxl && x[i] <= cxl) ||
                                               (flip_x == 1 && x[i - 1] > cxr && x[i] >= cxr) ||
                                               (flip_x == 0 && x[i - 1] > cxr) || (flip_x == 1 && x[i - 1] < cxl)))
                      {
                        continue;
                      }
                    if (clsw == GKS_K_CLIP && ((flip_y == 0 && y[j - 1] > cyb) || (flip_y == 1 && y[j - 1] < cyf) ||
                                               (flip_y == 0 && y[j - 1] < cyf && y[j] <= cyf) ||
                                               (flip_y == 1 && y[j - 1] > cyb && y[j] >= cyb)))
                      {
                        continue;
                      }

                    xn[0] = x[i - 1];
                    yn[0] = y[j];
                    zn[0] = Z(i - 1, j);
                    if (is_nan(zn[0])) continue;

                    xn[1] = x[i - 1];
                    yn[1] = y[j - 1];
                    zn[1] = Z(i - 1, j - 1);
                    if (is_nan(zn[1])) continue;

                    xn[2] = x[i];
                    yn[2] = y[j - 1];
                    zn[2] = Z(i, j - 1);
                    if (is_nan(zn[2])) continue;

                    xn[3] = x[i];
                    yn[3] = y[j];
                    zn[3] = Z(i, j);
                    if (is_nan(zn[3])) continue;

                    if (clsw == GKS_K_CLIP)
                      {
                        int l;
                        if ((zn[0] > czt && zn[1] > czt && zn[2] > czt && zn[3] > czt) ||
                            (zn[0] < czb && zn[1] < czb && zn[2] < czb && zn[3] < czb))
                          {
                            continue;
                          }

                        clip3d_for_surface(&xn[0], &xn[1], &yn[0], &yn[1], &zn[0], &zn[1]);
                        clip3d_for_surface(&xn[2], &xn[3], &yn[2], &yn[3], &zn[2], &zn[3]);
                        clip3d_for_surface(&xn[1], &xn[2], &yn[1], &yn[2], &zn[1], &zn[2]);
                        clip3d_for_surface(&xn[3], &xn[0], &yn[3], &yn[0], &zn[3], &zn[0]);
                        if ((xn[0] > cxr && xn[1] > cxr) || (xn[1] > cxr && xn[2] > cxr) ||
                            (xn[2] > cxr && xn[3] > cxr) || (xn[3] > cxr && xn[0] > cxr))
                          {
                            continue;
                          }
                        if ((xn[0] < cxl && xn[1] < cxl) || (xn[1] < cxl && xn[2] < cxl) ||
                            (xn[2] < cxl && xn[3] < cxl) || (xn[3] < cxl && xn[0] < cxl))
                          {
                            continue;
                          }
                        if ((yn[0] > cyb && yn[1] > cyb) || (yn[1] > cyb && yn[2] > cyb) ||
                            (yn[2] > cyb && yn[3] > cyb) || (yn[3] > cyb && yn[0] > cyb))
                          {
                            continue;
                          }
                        if ((yn[0] < cyf && yn[1] < cyf) || (yn[1] < cyf && yn[2] < cyf) ||
                            (yn[2] < cyf && yn[3] < cyf) || (yn[3] < cyf && yn[0] < cyf))
                          {
                            continue;
                          }
                        if ((zn[0] > czt && zn[1] > czt) || (zn[1] > czt && zn[2] > czt) ||
                            (zn[2] > czt && zn[3] > czt) || (zn[3] > czt && zn[0] > czt))
                          {
                            continue;
                          }
                        if ((zn[0] < czb && zn[1] < czb) || (zn[1] < czb && zn[2] < czb) ||
                            (zn[2] < czb && zn[3] < czb) || (zn[3] < czb && zn[0] < czb))
                          {
                            continue;
                          }
                        for (l = 0; l < 4; l++)
                          {
                            if ((zn[l] > czt && zn[(l + 1) % 4] == czt && zn[(l == 0) ? 3 : l - 1] == czt))
                              {
                                xn[l] = xn[(l + 1) % 4];
                                yn[l] = yn[(l + 1) % 4];
                                zn[l] = zn[(l + 1) % 4];
                              }
                            if ((zn[l] < czb && zn[(l + 1) % 4] == czb && zn[(l == 0) ? 3 : l - 1] == czb))
                              {
                                xn[l] = xn[(l + 1) % 4];
                                yn[l] = yn[(l + 1) % 4];
                                zn[l] = zn[(l + 1) % 4];
                              }
                          }
                      }

                    xn[4] = xn[0];
                    yn[4] = yn[0];
                    zn[4] = zn[0];

                    if (option == GR_OPTION_SHADED_MESH)
                      {
                        for (k = 0; k < 4; k++)
                          {
                            facex[k] = a * xn[k] + b;
                            facey[k] = c * yn[k] + d;
                            facez[k] = e * zn[k] + f;
                          }
                        get_intensity(facex, facey, facez, light_source, &intensity);
                      }

                    for (k = 0; k <= 4; k++) apply_world_xform(xn + k, yn + k, zn + k);

                    meanz = 0.25 * (Z(i - 1, j - 1) + Z(i, j - 1) + Z(i, j) + Z(i - 1, j));

                    if (option == GR_OPTION_Z_SHADED_MESH)
                      {
                        color = iround(meanz) + first_color;

                        if (color < first_color)
                          color = first_color;
                        else if (color > last_color)
                          color = last_color;

                        gks_set_fill_color_index(color);
                      }

                    else if (option == GR_OPTION_COLORED_MESH)
                      {
                        color = iround((meanz - color_min) / (color_max - color_min) * (last_color - first_color)) +
                                first_color;

                        if (color < first_color)
                          color = first_color;
                        else if (color > last_color)
                          color = last_color;

                        gks_set_fill_color_index(color);
                      }

                    else if (option == GR_OPTION_SHADED_MESH)
                      {
                        color = iround(intensity * (last_color - first_color)) + first_color;

                        if (color < first_color)
                          color = first_color;
                        else if (color > last_color)
                          color = last_color;

                        gks_set_fill_color_index(color);
                      }

                    gks_select_xform(MODERN_NDC);

                    np = 4;
                    gks_fillarea(np, xn, yn);

                    if (option == GR_OPTION_FILLED_MESH)
                      {
                        np = 5;
                        gks_polyline(np, xn, yn);
                      }

                    gks_select_xform(tnr);
                  }

                j--;
              }

            break;
          }

        case GR_OPTION_CELL_ARRAY:

          colia = (int *)xmalloc(nx * ny * sizeof(int));
          k = 0;
          for (j = 0; j < ny; j++)
            for (i = 0; i < nx; i++)
              {
                if (!is_nan(Z(i, j)))
                  {
                    color = first_color + (int)((Z(i, j) - wx.zmin) / (wx.zmax - wx.zmin) * (last_color - first_color));

                    if (color < first_color)
                      color = first_color;
                    else if (color > last_color)
                      color = last_color;
                  }
                else
                  color = BACKGROUND;

                colia[k++] = color;
              }

          w = (nx < 256) ? nx * (255 / nx + 1) - 1 : nx - 1;
          h = (ny < 256) ? ny * (255 / ny + 1) - 1 : ny - 1;
          ca = (int *)xmalloc((w + 1) * (h + 1) * sizeof(int));

          dwk = w;
          if (h > dwk) dwk = h;
          if (nx > dwk) dwk = nx;
          if (ny > dwk) dwk = ny;
          dwk += 1;
          wk1 = (int *)xmalloc(dwk * sizeof(int));
          wk2 = (int *)xmalloc(dwk * sizeof(int));

          pixel(hlr.xmin, hlr.xmax, ymin, ymax, nx, ny, colia, w, h, ca, dwk, wk1, wk2);

          free(wk2);
          free(wk1);
          free(ca);
          free(colia);

          break;
        }

      gks_set_pline_linetype(flip_z ? GKS_K_LINETYPE_SOLID : GKS_K_LINETYPE_DOTTED);
    }
  while ((hlr.sign >= 0) && ((int)option <= (int)GR_OPTION_MESH));

#undef Z

  free(z);
  free(y);
  free(x);
  free(zn);
  free(yn);
  free(xn);
  if (clsw == GKS_K_CLIP)
    {
      free(clipx);
      free(clipy);
      free(clipz);
    }

  /* restore linetype, fill area interior style and color index */

  gks_set_pline_linetype(ltype);
  gks_set_fill_int_style(int_style);
  gks_set_fill_color_index(coli);

  if (flag_stream)
    {
      gr_writestream("<surface nx=\"%d\" ny=\"%d\"", nx, ny);
      print_float_array("x", nx, px);
      print_float_array("y", ny, py);
      print_float_array("z", nx * ny, pz);
      gr_writestream(" option=\"%d\"/>\n", option);
    }
}

static const double *xp, *yp;

static int compar(const void *a, const void *b)
{
  /* TODO: Implement a version which works for every case. At the moment the GR_PROJECTION_DEFAULT has the problem, that
  the current camera position is not considered. For the other projection types the algorithm has some mistakes at the
  edge of the surface. */
  int ret = -1;
  if (GR_PROJECTION_DEFAULT == gpx.projection_type)
    {
      if (xp[*(int *)a] > xp[*(int *)b]) ret = 1;
      if (yp[*(int *)a] < yp[*(int *)b]) ret = 1;
    }
  else
    {
      if (((triangle_with_distance *)b)->sp > ((triangle_with_distance *)a)->sp)
        {
          ret = 1;
        }
    }
  return ret;
}

/*!
 * Draw a triangular surface plot for the given data points.
 *
 * \param[in] n The number of points
 * \param[in] px A pointer to the X coordinates
 * \param[in] py A pointer to the Y coordinates
 * \param[in] pz A pointer to the Z coordinates
 */
void gr_trisurface(int n, double *px, double *py, double *pz)
{
  int errind, tnr, coli, int_style;
  int modern_projection_type;
  int ntri, *triangles = NULL;
  double x[4], y[4], z[4], meanz;
  int i, j, color;

  if (n < 3)
    {
      fprintf(stderr, "invalid number of points\n");
      return;
    }

  check_autoinit;

  gks_inq_current_xformno(&errind, &tnr);

  setscale(lx.scale_options);

  modern_projection_type =
      gpx.projection_type == GR_PROJECTION_PERSPECTIVE || gpx.projection_type == GR_PROJECTION_ORTHOGRAPHIC;

  if (modern_projection_type)
    {
      lx.xmin = ix.xmin;
      lx.xmax = ix.xmax;
      lx.ymin = ix.ymin;
      lx.ymax = ix.ymax;
      lx.zmin = ix.zmin;
      lx.zmax = ix.zmax;
    }

  /* save fill area interior style and color index */

  gks_inq_fill_int_style(&errind, &int_style);
  gks_inq_fill_color_index(&errind, &coli);

  gks_set_fill_int_style(GKS_K_INTSTYLE_SOLID);

  gr_delaunay(n, px, py, &ntri, &triangles);

  if (gpx.projection_type == GR_PROJECTION_ORTHOGRAPHIC || gpx.projection_type == GR_PROJECTION_PERSPECTIVE)
    {
      triangle_with_distance *ps = (triangle_with_distance *)gks_malloc(ntri * (sizeof(triangle_with_distance)));
      double f[3];
      f[0] = tx.focus_point_x - tx.camera_pos_x;
      f[1] = tx.focus_point_y - tx.camera_pos_y;
      f[2] = tx.focus_point_z - tx.camera_pos_z;

      for (i = 0; i < ntri; i++)
        {
          double x_cord, y_cord, z_cord, edge_01_scalar, edge_12_scalar, edge_20_scalar, nearest_edge_distance;
          double xa[3], ya[3], za[3];

          /* simplify the access for each triangle point */
          for (j = 0; j < 3; j++)
            {
              xa[j] = px[triangles[3 * i + j]];
              ya[j] = py[triangles[3 * i + j]];
              za[j] = pz[triangles[3 * i + j]];
            }
          if (is_nan(xa[0]) || is_nan(xa[1]) || is_nan(xa[2])) continue;
          if (is_nan(ya[0]) || is_nan(ya[1]) || is_nan(ya[2])) continue;

          /* calculate the distance of each edge midpoint */
          x_cord = (xa[1] + xa[0]) / 2;
          y_cord = (ya[1] + ya[0]) / 2;
          z_cord = (za[1] + za[0]) / 2;
          edge_01_scalar =
              (x_cord - tx.camera_pos_x) * f[0] + (y_cord - tx.camera_pos_y) * f[1] + (z_cord - tx.camera_pos_z) * f[2];

          x_cord = (xa[1] + xa[2]) / 2;
          y_cord = (ya[1] + ya[2]) / 2;
          z_cord = (za[1] + za[2]) / 2;
          edge_12_scalar =
              (x_cord - tx.camera_pos_x) * f[0] + (y_cord - tx.camera_pos_y) * f[1] + (z_cord - tx.camera_pos_z) * f[2];

          x_cord = (xa[0] + xa[2]) / 2;
          y_cord = (ya[0] + ya[2]) / 2;
          z_cord = (za[0] + za[2]) / 2;
          edge_20_scalar =
              (x_cord - tx.camera_pos_x) * f[0] + (y_cord - tx.camera_pos_y) * f[1] + (z_cord - tx.camera_pos_z) * f[2];

          nearest_edge_distance = edge_01_scalar;
          if (nearest_edge_distance > edge_12_scalar)
            {
              nearest_edge_distance = edge_12_scalar;
            }
          if (nearest_edge_distance > edge_20_scalar)
            {
              nearest_edge_distance = edge_20_scalar;
            }

          /* create now ntri triangles with the nearest distance attribut */
          ps[i].a = triangles[3 * i + 0];
          ps[i].b = triangles[3 * i + 1];
          ps[i].c = triangles[3 * i + 2];
          ps[i].sp = nearest_edge_distance;
        }

      qsort(ps, ntri, sizeof(triangle_with_distance), compar);
      /* uses the sorted ps to get the sorted triangle which is need for the next steps */
      for (i = 0; i < ntri; i++)
        {
          triangles[3 * i + 0] = ps[i].a;
          triangles[3 * i + 1] = ps[i].b;
          triangles[3 * i + 2] = ps[i].c;
        }
      gks_free(ps);
    }
  else
    {
      xp = px;
      yp = py;

      qsort(triangles, ntri, 3 * sizeof(int), compar);
    }

  for (i = 0; i < ntri; i++)
    {
      meanz = 0.0;
      for (j = 0; j < 3; j++)
        {
          x[j] = x_lin(px[triangles[3 * i + j]]);
          y[j] = y_lin(py[triangles[3 * i + j]]);
          z[j] = z_lin(pz[triangles[3 * i + j]]);
          meanz += z[j];

          apply_world_xform(x + j, y + j, z + j);
        }
      meanz /= 3.0;

      color = iround((meanz - wx.zmin) / (wx.zmax - wx.zmin) * (last_color - first_color)) + first_color;

      if (color < first_color)
        color = first_color;
      else if (color > last_color)
        color = last_color;

      gks_select_xform(MODERN_NDC);

      gks_set_fill_color_index(color);
      gks_fillarea(3, x, y);

      x[3] = x[0];
      y[3] = y[0];
      gks_polyline(4, x, y);

      gks_select_xform(tnr);
    }

  /* restore fill area interior style and color index */
  gks_set_fill_int_style(int_style);
  gks_set_fill_color_index(coli);

  free(triangles);

  if (flag_stream)
    {
      gr_writestream("<trisurface len=\"%d\"", n);
      print_float_array("x", n, px);
      print_float_array("y", n, py);
      print_float_array("z", n, pz);
      gr_writestream("/>\n");
    }
}

void gr_gradient(int nx, int ny, double *x, double *y, double *z, double *u, double *v)
{
  int im1, i, ip1, jm1, j, jp1;
  double dx, dy, sx, sy;

  if ((nx <= 0) || (ny <= 0))
    {
      fprintf(stderr, "invalid number of points\n");
      return;
    }

  /* be sure that points ordinates are sorted in ascending order */

  for (i = 1; i < nx; i++)
    if (x[i - 1] >= x[i])
      {
        fprintf(stderr, "points not sorted in ascending order\n");
        return;
      }

  for (j = 1; j < ny; j++)
    if (y[j - 1] >= y[j])
      {
        fprintf(stderr, "points not sorted in ascending order\n");
        return;
      }

  check_autoinit;

#define Z(i, j) (z[(nx * (j) + (i))])
#define U(i, j) (u[(nx * (j) + (i))])
#define V(i, j) (v[(nx * (j) + (i))])

  dx = (x[nx - 1] - x[0]) / (nx - 1);
  dy = (y[ny - 1] - y[0]) / (ny - 1);

  for (j = 0; j < ny; j++)
    {
      jm1 = j > 0 ? j - 1 : 0;
      jp1 = j < ny - 1 ? j + 1 : ny - 1;
      sy = j > 0 && j < ny - 1 ? 2 * dy : dy;
      for (i = 0; i < nx; i++)
        {
          im1 = i > 0 ? i - 1 : 0;
          ip1 = i < nx - 1 ? i + 1 : nx - 1;
          sx = i > 0 && i < nx - 1 ? 2 * dx : dx;
          U(i, j) = (Z(ip1, j) - Z(im1, j)) / sx;
          V(i, j) = (Z(i, jp1) - Z(i, jm1)) / sy;
        }
    }

#undef V
#undef U
#undef Z
}

void gr_quiver(int nx, int ny, double *x, double *y, double *u, double *v, int color)
{
  int i, j, ci;
  double gnorm, gmax = 0;
  double dx = 0, dy = 0;
  int errind, linecolor, fillcolor;

  if ((nx <= 0) || (ny <= 0))
    {
      fprintf(stderr, "invalid number of points\n");
      return;
    }

  /* be sure that points ordinates are sorted in ascending order */

  for (i = 1; i < nx; i++)
    if (x[i - 1] >= x[i])
      {
        fprintf(stderr, "points not sorted in ascending order\n");
        return;
      }

  for (j = 1; j < ny; j++)
    if (y[j - 1] >= y[j])
      {
        fprintf(stderr, "points not sorted in ascending order\n");
        return;
      }

  check_autoinit;

  setscale(lx.scale_options);

  /* save line color and fill color */

  gks_inq_pline_color_index(&errind, &linecolor);
  gks_inq_fill_color_index(&errind, &fillcolor);

#define Z(i, j) (z[(nx * (j) + (i))])
#define U(i, j) (u[(nx * (j) + (i))])
#define V(i, j) (v[(nx * (j) + (i))])

  for (j = 0; j < ny; j++)
    for (i = 0; i < nx; i++)
      {
        gmax = max(U(i, j) * U(i, j) + V(i, j) * V(i, j), gmax);
      }
  gmax = sqrt(gmax);

  for (j = 0; j < ny; j++)
    {
      if (dy == 0 && !is_nan(y[j]))
        {
          dy = (y[ny - 1] - y[j]) / (ny - 1 - j);
          break;
        }
    }
  for (i = 0; i < nx; i++)
    {
      if (dx == 0 && !is_nan(x[i]))
        {
          dx = (x[nx - 1] - x[i]) / (nx - 1 - i);
          break;
        }
    }

  for (j = 0; j < ny; j++)
    for (i = 0; i < nx; i++)
      {
        gnorm = sqrt(U(i, j) * U(i, j) + V(i, j) * V(i, j)) / gmax;
        if (color)
          {
            ci = first_color + (int)((last_color - first_color) * gnorm);
            gr_setlinecolorind(ci);
            gr_setfillcolorind(ci);
          }
        gr_setarrowsize(gnorm);
        gr_drawarrow(x[i], y[j], x[i] + dx * U(i, j) / gmax, y[j] + dy * V(i, j) / gmax);
      }

#undef V
#undef U
#undef Z

  /* restore line color and fill color */

  gks_set_pline_color_index(linecolor);
  gks_set_fill_color_index(fillcolor);

  if (flag_stream)
    {
      gr_writestream("<quiver nx=\"%d\" ny=\"%d\"", nx, ny);
      print_float_array("x", nx, x);
      print_float_array("y", ny, y);
      print_float_array("u", nx * ny, u);
      print_float_array("v", nx * ny, v);
      gr_writestream(" color=\"%d\"/>\n", color);
    }
}

static int islinspace(int n, double *a)
{
  double step, feps;
  int i;

  if (n < 2) return 0;
  step = (a[n - 1] - a[0]) / (n - 1);
  feps = step * FEPS;
  for (i = 1; i < n; i++)
    {
      if (is_nan(a[i]) || is_nan(a[i - 1])) return 0;
      if (fabs(a[i] - a[i - 1] - step) > feps) return 0;
    }

  return 1;
}

static void rebin(int nx, int ny, double *px, double *py, double *pz, int *nxq, int *nyq, double **xq, double **yq,
                  double **zq)
{
  double step, *x, *y, *z;
  int i;
  int xcnt = 0, ycnt = 0;

  *nxq = 500;
  *nyq = 500;

  x = *xq = (double *)xmalloc(sizeof(double) * *nxq);
  y = *yq = (double *)xmalloc(sizeof(double) * *nyq);
  z = *zq = (double *)xmalloc(sizeof(double) * *nxq * *nyq);

  for (i = 0; i < *nxq; i++)
    {
      if (is_nan(px[i]))
        xcnt += 1;
      else
        break;
    }
  step = (px[nx - 1] - px[xcnt]) / (*nxq - 1 - xcnt);
  for (i = 0; i < *nxq; i++) x[i] = (i < xcnt) ? NAN : px[xcnt] + i * step;

  for (i = 0; i < *nyq; i++)
    {
      if (is_nan(py[i]))
        ycnt += 1;
      else
        break;
    }
  step = (py[ny - 1] - py[ycnt]) / (*nyq - 1 - ycnt);
  for (i = 0; i < *nyq; i++) y[i] = (i < ycnt) ? NAN : py[ycnt] + i * step;

  gr_interp2(nx, ny, px, py, pz, *nxq, *nyq, x, y, z, 1, 0.0);
}

/*!
 * Draw contours of a three-dimensional data set whose values are specified over a
 rectangular mesh. Contour lines may optionally be labeled.
 *
 * \param[in] nx The number of points along the X axis
 * \param[in] ny The number of points along the Y axis
 * \param[in] nh The number of height values. If less than 1, 16 evenly spaced
 *               values will be used instead of h, which can safely be NULL
 * \param[in] px A pointer to the X coordinates
 * \param[in] py A pointer to the Y coordinates
 * \param[in] h A pointer to the height values
 * \param[in] pz A pointer to the Z coordinates (at least nx * ny)
 * \param[in] major_h Directs GR to label contour lines. For example, a value of
 *                    3 would label every third line. A value of 1 will label
 *                    every line. A value of 0 produces no labels. To produce
 *                    colored contour lines, add an offset of 1000 to major_h
 */
void gr_contour(int nx, int ny, int nh, double *px, double *py, double *h, double *pz, int major_h)
{
  int i, j;
  int errind, tnr, ltype, color, halign, valign;
  double chux, chuy;
  int nxq, nyq;
  double *xq = NULL, *yq = NULL, *zq = NULL;
  int scale_options;
  double *x = NULL, *y = NULL;

  if ((nx <= 0) || (ny <= 0))
    {
      fprintf(stderr, "invalid number of points\n");
      return;
    }

  /* be sure that points ordinates are sorted in ascending order */

  for (i = 1; i < nx; i++)
    if (px[i - 1] >= px[i])
      {
        fprintf(stderr, "points not sorted in ascending order\n");
        return;
      }

  for (j = 1; j < ny; j++)
    if (py[j - 1] >= py[j])
      {
        fprintf(stderr, "points not sorted in ascending order\n");
        return;
      }

  check_autoinit;

  scale_options = lx.scale_options;

  /* calculate the position of the contour labels when the axes are logarithmic for example */
  if (scale_options != 0)
    {
      setscale(scale_options & ~(GR_OPTION_FLIP_X | GR_OPTION_FLIP_Y));

      x = (double *)xcalloc(nx, sizeof(double));
      for (i = 0; i < nx; i++) x[i] = x_lin(px[i]);

      y = (double *)xcalloc(ny, sizeof(double));
      for (i = 0; i < ny; i++) y[i] = y_lin(py[i]);

      setscale(scale_options & ~(GR_OPTION_X_LOG | GR_OPTION_Y_LOG | GR_OPTION_X_LOG2 | GR_OPTION_Y_LOG2 |
                                 GR_OPTION_X_LN | GR_OPTION_Y_LN));
    }
  else
    {
      x = px;
      y = py;
    }

  /* save linetype, line color, text alignment and character-up vector */

  gks_inq_pline_linetype(&errind, &ltype);
  gks_inq_pline_color_index(&errind, &color);
  gks_inq_text_align(&errind, &halign, &valign);
  gks_inq_text_upvec(&errind, &chux, &chuy);

  gks_set_text_align(GKS_K_TEXT_HALIGN_CENTER, GKS_K_TEXT_VALIGN_HALF);

  if (!islinspace(nx, x) || !islinspace(ny, y))
    {
      rebin(nx, ny, x, y, pz, &nxq, &nyq, &xq, &yq, &zq);

      gr_draw_contours(nxq, nyq, nh, xq, yq, h, zq, major_h);

      free(zq);
      free(yq);
      free(xq);
    }
  else
    gr_draw_contours(nx, ny, nh, x, y, h, pz, major_h);

  if (x != px) free(x);
  if (y != py) free(y);

  /* restore scale options, linetype, line color, character-up vector and text alignment */

  if (scale_options != 0)
    {
      setscale(scale_options);
    }
  gks_set_pline_linetype(ltype);
  gks_set_pline_color_index(color);
  gks_set_text_align(halign, valign);
  gks_set_text_upvec(chux, chuy);

  if (flag_stream)
    {
      gr_writestream("<contour nx=\"%d\" ny=\"%d\" nh=\"%d\"", nx, ny, nh);
      print_float_array("x", nx, px);
      print_float_array("y", ny, py);
      print_float_array("h", nh, h);
      print_float_array("z", nx * ny, pz);
      gr_writestream(" majorh=\"%d\"/>\n", major_h);
    }
}

/*!
 * Draw filled contour plot of a three-dimensional data set whose values are
 * specified over a rectangular mesh.
 *
 * \param[in] nx The number of points along the X axis
 * \param[in] ny The number of points along the Y axis
 * \param[in] nh The number of height values. 0 for default contours.
 * \param[in] px A pointer to the X coordinates
 * \param[in] py A pointer to the Y coordinates
 * \param[in] h A pointer to the height values in ascending order. If NULL, use nh
 *              evenly distributed height values between minimum and maximum Z value.
 * \param[in] pz A pointer to the Z coordinates (at least nx * ny)
 * \param[in] major_h Directs GR to label contour lines. For example, a value of
 *                    3 would label every third line. A value of 1 will label
 *                    every line. A value of 0 produces no labels. To produce
 *                    colored contour lines, add an offset of 1000 to major_h.
 *                    Use a value of -1 to disable contour lines and labels.
 */
void gr_contourf(int nx, int ny, int nh, double *px, double *py, double *h, double *pz, int major_h)
{
  int i, j;
  int errind;
  int nxq, nyq;
  int fillintstyle, fillcolorind;
  double *xq = NULL, *yq = NULL, *zq = NULL;
  int scale_options;
  double *x = NULL, *y = NULL;

  if ((nx <= 0) || (ny <= 0))
    {
      fprintf(stderr, "invalid number of points\n");
      return;
    }

  /* be sure that points ordinates are sorted in ascending order */

  for (i = 1; i < nx; i++)
    if (px[i - 1] >= px[i])
      {
        fprintf(stderr, "points not sorted in ascending order\n");
        return;
      }

  for (j = 1; j < ny; j++)
    if (py[j - 1] >= py[j])
      {
        fprintf(stderr, "points not sorted in ascending order\n");
        return;
      }

  if (nh > 0 && h)
    {
      for (i = 1; i < nh; i++)
        if (h[i - 1] >= h[i])
          {
            fprintf(stderr, "contours not sorted in ascending order\n");
            return;
          }
    }

  check_autoinit;

  scale_options = lx.scale_options;
  /* calculate the position of the contour labels when the axes are logarithmic for example */
  if (scale_options != 0)
    {
      setscale(scale_options & ~(GR_OPTION_FLIP_X | GR_OPTION_FLIP_Y));

      x = (double *)xcalloc(nx, sizeof(double));
      for (i = 0; i < nx; i++) x[i] = x_lin(px[i]);

      y = (double *)xcalloc(ny, sizeof(double));
      for (i = 0; i < ny; i++) y[i] = y_lin(py[i]);

      setscale(scale_options & ~(GR_OPTION_X_LOG | GR_OPTION_Y_LOG | GR_OPTION_X_LOG2 | GR_OPTION_Y_LOG2 |
                                 GR_OPTION_X_LN | GR_OPTION_Y_LN));
    }
  else
    {
      x = px;
      y = py;
    }

  /* save fill style and color */

  gks_inq_fill_style_index(&errind, &fillintstyle);
  gks_inq_fill_color_index(&errind, &fillcolorind);

  if (!islinspace(nx, x) || !islinspace(ny, y))
    {
      rebin(nx, ny, x, y, pz, &nxq, &nyq, &xq, &yq, &zq);

      gr_draw_contourf(nxq, nyq, nh, xq, yq, h, zq, first_color, last_color, major_h);

      free(zq);
      free(yq);
      free(xq);
    }
  else
    gr_draw_contourf(nx, ny, nh, x, y, h, pz, first_color, last_color, major_h);

  if (x != px) free(x);
  if (y != py) free(y);

  /* restore fill style and color */
  if (scale_options != 0)
    {
      setscale(scale_options);
    }
  gks_set_fill_style_index(fillintstyle);
  gks_set_fill_color_index(fillcolorind);

  if (flag_stream)
    {
      gr_writestream("<contourf nx=\"%d\" ny=\"%d\" nh=\"%d\"", nx, ny, nh);
      print_float_array("x", nx, px);
      print_float_array("y", ny, py);
      print_float_array("h", nh, h);
      print_float_array("z", nx * ny, pz);
      gr_writestream(" majorh=\"%d\"/>\n", major_h);
    }
}

/*!
 * Draw a contour plot for the given triangle mesh.
 *
 * \param[in] npoints The number of points
 * \param[in] x A pointer to the X coordinates
 * \param[in] y A pointer to the Y coordinates
 * \param[in] z A pointer to the Z coordinates
 * \param[in] nlevels The number of contour levels
 * \param[in] levels A pointer to the contour levels
 */
void gr_tricontour(int npoints, double *x, double *y, double *z, int nlevels, double *levels)
{
  int i, *colors;

  if (npoints < 3)
    {
      fprintf(stderr, "invalid number of points\n");
      return;
    }

  if (nlevels < 1)
    {
      fprintf(stderr, "invalid number of iso levels\n");
      return;
    }

  check_autoinit;

  setscale(lx.scale_options);

  colors = (int *)xmalloc(nlevels * sizeof(int));
  if (nlevels > 1)
    {
      for (i = 0; i < nlevels; i++)
        {
          colors[i] = first_color + (int)((double)i / (nlevels - 1) * (last_color - first_color));
        }
    }
  else
    colors[0] = 1;

  gr_draw_tricont(npoints, x, y, z, nlevels, levels, colors);

  free(colors);

  if (flag_stream)
    {
      gr_writestream("<tricont npoints=\"%d\"", npoints);
      print_float_array("x", npoints, x);
      print_float_array("y", npoints, y);
      print_float_array("z", npoints, z);
      print_float_array("levels", nlevels, levels);
      gr_writestream("/>\n");
    }
}

static int binning(double x[], double y[], int *cell, int *cnt, double size, double shape, double rx[2], double ry[2],
                   int bnd[2], int n, double ycorr)
{
  int nc;
  double xi, yi;
  int i, i1, i2, iinc;
  int j1, j2, jinc;
  int L, lmax, lat;
  double c1, c2, con1, con2, dist1;
  double sx, sy, xmin, ymin, xr, yr;

  xmin = rx[0];
  ymin = ry[0] + ycorr;
  xr = rx[1] - xmin;
  yr = ry[1] + ycorr - ymin;
  c1 = size / xr;
  c2 = size * shape / (yr * sqrt(3.));

  jinc = bnd[1];
  lat = jinc + 1;
  iinc = 2 * jinc;
  lmax = bnd[0] * bnd[1];
  con1 = 0.25;
  con2 = 1. / 3.;

  for (i = 0; i < n; i++)
    {
      if (is_nan(x[i]) || is_nan(y[i])) continue;
      xi = x[i];
      yi = y[i];
      gr_wctondc(&xi, &yi);
      if (xi < vxmin || xi > vxmax || yi < vymin || yi > vymax)
        {
          continue;
        }
      sx = c1 * (xi - xmin);
      sy = c2 * (yi - ymin);
      j1 = sx + 0.5;
      i1 = sy + 0.5;
      dist1 = pow((sx - j1), 2) + 3.0 * pow((sy - i1), 2);
      if (dist1 < con1)
        L = i1 * iinc + j1 + 1;
      else if (dist1 > con2)
        L = (int)sy * iinc + (int)sx + lat;
      else
        {
          j2 = sx;
          i2 = sy;
          if (dist1 <= pow((sx - j2 - 0.5), 2) + 3.0 * pow((sy - i2 - 0.5), 2))
            L = i1 * iinc + j1 + 1;
          else
            L = i2 * iinc + j2 + lat;
        }

      cnt[L] = cnt[L] + 1;
    }

  nc = 0;
  for (L = 1; L <= lmax; L++)
    {
      if (cnt[L] > 0)
        {
          nc++;
          cell[nc] = L;
          cnt[nc] = cnt[L];
        }
    }
  bnd[0] = (cell[nc] - 1) / bnd[1] + 1;
  return nc;
}

static int hcell2xy(int nbins, double rx[2], double ry[2], double shape, int bnd[2], int *cell, double *x, double *y,
                    int *cnt, double ycorr)
{
  double c3, c4, tmp;
  int jmax, lmax, L;
  int cntmax;

  c3 = (rx[1] - rx[0]) / nbins;
  c4 = ((ry[1] - ry[0]) * sqrt(3)) / (2 * shape * nbins);
  jmax = bnd[1];
  lmax = bnd[0] * bnd[1];

  cntmax = 0;
  for (L = 0; L <= lmax; L++)
    {
      y[L] = c4 * ((cell[L] - 1) / jmax) + ry[0] + ycorr;
      tmp = ((cell[L] - 1) / jmax) % 2 == 0 ? ((cell[L] - 1) % jmax) : ((cell[L] - 1) % jmax + 0.5);
      x[L] = c3 * tmp + rx[0];
      if (cnt[L] > cntmax) cntmax = cnt[L];
    }
  return cntmax;
}

int gr_hexbin(int n, double *x, double *y, int nbins)
{
  const hexbin_2pass_t *context;
  int cntmax;

  context = gr_hexbin_2pass(n, x, y, nbins, NULL);
  if (context == NULL)
    {
      return -1;
    }
  cntmax = context->cntmax;
  gr_hexbin_2pass(n, x, y, nbins, context);

  return cntmax;
}

const hexbin_2pass_t *gr_hexbin_2pass(int n, double *x, double *y, int nbins, const hexbin_2pass_t *context)
{
  hexbin_2pass_t *context_;
  double d, R;

  if (n <= 2)
    {
      fprintf(stderr, "invalid number of points\n");
      return NULL;
    }
  else if (nbins <= 2)
    {
      fprintf(stderr, "invalid number of bins\n");
      return NULL;
    }

  check_autoinit;

  d = (vxmax - vxmin) / nbins;
  R = 1. / sqrt(3) * d;

  if (context == NULL)
    {
      int jmax, c1, imax, lmax;
      double size, shape;
      double ycorr;
      int *cell, *cnt;
      double *xcm, *ycm;
      double rx[2], ry[2];
      int bnd[2];
      int nc, cntmax;

      size = nbins;
      shape = (vymax - vymin) / (vxmax - vxmin);

      jmax = floor(nbins + 1.5001);
      c1 = 2 * floor((nbins * shape) / sqrt(3) + 1.5001);
      imax = floor((jmax * c1 - 1) / jmax + 1);
      lmax = jmax * imax;

      ycorr = (vymax - vymin) - ((imax - 2) * 1.5 * R + (imax % 2) * R);
      ycorr = ycorr / 2;

      cell = (int *)xcalloc(lmax + 1, sizeof(int));
      cnt = (int *)xcalloc(lmax + 1, sizeof(int));
      xcm = (double *)xcalloc(lmax + 1, sizeof(double));
      ycm = (double *)xcalloc(lmax + 1, sizeof(double));

      rx[0] = vxmin;
      rx[1] = vxmax;
      ry[0] = vymin;
      ry[1] = vymax;

      bnd[0] = imax;
      bnd[1] = jmax;

      nc = binning(x, y, cell, cnt, size, shape, rx, ry, bnd, n, ycorr);

      cntmax = hcell2xy(nbins, rx, ry, shape, bnd, cell, xcm, ycm, cnt, ycorr);

      context_ = (hexbin_2pass_t *)xmalloc(sizeof(hexbin_2pass_t));
      context_->nc = nc;
      context_->cntmax = cntmax;
      context_->action = GR_2PASS_CLEANUP | GR_2PASS_RENDER; /* render and clean up by default */
      context_->priv = (hexbin_2pass_priv_t *)xmalloc(sizeof(hexbin_2pass_priv_t));
      context_->priv->cell = cell;
      context_->priv->cnt = cnt;
      context_->priv->xcm = xcm;
      context_->priv->ycm = ycm;
    }
  else
    {
      if (context->action & GR_2PASS_RENDER)
        {
          int errind, int_style, coli;
          int nc, cntmax;
          int *cell, *cnt;
          double *xcm, *ycm;
          double xlist[7], ylist[7], xdelta[6], ydelta[6];
          int i, j;

          nc = context->nc;
          cntmax = context->cntmax;
          cell = context->priv->cell;
          cnt = context->priv->cnt;
          xcm = context->priv->xcm;
          ycm = context->priv->ycm;

          for (j = 0; j < 6; j++)
            {
              xdelta[j] = sin(M_PI / 3 * j) * R;
              ydelta[j] = cos(M_PI / 3 * j) * R;
            }

          setscale(lx.scale_options);

          /* save fill area interior style and color index */
          gks_inq_fill_int_style(&errind, &int_style);
          gks_inq_fill_color_index(&errind, &coli);

          gks_set_fill_int_style(GKS_K_INTSTYLE_SOLID);

          for (i = 1; i <= nc; i++)
            {
              for (j = 0; j < 6; j++)
                {
                  xlist[j] = xcm[i] + xdelta[j];
                  ylist[j] = ycm[i] + ydelta[j];
                  gr_ndctowc(xlist + j, ylist + j);
                }
              xlist[6] = xlist[0];
              ylist[6] = ylist[0];

              gks_set_fill_color_index(first_color + (last_color - first_color) * ((double)cnt[i] / cntmax));
              gks_fillarea(6, xlist, ylist);
              gks_polyline(7, xlist, ylist);
            }
          free(ycm);
          free(xcm);
          free(cnt);
          free(cell);
          /* restore fill area interior style and color index */

          gks_set_fill_int_style(int_style);
          gks_set_fill_color_index(coli);
          if (flag_stream)
            {
              gr_writestream("<hexbin len=\"%d\"", n);
              print_float_array("x", n, x);
              print_float_array("y", n, y);
              gr_writestream(" nbins=\"%d\"/>\n", nbins);
            }
        }

      if (context->action & GR_2PASS_CLEANUP)
        {
          free(context->priv);
          free((hexbin_2pass_t *)context);
        }
      context_ = NULL;
    }

  return context_;
}
/*!
 * Set the currently used colormap.
 *
 * \param[in] index Colormap index
 *
 * A list of colormaps can be found at: https://gr-framework.org/colormaps.html
 *
 * Using a negative index will use the reverse of the selected colormap.
 */
void gr_setcolormap(int index)
{
  int ind = index, reverse, i, j;
  double r, g, b;

  colormap = index;

  check_autoinit;

  reverse = 0;
  r = g = b = 0;
  if (ind < 0)
    {
      ind = -ind;
      reverse = 1;
    }

  if (ind >= 100)
    {
      ind %= 100;
      first_color = 1000;
      last_color = 1255;
    }
  else
    {
      first_color = DEFAULT_FIRST_COLOR;
      last_color = DEFAULT_LAST_COLOR;
    }

  if (ind >= (int)(sizeof(cmap) / sizeof(cmap[0]))) ind = 0;

  for (i = 0; i <= DEFAULT_LAST_COLOR - DEFAULT_FIRST_COLOR; i++)
    {
      j = reverse ? DEFAULT_LAST_COLOR - DEFAULT_FIRST_COLOR - 1 - i : i;
      r = ((cmap[ind][j] >> 16) & 0xff) / 255.0;
      g = ((cmap[ind][j] >> 8) & 0xff) / 255.0;
      b = (cmap[ind][j] & 0xff) / 255.0;

      setcolorrep(DEFAULT_FIRST_COLOR + i, r, g, b);
    }

  for (i = 0; i < 256; i++)
    {
      j = reverse ? 255 - i : i;
      r = ((cmap_h[ind][j] >> 16) & 0xff) / 255.0;
      g = ((cmap_h[ind][j] >> 8) & 0xff) / 255.0;
      b = (cmap_h[ind][j] & 0xff) / 255.0;

      setcolorrep(1000 + i, r, g, b);
    }

  if (flag_stream) gr_writestream("<setcolormap index=\"%d\"/>\n", index);
}

void gr_inqcolormap(int *index)
{
  check_autoinit;

  *index = colormap;
}

/*!
 * Define a colormap by a list of RGB colors.
 *
 * \param[in] n The number of colors
 * \param[in] r A pointer to the red intensities in range 0.0 to 1.0
 * \param[in] g A pointer to the green intensities in range 0.0 to 1.0
 * \param[in] b A pointer to the blue intensities in range 0.0 to 1.0
 * \param[in] x A pointer to the positions of the corresponding color in the resulting colormap or NULL. The values of
 * x must increase monotonically from 0.0 to 1.0. If x is NULL the given colors are evenly distributed in the colormap.
 *
 * This function defines a colormap using the n given color intensities. If less than 256 colors are provided the
 * colors intensities are linear interpolated. If x is NULL the given color values are evenly distributed in the
 * colormap. Otherwise the normalized value of x defines the position of the color in the colormap.
 */
void gr_setcolormapfromrgb(int n, double *r, double *g, double *b, double *x)
{
  int i, j;
  int start_index, end_index;

  check_autoinit;

  if (n < 2)
    {
      fprintf(stderr, "Not enough colors provided.\n");
      return;
    }

  /* make sure x is in ascending order starting at 0 and ending at 1 */
  if (x != NULL)
    {
      if (x[0] != 0.0)
        {
          fprintf(stderr, "x must start at 0.0\n");
          return;
        }
      if (x[n - 1] != 1.0)
        {
          fprintf(stderr, "x must end at 1.0\n");
          return;
        }
      for (i = 0; i < n - 1; i++)
        {
          if (x[i] >= x[i + 1])
            {
              fprintf(stderr, "x not sorted in ascending order\n");
              return;
            }
        }
    }
  first_color = 1000;
  last_color = 1255;
  for (i = 0; i < n - 1; i++)
    {
      if (x == NULL)
        {
          start_index = nint(i * 256. / (n - 1));
          end_index = nint((i + 1) * 256. / (n - 1));
        }
      else
        {
          start_index = nint(x[i] * 256);
          end_index = nint(x[i + 1] * 256);
        }
      for (j = start_index; j < end_index; j++)
        {
          double a = ((double)j - start_index) / (end_index - start_index);
          double rj = r[i] * (1 - a) + r[i + 1] * a;
          double gj = g[i] * (1 - a) + g[i + 1] * a;
          double bj = b[i] * (1 - a) + b[i + 1] * a;
          gr_setcolorrep(1000 + j, rj, gj, bj);
        }
    }
}

/*!
 * Inquire the color index range of the current colormap.
 *
 * \param[out] first_color_ind The color index of the first color
 * \param[out] last_color_ind The color index of the last color
 */
void gr_inqcolormapinds(int *first_color_ind, int *last_color_ind)
{
  check_autoinit;
  if (first_color_ind != NULL)
    {
      *first_color_ind = first_color;
    }
  if (last_color_ind != NULL)
    {
      *last_color_ind = last_color;
    }
}

void gr_colorbar(void)
{
  int errind, halign, valign, clsw, tnr;
  double clrt[4], wn[4], vp[4];
  double xmin, xmax, ymin, ymax, zmin, zmax;
  int w, h, sx, sy, nx, ny, colia[256];
  int i, nz, ci, cells;
  double x, y, z, dy, dz;
  char text[256];
  format_reference_t format_reference;

  check_autoinit;

  setscale(lx.scale_options);

  /* save text alignment and clipping indicator */

  gks_inq_text_align(&errind, &halign, &valign);
  gks_inq_clip(&errind, &clsw, clrt);

  /* inquire current normalization transformation */

  gks_inq_current_xformno(&errind, &tnr);
  gks_inq_xform(tnr, &errind, wn, vp);

  cells = last_color - first_color + 1;
  for (ci = first_color; ci <= last_color; ci++) colia[ci - first_color] = ci;

  xmin = lx.xmin;
  xmax = lx.xmax;
  ymin = lx.ymin;
  ymax = lx.ymax;
  zmin = wx.zmin;
  zmax = wx.zmax;

  w = nx = 1;
  h = ny = cells;
  sx = sy = 1;

  gks_cellarray(xmin, ymin, xmax, ymax, w, h, sx, sy, nx, ny, colia);

  dz = 0.5 * gr_tick(zmin, zmax);
  nz = (int)((zmax - zmin) / dz + 0.5);
  dy = (ymax - ymin) / nz;

  gks_set_text_align(GKS_K_TEXT_HALIGN_LEFT, GKS_K_TEXT_VALIGN_HALF);
  gks_set_clipping(GKS_K_NOCLIP);

  x = xmax + 0.01 * (xmax - xmin) / (vp[1] - vp[0]);
  gr_getformat(&format_reference, 0, zmin, zmax, dz, 0);

  for (i = 0; i <= nz; i++)
    {
      y = ymin + i * dy;
      z = zmin + i * dz;
      text2d(x, y, gr_ftoa(text, z, &format_reference));
    }

  /* restore text alignment and clipping indicator */

  gks_set_text_align(halign, valign);
  gks_set_clipping(clsw);

  if (flag_stream) gr_writestream("<colorbar/>\n");
}

void gr_inqcolor(int color, int *rgb)
{
  int wkid = 1, errind;
  double r, g, b;

  check_autoinit;

  gks_inq_color_rep(wkid, color, GKS_K_VALUE_SET, &errind, &r, &g, &b);
  *rgb = ((nint(r * 255) & 0xff)) | ((nint(g * 255) & 0xff) << 8) | ((nint(b * 255) & 0xff) << 16);
}

int gr_inqcolorfromrgb(double red, double green, double blue)
{
  int wkid = 1, color, errind, ind = 0;
  unsigned int rgbmask;
  double r, g, b, dmin = FLT_MAX, d, dr, dg, db;

  check_autoinit;

  rgbmask = ((nint(red * 255) & 0xff)) | ((nint(green * 255) & 0xff) << 8) | ((nint(blue * 255) & 0xff) << 16);

  for (color = 80; color < 980; color++)
    if (rgb[color] == rgbmask)
      {
        setcolorrep(color, red, green, blue);
        used[color] = 1;
        return color;
      }

  for (color = 80; color < 980; color++)
    {
      if (!used[color])
        {
          setcolorrep(color, red, green, blue);
          used[color] = 1;
          return color;
        }
    }

  for (color = 80; color < 980; color++)
    {
      gks_inq_color_rep(wkid, color, GKS_K_VALUE_SET, &errind, &r, &g, &b);
      dr = 0.30 * (r - red);
      dg = 0.59 * (g - green);
      db = 0.11 * (b - blue);
      d = dr * dr + dg * dg + db * db;
      if (d < dmin)
        {
          ind = color;
          dmin = d;
          if (d < FEPS) break;
        }
    }

  return ind;
}

void gr_hsvtorgb(double h, double s, double v, double *r, double *g, double *b)
{
  int i;
  double f, p, q, t;

  if (s == 0)
    {
      *r = *g = *b = v;
    }
  else
    {
      h *= 6;
      i = floor(h);
      f = h - i;
      p = v * (1 - s);
      q = v * (1 - s * f);
      t = v * (1 - s * (1 - f));

      switch (i)
        {
        case 0:
          *r = v;
          *g = t;
          *b = p;
          break;
        case 1:
          *r = q;
          *g = v;
          *b = p;
          break;
        case 2:
          *r = p;
          *g = v;
          *b = t;
          break;
        case 3:
          *r = p;
          *g = q;
          *b = v;
          break;
        case 4:
          *r = t;
          *g = p;
          *b = v;
          break;
        case 5:
          *r = v;
          *g = p;
          *b = q;
          break;
        }
    }
}

double gr_tick(double amin, double amax)
{
  double exponent, fractpart, intpart, factor, tick_unit;
  int n;

  if (amax > amin)
    {
      exponent = log10(amax - amin);
      fractpart = modf(exponent, &intpart);
      GR_UNUSED(fractpart); /* silence compiler warning */
      n = (int)intpart;

      factor = pow(10.0, exponent - n);

      if (factor > 5)
        tick_unit = 2;
      else if (factor > 2.5)
        tick_unit = 1;
      else if (factor > 1)
        tick_unit = 0.5;
      else if (factor > 0.5)
        tick_unit = 0.2;
      else if (factor > 0.25)
        tick_unit = 0.1;
      else
        tick_unit = 0.05;

      tick_unit = tick_unit * pow(10.0, (double)n);
    }
  else
    {
      fprintf(stderr, "invalid range\n");
      tick_unit = 0;
    }

  return (tick_unit); /* return a tick unit that evenly divides into the
                         difference between the minimum and maximum value */
}

static int check_range(double a, double b)
{
  double d;

  if (a != 0)
    d = a;
  else if (b != 0)
    d = b;
  else
    d = 1;

  return fabs((b - a) / d) * 0.000001 > DBL_EPSILON;
}

int gr_validaterange(double amin, double amax)
{
  /* Check whether the given coordinate range does not lead
     to loss of precision in subsequent GR functions, e.g.
     when applying normalization or device transformations. */
  return check_range(amin, amax);
}

#ifdef _MSC_VER
#if _MSC_VER < 1700
static double trunc(double d)
{
  return (d > 0) ? floor(d) : ceil(d);
}
#endif
#endif

void gr_adjustrange(double *amin, double *amax)
{
  double tick;

  if (*amin == *amax)
    {
      if (*amin != 0)
        tick = pow(10.0, trunc(log10(fabs(*amin))));
      else
        tick = 0.1;

      *amin = *amin - tick;
      *amax = *amax + tick;
    }

  tick = gr_tick(*amin, *amax);

  if (fract(*amin / tick) != 0) *amin = tick * gauss(*amin / tick);

  if (fract(*amax / tick) != 0) *amax = tick * (gauss(*amax / tick) + 1);
}

static int gks_wstype(char *type)
{
  int wstype;

  if (!str_casecmp(type, "ps") || !str_casecmp(type, "eps"))
    wstype = 62;
  else if (!str_casecmp(type, "pdf"))
    wstype = 102;
  else if (!str_casecmp(type, "mov"))
    wstype = 120;
  else if (!str_casecmp(type, "gif"))
    wstype = 130;
  else if (!str_casecmp(type, "bmp"))
    wstype = 145;
  else if (!str_casecmp(type, "jpeg") || !str_casecmp(type, "jpg"))
    wstype = 144;
  else if (!str_casecmp(type, "png"))
    wstype = 140;
  else if (!str_casecmp(type, "mem"))
    wstype = 143;
  else if (!str_casecmp(type, "mp4"))
    wstype = 160;
  else if (!str_casecmp(type, "webm"))
    wstype = 161;
  else if (!str_casecmp(type, "ogg"))
    wstype = 162;
  else if (!str_casecmp(type, "tiff") || !str_casecmp(type, "tif"))
    wstype = 146;
  else if (!str_casecmp(type, "svg"))
    wstype = 382;
  else if (!str_casecmp(type, "wmf"))
    wstype = 390;
  else if (!str_casecmp(type, "pgf"))
    wstype = 314;
  else if (!str_casecmp(type, "ppm"))
    wstype = 170;
  else
    {
      fprintf(stderr, "%s: unrecognized file type\nAvailable formats: \
bmp, eps, jpeg, mov, mp4, webm, ogg, pdf, pgf, png, ps, svg, tiff, wmf or ppm\n",
              type);
      wstype = -1;
    }

  if (wstype == 145 && gks_getenv("GKS_USE_GS_BMP") != NULL) wstype = 320;

  if (wstype == 144 && gks_getenv("GKS_USE_GS_JPG") != NULL) wstype = 321;
  if (wstype == 144 && gks_getenv("GKS_USE_AGG_JPG") != NULL) wstype = 172;

  if (wstype == 140 && gks_getenv("GKS_USE_GS_PNG") != NULL) wstype = 322;
  if (wstype == 140 && gks_getenv("GKS_USE_AGG_PNG") != NULL) wstype = 171;

  if (wstype == 146 && gks_getenv("GKS_USE_GS_TIF") != NULL) wstype = 323;

  if (wstype == 143 && gks_getenv("GKS_USE_AGG_MEM") != NULL) wstype = 173;

  return wstype;
}

/*!
 * Open and activate a print device.
 *
 * \param[in] pathname Filename for the print device.
 *
 * This function opens an additional graphics output device. The device type is
 * obtained from the given file extension. The following file types are
 * supported:
 *
 * \verbatim embed:rst:leading-asterisk
 *
 * The following file types are supported:
 *
 * +-------------+---------------------------------------+
 * |.ps, .eps    |PostScript                             |
 * +-------------+---------------------------------------+
 * |.pdf         |Portable Document Format               |
 * +-------------+---------------------------------------+
 * |.bmp         |Windows Bitmap (BMP)                   |
 * +-------------+---------------------------------------+
 * |.jpeg, .jpg  |JPEG image file                        |
 * +-------------+---------------------------------------+
 * |.png         |Portable Network Graphics file (PNG)   |
 * +-------------+---------------------------------------+
 * |.tiff, .tif  |Tagged Image File Format (TIFF)        |
 * +-------------+---------------------------------------+
 * |.svg         |Scalable Vector Graphics               |
 * +-------------+---------------------------------------+
 * |.wmf         |Windows Metafile                       |
 * +-------------+---------------------------------------+
 * |.mp4         |MPEG-4 video file                      |
 * +-------------+---------------------------------------+
 * |.webm        |WebM video file                        |
 * +-------------+---------------------------------------+
 * |.ogg         |Ogg video file                         |
 * +-------------+---------------------------------------+
 *
 * \endverbatim
 */
void gr_beginprint(char *pathname)
{
  int wkid = 6, wstype = 62;
  char *type;

  check_autoinit;

  if (!flag_printing)
    {
      if ((type = strrchr(pathname, '.')) != NULL) wstype = gks_wstype(type + 1);

      if (wstype >= 0)
        {
          gks_open_ws(wkid, pathname, wstype);
          gks_activate_ws(wkid);
          flag_printing = 1;
        }
    }
  else
    fprintf(stderr, "print device already activated\n");
}

/*!
 * Open and activate a print device with the given layout attributes.
 *
 * \param[in] pathname Filename for the print device.
 * \param[in] mode Output mode (Color, GrayScale)
 * \param[in] format Output format (see table)
 * \param[in] orientation Page orientation (Landscape, Portrait)
 *
 * \verbatim embed:rst:leading-asterisk
 *
 * The available formats are:
 *
 * +-----------+---------------+
 * |A4         |0.210 x 0.297  |
 * +-----------+---------------+
 * |B5         |0.176 x 0.250  |
 * +-----------+---------------+
 * |Letter     |0.216 x 0.279  |
 * +-----------+---------------+
 * |Legal      |0.216 x 0.356  |
 * +-----------+---------------+
 * |Executive  |0.191 x 0.254  |
 * +-----------+---------------+
 * |A0         |0.841 x 1.189  |
 * +-----------+---------------+
 * |A1         |0.594 x 0.841  |
 * +-----------+---------------+
 * |A2         |0.420 x 0.594  |
 * +-----------+---------------+
 * |A3         |0.297 x 0.420  |
 * +-----------+---------------+
 * |A5         |0.148 x 0.210  |
 * +-----------+---------------+
 * |A6         |0.105 x 0.148  |
 * +-----------+---------------+
 * |A7         |0.074 x 0.105  |
 * +-----------+---------------+
 * |A8         |0.052 x 0.074  |
 * +-----------+---------------+
 * |A9         |0.037 x 0.052  |
 * +-----------+---------------+
 * |B0         |1.000 x 1.414  |
 * +-----------+---------------+
 * |B1         |0.500 x 0.707  |
 * +-----------+---------------+
 * |B10        |0.031 x 0.044  |
 * +-----------+---------------+
 * |B2         |0.500 x 0.707  |
 * +-----------+---------------+
 * |B3         |0.353 x 0.500  |
 * +-----------+---------------+
 * |B4         |0.250 x 0.353  |
 * +-----------+---------------+
 * |B6         |0.125 x 0.176  |
 * +-----------+---------------+
 * |B7         |0.088 x 0.125  |
 * +-----------+---------------+
 * |B8         |0.062 x 0.088  |
 * +-----------+---------------+
 * |B9         |0.044 x 0.062  |
 * +-----------+---------------+
 * |C5E        |0.163 x 0.229  |
 * +-----------+---------------+
 * |Comm10E    |0.105 x 0.241  |
 * +-----------+---------------+
 * |DLE        |0.110 x 0.220  |
 * +-----------+---------------+
 * |Folio      |0.210 x 0.330  |
 * +-----------+---------------+
 * |Ledger     |0.432 x 0.279  |
 * +-----------+---------------+
 * |Tabloid    |0.279 x 0.432  |
 * +-----------+---------------+
 *
 * \endverbatim
 */
void gr_beginprintext(char *pathname, char *mode, char *format, char *orientation)
{
  int wkid = 6, wstype = 62;
  char *type;
  double width = 0.210, height = 0.297;
  format_t *p = formats;
  int color = 0, landscape = 0;

  check_autoinit;

  if (!flag_printing)
    {
      if ((type = strrchr(pathname, '.')) != NULL) wstype = gks_wstype(type + 1);

      if (wstype >= 0)
        {
          if (str_casecmp(mode, "Color") == 0)
            color = 1;
          else if (str_casecmp(mode, "GrayScale") != 0)
            fprintf(stderr, "%s: invalid color mode\n", mode);

          while (p->format != NULL)
            {
              if (str_casecmp(p->format, format) == 0)
                {
                  width = p->width * 0.9;
                  height = p->height * 0.9;
                  break;
                }
              p++;
            }
          if (p->format == NULL) fprintf(stderr, "%s: invalid page size\n", format);

          if (str_casecmp(orientation, "Landscape") == 0)
            landscape = 1;
          else if (str_casecmp(orientation, "Portrait") != 0)
            fprintf(stderr, "%s: invalid page orientation\n", orientation);

          if (wstype == 62)
            {
              if (!color) wstype -= 1;
              if (landscape) wstype += 2;
            }

          gks_open_ws(wkid, pathname, wstype);
          gks_activate_ws(wkid);

          if (!landscape)
            {
              gks_set_ws_viewport(wkid, 0.0, width, 0.0, height);
              if (width < height)
                gks_set_ws_window(wkid, 0.0, width / height, 0.0, 1.0);
              else
                gks_set_ws_window(wkid, 0.0, 1.0, 0.0, height / width);
            }
          else
            {
              gks_set_ws_viewport(wkid, 0.0, height, 0.0, width);
              if (width < height)
                gks_set_ws_window(wkid, 0.0, 1.0, 0.0, width / height);
              else
                gks_set_ws_window(wkid, 0.0, height / width, 0.0, 1.0);
            }

          flag_printing = 1;
        }
    }
  else
    fprintf(stderr, "print device already activated\n");
}

void gr_endprint(void)
{
  int wkid = 6;

  if (flag_printing)
    {
      if (!autoinit) /* GKS may have been closed by gr_emergencyclosegks() */
        {
          gks_deactivate_ws(wkid);
          gks_close_ws(wkid);
        }
      flag_printing = 0;
    }
  else
    fprintf(stderr, "no print device activated\n");
}

void gr_ndctowc(double *x, double *y)
{
  check_autoinit;

  *x = x_log((*x - nx.b) / nx.a);
  *y = y_log((*y - nx.d) / nx.c);
}

void gr_wctondc(double *x, double *y)
{
  check_autoinit;

  *x = nx.a * x_lin(*x) + nx.b;
  *y = nx.c * y_lin(*y) + nx.d;
}

void gr_wc3towc(double *x, double *y, double *z)
{
  check_autoinit;

  apply_world_xform(x, y, z);
}

/*!
 * Draw a rectangle using the current line attributes.
 *
 * \param[in] xmin Left edge of the rectangle
 * \param[in] xmax Right edge of the rectangle
 * \param[in] ymin Bottom edge of the rectangle
 * \param[in] ymax Upper edge of the rectangle
 */
void gr_drawrect(double xmin, double xmax, double ymin, double ymax)
{
  int errind, style;
  double x[5], y[5];
  int codes[] = {'M', 'L', 'L', 'L', 'S'};

  check_autoinit;

  gks_inq_fill_int_style(&errind, &style);

  if (style != GKS_K_INTSTYLE_SOLID_WITH_BORDER)
    {
      x[0] = x[3] = min(xmin, xmax);
      x[1] = x[2] = max(xmin, xmax);
      x[4] = x[0];
      y[0] = y[1] = min(ymin, ymax);
      y[2] = y[3] = max(ymin, ymax);
      y[4] = y[0];

      polyline(5, x, y);
    }
  else
    {
      x[1] = x[2] = x_lin(max(xmin, xmax));
      x[0] = x[3] = x_lin(min(xmin, xmax));
      y[2] = y[3] = y_lin(max(ymin, ymax));
      y[0] = y[1] = y_lin(min(ymin, ymax));

      gks_gdp(4, x, y, GKS_K_GDP_DRAW_PATH, 5, codes);
    }

  if (flag_stream)
    gr_writestream("<drawrect xmin=\"%g\" xmax=\"%g\" ymin=\"%g\" ymax=\"%g\"/>\n", xmin, xmax, ymin, ymax);
}

/*!
 * Draw a filled rectangle using the current fill attributes.
 *
 * \param[in] xmin Left edge of the rectangle
 * \param[in] xmax Right edge of the rectangle
 * \param[in] ymin Bottom edge of the rectangle
 * \param[in] ymax Upper edge of the rectangle
 */
void gr_fillrect(double xmin, double xmax, double ymin, double ymax)
{
  int errind, style;
  double bwidth, x[4], y[4];
  int codes[] = {'M', 'L', 'L', 'L', 'f'};

  check_autoinit;

  gks_inq_fill_int_style(&errind, &style);

  if (style != GKS_K_INTSTYLE_SOLID_WITH_BORDER)
    {
      x[0] = x[3] = min(xmin, xmax);
      x[1] = x[2] = max(xmin, xmax);
      y[0] = y[1] = min(ymin, ymax);
      y[2] = y[3] = max(ymin, ymax);

      fillarea(4, x, y);
    }
  else
    {
      x[0] = min(x_lin(xmin), x_lin(xmax));
      y[0] = min(y_lin(ymin), y_lin(ymax));
      x[1] = max(x_lin(xmin), x_lin(xmax));
      y[1] = max(y_lin(ymin), y_lin(ymax));

      x[1] = x[2] = x_lin(max(xmin, xmax));
      x[0] = x[3] = x_lin(min(xmin, xmax));
      y[2] = y[3] = y_lin(max(ymin, ymax));
      y[0] = y[1] = y_lin(min(ymin, ymax));

      gr_inqborderwidth(&bwidth);
      if (bwidth != 0) codes[4] = 'F';

      gks_gdp(4, x, y, GKS_K_GDP_DRAW_PATH, 5, codes);
    }

  if (flag_stream)
    gr_writestream("<fillrect xmin=\"%g\" xmax=\"%g\" ymin=\"%g\" ymax=\"%g\"/>\n", xmin, xmax, ymin, ymax);
}

/*!
 * Draw a circular or elliptical arc covering the specified rectangle.
 *
 * \param[in] xmin Left edge of the rectangle
 * \param[in] xmax Right edge of the rectangle
 * \param[in] ymin Bottom edge of the rectangle
 * \param[in] ymax Upper edge of the rectangle
 * \param[in] a1 The start angle
 * \param[in] a2 The end angle
 *
 * The resulting arc begins at a1 and ends at a2 degrees. Angles are
 * interpreted such that 0 degrees is at the 3 o'clock position. The center of
 * the arc is the center of the given rectangle.
 */
void gr_drawarc(double xmin, double xmax, double ymin, double ymax, double a1, double a2)
{
  int errind, style;
  double xcenter, ycenter, width, height, start, end, a;
  int n;
  double x[361], y[361];
  int codes[3] = {'M', 'A', 'S'};

  check_autoinit;

  gks_inq_fill_int_style(&errind, &style);

  xcenter = (x_lin(xmin) + x_lin(xmax)) / 2.0;
  ycenter = (y_lin(ymin) + y_lin(ymax)) / 2.0;
  width = fabs(x_lin(xmax) - x_lin(xmin)) / 2.0;
  height = fabs(y_lin(ymax) - y_lin(ymin)) / 2.0;

  if (style != GKS_K_INTSTYLE_SOLID_WITH_BORDER)
    {
      start = min(a1, a2);
      end = max(a1, a2);
      start += ((int)(end - start)) / 360 * 360;
      /* Ensure that two equivalent but unequal angles result in a full arc. */
      if (fabs(end - start) < FEPS && fabs(a1 - a2) > FEPS)
        {
          end += 360;
        }

      n = 0;
      for (a = start; a <= end; a++)
        {
          x[n] = x_log(xcenter + width * cos(a * M_PI / 180));
          y[n] = y_log(ycenter + height * sin(a * M_PI / 180));
          n++;
        }
      if (fabs((a - 1) - end) > FEPS)
        {
          x[n] = x_log(xcenter + width * cos(end * M_PI / 180));
          y[n] = y_log(ycenter + height * sin(end * M_PI / 180));
          n++;
        }

      if (n > 1)
        {
          polyline(n, x, y);
        }
    }
  else
    {
      x[0] = xcenter + width * cos(a1);
      y[0] = ycenter + height * sin(a1);
      x[1] = width;
      y[1] = height;
      x[2] = a1 * M_PI / 180;
      y[2] = a2 * M_PI / 180;
      x[3] = y[3] = 0;

      gks_gdp(4, x, y, GKS_K_GDP_DRAW_PATH, 3, codes);
    }

  if (flag_stream)
    {
      gr_writestream("<drawarc xmin=\"%g\" xmax=\"%g\" ymin=\"%g\" ymax=\"%g\" "
                     "a1=\"%g\" a2=\"%g\"/>\n",
                     xmin, xmax, ymin, ymax, a1, a2);
    }
}

/*!
 * Fill a circular or elliptical arc covering the specified rectangle.
 *
 * \param[in] xmin Left edge of the rectangle
 * \param[in] xmax Right edge of the rectangle
 * \param[in] ymin Bottom edge of the rectangle
 * \param[in] ymax Upper edge of the rectangle
 * \param[in] a1 The start angle
 * \param[in] a2 The end angle
 *
 * The resulting arc begins at a1 and ends at a2 degrees. Angles are
 * interpreted such that 0 degrees is at the 3 o'clock position. The center of
 * the arc is the center of the given rectangle.
 */
void gr_fillarc(double xmin, double xmax, double ymin, double ymax, double a1, double a2)
{
  int errind, style;
  double xcenter, ycenter, width, height, start, end, a;
  int n;
  double bwidth, x[362], y[362];
  int codes[3] = {'M', 'A', 'f'};

  check_autoinit;

  gks_inq_fill_int_style(&errind, &style);

  xcenter = (x_lin(xmin) + x_lin(xmax)) / 2.0;
  ycenter = (y_lin(ymin) + y_lin(ymax)) / 2.0;
  width = fabs(x_lin(xmax) - x_lin(xmin)) / 2.0;
  height = fabs(y_lin(ymax) - y_lin(ymin)) / 2.0;

  if (style != GKS_K_INTSTYLE_SOLID_WITH_BORDER)
    {
      start = min(a1, a2);
      end = max(a1, a2);
      start += ((int)(end - start)) / 360 * 360;
      /* Ensure that two equivalent but unequal angles result in a full arc. */
      if (fabs(end - start) < FEPS && fabs(a1 - a2) > FEPS)
        {
          end += 360;
        }

      x[0] = x_log(xcenter);
      y[0] = x_log(ycenter);
      n = 1;
      for (a = start; a <= end; a++)
        {
          x[n] = x_log(xcenter + width * cos(a * M_PI / 180));
          y[n] = y_log(ycenter + height * sin(a * M_PI / 180));
          n++;
        }
      if (fabs((a - 1) - end) > FEPS)
        {
          x[n] = x_log(xcenter + width * cos(end * M_PI / 180));
          y[n] = y_log(ycenter + height * sin(end * M_PI / 180));
          n++;
        }

      if (n > 2)
        {
          fillarea(n, x, y);
        }
    }
  else
    {
      x[0] = xcenter + width * cos(a1);
      y[0] = ycenter + height * sin(a1);
      x[1] = width;
      y[1] = height;
      x[2] = a1 * M_PI / 180;
      y[2] = a2 * M_PI / 180;
      x[3] = y[3] = 0;

      gr_inqborderwidth(&bwidth);
      if (bwidth != 0) codes[2] = 'F';

      gks_gdp(4, x, y, GKS_K_GDP_DRAW_PATH, 3, codes);
    }

  if (flag_stream)
    {
      gr_writestream("<fillarc xmin=\"%g\" xmax=\"%g\" ymin=\"%g\" ymax=\"%g\" "
                     "a1=\"%g\" a2=\"%g\"/>\n",
                     xmin, xmax, ymin, ymax, a1, a2);
    }
}

static void addpath(double x, double y)
{
  xpath[npath] = x;
  ypath[npath] = y;
  npath += 1;
}

static void closepath(int fill)
{
  if (fill)
    {
      if (npath > 2) gks_fillarea(npath, xpath, ypath);
    }
  else if (npath > 1)
    gks_polyline(npath, xpath, ypath);
  npath = 0;
}

static void quad_bezier(double x[3], double y[3], int n)
{
  int i;
  double t, a, b, c;

  if (npath + n >= maxpath) reallocate(npath + n);

  for (i = 0; i < n; i++)
    {
      t = (double)i / (n - 1);
      a = pow((1.0 - t), 2.0);
      b = 2.0 * t * (1.0 - t);
      c = pow(t, 2.0);
      addpath(a * x[0] + b * x[1] + c * x[2], a * y[0] + b * y[1] + c * y[2]);
    }
}

static void cubic_bezier(double x[4], double y[4], int n)
{
  int i;
  double t, a, b, c, d;

  if (npath + n >= maxpath) reallocate(npath + n);

  for (i = 0; i < n; i++)
    {
      t = (double)i / (n - 1);
      a = pow((1.0 - t), 3.0);
      b = 3.0 * t * pow((1.0 - t), 2.0);
      c = 3.0 * pow(t, 2.0) * (1.0 - t);
      d = pow(t, 3.0);
      addpath(a * x[0] + b * x[1] + c * x[2] + d * x[3], a * y[0] + b * y[1] + c * y[2] + d * y[3]);
    }
}

/*!
 * Draw simple and compound outlines consisting of line segments and bezier
 * curves.
 *
 * \param[in] n The number of vertices
 * \param[in] vertices A pointer to the vertices
 * \param[in] codes A pointer to the path codes
 * \param[in] fill A flag indication whether resulting path is to be filled or
 *                 not
 *
 * \verbatim embed:rst:leading-asterisk
 *
 * The following path codes are recognized:
 *
 * +----------+-----------------------------------------------------------+
 * |      STOP|end the entire path                                        |
 * +----------+-----------------------------------------------------------+
 * |    MOVETO|move to the given vertex                                   |
 * +----------+-----------------------------------------------------------+
 * |    LINETO|draw a line from the current position to the given vertex  |
 * +----------+-----------------------------------------------------------+
 * |    CURVE3|draw a quadratic Bezier curve                              |
 * +----------+-----------------------------------------------------------+
 * |    CURVE4|draw a cubic Bezier curve                                  |
 * +----------+-----------------------------------------------------------+
 * | CLOSEPOLY|draw a line segment to the start point of the current path |
 * +----------+-----------------------------------------------------------+
 *
 * \endverbatim
 */
void gr_drawpath(int n, vertex_t *vertices, unsigned char *codes, int fill)
{
  int i, j = 0, code, nan = 0;

  check_autoinit;

  if (n >= maxpath) reallocate(n);

  if (codes == NULL)
    {
      memset(opcode, GR_LINETO, n);
      opcode[0] = GR_MOVETO;
    }
  else
    memmove(opcode, codes, n);

  for (i = 0; i < n; i++)
    {
      if (is_nan(vertices[i].x) || is_nan(vertices[i].y))
        {
          nan = 1;
          continue;
        }
      else
        {
          opcode[j] = nan ? GR_MOVETO : opcode[i];
          nan = 0;
        }
      xpoint[j] = vertices[i].x;
      ypoint[j] = vertices[i].y;
      j++;
    }

  for (i = 0; i < j; i++)
    {
      code = opcode[i];
      if (code == GR_STOP)
        break;
      else if (code == GR_MOVETO)
        {
          closepath(fill);
          addpath(xpoint[i], ypoint[i]);
        }
      else if (code == GR_LINETO)
        addpath(xpoint[i], ypoint[i]);
      else if (code == GR_CURVE3)
        {
          quad_bezier(xpoint + i - 1, ypoint + i - 1, 20);
          i += 1;
        }
      else if (code == GR_CURVE4)
        {
          cubic_bezier(xpoint + i - 1, ypoint + i - 1, 20);
          i += 2;
        }
      else if (code == GR_CLOSEPOLY)
        {
          addpath(xpoint[i], ypoint[i]);
          closepath(fill);
        }
    }
  closepath(fill);

  if (flag_stream)
    {
      gr_writestream("<drawpath len=\"%d\"", n);
      print_vertex_array("vertices", n, vertices);
      print_byte_array("codes", codes != NULL ? n : 0, codes);
      gr_writestream(" fill=\"%d\"/>\n", fill);
    }
}

/*!
 * Set the arrow style to be used for subsequent arrow commands.
 *
 * \param[in] style The arrow style to be used
 *
 * This function defines the arrow style for subsequent arrow primitives.
 * The default arrow style is 1.
 *
 * \verbatim embed:rst:leading-asterisk
 *
 * +---+----------------------------------+
 * |  1|simple, single-ended              |
 * +---+----------------------------------+
 * |  2|simple, single-ended, acute head  |
 * +---+----------------------------------+
 * |  3|hollow, single-ended              |
 * +---+----------------------------------+
 * |  4|filled, single-ended              |
 * +---+----------------------------------+
 * |  5|triangle, single-ended            |
 * +---+----------------------------------+
 * |  6|filled triangle, single-ended     |
 * +---+----------------------------------+
 * |  7|kite, single-ended                |
 * +---+----------------------------------+
 * |  8|filled kite, single-ended         |
 * +---+----------------------------------+
 * |  9|simple, double-ended              |
 * +---+----------------------------------+
 * | 10|simple, double-ended, acute head  |
 * +---+----------------------------------+
 * | 11|hollow, double-ended              |
 * +---+----------------------------------+
 * | 12|filled, double-ended              |
 * +---+----------------------------------+
 * | 13|triangle, double-ended            |
 * +---+----------------------------------+
 * | 14|filled triangle, double-ended     |
 * +---+----------------------------------+
 * | 15|kite, double-ended                |
 * +---+----------------------------------+
 * | 16|filled kite, double-ended         |
 * +---+----------------------------------+
 * | 17|double line, single-ended         |
 * +---+----------------------------------+
 * | 18|double line, double-ended         |
 * +---+----------------------------------+
 *
 * \endverbatim
 */
void gr_setarrowstyle(int style)
{
  check_autoinit;

  if (style >= 1 && style <= 18) arrow_style = style - 1;

  if (flag_stream) gr_writestream("<setarrowstyle style=\"%d\"/>\n", style);
}

/*!
 * Set the arrow size to be used for subsequent arrow commands.
 *
 * \param[in] size The arrow size to be used
 *
 * This function defines the arrow size for subsequent arrow primitives.
 * The default arrow size is 1.
 */
void gr_setarrowsize(double size)
{
  check_autoinit;

  if (size > 0) arrow_size = size;

  if (flag_stream) gr_writestream("<setarrowsize size=\"%g\"/>\n", size);
}

/*!
 * Draw an arrow between two points.
 *
 * \param[in] x1 The X coordinate of the arrow start point (tail)
 * \param[in] y1 The Y coordinate of the arrow start point (tail)
 * \param[in] x2 The X coordinate of the arrow end point (head)
 * \param[in] y2 The Y coordinate of the arrow end point (head)
 *
 * Different arrow styles (angles between arrow tail and wing, optionally filled
 * heads, double headed arrows) are available and can be set with the
 * gr_setarrowstyle function.
 */
void gr_drawarrow(double x1, double y1, double x2, double y2)
{
  double xs, ys, xe, ye;
  int errind, ltype, intstyle, tnr;
  double a, c, xc, yc, f, fh;
  int fill, i, j, n;
  double xi, yi, x[10], y[10];

  check_autoinit;

  gks_inq_pline_linetype(&errind, &ltype);
  gks_inq_fill_int_style(&errind, &intstyle);
  gks_inq_current_xformno(&errind, &tnr);

  if (tnr != NDC)
    {
      xs = nx.a * x_lin(x1) + nx.b;
      ys = nx.c * y_lin(y1) + nx.d;
      xe = nx.a * x_lin(x2) + nx.b;
      ye = nx.c * y_lin(y2) + nx.d;
    }
  else
    {
      xs = x1;
      ys = y1;
      xe = x2;
      ye = y2;
    }

  gks_set_fill_int_style(GKS_K_INTSTYLE_SOLID);

  c = sqrt((xe - xs) * (xe - xs) + (ye - ys) * (ye - ys));
  if (ys != ye)
    a = acos(fabs(xe - xs) / c);
  else
    a = 0;
  if (ye < ys) a = 2 * M_PI - a;
  if (xe < xs) a = M_PI - a;
  a -= M_PI / 2;

  xc = (xs + xe) / 2;
  yc = (ys + ye) / 2;
  f = 0.01 * c / 2;
  fh = 0.15 / c * arrow_size;

  j = 0;
  while ((n = vertex_list[arrow_style][j++]) != 0)
    {
      fill = n < 0;
      n = abs(n);
      gks_set_pline_linetype(n > 2 ? GKS_K_LINETYPE_SOLID : ltype);
      for (i = 0; i < n; i++)
        {
          xi = vertex_list[arrow_style][j++];
          yi = vertex_list[arrow_style][j++];
          xi *= fh;
          if (yi < 0)
            yi = (yi + 100) * fh - 100;
          else
            yi = (yi - 100) * fh + 100;
          xi *= f;
          yi *= f;
          x[i] = xc + cos(a) * xi - sin(a) * yi;
          y[i] = yc + sin(a) * xi + cos(a) * yi;
          if (tnr != NDC)
            {
              x[i] = (x[i] - nx.b) / nx.a;
              y[i] = (y[i] - nx.d) / nx.c;
              if (lx.scale_options)
                {
                  x[i] = x_log(x[i]);
                  y[i] = y_log(y[i]);
                }
            }
        }
      if (fill)
        gks_fillarea(n, x, y);
      else
        gks_polyline(n, x, y);
    }

  gks_set_fill_int_style(intstyle);
  gks_set_pline_linetype(ltype);

  if (flag_stream) gr_writestream("<drawarrow x1=\"%g\" y1=\"%g\" x2=\"%g\" y2=\"%g\"/>\n", x1, y1, x2, y2);
}

static void drawimage_calculation(double xmin, double xmax, double ymin, double ymax, int width, int height, int *data,
                                  int model)
{
  int *img = data, *imgT;
  int n, i, j, w, h;
  double hue, saturation, value, red, green, blue, x, y;

  if (model == GR_MODEL_HSV)
    {
      n = width * height;
      img = (int *)xmalloc(n * sizeof(int));
      for (i = 0; i < n; i++)
        {
          hue = (data[i] & 0xff) / 255.0;
          saturation = ((data[i] & 0xff00) >> 8) / 255.0;
          value = ((data[i] & 0xff0000) >> 16) / 255.0;
          gr_hsvtorgb(hue, saturation, value, &red, &green, &blue);
          img[i] = (data[i] & 0xff000000) | ((int)(red * 255) << 16) | ((int)(green * 255) << 8) | ((int)(blue * 255));
        }
    }

  if ((lx.scale_options & ~(GR_OPTION_FLIP_X | GR_OPTION_FLIP_Y | GR_OPTION_FLIP_Z)) != 0)
    {
      linear_xform lx_original;
      w = max(width, 2000);
      h = max(height, 2000);
      lx_original = lx;
      lx.xmin = xmin;
      lx.xmax = xmax;
      lx.a = (xmax - xmin) / blog(lx.basex, xmax / xmin);
      lx.b = xmin - lx.a * blog(lx.basex, xmin);
      lx.ymin = ymin;
      lx.ymax = ymax;
      lx.c = (ymax - ymin) / blog(lx.basey, ymax / ymin);
      lx.d = ymin - lx.c * blog(lx.basey, ymin);
      imgT = (int *)xmalloc(w * h * sizeof(int));
      for (i = 0; i < w; i++)
        {
          if (w > 1)
            {
              x = (x_log(xmin + i * (xmax - xmin) / (w - 1)) - xmin) / (xmax - xmin);
              if (x < 0)
                x = 0;
              else if (x > 1)
                x = 1;
            }
          else
            x = 0;
          for (j = 0; j < h; j++)
            {
              if (h > 1)
                {
                  y = (y_log(ymin + (h - 1 - j) * (ymax - ymin) / (h - 1)) - ymin) / (ymax - ymin);
                  if (y < 0)
                    y = 0;
                  else if (y > 1)
                    y = 1;
                }
              else
                y = 0;
              imgT[i + j * w] = img[(int)min(x * width, width - 1) + (int)min((1 - y) * height, height - 1) * width];
            }
        }
      lx = lx_original;
      if (lx.scale_options & GR_OPTION_FLIP_X)
        {
          double t = xmin;
          xmin = xmax;
          xmax = t;
        }
      if (lx.scale_options & GR_OPTION_FLIP_Y)
        {
          double t = ymin;
          ymin = ymax;
          ymax = t;
        }
      gks_draw_image(x_lin(xmin), y_lin(ymax), x_lin(xmax), y_lin(ymin), w, h, imgT);
      free(imgT);
    }
  else
    {
      if (lx.scale_options & GR_OPTION_FLIP_X)
        {
          double tmp = xmin;
          xmin = xmax;
          xmax = tmp;
        }
      if (lx.scale_options & GR_OPTION_FLIP_Y)
        {
          double tmp = ymin;
          ymin = ymax;
          ymax = tmp;
        }
      gks_draw_image(xmin, ymax, xmax, ymin, width, height, img);
    }
}

/*!
 * Draw an image into a given rectangular area.
 *
 * \param[in] xmin X coordinate of the lower left point of the rectangle
 * \param[in] ymin Y coordinate of the lower left point of the rectangle
 * \param[in] xmax X coordinate of the upper right point of the rectangle
 * \param[in] ymax Y coordinate of the upper right point of the rectangle
 * \param[in] width X dimension of the color index array
 * \param[in] height Y dimension of the color index array
 * \param[in] data color array
 * \param[in] model color model
 *
 * The points (xmin, ymin) and (xmax, ymax) are world coordinates defining
 * diagonally opposite corner points of a rectangle. This rectangle is divided
 * into width by height cells. The two-dimensional array data specifies colors
 * for each cell.
 *
 * \verbatim embed:rst:leading-asterisk
 *
 * The available color models are:
 *
 * +--------------------------+---+-----------+
 * |GR_MODEL_RGB              |  0|   AABBGGRR|
 * +--------------------------+---+-----------+
 * |GR_MODEL_HSV              |  1|   AAVVSSHH|
 * +--------------------------+---+-----------+
 *
 * \endverbatim
 */
void gr_drawimage(double xmin, double xmax, double ymin, double ymax, int width, int height, int *data, int model)
{
  int n;

  check_autoinit;

  drawimage_calculation(xmin, xmax, ymin, ymax, width, height, data, model);

  if (flag_stream)
    {
      n = width * height;
      gr_writestream("<drawimage xmin=\"%g\" xmax=\"%g\" ymin=\"%g\" ymax=\"%g\" "
                     "width=\"%d\" height=\"%d\"",
                     xmin, xmax, ymin, ymax, width, height);
      print_int_array("data", n, data);
      gr_writestream("model=\"%d\"/>\n", model);
    }
}

/*!
 * Allows drawing of shadows, realized by images painted underneath,
 * and offset from, graphics objects such that the shadow mimics the effect of
 * a light source cast on the graphics objects.
 *
 * \param[in] offsetx An x-offset, which specifies how far in the horizontal
 *                    direction the shadow is offset from the object
 * \param[in] offsety A y-offset, which specifies how far in the vertical
 *                    direction the shadow is offset from the object
 * \param[in] blur A blur value, which specifies whether the object has a
 *                    hard or a diffuse edge
 */
void gr_setshadow(double offsetx, double offsety, double blur)
{
  check_autoinit;

  gks_set_shadow(offsetx, offsety, blur);
}

/*!
 * Set the value of the alpha component associated with GR colors.
 *
 * \param[in] alpha An alpha value (0.0 - 1.0)
 */
void gr_settransparency(double alpha)
{
  check_autoinit;

  gks_set_transparency(alpha);
}

/*!
 * Inquire the value of the alpha component associated with GR colors.
 *
 * \param[out] alpha A pointer to a double value which will hold the transparency value after the function call
 */
void gr_inqtransparency(double *alpha)
{
  int errind;

  check_autoinit;

  gks_inq_transparency(&errind, alpha);
}

/*!
 * Change the coordinate transformation according to the given matrix.
 *
 * \param[in] mat 2D transformation matrix
 */
void gr_setcoordxform(double mat[3][2])
{
  check_autoinit;

  gks_set_coord_xform(mat);
}

/*!
 * Open a file for graphics output.
 *
 * \param[in] path Filename for the graphics file.
 *
 * gr_begingraphics allows to write all graphics output into a XML-formatted
 * file until the gr_endgraphics functions is called. The resulting file may
 * later be imported with the gr_importgraphics function.
 */
void gr_begingraphics(char *path)
{
  if (!flag_graphics)
    {
      if (gr_openstream(path) == 0)
        {
          gr_writestream(XML_HEADER);
          gr_writestream(GR_HEADER);
          flag_stream = flag_graphics = 1;
        }
      else
        fprintf(stderr, "%s: open failed\n", path);
    }
}

void gr_endgraphics(void)
{
  if (flag_graphics)
    {
      gr_writestream(GR_TRAILER);
      gr_closestream();
      flag_stream = debug != NULL;
      flag_graphics = 0;
    }
}

static void latex2image(char *string, int pointSize, double *rgb, int *width, int *height, int **data)
{
  static char *temp = NULL;
  int color;
  char s[FILENAME_MAX], path[FILENAME_MAX], cache[33];
  char *null, cmd[2 * FILENAME_MAX + 200];
  static char *preamble = NULL;
  char tex[FILENAME_MAX], dvi[FILENAME_MAX], png[FILENAME_MAX];
  FILE *stream;
  int math, ret;
#ifdef _WIN32
  wchar_t w_path[MAX_PATH];
#endif

  color = ((int)(rgb[0] * 255)) + ((int)(rgb[1] * 255) << 8) + ((int)(rgb[2] * 255) << 16) + (255 << 24);
  snprintf(s, FILENAME_MAX, "%d%x%s", pointSize, color, string);
  md5(s, cache, FILENAME_MAX);
  if (temp == NULL)
    {
#ifdef _WIN32
      temp = (char *)gks_getenv("TEMP");
#else
      temp = mkdtemp("gr-temp");
#endif
      if (temp == NULL) temp = TMPDIR;
    }
  snprintf(path, FILENAME_MAX, "%s%sgr-cache-%s.png", temp, DIRDELIM, cache);

#ifdef _WIN32
  MultiByteToWideChar(CP_UTF8, 0, path, strlen(path) + 1, w_path, MAX_PATH);
  if (_waccess(w_path, R_OK) != 0)
#else
  if (access(path, R_OK) != 0)
#endif
    {
      math = strstr(string, "\\(") == NULL;
      snprintf(tex, FILENAME_MAX, "%s%s%s.tex", temp, DIRDELIM, cache);
      snprintf(dvi, FILENAME_MAX, "%s%s%s.dvi", temp, DIRDELIM, cache);
      snprintf(png, FILENAME_MAX, "%s%s%s.png", temp, DIRDELIM, cache);
#ifdef _WIN32
      null = "NUL";
      MultiByteToWideChar(CP_UTF8, 0, tex, strlen(tex) + 1, w_path, MAX_PATH);
      stream = _wfopen(w_path, L"w");
#else
      null = "/dev/null";
      stream = fopen(tex, "w");
#endif
      if (preamble == NULL)
        {
          preamble = (char *)gks_getenv("GR_LATEX_PREAMBLE");
        }
      if (preamble != NULL)
        {
          if (strcmp(preamble, "AMS") == 0)
            {
              preamble = "\
\\documentclass{article}\n\
\\pagestyle{empty}\n\
\\usepackage{amssymb}\n\
\\usepackage{amsmath}\n\
\\usepackage[dvips]{color}\n\
\\begin{document}\n";
            }
        }
      else
        {
          preamble = "\
\\documentclass{article}\n\
\\pagestyle{empty}\n\
\\usepackage[dvips]{color}\n\
\\begin{document}\n";
        }
      fprintf(stream, "%s", preamble);
      if (math) fprintf(stream, "\\[\n");
      fprintf(stream, "\\color[rgb]{%.3f,%.3f,%.3f} {\n", rgb[0], rgb[1], rgb[2]);
      fwrite(string, strlen(string), 1, stream);
      fprintf(stream, "}\n");
      if (math) fprintf(stream, "\\]\n");
      fprintf(stream, "\\end{document}");
      fclose(stream);

      snprintf(cmd, 2 * FILENAME_MAX + 200, "latex -interaction=batchmode -halt-on-error -output-directory=%s %s >%s",
               temp, tex, null);
      ret = system(cmd);

#ifdef _WIN32
      MultiByteToWideChar(CP_UTF8, 0, dvi, strlen(dvi) + 1, w_path, MAX_PATH);
      if (ret == 0 && _waccess(w_path, R_OK) == 0)
#else
      if (ret == 0 && access(dvi, R_OK) == 0)
#endif
        {
          snprintf(cmd, 2 * FILENAME_MAX + 200, "dvipng -bg transparent -q -T tight -x %d %s -o %s >%s",
                   pointSize * 100, dvi, png, null);
          ret = system(cmd);
          if (ret == 0)
            {
              rename(png, path);
              if (remove(tex) != 0 || remove(dvi) != 0)
                {
                  fprintf(stderr, "error deleting temprorary files\n");
                }
            }
          else
            fprintf(stderr, "dvipng: PNG conversion failed\n");
        }
      else
        fprintf(stderr, "latex: failed to create a dvi file\n");
    }

#ifdef _WIN32
  MultiByteToWideChar(CP_UTF8, 0, path, strlen(path) + 1, w_path, MAX_PATH);
  if (_waccess(w_path, R_OK) == 0)
#else
  if (access(path, R_OK) == 0)
#endif
    {
      gr_readimage(path, width, height, data);
    }
}

int *rotl90(int m, int n, int *mat)
{
  int *trans = (int *)xcalloc(m * n, sizeof(int));
  int i, j;

  for (j = 0; j < n; j++)
    for (i = 0; i < m; i++) trans[(m - 1 - i) * n + j] = mat[j * m + i];

  return trans;
}

static int *rot180(int m, int n, int *mat)
{
  int *trans = (int *)xcalloc(m * n, sizeof(int));
  int i, j;

  for (j = 0; j < n; j++)
    for (i = 0; i < m; i++) trans[(n - 1 - j) * m + m - 1 - i] = mat[j * m + i];

  return trans;
}

static int *rotr90(int m, int n, int *mat)
{
  int *trans = (int *)xcalloc(m * n, sizeof(int));
  int i, j;

  for (j = 0; j < n; j++)
    for (i = 0; i < m; i++) trans[i * n + n - 1 - j] = mat[j * m + i];

  return trans;
}

static void mathtex(double x, double y, char *string, int inquire, double *tbx, double *tby)
{
  int wkid = 1, errind, conid, wtype, dcunit;
  int pointSize, pixels, color;
  double chh, rgb[3], ux, uy;
  int width, height, *data = NULL, w, h, *trans = NULL;
  double rad, rw, rh, rx, ry, xx, yy, bbx[4], bby[4];
  double x1, x2, y1, y2, midx, midy, sinf, cosf;
  int i, j, ii, jj, angle, path, halign, valign, tnr;

  gks_inq_ws_conntype(wkid, &errind, &conid, &wtype);
  gks_inq_max_ds_size(wtype, &errind, &dcunit, &rw, &rh, &width, &height);
  if (sizex > 0)
    pixels = sizex / rh * height;
  else
    pixels = 500;
  if (wtype == 101 || wtype == 102 || wtype == 120 || wtype == 382) pixels *= 8;

  gks_inq_text_height(&errind, &chh);
  gks_inq_text_color_index(&errind, &color);
  gks_inq_color_rep(wkid, color, GKS_K_VALUE_SET, &errind, &rgb[0], &rgb[1], &rgb[2]);

  pointSize = chh * pixels;
  latex2image(string, pointSize, rgb, &width, &height, &data);

  gks_inq_text_upvec(&errind, &ux, &uy);
  rad = -atan2(ux, uy);
  angle = (int)(rad * 180 / M_PI + 0.5);
  if (angle < 0) angle += 360;
  path = ((angle + 45) / 90) % 4;

  if (data != NULL)
    {
      rw = width / (double)pixels;
      rh = height / (double)pixels;

      gks_inq_text_align(&errind, &halign, &valign);

      rx = x;
      switch (halign)
        {
        case 2:
          rx -= 0.5 * rw;
          break;
        case 3:
          rx -= rw;
          break;
        }
      ry = y;
      switch (valign)
        {
        case 1:
          ry -= rh - chh * 0.04;
          break;
        case 2:
          ry -= rh;
          break;
        case 3:
          ry -= 0.5 * rh;
          break;
        case 5:
          ry -= chh * 0.04;
          break;
        }
      bbx[0] = rx;
      bbx[1] = rx + rw;
      bbx[2] = bbx[1];
      bbx[3] = bbx[0];
      bby[0] = ry;
      bby[1] = bby[0];
      bby[2] = ry + rh;
      bby[3] = bby[2];

      x1 = y1 = FLT_MAX;
      x2 = y2 = -FLT_MAX;

      for (i = 0; i < 4; i++)
        {
          xx = bbx[i] - x;
          yy = bby[i] - y;
          bbx[i] = x + cos(rad) * xx - sin(rad) * yy;
          bby[i] = y + sin(rad) * xx + cos(rad) * yy;

          x1 = min(x1, bbx[i]);
          x2 = max(x2, bbx[i]);
          y1 = min(y1, bby[i]);
          y2 = max(y2, bby[i]);
        }

      if (inquire)
        {
          for (i = 0; i < 4; i++)
            {
              tbx[i] = bbx[i];
              tby[i] = bby[i];
            }
        }
      else
        {
          gks_inq_current_xformno(&errind, &tnr);
          if (tnr != NDC) gks_select_xform(NDC);

          if (angle % 90 == 0)
            {
              switch (path)
                {
                case 0:
                  gks_draw_image(x1, y2, x2, y1, width, height, data);
                  break;
                case 1:
                  trans = rotl90(width, height, data);
                  gks_draw_image(x1, y2, x2, y1, height, width, trans);
                  free(trans);
                  break;
                case 2:
                  trans = rot180(width, height, data);
                  gks_draw_image(x1, y2, x2, y1, width, height, trans);
                  free(trans);
                  break;
                case 3:
                  trans = rotr90(width, height, data);
                  gks_draw_image(x1, y2, x2, y1, height, width, trans);
                  free(trans);
                  break;
                }
            }
          else
            {
              w = (int)((x2 - x1) * pixels + 0.5), h = (int)((y2 - y1) * pixels + 0.5);
              trans = (int *)xcalloc(w * h, sizeof(int));
              midx = ceil(0.5 * w);
              midy = ceil(0.5 * h);
              sinf = sin(rad);
              cosf = cos(rad);
              for (j = 0; j < h; j++)
                for (i = 0; i < w; i++)
                  {
                    xx = (i - midx) * cosf - (j - midy) * sinf;
                    yy = (i - midx) * sinf + (j - midy) * cosf;
                    ii = round(xx) + ceil(0.5 * width);
                    jj = round(yy) + ceil(0.5 * height);
                    if (ii >= 0 && jj >= 0 && ii < width && jj < height) trans[j * w + i] = data[jj * width + ii];
                  }
              gks_draw_image(x1, y2, x2, y1, w, h, trans);
              free(trans);
            }

          if (tnr != NDC) gks_select_xform(tnr);
        }

      free(data);
    }
}

void mathtex2(double x, double y, const char *formula, int inquire, double *tbx, double *tby, double *baseline);

/*!
 * Generate a character string starting at the given location. Strings can be
 * defined to create mathematical symbols and Greek letters using LaTeX syntax.
 *
 * \param[in] x The X coordinate of the starting position of the text string
 * \param[in] y The Y coordinate of the starting position of the text string
 * \param[in] string The text string to be drawn
 */
void gr_mathtex(double x, double y, char *string)
{
  char *s, *start;
  int len;
  int unused;
  int prec;

  check_autoinit;

  s = start = strdup(string);
  len = strlen(s);
  if (*s == '$' && s[len - 1] == '$')
    {
      s[len - 1] = '\0';
      start = s + 1;
    }

  gks_inq_text_fontprec(&unused, &unused, &prec);
  if (prec == 3)
    {
      mathtex2(x, y, start, 0, NULL, NULL, NULL);
    }
  else
    {
      mathtex(x, y, start, 0, NULL, NULL);
    }

  if (flag_stream) gr_writestream("<mathtex x=\"%g\" y=\"%g\" text=\"%s\"/>\n", x, y, string);

  free(s);
}

void gr_inqmathtex(double x, double y, char *string, double *tbx, double *tby)
{
  char *s, *start;
  int len;
  int unused;
  int prec;

  check_autoinit;

  s = start = strdup(string);
  len = strlen(s);
  if (*s == '$' && s[len - 1] == '$')
    {
      s[len - 1] = '\0';
      start = s + 1;
    }

  gks_inq_text_fontprec(&unused, &unused, &prec);
  if (prec == 3)
    {
      mathtex2(x, y, start, 1, tbx, tby, NULL);
    }
  else
    {
      mathtex(x, y, start, 1, tbx, tby);
    }

  free(s);
}

void mathtex2_3d(double x, double y, double z, const char *formula, int axis, double textScale, int inquire,
                 double *tbx, double *tby, double *tbz, double *baseline);

/*!
 * Generate a character string starting at the given location. Strings can be
 * defined to create mathematical symbols and Greek letters using a limited LaTeX syntax.
 *
 * \param[in] x The X coordinate of the starting position of the text string
 * \param[in] y The Y coordinate of the starting position of the text string
 * \param[in] z The Z coordinate of the starting position of the text string
 * \param[in] string The text string to be drawn
 * \param[in] axis The plane to draw on (1: YX-plane, 2: XY plane, 3: YZ plane, 4: XZ plane), negative flips direction
 */
void gr_mathtex3d(double x, double y, double z, char *string, int axis)
{
  char *s, *start;
  int len;

  check_autoinit;

  s = start = strdup(string);
  len = strlen(s);
  if (*s == '$' && s[len - 1] == '$')
    {
      s[len - 1] = '\0';
      start = s + 1;
    }

  mathtex2_3d(x, y, z, start, axis, text3d_get_height(), 0, NULL, NULL, NULL, NULL);

  if (flag_stream)
    gr_writestream("<mathtex3d x=\"%g\" y=\"%g\" z=\"%g\" text=\"%s\" axis=\"%d\"/>\n", x, y, z, string, axis);

  free(s);
}

/*!
 * This function calculates the bounding box of the text that would be drawn using gr_mathtex3d. tbx, tby, tbz contain
 * the corner coordinates, while baseline contains the baseline point.
 *
 * \param[in] x The X coordinate of the starting position of the text string in world coordinates
 * \param[in] y The Y coordinate of the starting position of the text string in world coordinates
 * \param[in] z The Z coordinate of the starting position of the text string in world coordinates
 * \param[in] string The text string that would be drawn
 * \param[in] axis The plane to draw on (1: YX-plane, 2: XY plane, 3: YZ plane, 4: XZ plane), negative flips direction
 * \param[in] tbx A 4-element double array to write the x-coordinates of the corners
 * \param[in] tby A 4-element double array to write the y-coordinates of the corners
 * \param[in] tbz A 4-element double array to write the z-coordinates of the corners
 * \param[in] baseline A 3-element (x, y, z) array to write the baseline point coordinates to
 */
void gr_inqmathtex3d(double x, double y, double z, char *string, int axis, double *tbx, double *tby, double *tbz,
                     double *baseline)
{
  char *s, *start;
  int len;

  check_autoinit;

  s = start = strdup(string);
  len = strlen(s);
  if (*s == '$' && s[len - 1] == '$')
    {
      s[len - 1] = '\0';
      start = s + 1;
    }

  mathtex2_3d(x, y, z, start, axis, text3d_get_height(), 1, tbx, tby, tbz, baseline);

  free(s);
}

static void append(double x, double y, char *string, int line_number, int math)
{
  text_node_t *prev = text;
  int errInd, n, wkId, font, prec;
  double cpx, cpy, tbx[4], tby[4];
  char *src, *dest;

  text = (text_node_t *)xcalloc(1, sizeof(text_node_t));
  text->next = NULL;
  if (head == NULL)
    head = text;
  else if (prev != NULL)
    prev->next = text;

  text->x = x;
  text->y = y;
  text->string = (char *)xcalloc(strlen(string) + 1, sizeof(char));
  src = string;
  dest = text->string;
  while (*src)
    {
      if (*src == '$' && *(src + 1) == '$') src++;
      *dest++ = *src++;
    }
  *dest = '\0';
  text->line_number = line_number;
  text->line_width = 0;
  text->math = math;

  gks_inq_open_ws(1, &errInd, &n, &wkId);
  if (math)
    {
      gks_inq_text_fontprec(&errInd, &font, &prec);
      if (prec == 3)
        {
          mathtex2(0, 0, text->string, 1, tbx, tby, text->baseline);
        }
      else
        {
          mathtex(0, 0, text->string, 1, tbx, tby);
        }
    }
  else
    {
      if (*text->string)
        gks_inq_text_extent(wkId, 0, 0, text->string, &errInd, &cpx, &cpy, tbx, tby);
      else
        {
          gks_inq_text_extent(wkId, 0, 0, "Ag", &errInd, &cpx, &cpy, tbx, tby);
          tbx[0] = tbx[1] = 0;
        }
    }

  text->width = tbx[1] - tbx[0];
  text->height = tby[2] - tby[1];
}

static text_node_t *parse(double x, double y, char *string, int inline_math)
{
  char *s, *start, *end;
  int line_number, math;

  head = text = NULL;
  line_number = 1;
  math = 0;

  s = (char *)xcalloc(strlen(string) + 1, sizeof(char));
  strcpy(s, string);

  start = end = s;
  while (*end)
    {
      if (*end == '\n')
        {
          math = 0;
          *end++ = '\0';
          append(x, y, start, line_number, math);
          start = end;
          line_number++;
        }
      else if (inline_math && !math && *end == '$' && *(end + 1) == '$')
        {
          end += 2;
        }
      else if (inline_math && *end == '$')
        {
          *end++ = '\0';
          append(x, y, start, line_number, math);
          math = !math;
          start = end;
        }
      else if (inline_math && *end == '\\' && *(end + 1) == '(')
        {
          *end++ = '\0';
          append(x, y, start, line_number, 0);
          start = ++end;
        }
      else if (inline_math && *end == '\\' && *(end + 1) == ')')
        {
          *end++ = '\0';
          append(x, y, start, line_number, 1);
          start = ++end;
        }
      else
        end++;
    }
  append(x, y, start, line_number, math);
  free(s);

  return head;
}

static void text_impl(double x, double y, char *string, int inline_math, int inquire, double *tbx, double *tby)
{
  int errInd, hAlign, vAlign;
  double chuX, chuY, angle, charHeight, xOff, yOff, lineWidth, lineHeight;
  text_node_t *textP, *p;
  int lineNumber = 1;
  double totalWidth = 0, totalHeight = 0, *baseLine;
  double xx, yy, sx, sy;
  int i;

  gks_inq_text_upvec(&errInd, &chuX, &chuY);
  gks_set_text_upvec(0, 1);
  angle = -atan2(chuX, chuY);

  gks_inq_text_height(&errInd, &charHeight);

  gks_inq_text_align(&errInd, &hAlign, &vAlign);
  gks_set_text_align(GKS_K_TEXT_HALIGN_LEFT, GKS_K_TEXT_VALIGN_HALF);

  text = textP = parse(x, y, string, inline_math);
  yOff = 0;
  while (textP != NULL)
    {
      lineWidth = 0;
      lineHeight = 0;
      p = textP;
      while (p != NULL)
        {
          if (p->line_number != lineNumber) break;
          lineHeight = max(p->height, lineHeight);
          lineWidth += p->width;
          p = p->next;
        }
      xOff = 0;
      yOff += 0.5 * lineHeight;

      totalWidth = max(totalWidth, lineWidth);
      totalHeight += lineHeight;

      while (textP != NULL && textP->line_number == lineNumber)
        {
          textP->x += xOff;
          textP->y -= yOff;

          xOff += textP->width;
          totalWidth = max(totalWidth, xOff);

          textP->line_width = lineWidth;
          textP = textP->next;
        }
      yOff += 0.5 * lineHeight;
      lineNumber += 1;
    }

  gks_set_text_upvec(chuX, chuY);

  if (!inquire)
    {
      p = text;
      while (p != NULL)
        {
          if (hAlign == 2)
            p->x += 0.5 * (totalWidth - p->line_width);
          else if (hAlign == 3)
            p->x += totalWidth - p->line_width;
          p = p->next;
        }

      textP = text;
      while (textP != NULL)
        {
          baseLine = NULL;
          p = text;
          while (p != NULL && p->line_number != textP->line_number)
            {
              p = p->next;
            }
          while (p != NULL && p->line_number == textP->line_number)
            {
              if (p->math)
                {
                  baseLine = p->baseline + 1;
                  break;
                }
              else
                p = p->next;
            }

          xx = textP->x - x;
          switch (hAlign)
            {
            case 2:
              xx -= 0.5 * totalWidth;
              break;
            case 3:
              xx -= totalWidth;
              break;
            default:
              break;
            }

          yy = textP->y - y;
          if (!textP->math && baseLine != NULL)
            {
              yy += *baseLine + 0.5 * charHeight;
            }
          switch (vAlign)
            {
            case 1:
              yy += -totalHeight * 0.1;
              break;
            case 2:
              yy += 0;
              break;
            case 3:
              yy += 0.5 * totalHeight;
              break;
            case 4:
              yy += totalHeight;
              break;
            case 5:
              yy += totalHeight * 1.1;
              break;
            default:
              break;
            }

          sx = x + cos(angle) * xx - sin(angle) * yy;
          sy = y + sin(angle) * xx + cos(angle) * yy;

          if (textP->math)
            gr_mathtex(sx, sy, textP->string);
          else
            gks_text(sx, sy, textP->string);

          textP = textP->next;
        }
    }
  else
    {
      xx = x;
      switch (hAlign)
        {
        case 2:
          xx -= 0.5 * totalWidth;
          break;
        case 3:
          xx -= totalWidth;
          break;
        default:
          break;
        }
      yy = y;
      switch (vAlign)
        {
        case 1:
          yy += -totalHeight * 0.1;
        case 2:
          break;
        case 3:
          yy += 0.5 * totalHeight;
          break;
        case 4:
          yy += totalHeight;
          break;
        case 5:
          yy += totalHeight * 1.1;
          break;
        default:
          break;
        }

      tbx[0] = xx;
      tby[0] = yy;
      tbx[1] = tbx[0] + totalWidth;
      tby[1] = tby[0];
      tbx[2] = tbx[1];
      tby[2] = tby[1] - totalHeight;
      tbx[3] = tbx[0];
      tby[3] = tby[2];

      for (i = 0; i < 4; i++)
        {
          xx = tbx[i] - x;
          yy = tby[i] - y;
          tbx[i] = x + cos(angle) * xx - sin(angle) * yy;
          tby[i] = y + sin(angle) * xx + cos(angle) * yy;
        }
    }

  while (text != NULL)
    {
      text_node_t *next = text->next;
      free(text->string);
      free(text);
      text = next;
    }

  gks_set_text_align(hAlign, vAlign);
}

static int is_math_text(char *s)
{
  if (strchr(s, '$') != NULL)
    {
      int dollar_count = 0;
      while (*s)
        {
          if (*s == '$')
            {
              if (*(s + 1) != '$')
                dollar_count++;
              else
                s++;
            }
          s++;
        }
      return dollar_count > 0 && dollar_count % 2 == 0 ? 1 : 0;
    }
  else if (strstr(s, "\\(") != NULL)
    return 1;
  else
    return 0;
}

/*!
 * Draw a text at position `x`, `y` using the current text attributes.
 *
 * \param[in] x The X coordinate of the starting position of the text string
 * \param[in] y The Y coordinate of the starting position of the text string
 * \param[in] string The text to be drawn
 *
 * The values for `x` and `y` are in normalized device coordinates.
 * The attributes that control the appearance of text are text font and
 * precision, character expansion factor, character spacing, text color index,
 * character height, character up vector, text path and text alignment.
 */
void gr_text(double x, double y, char *string)
{
  int errind, tnr;
  double tx, ty;

  check_autoinit;

  gks_inq_current_xformno(&errind, &tnr);
  if (tnr != NDC) gks_select_xform(NDC);

  tx = x + txoff[0];
  ty = y + txoff[1];

  if (strchr(string, '\n') != NULL || is_math_text(string))
    text_impl(tx, ty, string, 1, 0, NULL, NULL);
  else
    gks_text(tx, ty, string);

  if (tnr != NDC) gks_select_xform(tnr);

  if (flag_stream) gr_writestream("<text x=\"%g\" y=\"%g\" text=\"%s\"/>\n", x, y, string);
}

/*!
 * Draw a text at position `x`, `y` using the given options and current text
 * attributes.
 *
 * \param[in] x The X coordinate of the starting position of the text string
 * \param[in] y The Y coordinate of the starting position of the text string
 * \param[in] string The text to be drawn
 * \param[in] opts Bit mask including text options (GR_TEXT_USE_WC,
 * GR_TEXT_ENABLE_INLINE_MATH)
 *
 * The values for `x` and `y` specify the text position. If the GR_TEXT_USE_WC
 * option is set, they are interpreted as world cordinates, otherwise as
 * normalized device coordinates. The string may contain new line characters
 * and inline math expressions ($...$). The latter are only taken into account,
 * if the GR_TEXT_ENABLE_INLINE_MATH option is set.
 * The attributes that control the appearance of text are text font and
 * precision, character expansion factor, character spacing, text color index,
 * character height, character up vector, text path and text alignment.
 */
void gr_textx(double x, double y, char *string, int opts)
{
  int errind, tnr;
  double xn = x, yn = y;
  int inline_math = (opts & GR_TEXT_ENABLE_INLINE_MATH) != 0;

  check_autoinit;

  gks_inq_current_xformno(&errind, &tnr);
  if (tnr != NDC)
    {
      if ((opts & GR_TEXT_USE_WC) != 0) gr_wctondc(&xn, &yn);
      gks_select_xform(NDC);
    }

  if (strchr(string, '\n') != NULL || (is_math_text(string) && inline_math))
    text_impl(xn, yn, string, inline_math, 0, NULL, NULL);
  else
    gks_text(xn, yn, string);

  if (tnr != NDC) gks_select_xform(tnr);

  if (flag_stream) gr_writestream("<textx x=\"%g\" y=\"%g\" text=\"%s\" opts=\"%d\"/>\n", x, y, string, opts);
}

void gr_inqtext(double x, double y, char *string, double *tbx, double *tby)
{
  int errind, tnr, n, wkid;
  double tx, ty;
  double cpx, cpy;

  check_autoinit;

  gks_inq_current_xformno(&errind, &tnr);
  if (tnr != NDC) gks_select_xform(NDC);

  tx = x + txoff[0];
  ty = y + txoff[1];

  if (strchr(string, '\n') != NULL || is_math_text(string))
    text_impl(tx, ty, string, 1, 1, tbx, tby);
  else
    {
      gks_inq_open_ws(1, &errind, &n, &wkid);
      gks_inq_text_extent(wkid, tx, ty, string, &errind, &cpx, &cpy, tbx, tby);
    }

  if (tnr != NDC) gks_select_xform(tnr);
}

void gr_inqtextx(double x, double y, char *string, int opts, double *tbx, double *tby)
{
  int errind, tnr, n, wkid, i;
  double xn = x, yn = y, cpx, cpy;
  int inline_math = (opts & GR_TEXT_ENABLE_INLINE_MATH) != 0;

  check_autoinit;

  gks_inq_current_xformno(&errind, &tnr);
  if (tnr != NDC)
    {
      if ((opts & GR_TEXT_USE_WC) != 0) gr_wctondc(&xn, &yn);
      gks_select_xform(NDC);
    }

  if (strchr(string, '\n') != NULL || (is_math_text(string) && inline_math))
    text_impl(xn, yn, string, inline_math, 1, tbx, tby);
  else
    {
      gks_inq_open_ws(1, &errind, &n, &wkid);
      gks_inq_text_extent(wkid, xn, yn, string, &errind, &cpx, &cpy, tbx, tby);
    }

  if (tnr != NDC)
    {
      gks_select_xform(tnr);

      if ((opts & GR_TEXT_USE_WC) != 0)
        {
          for (i = 0; i < 4; i++)
            {
              tbx[i] = (tbx[i] - nx.b) / nx.a;
              tby[i] = (tby[i] - nx.d) / nx.c;
              if (lx.scale_options)
                {
                  tbx[i] = x_log(tbx[i]);
                  tby[i] = y_log(tby[i]);
                }
            }
        }
    }
}

void gr_beginselection(int index, int type)
{
  check_autoinit;

  gks_begin_selection(index, type);
}

void gr_endselection(void)
{
  check_autoinit;

  gks_end_selection();
}

void gr_setbboxcallback(int id, void (*callback)(int, double, double, double, double))
{
  check_autoinit;

  gks_set_bbox_callback(id, callback);
}

void gr_cancelbboxcallback(void)
{
  check_autoinit;

  gks_cancel_bbox_callback();
}

void gr_moveselection(double x, double y)
{
  check_autoinit;

  gks_move_selection(x, y);
}

void gr_resizeselection(int type, double x, double y)
{
  check_autoinit;

  gks_resize_selection(type, x, y);
}

void gr_inqbbox(double *xmin, double *xmax, double *ymin, double *ymax)
{
  int errind;

  check_autoinit;

  gks_inq_bbox(&errind, xmin, xmax, ymin, ymax);
}

double gr_precision(void)
{
  /* check_autoinit is intentionally not called here, because
   *  wrappers might call gr_precision on top-level. */

  return gks_precision();
}

int gr_text_maxsize(void)
{
  return gks_text_maxsize();
}

void gr_setregenflags(int flags)
{
  check_autoinit;

  regeneration_flags = flags;
}

int gr_inqregenflags(void)
{
  check_autoinit;

  return regeneration_flags;
}

void gr_savestate(void)
{
  int errind;
  state_list *s = NULL;

  check_autoinit;

  if (state_saved < MAX_SAVESTATE)
    {
      if (state == NULL) state = (state_list *)xmalloc(sizeof(state_list) * MAX_SAVESTATE);

      s = state + state_saved;
      state_saved += 1;

      gks_inq_pline_linetype(&errind, &s->ltype);
      gks_inq_pline_linewidth(&errind, &s->lwidth);
      gks_inq_pline_color_index(&errind, &s->plcoli);
      gks_inq_pmark_type(&errind, &s->mtype);
      gks_inq_pmark_size(&errind, &s->mszsc);
      gks_inq_pmark_color_index(&errind, &s->pmcoli);
      gks_inq_text_fontprec(&errind, &s->txfont, &s->txprec);
      gks_inq_text_expfac(&errind, &s->chxp);
      gks_inq_text_spacing(&errind, &s->chsp);
      gks_inq_text_color_index(&errind, &s->txcoli);
      gks_inq_text_height(&errind, &s->chh);
      gks_inq_text_upvec(&errind, &s->chup[0], &s->chup[1]);
      gks_inq_text_path(&errind, &s->txp);
      gks_inq_text_align(&errind, &s->txal[0], &s->txal[1]);
      gks_inq_fill_int_style(&errind, &s->ints);
      gks_inq_fill_style_index(&errind, &s->styli);
      gks_inq_fill_color_index(&errind, &s->facoli);
      gks_inq_transparency(&errind, &s->alpha);

      gks_inq_current_xformno(&errind, &s->tnr);
      gks_inq_xform(WC, &errind, s->wn, s->vp);

      s->scale_options = lx.scale_options;

      gks_inq_border_width(&errind, &s->bwidth);
      gks_inq_border_color_index(&errind, &s->bcoli);
      gks_inq_clip_xform(&errind, &s->clip_tnr);
      gks_inq_resize_behaviour(&s->resize_behaviour);
      gks_inq_clip_region(&errind, &s->clip_region);

      s->txoff[0] = txoff[0];
      s->txoff[1] = txoff[1];
    }
  else
    fprintf(stderr, "attempt to save state beyond implementation limit\n");

  if (flag_stream) gr_writestream("<savestate/>\n");
}

void gr_restorestate(void)
{
  state_list *s = NULL;

  check_autoinit;

  if (state_saved > 0)
    {
      state_saved -= 1;
      s = state + state_saved;

      gks_set_pline_linetype(s->ltype);
      gks_set_pline_linewidth(s->lwidth);
      gks_set_pline_color_index(s->plcoli);
      gks_set_pmark_type(s->mtype);
      gks_set_pmark_size(s->mszsc);
      gks_set_pmark_color_index(s->pmcoli);
      gks_set_text_fontprec(s->txfont, s->txprec);
      gks_set_text_expfac(s->chxp);
      gks_set_text_spacing(s->chsp);
      gks_set_text_color_index(s->txcoli);
      gks_set_text_height(s->chh);
      gks_set_text_upvec(s->chup[0], s->chup[1]);
      gks_set_text_path(s->txp);
      gks_set_text_align(s->txal[0], s->txal[1]);
      gks_set_fill_int_style(s->ints);
      gks_set_fill_style_index(s->styli);
      gks_set_fill_color_index(s->facoli);
      gks_set_transparency(s->alpha);

      gks_select_xform(s->tnr);
      gks_set_window(WC, s->wn[0], s->wn[1], s->wn[2], s->wn[3]);
      gks_set_window(MODERN_NDC, -1, 1, -1, 1);
      gks_set_viewport(WC, s->vp[0], s->vp[1], s->vp[2], s->vp[3]);
      gks_set_viewport(MODERN_NDC, s->vp[0], s->vp[1], s->vp[2], s->vp[3]);
      vxmin = s->vp[0];
      vxmax = s->vp[1];
      vymin = s->vp[2];
      vymax = s->vp[3];

      setscale(s->scale_options);

      gks_set_border_width(s->bwidth);
      gks_set_border_color_index(s->bcoli);
      gks_select_clip_xform(s->clip_tnr);
      gks_set_resize_behaviour(s->resize_behaviour);
      gks_set_clip_region(s->clip_region);

      s->txoff[0] = txoff[0];
      s->txoff[1] = txoff[1];

      if (ctx)
        {
          ctx->ltype = s->ltype;
          ctx->lwidth = s->lwidth;
          ctx->plcoli = s->plcoli;
          ctx->mtype = s->mtype;
          ctx->mszsc = s->mszsc;
          ctx->pmcoli = s->pmcoli;
          ctx->txfont = s->txfont;
          ctx->txprec = s->txprec;
          ctx->chxp = s->chxp;
          ctx->chsp = s->chsp;
          ctx->txcoli = s->txcoli;
          ctx->chh = s->chh;
          ctx->chup[0] = s->chup[0];
          ctx->chup[1] = s->chup[1];
          ctx->txp = s->txp;
          ctx->txal[0] = s->txal[0];
          ctx->txal[1] = s->txal[1];
          ctx->ints = s->ints;
          ctx->styli = s->styli;
          ctx->facoli = s->facoli;

          ctx->tnr = s->tnr;
          ctx->wn[0] = s->wn[0];
          ctx->wn[2] = s->wn[2];
          ctx->wn[1] = s->wn[1];
          ctx->wn[3] = s->wn[3];
          ctx->vp[0] = s->vp[0];
          ctx->vp[2] = s->vp[2];
          ctx->vp[1] = s->vp[1];
          ctx->vp[3] = s->vp[3];

          ctx->scale_options = s->scale_options;

          ctx->bwidth = s->bwidth;
          ctx->bcoli = s->bcoli;
          ctx->clip_tnr = s->clip_tnr;
          ctx->resize_behaviour = s->resize_behaviour;
          ctx->clip_region = s->clip_region;

          ctx->txoff[0] = s->txoff[0];
          ctx->txoff[1] = s->txoff[1];
        }
    }
  else
    fprintf(stderr, "attempt to restore unsaved state\n");

  if (flag_stream) gr_writestream("<restorestate/>\n");
}

void gr_selectcontext(int context)
{
  int id;

  check_autoinit;

  if (context >= 1 && context <= GR_MAX_CONTEXT)
    {
      if (app_context == NULL)
        {
          int i;
          app_context = (state_list_vector *)xmalloc(sizeof(state_list_vector));
          app_context->max_non_null_id = -1;
          app_context->capacity = max(CONTEXT_VECTOR_INCREMENT, context);
          app_context->buf = (state_list **)xmalloc(app_context->capacity * sizeof(state_list));
          for (i = 0; i < app_context->capacity; ++i)
            {
              app_context->buf[i] = NULL;
            }
        }
      else if (app_context->capacity < context)
        {
          int i = app_context->capacity;
          app_context->capacity = max(app_context->capacity + CONTEXT_VECTOR_INCREMENT, context);
          app_context->buf = (state_list **)xrealloc(app_context->buf, app_context->capacity * sizeof(state_list));
          for (; i < app_context->capacity; ++i)
            {
              app_context->buf[i] = NULL;
            }
        }
      id = context - 1;
      if (app_context->buf[id] == NULL)
        {
          app_context->buf[id] = (state_list *)xmalloc(sizeof(state_list));
          app_context->max_non_null_id = max(app_context->max_non_null_id, id);
          ctx = app_context->buf[id];

          ctx->ltype = GKS_K_LINETYPE_SOLID;
          ctx->lwidth = 1;
          ctx->plcoli = 1;
          ctx->mtype = GKS_K_MARKERTYPE_ASTERISK;
          ctx->mszsc = 2;
          ctx->pmcoli = 1;
          ctx->txfont = 3;
          ctx->txprec = GKS_K_TEXT_PRECISION_STRING;
          ctx->chxp = 1;
          ctx->chsp = 0;
          ctx->txcoli = 1;
          ctx->chh = 0.027;
          ctx->chup[0] = 0;
          ctx->chup[1] = 1;
          ctx->txp = GKS_K_TEXT_PATH_RIGHT;
          ctx->txal[0] = GKS_K_TEXT_HALIGN_LEFT;
          ctx->txal[1] = GKS_K_TEXT_VALIGN_BASE;
          ctx->ints = GKS_K_INTSTYLE_HOLLOW;
          ctx->styli = 1;
          ctx->facoli = 1;
          ctx->alpha = 1.0;

          ctx->tnr = WC;
          ctx->wn[0] = ctx->wn[2] = 0;
          ctx->wn[1] = ctx->wn[3] = 1;
          ctx->vp[0] = ctx->vp[2] = 0.2;
          ctx->vp[1] = ctx->vp[3] = 0.9;

          ctx->scale_options = 0;

          ctx->bwidth = 1;
          ctx->bcoli = 1;
          ctx->clip_tnr = 0;
          ctx->resize_behaviour = GKS_K_RESIZE;
          ctx->clip_region = GKS_K_REGION_RECTANGLE;

          ctx->txoff[0] = 0;
          ctx->txoff[1] = 0;
        }
      else
        {
          ctx = app_context->buf[id];
        }

      gks_set_pline_linetype(ctx->ltype);
      gks_set_pline_linewidth(ctx->lwidth);
      gks_set_pline_color_index(ctx->plcoli);
      gks_set_pmark_type(ctx->mtype);
      gks_set_pmark_size(ctx->mszsc);
      gks_set_pmark_color_index(ctx->pmcoli);
      gks_set_text_fontprec(ctx->txfont, ctx->txprec);
      gks_set_text_expfac(ctx->chxp);
      gks_set_text_spacing(ctx->chsp);
      gks_set_text_color_index(ctx->txcoli);
      gks_set_text_height(ctx->chh);
      gks_set_text_upvec(ctx->chup[0], ctx->chup[1]);
      gks_set_text_path(ctx->txp);
      gks_set_text_align(ctx->txal[0], ctx->txal[1]);
      gks_set_fill_int_style(ctx->ints);
      gks_set_fill_style_index(ctx->styli);
      gks_set_fill_color_index(ctx->facoli);
      gks_set_transparency(ctx->alpha);

      gks_select_xform(ctx->tnr);
      gks_set_window(WC, ctx->wn[0], ctx->wn[1], ctx->wn[2], ctx->wn[3]);
      gks_set_window(MODERN_NDC, -1, 1, -1, 1);
      gks_set_viewport(WC, ctx->vp[0], ctx->vp[1], ctx->vp[2], ctx->vp[3]);
      gks_set_viewport(MODERN_NDC, ctx->vp[0], ctx->vp[1], ctx->vp[2], ctx->vp[3]);
      vxmin = ctx->vp[0];
      vxmax = ctx->vp[1];
      vymin = ctx->vp[2];
      vymax = ctx->vp[3];

      setscale(ctx->scale_options);

      gks_set_border_width(ctx->bwidth);
      gks_set_border_color_index(ctx->bcoli);
      gks_select_clip_xform(ctx->clip_tnr);
      gks_set_resize_behaviour(ctx->resize_behaviour);
      gks_set_clip_region(ctx->clip_region);

      txoff[0] = ctx->txoff[0];
      txoff[1] = ctx->txoff[1];
    }
  else
    {
      fprintf(stderr, "invalid context id\n");
      ctx = NULL;
    }
}

void gr_savecontext(int context)
{
  int errind;
  int id;

  check_autoinit;

  if (context >= 1 && context <= GR_MAX_CONTEXT)
    {
      if (app_context == NULL)
        {
          int i;
          app_context = (state_list_vector *)xmalloc(sizeof(state_list_vector));
          app_context->max_non_null_id = -1;
          app_context->capacity = max(CONTEXT_VECTOR_INCREMENT, context);
          app_context->buf = (state_list **)xmalloc(app_context->capacity * sizeof(state_list));
          for (i = 0; i < app_context->capacity; ++i)
            {
              app_context->buf[i] = NULL;
            }
        }
      else if (app_context->capacity < context)
        {
          int i = app_context->capacity;
          app_context->capacity = max(app_context->capacity + CONTEXT_VECTOR_INCREMENT, context);
          app_context->buf = (state_list **)xrealloc(app_context->buf, app_context->capacity * sizeof(state_list));
          for (; i < app_context->capacity; ++i)
            {
              app_context->buf[i] = NULL;
            }
        }
      id = context - 1;
      if (app_context->buf[id] == NULL)
        {
          app_context->buf[id] = (state_list *)xmalloc(sizeof(state_list));
          app_context->max_non_null_id = max(app_context->max_non_null_id, id);
        }

      gks_inq_pline_linetype(&errind, &app_context->buf[id]->ltype);
      gks_inq_pline_linewidth(&errind, &app_context->buf[id]->lwidth);
      gks_inq_pline_color_index(&errind, &app_context->buf[id]->plcoli);
      gks_inq_pmark_type(&errind, &app_context->buf[id]->mtype);
      gks_inq_pmark_size(&errind, &app_context->buf[id]->mszsc);
      gks_inq_pmark_color_index(&errind, &app_context->buf[id]->pmcoli);
      gks_inq_text_fontprec(&errind, &app_context->buf[id]->txfont, &app_context->buf[id]->txprec);
      gks_inq_text_expfac(&errind, &app_context->buf[id]->chxp);
      gks_inq_text_spacing(&errind, &app_context->buf[id]->chsp);
      gks_inq_text_color_index(&errind, &app_context->buf[id]->txcoli);
      gks_inq_text_height(&errind, &app_context->buf[id]->chh);
      gks_inq_text_upvec(&errind, &app_context->buf[id]->chup[0], &app_context->buf[id]->chup[1]);
      gks_inq_text_path(&errind, &app_context->buf[id]->txp);
      gks_inq_text_align(&errind, &app_context->buf[id]->txal[0], &app_context->buf[id]->txal[1]);
      gks_inq_fill_int_style(&errind, &app_context->buf[id]->ints);
      gks_inq_fill_style_index(&errind, &app_context->buf[id]->styli);
      gks_inq_fill_color_index(&errind, &app_context->buf[id]->facoli);
      gks_inq_transparency(&errind, &app_context->buf[id]->alpha);

      gks_inq_current_xformno(&errind, &app_context->buf[id]->tnr);
      gks_inq_xform(WC, &errind, app_context->buf[id]->wn, app_context->buf[id]->vp);

      app_context->buf[id]->scale_options = lx.scale_options;

      gks_inq_border_width(&errind, &app_context->buf[id]->bwidth);
      gks_inq_border_color_index(&errind, &app_context->buf[id]->bcoli);
      gks_inq_clip_xform(&errind, &app_context->buf[id]->clip_tnr);
      gks_inq_resize_behaviour(&app_context->buf[id]->resize_behaviour);
      gks_inq_clip_region(&errind, &app_context->buf[id]->clip_region);

      app_context->buf[id]->txoff[0] = txoff[0];
      app_context->buf[id]->txoff[1] = txoff[1];
    }
  else
    {
      fprintf(stderr, "invalid context id\n");
    }
}

void gr_destroycontext(int context)
{
  int errind;
  int id;

  check_autoinit;

  if (context >= 1 && context <= app_context->capacity)
    {
      if (app_context == NULL)
        {
          int i;
          app_context = (state_list_vector *)xmalloc(sizeof(state_list_vector));
          app_context->max_non_null_id = -1;
          app_context->capacity = max(CONTEXT_VECTOR_INCREMENT, context);
          app_context->buf = (state_list **)xmalloc(app_context->capacity * sizeof(state_list));
          for (i = 0; i < app_context->capacity; ++i)
            {
              app_context->buf[i] = NULL;
            }
        }
      else if (app_context->capacity < context)
        {
          int i = app_context->capacity;
          app_context->capacity = max(app_context->capacity + CONTEXT_VECTOR_INCREMENT, context);
          app_context->buf = (state_list **)xrealloc(app_context->buf, app_context->capacity * sizeof(state_list));
          for (; i < app_context->capacity; ++i)
            {
              app_context->buf[i] = NULL;
            }
        }
      id = context - 1;
      if (app_context->buf[id] == NULL)
        {
          app_context->buf[id] = (state_list *)xmalloc(sizeof(state_list));
          app_context->max_non_null_id = max(app_context->max_non_null_id, id);
        }

      gks_inq_pline_linetype(&errind, &app_context->buf[id]->ltype);
      gks_inq_pline_linewidth(&errind, &app_context->buf[id]->lwidth);
      gks_inq_pline_color_index(&errind, &app_context->buf[id]->plcoli);
      gks_inq_pmark_type(&errind, &app_context->buf[id]->mtype);
      gks_inq_pmark_size(&errind, &app_context->buf[id]->mszsc);
      gks_inq_pmark_color_index(&errind, &app_context->buf[id]->pmcoli);
      gks_inq_text_fontprec(&errind, &app_context->buf[id]->txfont, &app_context->buf[id]->txprec);
      gks_inq_text_expfac(&errind, &app_context->buf[id]->chxp);
      gks_inq_text_spacing(&errind, &app_context->buf[id]->chsp);
      gks_inq_text_color_index(&errind, &app_context->buf[id]->txcoli);
      gks_inq_text_height(&errind, &app_context->buf[id]->chh);
      gks_inq_text_upvec(&errind, &app_context->buf[id]->chup[0], &app_context->buf[id]->chup[1]);
      gks_inq_text_path(&errind, &app_context->buf[id]->txp);
      gks_inq_text_align(&errind, &app_context->buf[id]->txal[0], &app_context->buf[id]->txal[1]);
      gks_inq_fill_int_style(&errind, &app_context->buf[id]->ints);
      gks_inq_fill_style_index(&errind, &app_context->buf[id]->styli);
      gks_inq_fill_color_index(&errind, &app_context->buf[id]->facoli);
      gks_inq_transparency(&errind, &app_context->buf[id]->alpha);

      gks_inq_current_xformno(&errind, &app_context->buf[id]->tnr);
      gks_inq_xform(WC, &errind, app_context->buf[id]->wn, app_context->buf[id]->vp);

      app_context->buf[id]->scale_options = lx.scale_options;

      gks_inq_border_width(&errind, &app_context->buf[id]->bwidth);
      gks_inq_border_color_index(&errind, &app_context->buf[id]->bcoli);
      gks_inq_clip_xform(&errind, &app_context->buf[id]->clip_tnr);
      gks_inq_resize_behaviour(&app_context->buf[id]->resize_behaviour);
      gks_inq_clip_region(&errind, &app_context->buf[id]->clip_region);

      app_context->buf[id]->txoff[0] = txoff[0];
      app_context->buf[id]->txoff[1] = txoff[1];
    }
  else
    {
      fprintf(stderr, "invalid context id\n");
    }
}

void gr_unselectcontext(void)
{
  check_autoinit;

  if (ctx)
    {
      ctx = NULL;
    }
}

int gr_uselinespec(char *linespec)
{
  char *spec = linespec, lastspec = ' ';
  int result, linetype = 0, markertype = 0, color = -1;

  while (*spec)
    {
      switch (*spec)
        {
        case ' ':
          def_color = 0;
          break;
        case '-':
          if (lastspec == '-')
            linetype = GKS_K_LINETYPE_DASHED;
          else
            linetype = GKS_K_LINETYPE_SOLID;
          break;
        case ':':
          linetype = GKS_K_LINETYPE_DOTTED;
          break;
        case '.':
          if (lastspec == '-')
            linetype = GKS_K_LINETYPE_DASHED_DOTTED;
          else
            markertype = GKS_K_MARKERTYPE_DOT;
          break;

        case '+':
          markertype = GKS_K_MARKERTYPE_PLUS;
          break;
        case 'o':
          markertype = GKS_K_MARKERTYPE_CIRCLE;
          break;
        case '*':
          markertype = GKS_K_MARKERTYPE_ASTERISK;
          break;
        case 'x':
          markertype = GKS_K_MARKERTYPE_DIAGONAL_CROSS;
          break;
        case 's':
          markertype = GKS_K_MARKERTYPE_SOLID_SQUARE;
          break;
        case 'd':
          markertype = GKS_K_MARKERTYPE_SOLID_DIAMOND;
          break;
        case '^':
          markertype = GKS_K_MARKERTYPE_SOLID_TRI_UP;
          break;
        case 'v':
          markertype = GKS_K_MARKERTYPE_SOLID_TRI_DOWN;
          break;
        case '>':
          markertype = GKS_K_MARKERTYPE_SOLID_TRI_RIGHT;
          break;
        case '<':
          markertype = GKS_K_MARKERTYPE_SOLID_TRI_LEFT;
          break;
        case 'p':
          markertype = GKS_K_MARKERTYPE_SOLID_STAR;
          break;
        case 'h':
          markertype = GKS_K_MARKERTYPE_TRI_UP_DOWN;
          break;

        case 'r':
          color = 984;
          break;
        case 'g':
          color = 987;
          break;
        case 'b':
          color = 989;
          break;
        case 'c':
          color = 983;
          break;
        case 'm':
          color = 988;
          break;
        case 'y':
          color = 994;
          break;
        case 'k':
          color = 1;
          break;
        case 'w':
          color = 0;
          break;
        default:
          break;
        }
      lastspec = *spec++;
    }

  result = 0;
  if (linetype != 0)
    {
      result |= GR_SPEC_LINE;
      gr_setlinetype(linetype);
    }
  if (markertype != 0)
    {
      result |= GR_SPEC_MARKER;
      gr_setmarkertype(markertype);
    }
  if (color == -1)
    {
      color = 980 + predef_colors[def_color];
      if (strcmp(linespec, " ")) def_color = (def_color + 1) % 20;
    }
  else
    {
      if (result == 0) result = GR_SPEC_LINE;
      result |= GR_SPEC_COLOR;
    }

  gr_setlinecolorind(color);
  gr_setmarkercolorind(color);

  if (flag_stream) gr_writestream("<uselinespec linespec=\"%s\"/>\n", linespec);

  return result;
}

void gr_adjustlimits(double *amin, double *amax)
{
  double a = log10(*amax - *amin), b = 1;
  double quotient, remainder, exponent, scale;

  if (*amin == *amax)
    {
      *amin -= 1;
      *amax += 1;
    }

  remainder = fmod(a, b);
  quotient = (a - remainder) / b;
  if (remainder)
    {
      if ((b < 0) != (remainder < 0))
        {
          remainder += b;
          quotient -= 1;
        }
    }
  else
    {
      remainder *= remainder;
      if (b < 0) remainder = -remainder;
    }
  if (quotient)
    {
      exponent = floor(quotient);
      if (quotient - exponent > 0.5) exponent += 1;
    }
  else
    {
      quotient *= quotient;
      exponent = quotient * a / b;
    }
  if (remainder < 0.5) exponent -= 1;

  scale = pow(10.0, -exponent);
  *amin = floor(*amin * scale + FEPS) / scale;
  *amax = ceil(*amax * scale - FEPS) / scale;
}

/*!
 * Returns the version string of the GR runtime.
 *
 * \returns A pointer to the GR runtime version string.
 */
const char *gr_version(void)
{
  static const char *gr_version_str = GR_VERSION;
  return gr_version_str;
}

/*!
 * Finds the index of the minimum and maximum value in array.
 *
 * \param[out] min_index the index of the minimum value in array
 * \param[out] max_index the index of the maximum value in array
 * \param[in] n the number of values in array
 * \param[in] array the value array
 */
static void arg_min_max(int *min_index, int *max_index, int n, const double *array)
{
  int i;
  *min_index = 0;
  *max_index = 0;
  for (i = 1; i < n; i++)
    {
      if (array[i] < array[*min_index]) *min_index = i;
      if (array[i] > array[*max_index]) *max_index = i;
    }
}

/*!
 * Reduces the number of points of the x and y array.
 *
 * \param[in] n the number of points of the x and y arrays
 * \param[in] x the x value array
 * \param[in] y the y value array
 * \param[in] points the requested number of points
 * \param[out] x_array the return array for the x values
 * \param[out] y_array the return array for the y values
 */
void gr_reducepoints(int n, const double *x, const double *y, int points, double *x_array, double *y_array)
{
  int append_index = 0;
  int num_intervals = points / 2;
  double exact_interval_width = (double)n / num_intervals;
  int interval_width = n / num_intervals;
  int interval;
  if (n < points)
    {
      /* Copy the original array */
      memcpy(x_array, x, sizeof(double) * n);
      memcpy(y_array, y, sizeof(double) * n);
      fprintf(stderr, "Not enough points provided.\n");
      return;
    }
  for (interval = 0; interval < num_intervals; interval++)
    {
      int index = interval * exact_interval_width;
      int min_index, max_index;
      arg_min_max(&min_index, &max_index, min(interval_width, n - index - 1), y + index);
      x_array[append_index] = x[min_index + index];
      y_array[append_index] = y[min_index + index];
      append_index++;
      x_array[append_index] = x[max_index + index];
      y_array[append_index] = y[max_index + index];
      append_index++;
    }
}

/*!
 * Display a point set as a aggregated and rasterized image.
 *
 * \param[in] n The number of points
 * \param[in] x A pointer to the X coordinates
 * \param[in] y A pointer to the Y coordinates
 * \param[in] xform The transformation type used for color mapping
 * \param[in] w The width of the grid used for rasterization
 * \param[in] h The height of the grid used for rasterization
 *
 * The values for `x` and `y` are in world coordinates.
 *
 * \verbatim embed:rst:leading-asterisk
 *
 * The available transformation types are:
 *
 * +----------------+---+--------------------+
 * |XFORM_BOOLEAN   |  0|boolean             |
 * +----------------+---+--------------------+
 * |XFORM_LINEAR    |  1|linear              |
 * +----------------+---+--------------------+
 * |XFORM_LOG       |  2|logarithmic         |
 * +----------------+---+--------------------+
 * |XFORM_LOGLOG    |  3|double logarithmic  |
 * +----------------+---+--------------------+
 * |XFORM_CUBIC     |  4|cubic               |
 * +----------------+---+--------------------+
 * |XFORM_EQUALIZED |  5|histogram equalized |
 * +----------------+---+--------------------+
 *
 * \endverbatim
 */
void gr_shadepoints(int n, double *x, double *y, int xform, int w, int h)
{
  int *bins;
  double roi[4];

  if (n <= 2)
    {
      fprintf(stderr, "invalid number of points\n");
      return;
    }

  if (xform < 0 || xform > 5)
    {
      fprintf(stderr, "invalid transfer function\n");
      return;
    }

  if (w < 1 || h < 1)
    {
      fprintf(stderr, "invalid dimensions\n");
      return;
    }

  check_autoinit;

  roi[0] = lx.xmin;
  roi[1] = lx.xmax;
  roi[2] = lx.ymin;
  roi[3] = lx.ymax;
  bins = (int *)xcalloc(w * h, sizeof(int));

  gr_shade(n, x, y, 0, xform, roi, w, h, bins);

  gks_cellarray(lx.xmin, lx.ymax, lx.xmax, lx.ymin, w, h, 1, 1, w, h, bins);

  free(bins);

  if (flag_stream)
    {
      gr_writestream("<shadepoints len=\"%d\"", n);
      print_float_array("x", n, x);
      print_float_array("y", n, y);
      gr_writestream(" xform=\"%d\" w=\"%d\" h=\"%d\"/>\n", xform, w, h);
    }
}

/*!
 * Display a line set as a aggregated and rasterized image.
 *
 * \param[in] n The number of points
 * \param[in] x A pointer to the X coordinates
 * \param[in] y A pointer to the Y coordinates
 * \param[in] xform The transformation type used for color mapping
 * \param[in] w The width of the grid used for rasterization
 * \param[in] h The height of the grid used for rasterization
 *
 * The values for `x` and `y` are in world coordinates.
 * NaN values can be used to separate the point set into line segments.
 *
 * \verbatim embed:rst:leading-asterisk
 *
 * The available transformation types are:
 *
 * +----------------+---+--------------------+
 * |XFORM_BOOLEAN   |  0|boolean             |
 * +----------------+---+--------------------+
 * |XFORM_LINEAR    |  1|linear              |
 * +----------------+---+--------------------+
 * |XFORM_LOG       |  2|logarithmic         |
 * +----------------+---+--------------------+
 * |XFORM_LOGLOG    |  3|double logarithmic  |
 * +----------------+---+--------------------+
 * |XFORM_CUBIC     |  4|cubic               |
 * +----------------+---+--------------------+
 * |XFORM_EQUALIZED |  5|histogram equalized |
 * +----------------+---+--------------------+
 *
 * \endverbatim
 */
void gr_shadelines(int n, double *x, double *y, int xform, int w, int h)
{
  int *bins;
  double roi[4];

  if (n <= 2)
    {
      fprintf(stderr, "invalid number of points\n");
      return;
    }

  if (xform < 0 || xform > 5)
    {
      fprintf(stderr, "invalid transfer function\n");
      return;
    }

  if (w < 1 || h < 1)
    {
      fprintf(stderr, "invalid dimensions\n");
      return;
    }

  check_autoinit;

  roi[0] = lx.xmin;
  roi[1] = lx.xmax;
  roi[2] = lx.ymin;
  roi[3] = lx.ymax;
  bins = (int *)xcalloc(w * h, sizeof(int));

  gr_shade(n, x, y, 1, xform, roi, w, h, bins);

  gks_cellarray(lx.xmin, lx.ymax, lx.xmax, lx.ymin, w, h, 1, 1, w, h, bins);

  free(bins);

  if (flag_stream)
    {
      gr_writestream("<shadelines len=\"%d\"", n);
      print_float_array("x", n, x);
      print_float_array("y", n, y);
      gr_writestream(" xform=\"%d\" w=\"%d\" h=\"%d\"/>\n", xform, w, h);
    }
}

void gr_panzoom(double x, double y, double xzoom, double yzoom, double *xmin, double *xmax, double *ymin, double *ymax)
{
  int errind, tnr;
  double wn[4], vp[4];
  double x0, x1, y0, y1, tmp;

  check_autoinit;

  gks_inq_current_xformno(&errind, &tnr);
  gks_inq_xform(tnr, &errind, wn, vp);

  xzoom = fabs(xzoom);
  yzoom = fabs(yzoom);

  if (yzoom < FEPS)
    {
      yzoom = xzoom;
    }

  if (xzoom < FEPS)
    {
      x0 = vp[0] + x;
      x1 = vp[1] + x;
      y0 = vp[2] + y;
      y1 = vp[3] + y;
    }
  else
    {
      x0 = x1 = 0.5 * (vp[0] + vp[1]) + x;
      y0 = y1 = 0.5 * (vp[2] + vp[3]) + y;
    }

  gr_ndctowc(&x0, &y0);
  gr_ndctowc(&x1, &y1);

  if (GR_OPTION_FLIP_X & lx.scale_options)
    {
      tmp = x0;
      x0 = x1;
      x1 = tmp;
    }
  if (GR_OPTION_FLIP_Y & lx.scale_options)
    {
      tmp = y0;
      y0 = y1;
      y1 = tmp;
    }

  if (xzoom < FEPS)
    {
      *xmin = x0;
      *xmax = x1;
      *ymin = y0;
      *ymax = y1;
    }
  else
    {
      gr_inqwindow(xmin, xmax, ymin, ymax);
      gr_wctondc(xmin, ymin);
      gr_wctondc(xmax, ymax);
      gr_wctondc(&x0, &y0);
      *xmin = x0 - (x0 - *xmin) * xzoom;
      *xmax = x0 + (*xmax - x0) * xzoom;
      *ymin = y0 - (y0 - *ymin) * yzoom;
      *ymax = y0 + (*ymax - y0) * yzoom;
      gr_ndctowc(xmin, ymin);
      gr_ndctowc(xmax, ymax);
    }
}

/*!
 * Find a boundary around a given point set.
 *
 * The boundary is calculated using a 2 dimensional ball pivoting algorithm.
 *
 * \param[in] n The number of points
 * \param[in] x A pointer to the X coordinates
 * \param[in] y A pointer to the Y coordinates
 * \param[in] r A constant ball radius
 * \param[in] r_function A ball radius callback function
 * \param[in] n_contour The amount of memory allocated for the boundary points
 * \param[out] contour A pointer to allocated memory to store the indices of the boundary points
 *
 * \returns Number of points in the boundary contour
 *
 * The ball radius used in the algorithm can be either constant or position dependent. In the first case
 * `r` should contain the radius and `r_function` is NULL. Otherwise `r_function` should be a pointer to
 * a function returning the appropriate radius for a given position.
 *
 * If `r_function` is NULL and `r` has a value less or equal 0 the algorithm calculates a ball radius
 * based on the largest distance from a point to its nearest neighbor.
 *
 * The calculated boundary is represented as a list of indices in the given `x` and `y` arrays and is
 * stored in the `contour` array. `contour` must be a pointer to allocated memory for at least `n_contour`
 * integer indices. Normally less than `n` indices are needed for the boundary, in the worst case 2*`n`
 * indices are needed.
 *
 */
int gr_findboundary(int n, double *x, double *y, double r, double (*r_function)(double x, double y), int n_contour,
                    int *contour)
{
  int result;
  if (n < 2)
    {
      fprintf(stderr, "Not enough points provided.\n");
      return 0;
    }
  result = find_boundary(n, x, y, r, r_function, n_contour, contour);
  if (result < 0)
    {
      if (result == -1)
        {
          fprintf(stderr, "Ball radius is too small.\n");
        }
      else if (result == -2)
        {
          fprintf(stderr, "Ball radius is too large.\n");
        }
      else if (result == -3)
        {
          fprintf(stderr, "Not enough memory provided in contour array.\n");
        }
      else
        {
          fprintf(stderr, "An error occurred finding the boundary.\n");
        }
      result = 0;
    }
  return result;
}

/*!
 * Set the resample method for resampling.
 *
 * \param[in] flag Resample method
 *
 * The available options are:
 *
 * \verbatim embed:rst:leading-asterisk
 *
 * +------------------------+------------+--------------------+
 * |GKS_K_RESAMPLE_DEFAULT  | 0x00000000 |default             |
 * +------------------------+------------+--------------------+
 * |GKS_K_RESAMPLE_NEAREST  | 0x01010101 |nearest neighbour   |
 * +------------------------+------------+--------------------+
 * |GKS_K_RESAMPLE_LINEAR   | 0x02020202 |linear              |
 * +------------------------+------------+--------------------+
 * |GKS_K_RESAMPLE_LANCZOS  | 0x03030303 |Lanczos             |
 * +------------------------+------------+--------------------+
 *
 * \endverbatim
 *
 * Alternatively, combinations of these methods can be selected for horizontal or vertical upsampling or downsampling:
 *
 * \verbatim embed:rst:leading-asterisk
 *
 * +-------------------------------------+------------+----------------------------------------------+
 * | GKS_K_UPSAMPLE_VERTICAL_DEFAULT     | 0x00000000 | default for vertical upsampling              |
 * +-------------------------------------+------------+----------------------------------------------+
 * | GKS_K_UPSAMPLE_HORIZONTAL_DEFAULT   | 0x00000000 | default for horizontal upsampling            |
 * +-------------------------------------+------------+----------------------------------------------+
 * | GKS_K_DOWNSAMPLE_VERTICAL_DEFAULT   | 0x00000000 | default for vertical downsampling            |
 * +-------------------------------------+------------+----------------------------------------------+
 * | GKS_K_DOWNSAMPLE_HORIZONTAL_DEFAULT | 0x00000000 | default for horizontal downsampling          |
 * +-------------------------------------+------------+----------------------------------------------+
 * | GKS_K_UPSAMPLE_VERTICAL_NEAREST     | 0x00000001 | nearest neighbor for vertical upsampling     |
 * +-------------------------------------+------------+----------------------------------------------+
 * | GKS_K_UPSAMPLE_HORIZONTAL_NEAREST   | 0x00000100 | nearest neighbor for horizontal upsampling   |
 * +-------------------------------------+------------+----------------------------------------------+
 * | GKS_K_DOWNSAMPLE_VERTICAL_NEAREST   | 0x00010000 | nearest neighbor for vertical downsampling   |
 * +-------------------------------------+------------+----------------------------------------------+
 * | GKS_K_DOWNSAMPLE_HORIZONTAL_NEAREST | 0x01000000 | nearest neighbor for horizontal downsampling |
 * +-------------------------------------+------------+----------------------------------------------+
 * | GKS_K_UPSAMPLE_VERTICAL_LINEAR      | 0x00000002 | linear for vertical upsampling               |
 * +-------------------------------------+------------+----------------------------------------------+
 * | GKS_K_UPSAMPLE_HORIZONTAL_LINEAR    | 0x00000200 | linear for horizontal upsampling             |
 * +-------------------------------------+------------+----------------------------------------------+
 * | GKS_K_DOWNSAMPLE_VERTICAL_LINEAR    | 0x00020000 | linear for vertical downsampling             |
 * +-------------------------------------+------------+----------------------------------------------+
 * | GKS_K_DOWNSAMPLE_HORIZONTAL_LINEAR  | 0x02000000 | linear for horizontal downsampling           |
 * +-------------------------------------+------------+----------------------------------------------+
 * | GKS_K_UPSAMPLE_VERTICAL_LANCZOS     | 0x00000003 | lanczos for vertical upsampling              |
 * +-------------------------------------+------------+----------------------------------------------+
 * | GKS_K_UPSAMPLE_HORIZONTAL_LANCZOS   | 0x00000300 | lanczos for horizontal upsampling            |
 * +-------------------------------------+------------+----------------------------------------------+
 * | GKS_K_DOWNSAMPLE_VERTICAL_LANCZOS   | 0x00030000 | lanczos for vertical downsampling            |
 * +-------------------------------------+------------+----------------------------------------------+
 * | GKS_K_DOWNSAMPLE_HORIZONTAL_LANCZOS | 0x03000000 | lanczos for horizontal downsampling          |
 * +-------------------------------------+------------+----------------------------------------------+
 *
 * \endverbatim
 */
void gr_setresamplemethod(unsigned int flag)
{
  check_autoinit;

  gks_set_resample_method(flag);
}

/*!
 * Inquire the resample flag status.
 *
 * \returns Resample flag
 */
void gr_inqresamplemethod(unsigned int *flag)
{
  check_autoinit;

  gks_inq_resample_method(flag);
}

/*!
 * Draw paths using given vertices and path codes.
 *
 * \param[in] n The number of points
 * \param[in] x A pointer to the X coordinates
 * \param[in] y A pointer to the Y coordinates
 * \param[in] codes Path codes as a null-terminated string
 *
 * The values for `x` and `y` are in world coordinates. `n` is the number of vertices to use.
 * The `codes` describe several patch primitives that can be used to create compound paths.
 *
 * The following path codes are recognized:
 *
 * \verbatim embed:rst:leading-asterisk
 *
 * +----------+---------------------------------------+-------------------+-------------------+
 * | **Code** | **Description**                       | **x**             | **y**             |
 * +----------+---------------------------------------+-------------------+-------------------+
 * |     M, m | move                                  | x                 | y                 |
 * +----------+---------------------------------------+-------------------+-------------------+
 * |     L, l | line                                  | x                 | y                 |
 * +----------+---------------------------------------+-------------------+-------------------+
 * |     Q, q | quadratic Bezier                      | x1, x2            | y1, y2            |
 * +----------+---------------------------------------+-------------------+-------------------+
 * |     C, c | cubic Bezier                          | x1, x2, x3        | y1, y2, y3        |
 * +----------+---------------------------------------+-------------------+-------------------+
 * |     A, a | arc                                   | rx, a1, reserved  | ry, a2, reserved  |
 * +----------+---------------------------------------+-------------------+-------------------+
 * |        Z | close path                            |                   |                   |
 * +----------+---------------------------------------+-------------------+-------------------+
 * |        S | stroke                                |                   |                   |
 * +----------+---------------------------------------+-------------------+-------------------+
 * |        s | close path and stroke                 |                   |                   |
 * +----------+---------------------------------------+-------------------+-------------------+
 * |        f | close path and fill                   |                   |                   |
 * +----------+---------------------------------------+-------------------+-------------------+
 * |        F | close path, fill and stroke           |                   |                   |
 * +----------+---------------------------------------+-------------------+-------------------+
 * |        g | close path and fill (nonzero)         |                   |                   |
 * +----------+---------------------------------------+-------------------+-------------------+
 * |        G | close path, fill (nonzero) and stroke |                   |                   |
 * +----------+---------------------------------------+-------------------+-------------------+
 *
 * \endverbatim
 *
 *  - M, m
 *
 *    Moves the current position to (`x`, `y`). The new position is either absolute (`M`) or relative to the current
 *    position (`m`). The initial position of `gr_path` is (0, 0).
 *
 *    Example:
 *
 *        double x[2] = {0.5, -0.1};
 *        double y[2] = {0.2, 0.1};
 *        gr_path(2, x, y, "Mm");
 *
 *    The first move command in this example moves the current position to the absolute coordinates (0.5, 0.2). The
 *    second move to performs a movement by (-0.1, 0.1) relative to the current position resulting in the point
 *    (0.4, 0.3).
 *
 *
 *  - L, l
 *
 *    Draws a line from the current position to the given position (`x`, `y`). The end point of the line is either
 *    absolute (`L`) or relative to the current position (`l`). The current position is set to the end point of the
 *    line.
 *
 *    Example:
 *
 *        double x[3] = {0.1, 0.5, 0.0};
 *        double y[3] = {0.1, 0.1, 0.2};
 *        gr_path(3, x, y, "MLlS");
 *
 *    The first line to command draws a straight line from the current position (0.1, 0.1) to the absolute position
 *    (0.5, 0.1) resulting in a horizontal line. The second line to command draws a vertical line relative to the
 *    current position resulting in the end point (0.5, 0.3).
 *
 *
 *  - Q, q
 *
 *    Draws a quadratic bezier curve from the current position to the end point (`x2`, `y2`) using (`x1`, `y1`) as the
 *    control point. Both points are either absolute (`Q`) or relative to the current position (`q`). The current
 *    position is set to the end point of the bezier curve.
 *
 *    Example:
 *
 *        double x[5] = {0.1, 0.3, 0.5, 0.2, 0.4};
 *        double y[5] = {0.1, 0.2, 0.1, 0.1, 0.0};
 *        gr_path(5, x, y, "MQqS");
 *
 *    This example will generate two bezier curves whose start and end points are each located at y=0.1. As the control
 *    points are horizontally in the middle of each bezier curve with a higher y value both curves are symmetrical
 *    and bend slightly upwards in the middle. The current position is set to (0.9, 0.1) at the end.
 *
 *  - C, c
 *
 *    Draws a cubic bezier curve from the current position to the end point (`x3`, `y3`) using (`x1`, `y1`) and
 *    (`x2`, `y2`) as the control points. All three points are either absolute (`C`) or relative to the current position
 *    (`c`). The current position is set to the end point of the bezier curve.
 *
 *    Example:
 *
 *        double x[7] = {0.1, 0.2, 0.3, 0.4, 0.1, 0.2, 0.3};
 *        double y[7] = {0.1, 0.2, 0.0, 0.1, 0.1, -0.1, 0.0};
 *        gr_path(7, x, y, "MCcS");
 *
 *    This example will generate two bezier curves whose start and end points are each located at y=0.1. As the control
 *    points are equally spaced along the x-axis and the first is above and the second is below the start and end
 *    points this creates a wave-like shape for both bezier curves. The current position is set to (0.8, 0.1) at the
 *    end.
 *
 *
 *  - A, a
 *
 *    Draws an elliptical arc starting at the current position. The major axis of the ellipse is aligned with the x-axis
 *    and the minor axis is aligned with the y-axis of the plot. `rx` and `ry` are the ellipses radii along the major
 *    and minor axis. `a1` and `a2` define the start and end angle of the arc in radians. The current position is set
 *    to the end point of the arc. If `a2` is greater than `a1` the arc is drawn counter-clockwise, otherwise it is
 *    drawn clockwise. The `a` and `A` commands draw the same arc. The third coordinates of the `x` and `y` array are
 *    ignored and reserved for future use.
 *
 *    Examples:
 *
 *        double x[4] = {0.1, 0.2, -3.14159 / 2, 0.0};
 *        double y[4] = {0.1, 0.4, 3.14159 / 2, 0.0};
 *        gr_path(4, x, y, "MAS");
 *
 *    This example draws an arc starting at (0.1, 0.1). As the start angle -pi/2 is smaller than the end angle pi/2 the
 *    arc is drawn counter-clockwise. In this case the right half of an ellipse with an x radius of 0.2 and a y radius
 *    of 0.4 is shown. Therefore the current position is set to (0.1, 0.9) at the end.
 *
 *        double x[4] = {0.1, 0.2, 3.14159 / 2, 0.0};
 *        double y[4] = {0.9, 0.4, -3.14159 / 2, 0.0};
 *        gr_path(4, x, y, "MAS");
 *
 *    This examples draws the same arc as the previous one. The only difference is that the starting point is now at
 *    (0.1, 0.9) and the start angle pi/2 is greater than the end angle -pi/2 so that the ellipse arc is drawn
 * clockwise. Therefore the current position is set to (0.1, 0.1) at the end.
 *
 *  - Z
 *
 *    Closes the current path by connecting the current position to the target position of the last move command
 *    (`m` or `M`) with a straight line. If no move to was performed in this path it connects the current position to
 *    (0, 0). When the path is stroked this line will also be drawn.
 *
 *
 *  - S, s
 *
 *    Strokes the path with the current border width and border color (set with `gr_setborderwidth` and
 *    `gr_setbordercolorind`). In case of `s` the path is closed beforehand, which is equivalent to `ZS`.
 *
 *
 *  - F, f, G, g
 *
 *    Fills the current path using the even-odd-rule for `F` and `f` or the nonzero / winding rule for `G` and `g`
 *    in the current fill color. Filling a path implicitly closes the path. The fill color can be set using
 *    `gr_setfillcolorind`. In case of `F` and `G` the path is also stroked using the current border width and color
 *    afterwards.
 *
 */
void gr_path(int n, double *x, double *y, const char *codes)
{
  int i, len;

  check_autoinit;

  len = strlen(codes);
  if (len >= maxpath) reallocate(len);

  for (i = 0; i < len; i++) code[i] = (unsigned int)codes[i];

  gks_gdp(n, x, y, GKS_K_GDP_DRAW_PATH, len, code);
}

/*!
 * Return the position on the hyperboloid or sphere.
 */
static void gr_trackballposition(const double *mouse, double r, double *erg)
{
  double x, y, z;
  double fx, fy, fz, f_length;

  x = mouse[0];
  y = mouse[1];

  /* reverse projection */
  if (gpx.projection_type == GR_PROJECTION_ORTHOGRAPHIC)
    {
      x = (gpx.right - gpx.left) * (x + 1) * 0.5 + gpx.left;
      y = (gpx.bottom - gpx.top) * (-y + 1) * 0.5 + gpx.top;

      if (x * x + y * y <= r * r / sqrt(2))
        {
          /* sphere */
          z = sqrt(r * r - (x * x + y * y));
        }
      else
        {
          /* hyperboloid */
          z = r * r / (2 * sqrt(x * x + y * y));
        }
    }
  else
    {
      /* point on z_near */
      double opposite_catheter = tan(gpx.fov / 2);
      double factor_x = x * opposite_catheter * (ix.xmax - ix.xmin) / (ix.ymax - ix.ymin);
      double factor_y = y * opposite_catheter;
      double d[3], distance;
      d[0] = tx.focus_point_x - tx.camera_pos_x;
      d[1] = tx.focus_point_y - tx.camera_pos_y;
      d[2] = tx.focus_point_z - tx.camera_pos_z;
      /* distance to the focuspoint as offset for the calculated z */
      distance = sqrt(d[0] * d[0] + d[1] * d[1] + d[2] * d[2]);

      z = (distance - sqrt(-distance * distance * (factor_x * factor_x + factor_y * factor_y) +
                           r * r * (factor_x * factor_x + factor_y * factor_y + 1))) /
          (factor_x * factor_x + factor_y * factor_y + 1);
      x = factor_x * z;
      y = factor_y * z;

      if (x * x + y * y > r * r / sqrt(2))
        {
          /* position wasnt onside the trackball */
          z = distance / 2 -
              sqrt(distance * distance / 4 + r * r / (2 * sqrt(factor_x * factor_x + factor_y * factor_y)));
          x = factor_x * z;
          y = factor_y * z;
        }
    }

  /* calculate and normalize the forward direction */
  fx = tx.focus_point_x - tx.camera_pos_x;
  fy = tx.focus_point_y - tx.camera_pos_y;
  fz = tx.focus_point_z - tx.camera_pos_z;
  f_length = sqrt(fx * fx + fy * fy + fz * fz);
  fx /= f_length;
  fy /= f_length;
  fz /= f_length;

  /* transform the point into the camera system */
  erg[0] = x * tx.s_x + y * tx.up_x + z * fx;
  erg[1] = x * tx.s_y + y * tx.up_y + z * fy;
  erg[2] = x * tx.s_z + y * tx.up_z + z * fz;
}

/*!
 * Return the radius of the minimum bounding sphere for the current 3D window
 */
static void gr_calculateradius(double *radius)
{
  int i;
  double max = 0;
  double left = pow(ix.xmin - tx.focus_point_x, 2);
  double right = pow(ix.xmax - tx.focus_point_x, 2);
  double bottom = pow(ix.ymin - tx.focus_point_y, 2);
  double top = pow(ix.ymax - tx.focus_point_y, 2);
  double z_far = pow(ix.zmin - tx.focus_point_z, 2);
  double z_near = pow(ix.zmax - tx.focus_point_z, 2);

  double radii[8];

  /* all eight coordinates quadrants */
  radii[0] = sqrt(right + top + z_far);
  radii[1] = sqrt(right + top + z_near);
  radii[2] = sqrt(left + top + z_far);
  radii[3] = sqrt(left + top + z_near);
  radii[4] = sqrt(right + bottom + z_far);
  radii[5] = sqrt(right + bottom + z_near);
  radii[6] = sqrt(left + bottom + z_far);
  radii[7] = sqrt(left + bottom + z_near);

  /* find the max radius*/
  for (i = 0; i < 8; i++)
    {
      if (max < radii[i])
        {
          max = radii[i];
        }
    }

  *radius = max;
}

/*!
 * Rotate the current scene according to a virtual arcball.
 *
 * \param start_mouse_pos_x x component of the start mouse position
 * \param start_mouse_pos_y y component of the start mouse position
 * \param end_mouse_pos_x x component of the end mouse position
 * \param end_mouse_pos_y y component of the end mouse position
 *
 * This function requires values between 0 (left side or bottom of the drawing
 * area) and 1 (right side or top of the drawing area).
 */
void gr_camerainteraction(double start_mouse_pos_x, double start_mouse_pos_y, double end_mouse_pos_x,
                          double end_mouse_pos_y)
{
  check_autoinit;

  /* check if there is any mouse movement */
  if (start_mouse_pos_x != end_mouse_pos_x || start_mouse_pos_y != end_mouse_pos_y)
    {
      double start[3], end[3], mouse_start[3], mouse_end[3], rotation_mat[9];
      double radius, camera_distance;
      double start_length, end_length;
      double cos_angle, c, s;
      double axis_x, axis_y, axis_z, axis_length;
      double fx, fy, fz, f_length;
      double axis_projection_forward;
      double cam_x, cam_y, cam_z, up_x, up_y, up_z, sx, sy, sz;

      gr_calculateradius(&radius);

      camera_distance = radius;
      /* parameter for better overview */
      if (gpx.projection_type == GR_PROJECTION_PERSPECTIVE)
        {
          camera_distance = fabs(radius / sin((gpx.fov * M_PI / 180) / 2));
        }

      /* transform mouseposition onto [-1, 1] */
      mouse_start[0] = start_mouse_pos_x * 2 - 1;
      mouse_start[1] = 2 * start_mouse_pos_y - 1;
      mouse_start[2] = 0;
      mouse_end[0] = end_mouse_pos_x * 2 - 1;
      mouse_end[1] = 2 * end_mouse_pos_y - 1;
      mouse_end[2] = 0;

      /* get the trackball positions of the start and end mouseposition */
      gr_trackballposition(mouse_start, camera_distance, start);
      gr_trackballposition(mouse_end, camera_distance, end);

      /* calculate the rotation axis and the angle of the rotation */
      start_length = sqrt(start[0] * start[0] + start[1] * start[1] + start[2] * start[2]);
      end_length = sqrt(end[0] * end[0] + end[1] * end[1] + end[2] * end[2]);
      cos_angle = (start[0] * end[0] + start[1] * end[1] + start[2] * end[2]) / start_length / end_length;
      axis_x = start[1] * end[2] - end[1] * start[2];
      axis_y = start[2] * end[0] - end[2] * start[0];
      axis_z = start[0] * end[1] - end[0] * start[1];

      /* calculate and normalize the forward direction */
      fx = tx.focus_point_x - tx.camera_pos_x;
      fy = tx.focus_point_y - tx.camera_pos_y;
      fz = tx.focus_point_z - tx.camera_pos_z;
      f_length = sqrt(fx * fx + fy * fy + fz * fz);
      fx /= f_length;
      fy /= f_length;
      fz /= f_length;

      /* reverse the rotation axis around the forward axis */
      axis_projection_forward = axis_x * fx + axis_y * fy + axis_z * fz;
      axis_x -= fx * axis_projection_forward * 2;
      axis_y -= fy * axis_projection_forward * 2;
      axis_z -= fz * axis_projection_forward * 2;
      axis_length = sqrt(axis_x * axis_x + axis_y * axis_y + axis_z * axis_z);
      axis_x /= axis_length;
      axis_y /= axis_length;
      axis_z /= axis_length;

      /* shorter names for sin and cos to reduce the size of the matrix */
      c = cos_angle;
      s = sqrt(1 - c * c);

      rotation_mat[0] = axis_x * axis_x * (1 - c) + c;
      rotation_mat[1] = axis_x * axis_y * (1 - c) - axis_z * s;
      rotation_mat[2] = axis_x * axis_z * (1 - c) + axis_y * s;
      rotation_mat[3] = axis_y * axis_x * (1 - c) + axis_z * s;
      rotation_mat[4] = axis_y * axis_y * (1 - c) + c;
      rotation_mat[5] = axis_y * axis_z * (1 - c) - axis_x * s;
      rotation_mat[6] = axis_z * axis_x * (1 - c) - axis_y * s;
      rotation_mat[7] = axis_z * axis_y * (1 - c) + axis_x * s;
      rotation_mat[8] = axis_z * axis_z * (1 - c) + c;

      /* rotate camera position */
      cam_x = (tx.camera_pos_x - tx.focus_point_x) * rotation_mat[0] +
              (tx.camera_pos_y - tx.focus_point_y) * rotation_mat[1] +
              (tx.camera_pos_z - tx.focus_point_z) * rotation_mat[2] + tx.focus_point_x;
      cam_y = (tx.camera_pos_x - tx.focus_point_x) * rotation_mat[3] +
              (tx.camera_pos_y - tx.focus_point_y) * rotation_mat[4] +
              (tx.camera_pos_z - tx.focus_point_z) * rotation_mat[5] + tx.focus_point_y;
      cam_z = (tx.camera_pos_x - tx.focus_point_x) * rotation_mat[6] +
              (tx.camera_pos_y - tx.focus_point_y) * rotation_mat[7] +
              (tx.camera_pos_z - tx.focus_point_z) * rotation_mat[8] + tx.focus_point_z;

      /* rotate up and right camera axes */
      up_x = tx.up_x * rotation_mat[0] + tx.up_y * rotation_mat[1] + tx.up_z * rotation_mat[2];
      up_y = tx.up_x * rotation_mat[3] + tx.up_y * rotation_mat[4] + tx.up_z * rotation_mat[5];
      up_z = tx.up_x * rotation_mat[6] + tx.up_y * rotation_mat[7] + tx.up_z * rotation_mat[8];
      sx = tx.s_x * rotation_mat[0] + tx.s_y * rotation_mat[1] + tx.s_z * rotation_mat[2];
      sy = tx.s_x * rotation_mat[3] + tx.s_y * rotation_mat[4] + tx.s_z * rotation_mat[5];
      sz = tx.s_x * rotation_mat[6] + tx.s_y * rotation_mat[7] + tx.s_z * rotation_mat[8];

      /* save the new calculated values for the transformation */
      tx.camera_pos_x = cam_x;
      tx.camera_pos_y = cam_y;
      tx.camera_pos_z = cam_z;
      tx.up_x = up_x;
      tx.up_y = up_y;
      tx.up_z = up_z;
      tx.s_x = sx;
      tx.s_y = sy;
      tx.s_z = sz;
    }

  if (flag_stream)
    gr_writestream("<camerainteraction start_mouse_pos_x=\"%g\" start_mouse_pos_y=\"%g\" end_mouse_pos_x=\"%g\" "
                   "end_mouse_pos_y=\"%g\"/>\n",
                   start_mouse_pos_x, start_mouse_pos_y, end_mouse_pos_x, end_mouse_pos_y);
}

/*!
 * Set the three dimensional window. Only used for perspective and orthographic projection.
 *
 * \param xmin min x-value
 * \param xmax max x-value
 * \param ymin min y-value
 * \param ymax max y-value
 * \param zmin min z-value
 * \param zmax max z-value
 */
void gr_setwindow3d(double xmin, double xmax, double ymin, double ymax, double zmin, double zmax)
{
  check_autoinit;

  ix.xmin = xmin;
  ix.xmax = xmax;
  ix.ymin = ymin;
  ix.ymax = ymax;
  ix.zmin = zmin;
  ix.zmax = zmax;

  wx.zmin = zmin;
  wx.zmax = zmax;

  if (flag_stream)
    gr_writestream("<setwindow3d xmin=\"%g\" xmax=\"%g\" ymin=\"%g\" ymax=\"%g\" zmin=\"%g\" zmax=\"%g\"/>\n", xmin,
                   xmax, ymin, ymax, zmin, zmax);
}

static void setscalefactors3d(double x_axis_scale, double y_axis_scale, double z_axis_scale)
{
  tx.x_axis_scale = x_axis_scale;
  tx.y_axis_scale = y_axis_scale;
  tx.z_axis_scale = z_axis_scale;
  tx.use_setspace3d = 0;
}

/*!
 * Set the scale factor for each axis.
 *
 * \param x_axis_scale factor for scaling the x-axis
 * \param y_axis_scale factor for scaling the y-axis
 * \param z_axis_scale factor for scaling the z-axis
 *
 * The scaling factors must not be zero.
 */
void gr_setscalefactors3d(double x_axis_scale, double y_axis_scale, double z_axis_scale)
{
  check_autoinit;

  if (x_axis_scale == 0 || y_axis_scale == 0 || z_axis_scale == 0)
    {
      fprintf(stderr, "Invalid scale factor. Please check your parameters again.\n");
      return;
    }

  setscalefactors3d(x_axis_scale, y_axis_scale, z_axis_scale);

  if (flag_stream)
    gr_writestream("<setscalefactors3d x_axis_scale=\"%g\" y_axis_scale=\"%g\" z_axis_scale=\"%g\"/>\n", x_axis_scale,
                   y_axis_scale, z_axis_scale);
}

/*!
 * Returns the scaling factor for each axis.
 */
void gr_inqscalefactors3d(double *x_axis_scale, double *y_axis_scale, double *z_axis_scale)
{
  *x_axis_scale = tx.x_axis_scale;
  *y_axis_scale = tx.y_axis_scale;
  *z_axis_scale = tx.z_axis_scale;
}

/*!
 * Define the border width of subsequent path output primitives.
 *
 * \param[in] width The border width scale factor
 */
void gr_setborderwidth(double width)
{
  check_autoinit;

  gks_set_border_width(width);
  if (ctx) ctx->bwidth = width;

  if (flag_stream) gr_writestream("<setborderwidth width=\"%g\"/>\n", width);
}

void gr_inqborderwidth(double *width)
{
  int errind;

  check_autoinit;

  gks_inq_border_width(&errind, width);
}

/*!
 * Define the border color of subsequent path output primitives.
 *
 * \param[in] color The border color index (COLOR < 1256)
 */
void gr_setbordercolorind(int color)
{
  check_autoinit;

  gks_set_border_color_index(color);
  if (ctx) ctx->bcoli = color;

  if (flag_stream) gr_writestream("<setbordercolorind color=\"%d\"/>\n", color);
}

void gr_inqbordercolorind(int *coli)
{
  int errind;

  check_autoinit;

  gks_inq_border_color_index(&errind, coli);
}

void gr_selectclipxform(int tnr)
{
  check_autoinit;

  gks_select_clip_xform(tnr);
  if (ctx) ctx->clip_tnr = tnr;

  if (flag_stream) gr_writestream("<selectclipxform tnr=\"%d\"/>\n", tnr);
}

void gr_inqclipxform(int *tnr)
{
  int errind;

  check_autoinit;

  gks_inq_clip_xform(&errind, tnr);
}

void gr_setclipregion(int region)
{
  check_autoinit;

  gks_set_clip_region(region);
  if (ctx) ctx->clip_region = region;

  if (flag_stream) gr_writestream("<setclipregion region=\"%d\"/>\n", region);
}

void gr_inqclipregion(int *region)
{
  int errind;

  check_autoinit;

  gks_inq_clip_region(&errind, region);
}

void gr_settextoffset(double xoff, double yoff)
{
  check_autoinit;

  txoff[0] = xoff;
  txoff[1] = yoff;

  if (flag_stream) gr_writestream("<settextoffset xoff=\"%g\" yoff=\"%g\"/>\n", xoff, yoff);
}

/*!
 * Set the camera for orthographic or perspective projection.
 *
 * The center of the 3d window is used as the focus point and the camera is
 * positioned relative to it, using camera distance, azimuthal angle and polar
 * angle similar to gr_setspace.  This function can be used if the user
 * prefers spherical coordinates to setting the camera position directly, but
 * has reduced functionality in comparison to gr_settransformationparameters,
 * gr_setscalefactors3d, gr_setperspectiveprojection and
 * gr_setorthographicprojection.
 *
 * \param phi azimuthal angle of the spherical coordinates
 * \param theta polar angle of the spherical coordinates
 * \param fov vertical field of view(0 or NaN for orthographic projection)
 * \param cam distance between the camera and the focus point (in
 * arbitrary units, 0 or NaN for the radius of the object's smallest bounding
 * sphere)
 */
void gr_setspace3d(double phi, double theta, double fov, double cam)
{
  double scale_factor_x, scale_factor_y, scale_factor_z;
  double camera_distance = cam, bounding_sphere_radius;
  double eps = 1e-6;

  tx.focus_point_x = (ix.xmax + ix.xmin) / 2;
  tx.focus_point_y = (ix.ymin + ix.ymax) / 2;
  tx.focus_point_z = (ix.zmax + ix.zmin) / 2;

  bounding_sphere_radius = sqrt(3);
  if (is_nan(fov) || fov == 0)
    {
      if (camera_distance == 0 || is_nan(camera_distance))
        {
          camera_distance = bounding_sphere_radius;
        }
      setorthographicprojection(-camera_distance, camera_distance, -camera_distance, camera_distance,
                                -camera_distance * 2, camera_distance * 2);
    }
  else
    {
      if (camera_distance == 0 || is_nan(camera_distance))
        {
          camera_distance = fabs(bounding_sphere_radius / sin((fov * M_PI / 180) / 2));
        }
      setperspectiveprojection(max(eps, camera_distance - bounding_sphere_radius * 1.01),
                               camera_distance + bounding_sphere_radius * 2, fov);
    }

  scale_factor_x = 2.0 / (ix.xmax - ix.xmin);
  scale_factor_y = 2.0 / (ix.ymax - ix.ymin);
  scale_factor_z = 2.0 / (ix.zmax - ix.zmin);

  settransformationparameters(
      camera_distance * sin(theta * M_PI / 180) * cos(phi * M_PI / 180) + tx.focus_point_x * scale_factor_x,
      camera_distance * sin(theta * M_PI / 180) * sin(phi * M_PI / 180) + tx.focus_point_y * scale_factor_y,
      camera_distance * cos(theta * M_PI / 180) + tx.focus_point_z * scale_factor_z,
      -cos(phi * M_PI / 180) * cos(theta * M_PI / 180), -sin(phi * M_PI / 180) * cos(theta * M_PI / 180),
      sin(theta * M_PI / 180), tx.focus_point_x * scale_factor_x, tx.focus_point_y * scale_factor_y,
      tx.focus_point_z * scale_factor_z);

  setscalefactors3d(scale_factor_x, scale_factor_y, scale_factor_z);

  tx.use_setspace3d = 1;
  tx.setspace3d_phi = phi;
  tx.setspace3d_theta = theta;
  tx.setspace3d_fov = fov;
  tx.setspace3d_cam = cam;

  if (flag_stream)
    gr_writestream("<setspace3d phi=\"%g\" theta=\"%g\" fov=\"%g\" cam=\"%g\"/>\n", phi, theta, fov, cam);
}

void gr_inqspace3d(int *use_setspace3d, double *phi, double *theta, double *fov, double *cam)
{
  check_autoinit;

  *use_setspace3d = tx.use_setspace3d;
  if (tx.use_setspace3d)
    {
      *phi = tx.setspace3d_phi;
      *theta = tx.setspace3d_theta;
      *fov = tx.setspace3d_fov;
      *cam = tx.setspace3d_cam;
    }
  else
    {
      *phi = NAN;
      *theta = NAN;
      *fov = NAN;
      *cam = NAN;
    }
}

void gr_settextencoding(int encoding)
{
  check_autoinit;

  gks_set_encoding(encoding);

  if (flag_stream) gr_writestream("<settextencoding encoding=\"%d\"/>\n", encoding);
}

void gr_inqtextencoding(int *encoding)
{
  check_autoinit;

  gks_inq_encoding(encoding);
}

void gr_setcallback(char *(*callback)(const char *arg))
{
  check_autoinit;

  gks_set_callback(callback);
}

static void bilinear_interpolation(double c00, double c10, double c01, double c11, double x_dist, double y_dist,
                                   double *erg)
{
  double c0 = c00 * (1 - x_dist) + c10 * x_dist;
  double c1 = c01 * (1 - x_dist) + c11 * x_dist;

  *erg = c0 * (1 - y_dist) + c1 * y_dist;
}

/*!
 * Set the number of threads which can run parallel. The default value is the number of threads the cpu has.
 * The only usage right now is inside `gr_cpubasedvolume` and `gr_volume_nogrid`.
 *
 * \param[in] num number of threads
 */
void gr_setthreadnumber(int num)
{
  check_autoinit;

  vt.max_threads = max(1, num);
  vt.thread_size = 10 * (1.0 / (2.0 * num));

  if (flag_stream) gr_writestream("<setthreadnumber num=\"%i\"/>\n", num);
}

/*!
 * Set the width and height of the resulting picture. These values are only used for the volume rendering methods.
 * The default values are 1000 for both.
 *
 * \param[in] width  width of the resulting image
 * \param[in] height height of the resulting image
 */
void gr_setpicturesizeforvolume(int width, int height)
{
  check_autoinit;

  vt.picture_height = height;
  vt.picture_width = width;

  if (flag_stream) gr_writestream("<setpicturesizeforvolume width=\"%i\" height=\"%i\"/>\n", width, height);
}

/*!
 * Set if gr_cpubasedvolume is calculated approximative or exact. To use the exact calculation set
 * approximative_calculation to 0. The default value is the approximative version, which can be set with the number 1.
 *
 * \param[in] approximative_calculation exact or approximative calculation of the volume
 */
void gr_setapproximativecalculation(int approximative_calculation)
{
  check_autoinit;

  if (approximative_calculation == 0 || approximative_calculation == 1)
    {
      vt.approximative_calculation = approximative_calculation;
    }
  else
    {
      fprintf(stderr, "Invalid number for approximative_calculation. Valid numbers are 0 and 1.\n");
    }

  if (flag_stream)
    gr_writestream("<setapproximativecalculation approximative_calculation=\"%i\"", approximative_calculation);
}

/*!
 * Set the gr_volume border type with this flag. This inflicts how the volume is calculated.
 * When the flag is set to GR_VOLUME_WITH_BORDER the border will be calculated the same as the points inside the volume.
 *
 * \param[in] flag calculation of the gr_volume border
 *
 * The available options are:
 *
 * \verbatim embed:rst:leading-asterisk
 *
 * +---------------------------+---+-----------------------+
 * |GR_VOLUME_WITHOUT_BORDER   |  0|default value          |
 * +---------------------------+---+-----------------------+
 * |GR_VOLUME_WITH_BORDER      |  1|gr_volume with border  |
 * +---------------------------+---+-----------------------+
 *
 * \endverbatim
 */
void gr_setvolumebordercalculation(int flag)
{
  check_autoinit;

  if (flag == GR_VOLUME_WITHOUT_BORDER || flag == GR_VOLUME_WITH_BORDER)
    {
      vt.border = flag;
    }
  else
    {
      fprintf(stderr, "Invalid gr_volume bordercalculation flag. Possible options are GR_VOLUME_WITHOUT_BORDER, "
                      "GR_VOLUME_WITH_BORDER \n");
    }
  if (flag_stream) gr_writestream("<setvolumebordercalculation flag=\"%i\"/>\n", flag);
}

/*!
 * Inquire the parameters which can be set for gr_cpubasedvolume. The size of the resulting image,
 * the way the volumeborder is calculated and the amount of threads which are used.
 *
 * \param[out] border                       flag which tells how the border is calculated
 * \param[out] max_threads                  number of threads
 * \param[out] picture_width                width of the resulting image
 * \param[out] picture_height               height of the resulting image
 * \param[out] approximative_calculation    exact or approximative calculation of gr_cpubasedvolume
 */
void gr_inqvolumeflags(int *border, int *max_threads, int *picture_width, int *picture_height,
                       int *approximative_calculation)
{
  check_autoinit;

  *border = vt.border;
  *max_threads = vt.max_threads;
  *picture_width = vt.picture_width;
  *picture_height = vt.picture_height;
  *approximative_calculation = vt.approximative_calculation;
}

static void draw_volume(const double *pixels)
{
  int i;
  double dmax;
  double xmin, ymin, xmax, ymax;
  int *ipixels, *colormap;

  ipixels = (int *)gks_malloc(vt.picture_width * vt.picture_height * sizeof(int));

  dmax = pixels[0];
  for (i = 1; i < vt.picture_width * vt.picture_height; i++)
    {
      if (pixels[i] > dmax)
        {
          dmax = pixels[i];
        }
    }

  colormap = (int *)gks_malloc((last_color - first_color + 1) * sizeof(int));
  for (i = first_color; i <= last_color; i++)
    {
      gr_inqcolor(i, colormap + i - first_color);
    }

  for (i = 0; i < vt.picture_width * vt.picture_height; i++)
    {
      if (pixels[i] >= 0)
        {
          if (dmax == 0)
            {
              ipixels[i] = 0;
            }
          else
            {
              ipixels[i] = (255u << 24) + colormap[(int)(pixels[i] / dmax * (last_color - first_color))];
            }
        }
    }

  gr_inqwindow(&xmin, &xmax, &ymin, &ymax);
  drawimage_calculation(xmin, xmax, ymin, ymax, vt.picture_width, vt.picture_height, ipixels, 0);

  free(ipixels);
  free(colormap);
}

static void trilinear_interpolation(double c000, double c001, double c010, double c100, double c101, double c110,
                                    double c011, double c111, double x_dist, double y_dist, double z_dist, double *erg)
{
  double c00 = c000 * (1 - x_dist) + c100 * x_dist;
  double c01 = c001 * (1 - x_dist) + c101 * x_dist;
  double c10 = c010 * (1 - x_dist) + c110 * x_dist;
  double c11 = c011 * (1 - x_dist) + c111 * x_dist;

  double c0 = c00 * (1 - y_dist) + c10 * y_dist;
  double c1 = c01 * (1 - y_dist) + c11 * y_dist;

  *erg = c0 * (1 - z_dist) + c1 * z_dist;
}

static void ray_casting_thread(void *arg)
{
  int i, j, s;
  double ray_start[3] = {0, 0, 0}, ray_dir[3] = {0, 0, 0}, ray_dir_default[3], tmp[3];

  /* get the necessary attributes out of the structs */
  struct thread_attr *ta = (struct thread_attr *)arg;
  struct ray_casting_attr *rc = vt.ray_casting;

  int nx = rc->nx, ny = rc->ny, nz = rc->nz;
  int algorithm = rc->algorithm;
  double *data = rc->data, *pixels = rc->pixels;
  double *dmax_ptr = rc->dmax_ptr, *dmin_ptr = rc->dmin_ptr;
  double f_length, xaspect, yaspect, aspect_ratio;

  double eps = 1e-8; /* precision parameter for comparisons */
  double x_spacing = 1. / nx;
  double y_spacing = 1. / ny;
  double z_spacing = 1. / nz;
  double min_n = 25; /* number found by testing */
  double wdh = max(1., ceil(min_n / (double)min(nx, min(ny, nz))));

  /* transform values into integer */
  double min_val_t[3] = {0, 0, 0}, max_val_t[3];
  max_val_t[0] = nx - 1;
  max_val_t[1] = ny - 1;
  max_val_t[2] = nz - 1;
  if (vt.border == GR_VOLUME_WITH_BORDER)
    {
      min_val_t[0] = min_val_t[1] = min_val_t[2] = -0.5;
      max_val_t[0] = nx - 0.5;
      max_val_t[1] = ny - 0.5;
      max_val_t[2] = nz - 0.5;
    }

  /* the direction of each ray is the same when the projection_type is set to orthographic */
  ray_dir_default[0] = (tx.focus_point_x - tx.camera_pos_x);
  ray_dir_default[1] = (tx.focus_point_y - tx.camera_pos_y);
  ray_dir_default[2] = (tx.focus_point_z - tx.camera_pos_z);

  f_length = sqrt(ray_dir_default[0] * ray_dir_default[0] + ray_dir_default[1] * ray_dir_default[1] +
                  ray_dir_default[2] * ray_dir_default[2]);
  ray_dir_default[0] /= f_length;
  ray_dir_default[1] /= f_length;
  ray_dir_default[2] /= f_length;

  /* determine aspect_ratio */
  xaspect = (vxmax - vxmin) / (vymax - vymin);
  yaspect = 1.0 / xaspect;
  if (xaspect < 1.0)
    {
      xaspect = 1.0;
    }
  else
    {
      yaspect = 1.0;
    }
  aspect_ratio = xaspect / yaspect;

  if (gpx.projection_type == GR_PROJECTION_ORTHOGRAPHIC)
    {
      ray_dir[0] = ray_dir_default[0] / x_spacing;
      ray_dir[1] = ray_dir_default[1] / y_spacing;
      ray_dir[2] = ray_dir_default[2] / z_spacing;
    }
  for (i = ta->x_start; i < ta->x_end; i++)
    {
      for (j = ta->y_start; j < ta->y_end; j++)
        {
          double color = 0;
          double x_ortho = 0, y_ortho = 0, z_ortho = 0;
          double lambda[3] = {0};
          double start = NAN;
          double max_lambda;
          if (algorithm == 1)
            {
              /* absorption */
              color = 1;
            }

          /* cast ray */
          if (gpx.projection_type == GR_PROJECTION_ORTHOGRAPHIC)
            {
              double width_steps = (gpx.right - gpx.left) / vt.picture_width;
              double heigth_steps = (gpx.top - gpx.bottom) / vt.picture_height;

              /* uses the pixel mid point */
              if (aspect_ratio > 1)
                {
                  tmp[0] = (gpx.left + (0.5 + i) * width_steps) * aspect_ratio;
                  tmp[1] = gpx.bottom + (0.5 + j) * heigth_steps;
                }
              else
                {
                  tmp[0] = gpx.left + (0.5 + i) * width_steps;
                  tmp[1] = (gpx.bottom + (0.5 + j) * heigth_steps) / aspect_ratio;
                }
              tmp[2] = gpx.near_plane;

              /* transform the point into the camera system */
              ray_start[0] = tmp[0] * tx.s_x - tmp[1] * tx.up_x + tmp[2] * ray_dir_default[0];
              ray_start[1] = tmp[0] * tx.s_y - tmp[1] * tx.up_y + tmp[2] * ray_dir_default[1];
              ray_start[2] = tmp[0] * tx.s_z - tmp[1] * tx.up_z + tmp[2] * ray_dir_default[2];
            }
          else if (gpx.projection_type == GR_PROJECTION_PERSPECTIVE)
            {
              double near_plane[3], lam = NAN, near_plane_size;
              ray_start[0] = tx.camera_pos_x;
              ray_start[1] = tx.camera_pos_y;
              ray_start[2] = tx.camera_pos_z;

              /* calculate position on near_plane */
              near_plane[0] = gpx.near_plane / (gpx.far_plane - gpx.near_plane);
              near_plane[1] = gpx.near_plane / (gpx.far_plane - gpx.near_plane);
              near_plane[2] = gpx.near_plane / (gpx.far_plane - gpx.near_plane);

              if (fabs(ray_dir_default[0]) >= eps)
                {
                  lam = fabs((near_plane[0]) / ray_dir_default[0]);
                }
              if (fabs(ray_dir_default[1]) >= eps)
                {
                  double tmp_lam = fabs((near_plane[1]) / ray_dir_default[1]);
                  if ((lam != lam) || (lam == lam && tmp_lam < lam))
                    {
                      lam = tmp_lam;
                    }
                }
              if (fabs(ray_dir_default[2]) >= eps)
                {
                  double tmp_lam = fabs((near_plane[2]) / ray_dir_default[2]);
                  if ((lam != lam) || (lam == lam && tmp_lam < lam))
                    {
                      lam = tmp_lam;
                    }
                }

              /* calculate size of near plane with tan */
              near_plane_size = tan(gpx.fov * M_PI / 360.0) *
                                sqrt(pow(lam * ray_dir_default[0], 2) + pow(lam * ray_dir_default[1], 2) +
                                     pow(lam * ray_dir_default[2], 2));

              /* calculate the position where each ray starts on the near plane */
              if (aspect_ratio > 1)
                {
                  double x = (-near_plane_size + 2 * near_plane_size * (i + 0.5) / vt.picture_width) * aspect_ratio;
                  double y = (-near_plane_size + 2 * near_plane_size * (j + 0.5) / vt.picture_height);
                  ray_start[0] = tx.s_x * x - tx.up_x * y + ray_start[0] + lam * ray_dir_default[0];
                  ray_start[1] = tx.s_y * x - tx.up_y * y + ray_start[1] + lam * ray_dir_default[1];
                  ray_start[2] = tx.s_z * x - tx.up_z * y + ray_start[2] + lam * ray_dir_default[2];
                }
              else
                {
                  double x = (-near_plane_size + 2 * near_plane_size * (i + 0.5) / vt.picture_width);
                  double y = (-near_plane_size + 2 * near_plane_size * (j + 0.5) / vt.picture_height) / aspect_ratio;
                  ray_start[0] = tx.s_x * x - tx.up_x * y + ray_start[0] + lam * ray_dir_default[0];
                  ray_start[1] = tx.s_y * x - tx.up_y * y + ray_start[1] + lam * ray_dir_default[1];
                  ray_start[2] = tx.s_z * x - tx.up_z * y + ray_start[2] + lam * ray_dir_default[2];
                }

              /* ray_dir depending on point and angle */
              ray_dir[0] = (ray_start[0] - tx.camera_pos_x) / x_spacing;
              ray_dir[1] = (ray_start[1] - tx.camera_pos_y) / y_spacing;
              ray_dir[2] = (ray_start[2] - tx.camera_pos_z) / z_spacing;

              f_length = sqrt(ray_dir[0] * ray_dir[0] + ray_dir[1] * ray_dir[1] + ray_dir[2] * ray_dir[2]);
              ray_dir[0] /= f_length;
              ray_dir[1] /= f_length;
              ray_dir[2] /= f_length;
            }
          /* transform interval same like the original data points */
          if (gpx.projection_type == GR_PROJECTION_ORTHOGRAPHIC)
            {
              x_ortho = fabs(ix.xmax) - fabs(ix.xmin);
              y_ortho = fabs(ix.ymax) - fabs(ix.ymin);
              z_ortho = fabs(ix.zmax) - fabs(ix.zmin);
            }
          ray_start[0] =
              ((ray_start[0] - (ix.xmin * 2 - x_ortho) / (ix.xmax - ix.xmin)) / 2 * (max_val_t[0] - min_val_t[0])) +
              min_val_t[0];
          ray_start[1] =
              ((ray_start[1] - (ix.ymin * 2 - y_ortho) / (ix.ymax - ix.ymin)) / 2 * (max_val_t[1] - min_val_t[1])) +
              min_val_t[1];
          ray_start[2] =
              ((ray_start[2] - (ix.zmin * 2 - z_ortho) / (ix.zmax - ix.zmin)) / 2 * (max_val_t[2] - min_val_t[2])) +
              min_val_t[2];

          /* when or does the ray hits parts of the volume */
          /* calculate the lambda for each direction and take maximum of these three values */
          if (fabs(ray_dir[0]) >= eps)
            {
              double dirfrac = 1.0 / ray_dir[0];
              lambda[0] = min((min_val_t[0] - ray_start[0]) * dirfrac, (max_val_t[0] - ray_start[0]) * dirfrac);
            }
          if (fabs(ray_dir[1]) >= eps)
            {
              double dirfrac = 1.0 / ray_dir[1];
              lambda[1] = min((min_val_t[1] - ray_start[1]) * dirfrac, (max_val_t[1] - ray_start[1]) * dirfrac);
            }
          if (fabs(ray_dir[2]) >= eps)
            {
              double dirfrac = 1.0 / ray_dir[2];
              lambda[2] = min((min_val_t[2] - ray_start[2]) * dirfrac, (max_val_t[2] - ray_start[2]) * dirfrac);
            }
          max_lambda = max(lambda[0], max(lambda[1], lambda[2]));

          /* point where the ray enters the volume when possible */
          if (min_val_t[0] - (ray_start[0] + max_lambda * ray_dir[0]) > eps ||
              (ray_start[0] + max_lambda * ray_dir[0]) - max_val_t[0] > eps)
            {
              pixels[i + j * vt.picture_width] = -1;
              continue;
            }
          if (min_val_t[1] - (ray_start[1] + max_lambda * ray_dir[1]) > eps ||
              (ray_start[1] + max_lambda * ray_dir[1]) - max_val_t[1] > eps)
            {
              pixels[i + j * vt.picture_width] = -1;
              continue;
            }
          if (min_val_t[2] - (ray_start[2] + max_lambda * ray_dir[2]) > eps ||
              (ray_start[2] + max_lambda * ray_dir[2]) - max_val_t[2] > eps)
            {
              pixels[i + j * vt.picture_width] = -1;
              continue;
            }
          ray_start[0] += max_lambda * ray_dir[0];
          ray_start[1] += max_lambda * ray_dir[1];
          ray_start[2] += max_lambda * ray_dir[2];

          /* influence of the voxels which are passed by each ray */
          while (1)
            {
              double voxel_influ = 0;
              double ray_length, lambda_min, start_copy = NAN, voxel_sum = 0;
              double end, mid_left, mid_right;
              double x_dist, y_dist, z_dist;
              double ray_end[3];
              int x_0 = 0, y_0 = 0, z_0 = 0;
              int x_1 = 0, y_1 = 0, z_1 = 0;

              /* end point */
              if (ray_dir[0] < 0)
                {
                  lambda[0] = (max(RAYCASTING_FLOOR(ray_start[0]), min_val_t[0]) - ray_start[0]) / ray_dir[0];
                }
              else
                {
                  lambda[0] = (min(RAYCASTING_CEIL(ray_start[0]), max_val_t[0]) - ray_start[0]) / ray_dir[0];
                }
              if (ray_dir[1] < 0)
                {
                  lambda[1] = (max(RAYCASTING_FLOOR(ray_start[1]), min_val_t[1]) - ray_start[1]) / ray_dir[1];
                }
              else
                {
                  lambda[1] = (min(RAYCASTING_CEIL(ray_start[1]), max_val_t[1]) - ray_start[1]) / ray_dir[1];
                }
              if (ray_dir[2] < 0)
                {
                  lambda[2] = (max(RAYCASTING_FLOOR(ray_start[2]), min_val_t[2]) - ray_start[2]) / ray_dir[2];
                }
              else
                {
                  lambda[2] = (min(RAYCASTING_CEIL(ray_start[2]), max_val_t[2]) - ray_start[2]) / ray_dir[2];
                }
              lambda_min = lambda[0];
              if ((fabs(lambda_min) > fabs(lambda[1]) || lambda_min != lambda_min) && lambda[1] == lambda[1])
                lambda_min = lambda[1];
              if ((fabs(lambda_min) > fabs(lambda[2]) || lambda_min != lambda_min) && lambda[2] == lambda[2])
                lambda_min = lambda[2];

              ray_end[0] = ray_start[0] + lambda_min * ray_dir[0];
              ray_end[1] = ray_start[1] + lambda_min * ray_dir[1];
              ray_end[2] = ray_start[2] + lambda_min * ray_dir[2];

              /* identify voxel */
              if (ray_dir[0] >= -eps)
                {
                  if (fabs(ray_start[0]) > eps)
                    {
                      x_0 = min(nx - 1, (ray_start[0] - fmod(ray_start[0], 1)));
                    }
                  x_1 = x_0;
                  if (ray_end[0] < nx - 1 + eps)
                    {
                      x_1 = (int)min(nx - 1, max(0, RAYCASTING_CEIL(ray_start[0])));
                    }
                }
              else if (ray_dir[0] < eps)
                {
                  if (fabs(ray_start[0]) > eps)
                    {
                      x_0 = min(nx - 1, max(0, (ray_start[0] - fmod(ray_start[0] - ceil(ray_start[0]), 1))));
                    }
                  x_1 = x_0;
                  if (ray_end[0] >= -eps)
                    {
                      x_1 = (int)min(nx - 1, max(0, RAYCASTING_FLOOR(ray_start[0])));
                    }
                }

              if (ray_dir[1] >= -eps)
                {
                  if (fabs(ray_start[1]) > eps)
                    {
                      y_0 = min(ny - 1, (ray_start[1] - fmod(ray_start[1], 1)));
                    }
                  y_1 = y_0;
                  if (ray_end[1] < ny - 1 + eps)
                    {
                      y_1 = (int)min(ny - 1, max(0, RAYCASTING_CEIL(ray_start[1])));
                    }
                }
              else if (ray_dir[1] < eps)
                {
                  if (fabs(ray_start[1]) > eps)
                    {
                      y_0 = min(ny - 1, max(0, (ray_start[1] - fmod(ray_start[1] - ceil(ray_start[1]), 1))));
                    }
                  y_1 = y_0;
                  if (ray_end[1] >= -eps)
                    {
                      y_1 = (int)min(ny - 1, max(0, RAYCASTING_FLOOR(ray_start[1])));
                    }
                }

              if (ray_dir[2] >= -eps)
                {
                  if (fabs(ray_start[2]) > eps)
                    {
                      z_0 = min(nz - 1, (ray_start[2] - fmod(ray_start[2], 1)));
                    }
                  z_1 = z_0;
                  if (ray_end[2] < nz - 1 + eps)
                    {
                      z_1 = (int)min(nz - 1, max(0, RAYCASTING_CEIL(ray_start[2])));
                    }
                }
              else if (ray_dir[2] < eps)
                {
                  if (fabs(ray_start[2]) > eps)
                    {
                      z_0 = min(nz - 1, max(0, (ray_start[2] - fmod(ray_start[2] - ceil(ray_start[2]), 1))));
                    }
                  z_1 = z_0;
                  if (ray_end[2] >= -eps)
                    {
                      z_1 = (int)min(nz - 1, max(0, RAYCASTING_FLOOR(ray_start[2])));
                    }
                }

              ray_length = sqrt(pow((ray_end[0] - ray_start[0]) * x_spacing, 2) +
                                pow((ray_end[1] - ray_start[1]) * y_spacing, 2) +
                                pow((ray_end[2] - ray_start[2]) * z_spacing, 2));
              if (vt.approximative_calculation == 0)
                {
                  wdh = 1;
                }
              for (s = 0; s < (int)wdh; s++)
                {
                  int k, repeat = 1;
                  double *bilinear_ptr;
                  double dist_copy[3] = {NAN, NAN, NAN};
                  if (is_nan(start))
                    {
                      repeat = 0;
                    }
                  for (k = repeat; k < 4; k++)
                    {
                      double ray_position[3];
                      if (vt.approximative_calculation == 1 && (k == 1 || k == 2))
                        {
                          continue;
                        }
                      if (k == 0)
                        {
                          ray_position[0] = ray_start[0];
                          ray_position[1] = ray_start[1];
                          ray_position[2] = ray_start[2];
                        }
                      else if (vt.approximative_calculation == 0)
                        {
                          ray_position[0] = ray_start[0] + lambda_min * (double)(k) / 3. * ray_dir[0];
                          ray_position[1] = ray_start[1] + lambda_min * (double)(k) / 3. * ray_dir[1];
                          ray_position[2] = ray_start[2] + lambda_min * (double)(k) / 3. * ray_dir[2];
                        }
                      else
                        {
                          ray_position[0] = ray_start[0] + lambda_min * (s + 1.) / wdh * ray_dir[0];
                          ray_position[1] = ray_start[1] + lambda_min * (s + 1.) / wdh * ray_dir[1];
                          ray_position[2] = ray_start[2] + lambda_min * (s + 1.) / wdh * ray_dir[2];
                        }

                      if (k == 0)
                        {
                          bilinear_ptr = &start;
                        }
                      else if (k == 1)
                        {
                          bilinear_ptr = &mid_left;
                        }
                      else if (k == 2)
                        {
                          bilinear_ptr = &mid_right;
                        }
                      else
                        {
                          bilinear_ptr = &end;
                        }

                      if (ray_dir[0] >= -eps)
                        {
                          x_dist = fabs(min(nx, ray_position[0]) - x_0);
                          if (ray_position[0] <= 0)
                            {
                              x_dist = fabs(ray_position[0] - min_val_t[0]);
                            }
                        }
                      else
                        {
                          x_dist = fabs(max(ray_position[0], -1) - x_0);
                          if (ray_position[0] >= nx - 1)
                            {
                              x_dist = fabs(ray_position[0] - max_val_t[0]);
                            }
                        }

                      if (ray_dir[1] >= -eps)
                        {
                          y_dist = fabs(min(ny, ray_position[1]) - y_0);
                          if (ray_position[1] <= 0)
                            {
                              y_dist = fabs(ray_position[1] - min_val_t[1]);
                            }
                        }
                      else
                        {
                          y_dist = fabs(max(ray_position[1], -1) - y_0);
                          if (ray_position[1] >= ny - 1)
                            {
                              y_dist = fabs(ray_position[1] - max_val_t[1]);
                            }
                        }

                      if (ray_dir[2] >= -eps)
                        {
                          z_dist = fabs(min(nz, ray_position[2]) - z_0);
                          if (ray_position[2] <= 0)
                            {
                              z_dist = fabs(ray_position[2] - min_val_t[2]);
                            }
                        }
                      else
                        {
                          z_dist = fabs(max(ray_position[2], -1) - z_0);
                          if (ray_position[2] >= nz - 1)
                            {
                              z_dist = fabs(ray_position[2] - max_val_t[2]);
                            }
                        }

                      if (ray_position[0] > nx - 1 + sign(ray_dir[0]) * eps || ray_position[0] < sign(ray_dir[0]) * eps)
                        {
                          x_dist *= 2;
                        }
                      if (ray_position[1] > ny - 1 + sign(ray_dir[1]) * eps || ray_position[1] < sign(ray_dir[1]) * eps)
                        {
                          y_dist *= 2;
                        }
                      if (ray_position[2] > nz - 1 + sign(ray_dir[2]) * eps || ray_position[2] < sign(ray_dir[2]) * eps)
                        {
                          z_dist *= 2;
                        }

                      if ((s == 0 && k == 0) || (s == wdh - 1 && k == 3) ||
                          (wdh <= 1 && vt.approximative_calculation == 1))
                        {
                          if ((fabs(x_dist - 0) <= eps || fabs(x_dist - 1) <= eps) && fabs(ray_dir[0]) > eps)
                            {
                              int x_tmp = x_0;
                              if (fabs(x_dist - 1) <= eps)
                                {
                                  x_tmp = x_1;
                                }
                              bilinear_interpolation(
                                  data[x_tmp + y_0 * nx + z_0 * (nx * ny)], data[x_tmp + y_1 * nx + z_0 * (nx * ny)],
                                  data[x_tmp + y_0 * nx + z_1 * (nx * ny)], data[x_tmp + y_1 * nx + z_1 * (nx * ny)],
                                  y_dist, z_dist, bilinear_ptr);
                              if (dist_copy[0] == dist_copy[0])
                                {
                                  bilinear_interpolation(data[x_tmp + y_0 * nx + z_0 * (nx * ny)],
                                                         data[x_tmp + y_1 * nx + z_0 * (nx * ny)],
                                                         data[x_tmp + y_0 * nx + z_1 * (nx * ny)],
                                                         data[x_tmp + y_1 * nx + z_1 * (nx * ny)], dist_copy[1],
                                                         dist_copy[2], &start);
                                }
                            }
                          else if ((fabs(y_dist - 0) <= eps || fabs(y_dist - 1) <= eps) && fabs(ray_dir[1]) > eps)
                            {
                              int y_tmp = y_0;
                              if (fabs(y_dist - 1) <= eps)
                                {
                                  y_tmp = y_1;
                                }
                              bilinear_interpolation(
                                  data[x_0 + y_tmp * nx + z_0 * (nx * ny)], data[x_1 + y_tmp * nx + z_0 * (nx * ny)],
                                  data[x_0 + y_tmp * nx + z_1 * (nx * ny)], data[x_1 + y_tmp * nx + z_1 * (nx * ny)],
                                  x_dist, z_dist, bilinear_ptr);
                              if (dist_copy[0] == dist_copy[0])
                                {
                                  bilinear_interpolation(data[x_0 + y_tmp * nx + z_0 * (nx * ny)],
                                                         data[x_1 + y_tmp * nx + z_0 * (nx * ny)],
                                                         data[x_0 + y_tmp * nx + z_1 * (nx * ny)],
                                                         data[x_1 + y_tmp * nx + z_1 * (nx * ny)], dist_copy[0],
                                                         dist_copy[2], &start);
                                }
                            }
                          else if ((fabs(z_dist - 0) <= eps || fabs(z_dist - 1) <= eps) && fabs(ray_dir[2]) > eps)
                            {
                              int z_tmp = z_0;
                              if (fabs(z_dist - 1) <= eps)
                                {
                                  z_tmp = z_1;
                                }
                              bilinear_interpolation(
                                  data[x_0 + y_0 * nx + z_tmp * (nx * ny)], data[x_1 + y_0 * nx + z_tmp * (nx * ny)],
                                  data[x_0 + y_1 * nx + z_tmp * (nx * ny)], data[x_1 + y_1 * nx + z_tmp * (nx * ny)],
                                  x_dist, y_dist, bilinear_ptr);
                              if (dist_copy[0] == dist_copy[0])
                                {
                                  bilinear_interpolation(data[x_0 + y_0 * nx + z_tmp * (nx * ny)],
                                                         data[x_1 + y_0 * nx + z_tmp * (nx * ny)],
                                                         data[x_0 + y_1 * nx + z_tmp * (nx * ny)],
                                                         data[x_1 + y_1 * nx + z_tmp * (nx * ny)], dist_copy[0],
                                                         dist_copy[1], &start);
                                }
                            }
                          if (is_nan(start))
                            {
                              dist_copy[0] = x_dist;
                              dist_copy[1] = y_dist;
                              dist_copy[2] = z_dist;
                            }
                        }
                      else
                        {
                          trilinear_interpolation(
                              data[x_0 + y_0 * nx + z_0 * (nx * ny)], data[x_0 + y_0 * nx + z_1 * (nx * ny)],
                              data[x_0 + y_1 * nx + z_0 * (nx * ny)], data[x_1 + y_0 * nx + z_0 * (nx * ny)],
                              data[x_1 + y_0 * nx + z_1 * (nx * ny)], data[x_1 + y_1 * nx + z_0 * (nx * ny)],
                              data[x_0 + y_1 * nx + z_1 * (nx * ny)], data[x_1 + y_1 * nx + z_1 * (nx * ny)], x_dist,
                              y_dist, z_dist, bilinear_ptr);
                        }
                    }
                  /* set the values */
                  if (s == 0)
                    {
                      start_copy = start;
                    }
                  if (vt.approximative_calculation == 1)
                    {
                      voxel_sum += (start + end) / 2.;
                      start = end;
                    }
                }
              voxel_influ = voxel_sum / wdh * ray_length;

              if (vt.approximative_calculation == 0)
                {
                  double a = 27. / 6. * (end - 3. * mid_right + 3. * mid_left - start);
                  double b = 9. / 2. * (mid_right - 2. * mid_left + start - 6. / 27. * a);
                  double c = 3. * (mid_left - start - 1. / 9. * b - 1. / 27. * a);

                  if (algorithm == 0 || algorithm == 1)
                    {
                      voxel_influ = (0.25 * a + 1. / 3. * b + 0.5 * c + start) * ray_length;
                    }
                  else
                    {
                      double x1 = (-b + sqrt(b * b - 3 * a * c)) / (3 * a);
                      double x2 = (-b - sqrt(b * b - 3 * a * c)) / (3 * a);
                      if (0 > x1 || x1 > 1 || x1 != x1)
                        {
                          x1 = 0;
                        }
                      if (0 > x2 || x2 > 1 || x2 != x2)
                        {
                          x2 = 0;
                        }
                      voxel_influ = max(a * pow(x1, 3) + b * pow(x1, 2) + c * x1 + start,
                                        a * pow(x2, 3) + b * pow(x2, 2) + c * x2 + start);
                      color = max(color, voxel_influ);
                    }
                }

              if (algorithm == 0 || algorithm == 1)
                {
                  /* emission or absorption*/
                  color += voxel_influ;
                  if (rc->dmax_ptr != NULL && color >= *dmax_ptr) break;
                }
              else
                {
                  /* MIP */
                  start = start_copy;
                  color = max(color, max(start, end));
                  if (rc->dmax_ptr != NULL && color >= *dmax_ptr) break;
                }

              ray_start[0] = ray_end[0];
              ray_start[1] = ray_end[1];
              ray_start[2] = ray_end[2];
              start = end;

              /* can reuse end value */
              if (fabs(ray_start[0] - max_val_t[0]) <= eps || fabs(ray_start[1] - max_val_t[1]) <= eps ||
                  fabs(ray_start[2] - max_val_t[2]) <= eps)
                {
                  break;
                }
              if (fabs(ray_start[0] - min_val_t[0]) <= eps || fabs(ray_start[1] - min_val_t[1]) <= eps ||
                  fabs(ray_start[2] - min_val_t[2]) <= eps)
                {
                  break;
                }
            }

          if (algorithm == 1)
            {
              /* absorption */
              color = exp(-color);
            }
          if (rc->dmax_ptr != NULL && color > *dmax_ptr) color = *dmax_ptr;
          if (rc->dmin_ptr != NULL && color < *dmin_ptr) color = *dmin_ptr;
          pixels[i + j * vt.picture_width] = color;
        }
    }
}

static int system_processor_count(void)
{
#ifdef _WIN32
#ifndef _SC_NPROCESSORS_ONLN
  SYSTEM_INFO info;
  GetSystemInfo(&info);
#define sysconf(a) info.dwNumberOfProcessors
#define _SC_NPROCESSORS_ONLN
#endif
#endif
  return (int)sysconf(_SC_NPROCESSORS_ONLN);
}

/*!
 * Draw volume data with raycasting using the given algorithm and apply the current GR colormap.
 *
 * \param[in]     nx         number of points in x-direction
 * \param[in]     ny         number of points in y-direction
 * \param[in]     nz         number of points in z-direction
 * \param[in]     data       an array of shape nx * ny * nz containing the intensities for each point
 * \param[in]     algorithm  the algorithm to reduce the volume data
 * \param[in,out] dmin_ptr   The variable this parameter points at will be used as minimum data value when applying the
 *                            colormap. If it is negative, the variable will be set to the actual occuring minimum and
 *                            that value will be used instead. If dmin_ptr is NULL, it will be ignored.
 * \param[in,out] dmax_ptr   The variable this parameter points at will be used as maximum data value when applying the
 *                            colormap. If it is negative, the variable will be set to the actual occuring maximum and
 *                            that value will be used instead. If dmax_ptr is NULL, it will be ignored.
 *
 * \param[in]       min_val   array with the minimum coordinates of the volumedata
 * \param[in]       max_val   array with the maximum coordinates of the volumedata
 *
 * \verbatim embed:rst:leading-asterisk
 *
 * Available algorithms are:
 *
 * +---------------------+---+-----------------------------+
 * |GR_VOLUME_EMISSION   |  0|emission model               |
 * +---------------------+---+-----------------------------+
 * |GR_VOLUME_ABSORPTION |  1|absorption model             |
 * +---------------------+---+-----------------------------+
 * |GR_VOLUME_MIP        |  2|maximum intensity projection |
 * +---------------------+---+-----------------------------+
 *
 * \endverbatim
 */
void gr_cpubasedvolume(int nx, int ny, int nz, double *data, int algorithm, double *dmin_ptr, double *dmax_ptr,
                       double *dmin_val, double *dmax_val)
{
  const cpubasedvolume_2pass_t *context;

  context = gr_cpubasedvolume_2pass(nx, ny, nz, data, algorithm, dmin_ptr, dmax_ptr, dmin_val, dmax_val, NULL);
  if (context == NULL)
    {
      return;
    }
  gr_cpubasedvolume_2pass(nx, ny, nz, data, algorithm, dmin_ptr, dmax_ptr, dmin_val, dmax_val, context);
}

/*!
 * Draw volume data with raycasting using the given algorithm and apply the current GR colormap. This is the two pass
 * version of gr_cpubasedvolume and can be used to retrieve dmin and dmax in a first call before the actual volume is
 * drawn in the second call.
 *
 * \param[in]     nx         number of points in x-direction
 * \param[in]     ny         number of points in y-direction
 * \param[in]     nz         number of points in z-direction
 * \param[in]     data       an array of shape nx * ny * nz containing the intensities for each point
 * \param[in]     algorithm  the algorithm to reduce the volume data
 * \param[in,out] dmin_ptr   The variable this parameter points at will be used as minimum data value when applying the
 *                           colormap. If it is negative, the variable will be set to the actual occuring minimum and
 *                           that value will be used instead. If dmin_ptr is NULL, it will be ignored.
 * \param[in,out] dmax_ptr   The variable this parameter points at will be used as maximum data value when applying the
 *                           colormap. If it is negative, the variable will be set to the actual occuring maximum and
 *                           that value will be used instead. If dmax_ptr is NULL, it will be ignored.
 * \param[in]     min_val    array with the minimum coordinates of the volumedata
 * \param[in]     max_val    array with the maximum coordinates of the volumedata
 * \param[in,out] context    pointer to a cpubasedvolume_2pass_t context struct. In the first pass, this pointer must
 *                           be NULL. In the second pass, the return value of the first call must be used as context
 *                           parameter.
 * \returns                  a context struct in the first pass, NULL in the second pass.
 *
 * \verbatim embed:rst:leading-asterisk
 *
 * Available algorithms are:
 *
 * +---------------------+---+-----------------------------+
 * |GR_VOLUME_EMISSION   |  0|emission model               |
 * +---------------------+---+-----------------------------+
 * |GR_VOLUME_ABSORPTION |  1|absorption model             |
 * +---------------------+---+-----------------------------+
 * |GR_VOLUME_MIP        |  2|maximum intensity projection |
 * +---------------------+---+-----------------------------+
 *
 * \endverbatim
 */
const cpubasedvolume_2pass_t *gr_cpubasedvolume_2pass(int nx, int ny, int nz, double *data, int algorithm,
                                                      double *dmin_ptr, double *dmax_ptr, double *dmin_val,
                                                      double *dmax_val, const cpubasedvolume_2pass_t *context)
{
  cpubasedvolume_2pass_t *context_;
  int n_x, n_y, size;
  double *pixels, *min_ptr, *max_ptr;
  double min_val[3], max_val[3];
  int x_start = 0, x_end = 0, y_start = 0, y_end = 0;
  struct ray_casting_attr f;
#ifndef NO_THREADS
  threadpool_t *tp;
#endif
  struct thread_attr *jobs;
  int i, j = 0, threadnum;
  check_autoinit;

  if (context == NULL)
    {
      if (gpx.projection_type == GR_PROJECTION_DEFAULT)
        {
          fprintf(stderr, "gr_cpubasedvolume only runs when the projectiontype is set to GR_PROJECTION_ORTHOGRAPHIC or "
                          "GR_PROJECTION_PERSPECTIVE.\n");
          return NULL;
        }

      pixels = calloc(vt.picture_width * vt.picture_height, sizeof(double));
      if (pixels == 0)
        {
          fprintf(stderr, "can't allocate memory");
          return NULL;
        }
      /* size of each thread calculated out of threadnumber */
      size = (int)(max(10, (nx + ny + nz) / 3.0 * vt.thread_size));
      n_x = (int)ceil(1. * vt.picture_width / size);
      n_y = (int)ceil(1. * vt.picture_height / size);

      max_ptr = dmax_ptr;
      min_ptr = dmin_ptr;
      if (dmax_ptr && *dmax_ptr < 0) max_ptr = NULL;
      if (dmin_ptr && *dmin_ptr < 0) min_ptr = NULL;

      if (dmin_val == NULL)
        {
          min_val[0] = min_val[1] = min_val[2] = -1;
        }
      else
        {
          min_val[0] = dmin_val[0];
          min_val[1] = dmin_val[1];
          min_val[2] = dmin_val[2];
        }
      if (dmax_val == NULL)
        {
          max_val[0] = max_val[1] = max_val[2] = -1;
        }
      else
        {
          max_val[0] = dmax_val[0];
          max_val[1] = dmax_val[1];
          max_val[2] = dmax_val[2];
        }

      f.nx = nx;
      f.ny = ny;
      f.nz = nz;
      f.algorithm = algorithm;
      f.data = data;
      f.dmin_ptr = min_ptr;
      f.dmax_ptr = max_ptr;
      f.min_val = min_val;
      f.max_val = max_val;
      f.pixels = pixels;
      vt.ray_casting = &f;

/* creates the threadpool */
#ifndef NO_THREADS
      tp = calloc(1, sizeof(*tp));
      if (tp == 0)
        {
          fprintf(stderr, "can't allocate memory");
          return NULL;
        }
      threadnum = (system_processor_count() - 1) < 256 ? system_processor_count() - 1 : 256;
      if (vt.max_threads > 0)
        {
          threadnum = vt.max_threads;
        }
      threadpool_create(tp, threadnum, ray_casting_thread);
#endif
      jobs = (struct thread_attr *)gks_malloc(n_x * n_y * sizeof(struct thread_attr));

      for (i = 0; i < n_x; i++)
        {
          x_end = (int)min((i + 1.0) * size, vt.picture_width);
          for (j = 0; j < n_y; j++)
            {
              /* transfer data for each thread */
              y_end = (int)min((j + 1.0) * size, vt.picture_height);
              jobs[i + j * n_x].x_start = x_start;
              jobs[i + j * n_x].y_start = y_start;
              jobs[i + j * n_x].x_end = x_end;
              jobs[i + j * n_x].y_end = y_end;

#ifndef NO_THREADS
              threadpool_add_work(tp, jobs + i + j * n_x);
#else
              ray_casting_thread(jobs + i + j * n_x);
#endif
              y_start = y_end;
            }
          x_start = x_end;
          y_start = 0;
        }
#ifndef NO_THREADS
      threadpool_destroy(tp);
#endif

      /* calculate the min and max value of all pixels */
      if (dmax_ptr && *dmax_ptr < 0)
        {
          double max_color = 0;
          for (i = 0; i < vt.picture_width * vt.picture_height; i++)
            {
              if (pixels[i] > max_color) max_color = pixels[i];
            }
          *dmax_ptr = max_color;
        }
      if (dmin_ptr && *dmin_ptr < 0)
        {
          double min_color = pixels[0];
          for (i = 1; i < vt.picture_width * vt.picture_height; i++)
            {
              if (pixels[i] < min_color) min_color = pixels[i];
            }
          *dmin_ptr = max(0, min_color);
        }
      free(jobs);

      context_ = (cpubasedvolume_2pass_t *)xmalloc(sizeof(cpubasedvolume_2pass_t));
      context_->dmin = *dmin_ptr;
      context_->dmax = *dmax_ptr;
      context_->action = GR_2PASS_CLEANUP | GR_2PASS_RENDER; /* render and clean up by default */
      context_->priv = (cpubasedvolume_2pass_priv_t *)xmalloc(sizeof(cpubasedvolume_2pass_priv_t));
      context_->priv->pixels = pixels;
    }
  else
    {
      double *pixels = context->priv->pixels;

      if (context->action & GR_2PASS_RENDER)
        {
          draw_volume(pixels);
          if (flag_stream)
            {
              gr_writestream("<cpubasedvolume nx=\"%i\" ny=\"%i\" nz=\"%i\" />\n", nx, ny, nz);
              print_float_array("data", nx * ny * nz, data);
              gr_writestream(" algorithm=\"%i\" ", algorithm);
              print_float_array("dmin_ptr", 1, dmin_ptr);
              print_float_array("dmax_ptr", 1, dmax_ptr);
              print_float_array("dmin_val", 1, dmin_val);
              print_float_array("dmax_val", 1, dmax_val);
              gr_writestream("/>\n");
            }
        }

      if (context->action & GR_2PASS_CLEANUP)
        {
          free(pixels);
          free(context->priv);
          free((cpubasedvolume_2pass_t *)context);
        }
      context_ = NULL;
    }

  return context_;
}

void gr_inqvpsize(int *width, int *height, double *device_pixel_ratio)
{
  int n = 1, errind, wkid, ol, conid, wtype;

  check_autoinit;

  gks_inq_open_ws(n, &errind, &ol, &wkid);
  gks_inq_ws_conntype(wkid, &errind, &conid, &wtype);
  if (wtype == 381)
    {
      gks_update_ws(wkid, GKS_K_PERFORM_FLAG);
    }
  gks_inq_vp_size(wkid, &errind, width, height, device_pixel_ratio);
}

static double mean(const double *a, const int len, const int *connections)
{
  double sum = 0;
  int i;

  for (i = 0; i < len; i++)
    {
      sum += a[connections[i] - 1];
    }
  return sum / len;
}

static int compare_depth(const void *_a, const void *_b)
{
  double a = *(double *)_a, b = *(double *)_b;
  return a > b ? 1 : a < b ? -1 : 0;
}

void gr_polygonmesh3d(int num_points, const double *px, const double *py, const double *pz, int num_connections,
                      const int *connections, const int *colors)
{
  int i, j, k, len, maxlen = 0, len_connections;
  double *x, *y, *z;
  int *faces, *faceP, *attributes;
  double cam_x, cam_y, cam_z, up_x, up_y, up_z, foc_x, foc_y, foc_z, depth;

  x = (double *)xcalloc(num_points, sizeof(double));
  y = (double *)xcalloc(num_points, sizeof(double));
  z = (double *)xcalloc(num_points, sizeof(double));
  for (i = 0; i < num_points; i++)
    {
      x[i] = px[i];
      y[i] = py[i];
      z[i] = pz[i];
      gr_wc3towc(&x[i], &y[i], &z[i]);
    }

  j = 0;
  for (i = 0; i < num_connections; i++)
    {
      len = connections[j++];
      if (len > maxlen) maxlen = len;
      j += len;
    }
  len_connections = j;

  faces = (int *)xcalloc(num_connections, sizeof(double) + (1 + maxlen + 1) * sizeof(int));
  gr_inqtransformationparameters(&cam_x, &cam_y, &cam_z, &up_x, &up_y, &up_z, &foc_x, &foc_y, &foc_z);

  j = 0;
  faceP = faces;
  for (i = 0; i < num_connections; i++)
    {
      len = connections[j++];
      depth = mean(z, len, connections + j);
      memcpy(faceP, &depth, sizeof(double));
      faceP += sizeof(double) / sizeof(int);
      memcpy(faceP, &len, sizeof(int));
      faceP += 1;
      memcpy(faceP, connections + j, len * sizeof(int));
      faceP += maxlen;
      memcpy(faceP, &colors[i], sizeof(int));
      faceP += 1;
      j += len;
    }
  qsort(faces, num_connections, (sizeof(double) + (1 + maxlen + 1) * sizeof(int)), compare_depth);

  attributes = (int *)xcalloc(num_connections, (1 + maxlen + 1) * sizeof(int));
  k = 0;
  faceP = faces;
  for (i = 0; i < num_connections; i++)
    {
      faceP += sizeof(double) / sizeof(int);
      len = attributes[k++] = *faceP;
      faceP += 1;
      for (j = 0; j < len; j++)
        {
          attributes[k++] = faceP[j];
        }
      faceP += maxlen;
      attributes[k++] = *faceP;
      faceP += 1;
    }

  gks_gdp(num_points, x, y, GKS_K_GDP_FILL_POLYGONS, k, attributes);

  free(attributes);
  free(faces);
  free(z);
  free(y);
  free(x);

  if (flag_stream)
    {
      gr_writestream("<polygonmesh3d num_points=\"%d\"", num_points);
      print_float_array("x", num_points, (double *)px);
      print_float_array("y", num_points, (double *)py);
      print_float_array("z", num_points, (double *)pz);
      gr_writestream(" len_connections=\"%d\"", len_connections);
      print_int_array("connections", len_connections, (int *)connections);
      gr_writestream(" num_connections=\"%d\"", num_connections);
      print_int_array("colors", num_connections, (int *)colors);
      gr_writestream("/>\n");
    }
}

GR_INLINE static void pt_scale(point3d_t *self, double const other)
{
  self->x *= other;
  self->y *= other;
  self->z *= other;
}

GR_INLINE static void pt_mad(point3d_t *self, double const fac, point3d_t const *b)
{
  /* self <- self + fac * b */
  self->x += fac * b->x;
  self->y += fac * b->y;
  self->z += fac * b->z;
}

GR_INLINE static double pt_dot(point3d_t const *self, point3d_t const *other)
{
  return self->x * other->x + self->y * other->y + self->z * other->z;
}


GR_INLINE static double pt_length(point3d_t const *self)
{
  return sqrt(self->x * self->x + self->y * self->y + self->z * self->z);
}

GR_INLINE static double pt_smallest_mult(point3d_t const *self, point3d_t const *vec)
{
  double low = 1e15;
  double _x = vec->x / self->x;
  double _y = vec->y / self->y;
  double _z = vec->z / self->z;
  if (fabs(self->x) >= 1e-12)
    {
      low = _x;
    }
  if (fabs(self->y) >= 1e-12 && low > _y)
    {
      low = _y;
    }
  if (fabs(self->z) >= 1e-12 && low > _z)
    {
      low = _z;
    }
  return low;
}

GR_INLINE static void pt_sub(point3d_t *self, point3d_t const *other)
{
  self->x -= other->x;
  self->y -= other->y;
  self->z -= other->z;
}

GR_INLINE static double pt_biggest_mult(point3d_t const *self, point3d_t const *vec)
{
  double max = -1e15;
  double _x = vec->x / self->x;
  double _y = vec->y / self->y;
  double _z = vec->z / self->z;
  if (fabs(self->x) >= 1e-12)
    {
      max = _x;
    }
  if (fabs(self->y) >= 1e-12 && max < _y)
    {
      max = _y;
    }
  if (fabs(self->z) >= 1e-12 && max < _z)
    {
      max = _z;
    }
  return max;
}

GR_INLINE static void pt_matmul(point3d_t *self, point3d_t const *for_x, point3d_t const *for_y, point3d_t const *for_z)
{
  double tmp_x = self->x * for_x->x + self->y * for_y->x + self->z * for_z->x;
  double tmp_y = self->x * for_x->y + self->y * for_y->y + self->z * for_z->y;
  double tmp_z = self->x * for_x->z + self->y * for_y->z + self->z * for_z->z;
  self->x = tmp_x;
  self->y = tmp_y;
  self->z = tmp_z;
}

GR_INLINE static void pt_unitize(point3d_t *pt)
{
  double l = pt_length(pt);
  pt->x /= l;
  pt->y /= l;
  pt->z /= l;
}

/*!
 * Initializes default parameters for interpolation using the gaussian multivariate distribution.
 *
 * if \f$\Sigma\f$ is the covariance matrice:
 *
 * \param[in]       determinant   \f$\left|\Sigma\right|\f$
 * \param[in]       mat           \f$\Sigma^{-\frac{1}{2}}\f$
 */
void gr_volume_interp_gauss_init(double determinant, double *mat)
{
  interp_gauss_data.sqrt_det = sqrt(determinant);
  interp_gauss_data.gauss_sig_1.x = mat[0];
  interp_gauss_data.gauss_sig_2.x = mat[3];
  interp_gauss_data.gauss_sig_3.x = mat[6];
  interp_gauss_data.gauss_sig_1.y = mat[1];
  interp_gauss_data.gauss_sig_2.y = mat[4];
  interp_gauss_data.gauss_sig_3.y = mat[7];
  interp_gauss_data.gauss_sig_1.z = mat[2];
  interp_gauss_data.gauss_sig_2.z = mat[5];
  interp_gauss_data.gauss_sig_3.z = mat[8];
}

/*!
 * Integrates the given ray through a gaussian multivariate distribution.
 *
 * The parameters of the distribution are set using either `gr_volume_interp_gauss_init` or `extra_data` (as `gauss_t`)
 *
 * \param[in]       dt_pt   The data point with associated intensity and optional distribution parameters
 * \param[in]       extra_data  Optional extra data for data point
 * \param[in]       from    Start point of ray
 * \param[in]       len     The direction and length of ray
 * \returns                 The integrated density
 */
double gr_volume_interp_gauss(const data_point3d_t *dt_pt, const void *extra_data, const point3d_t *from,
                              const point3d_t *len)
{
  point3d_t rfrom = *from, dir = *len;
  point3d_t y_0, b;
  const gauss_t *d = extra_data == NULL ? &interp_gauss_data : (const gauss_t *)extra_data;
  double f, y_0b, ex;
  pt_sub(&rfrom, &dt_pt->pt);

  y_0 = rfrom;
  b = dir;
  pt_unitize(&b);

  pt_matmul(&y_0, &d->gauss_sig_1, &d->gauss_sig_2, &d->gauss_sig_3);
  pt_matmul(&b, &d->gauss_sig_1, &d->gauss_sig_2, &d->gauss_sig_3);

  f = 1. / pt_length(&b);
  pt_scale(&b, f);

  y_0b = pt_dot(&y_0, &b);
  ex = 0.5 * (y_0b * y_0b - pt_dot(&y_0, &y_0));

  return 2 * M_PI * d->sqrt_det * f * dt_pt->data * exp(ex);
}

/*!
 * Initializes default parameters for trilinear interpolation.
 *
 * \param[in]       grid_x   The extent of density
 * \param[in]       grid_y   The extent of density
 * \param[in]       grid_z   The extent of density
 */
void gr_volume_interp_tri_linear_init(double grid_x, double grid_y, double grid_z)
{
  interp_tri_linear_data.grid_x_re = 1. / grid_x;
  interp_tri_linear_data.grid_y_re = 1. / grid_y;
  interp_tri_linear_data.grid_z_re = 1. / grid_z;
}

/*!
 * Integrates the given ray through a axis-aligned trilinear interpolation density.
 *
 * The parameters of the density are set using either `gr_volume_interp_tri_linear_init` or `extra_data` (as
 * `tri_linear_t`)
 *
 * \param[in]       dt_pt       The data point with associated intensity and optional density parameters
 * \param[in]       extra_data  Optional extra data for data point
 * \param[in]       from        Start point of ray
 * \param[in]       len         The direction and length of ray
 * \returns                 The integrated density
 */
double gr_volume_interp_tri_linear(const data_point3d_t *dt_pt, const void *extra_data, const point3d_t *from,
                                   const point3d_t *len)
{
  point3d_t rfrom = *from, dir = *len;

  const tri_linear_t *d = extra_data == NULL ? &interp_tri_linear_data : (const tri_linear_t *)extra_data;

  double dirlen = 0.5 * sqrt((dir.x * tx.x_axis_scale) * (dir.x * tx.x_axis_scale) +
                             (dir.y * tx.y_axis_scale) * (dir.y * tx.y_axis_scale) +
                             (dir.z * tx.z_axis_scale) * (dir.z * tx.z_axis_scale));
  int i;
  double low, high;
  int current = 0;
  double val = 0;

  double steps[5] = {0., 0., 0., 0., 0.};

  /* convert ray to model space */
  pt_sub(&rfrom, &dt_pt->pt);

  if (dir.x < 0)
    {
      dir.x *= -d->grid_x_re;
      rfrom.x *= -d->grid_x_re;
    }
  else
    {
      dir.x *= d->grid_x_re;
      rfrom.x *= d->grid_x_re;
    }

  if (dir.y < 0)
    {
      dir.y *= -d->grid_y_re;
      rfrom.y *= -d->grid_y_re;
    }
  else
    {
      dir.y *= d->grid_y_re;
      rfrom.y *= d->grid_y_re;
    }

  if (dir.z < 0)
    {
      dir.z *= -d->grid_z_re;
      rfrom.z *= -d->grid_z_re;
    }
  else
    {
      dir.z *= d->grid_z_re;
      rfrom.z *= d->grid_z_re;
    }

  {
    point3d_t high_pt = {1, 1, 1};
    point3d_t low_pt = {-1, -1, -1};
    pt_sub(&high_pt, &rfrom);
    pt_sub(&low_pt, &rfrom);
    high = pt_smallest_mult(&dir, &high_pt);
    low = pt_biggest_mult(&dir, &low_pt);
  }

  /* check if ray even intersects density */
  if (low > high) return -1;

  {
    point3d_t middle = rfrom;
    pt_mad(&middle, 0.5 * (low + high), &dir);
    if (!((-1 <= middle.x && middle.x <= 1) && (-1 <= middle.y && middle.y <= 1) && (-1 <= middle.z && middle.z <= 1)))
      {
        return -1;
      }
  }

  {
    /* Find relevant segments along ray */
    point3d_t middir;
    middir.x = -rfrom.x / dir.x;
    middir.y = -rfrom.y / dir.y;
    middir.z = -rfrom.z / dir.z;

    steps[current++] = low;

    if (fabs(dir.x) >= 1e-12)
      {
        if (middir.x > low && middir.x < high) steps[current++] = middir.x;
      }

    if (fabs(dir.y) >= 1e-12)
      {
        if (middir.y > low && middir.y < high) steps[current++] = middir.y;
      }

    if (fabs(dir.z) >= 1e-12)
      {
        if (middir.z > low && middir.z < high) steps[current++] = middir.z;
      }

    if (current > 3 && steps[2] > steps[3])
      {
        float v = steps[3];
        steps[3] = steps[2];
        steps[2] = v;
      }
    if (current > 2 && steps[1] > steps[2])
      {
        float v = steps[2];
        steps[2] = steps[1];
        steps[1] = v;
      }
    if (current > 3 && steps[2] > steps[3])
      {
        float v = steps[3];
        steps[3] = steps[2];
        steps[2] = v;
      }

    steps[current] = high;
  }

  /* Integrate each segment */
  for (i = 0; i < current; ++i)
    {
      double l_from_seg = steps[i];
      double l_to_seg = steps[i + 1];
      double half;
      if (l_to_seg - l_from_seg < 1e-10) continue;
      half = 0.5 * (l_from_seg + l_to_seg);

      if (rfrom.x + half * dir.x < 0)
        {
          rfrom.x *= -1;
          dir.x *= -1;
        }
      if (rfrom.y + half * dir.y < 0)
        {
          rfrom.y *= -1;
          dir.y *= -1;
        }
      if (rfrom.z + half * dir.z < 0)
        {
          rfrom.z *= -1;
          dir.z *= -1;
        }

      {
        double a = 1 - rfrom.x - rfrom.y - rfrom.z + rfrom.x * rfrom.y + rfrom.x * rfrom.z + rfrom.y * rfrom.z -
                   rfrom.x * rfrom.y * rfrom.z;
        double b = -dir.x - dir.y - dir.z + dir.x * rfrom.y + rfrom.x * dir.y + dir.x * rfrom.z + rfrom.x * dir.z +
                   dir.y * rfrom.z + rfrom.y * dir.z - dir.x * rfrom.y * rfrom.z - rfrom.x * dir.y * rfrom.z -
                   rfrom.x * rfrom.y * dir.z;
        double c = dir.x * dir.y * (1 - rfrom.z) + dir.x * dir.z * (1 - rfrom.y) + dir.y * dir.z * (1 - rfrom.x);
        double d = -dir.x * dir.y * dir.z;
        double s_s_2 = l_from_seg * l_from_seg;
        double s_s_3 = s_s_2 * l_from_seg;
        double s_s_4 = s_s_3 * l_from_seg;
        double s_e_2 = l_to_seg * l_to_seg;
        double s_e_3 = s_e_2 * l_to_seg;
        double s_e_4 = s_e_3 * l_to_seg;
        val += 0.25 * d * (s_e_4 - s_s_4) + (1. / 3.) * c * (s_e_3 - s_s_3) + 0.5 * b * (s_e_2 - s_s_2) +
               a * (l_to_seg - l_from_seg);
      }
    }

  return dt_pt->data * val * dirlen;
}

static void *volume_nogrid_worker(void *data)
{
  volume_nogrid_data_struct *d = (volume_nogrid_data_struct *)data;
  int px_width = d->px_width, px_height = d->px_height;
  point3d_t ray_dir_init = *(d->ray_dir_init);
  point3d_t ray_dir_x = *(d->ray_dir_x);
  point3d_t ray_dir_y = *(d->ray_dir_y);
  point3d_t ray_from_init = *(d->ray_from_init);
  point3d_t ray_from_x = *(d->ray_from_x);
  point3d_t ray_from_y = *(d->ray_from_y);
  double *pixels = d->pixels;
  double x_factor = d->x_factor, y_factor = d->y_factor;
  kernel_f callback = d->callback;
  const data_point3d_t *curr_dt_pt = d->start;
  const void **extra_data = d->extra_data;

  /* Initialize pixel buffer */
  int my_x, my_y;
  for (my_y = 0; my_y < px_height; ++my_y)
    {
      for (my_x = 0; my_x < px_width; ++my_x)
        {
          pixels[my_x + my_y * px_width] = -1;
        }
    }

  while (curr_dt_pt < d->end)
    {
      int y_start, y_fin;
      double x, y, radius, x_radius, y_radius;
      point3d_t _z;

      /* Zero optimization */
      if (curr_dt_pt->data == 0)
        {
          ++curr_dt_pt;
          if (extra_data != NULL) ++extra_data;
          continue;
        }

      /* Calculate extent on image */
      radius = d->radius;
      if (d->radius_callback != NULL)
        {
          radius = d->radius_callback(curr_dt_pt, (const void *)extra_data);
        }

      _z = curr_dt_pt->pt;
      apply_world_xform(&_z.x, &_z.y, &_z.z);

      x = (_z.x + 1) * px_width / 2;
      y = (-_z.y + 1) * px_height / 2;

      x_radius = radius / x_factor;
      y_radius = radius / y_factor;

      y_start = ceil(y - y_radius);
      y_fin = ceil(y + y_radius);
      if (y_start < 0)
        {
          y_start = 0;
        }
      if (y_fin > px_height)
        {
          y_fin = px_height;
        }

      for (my_y = y_start; my_y < y_fin; ++my_y)
        {
          double tmp = (my_y - y) / y_radius;
          double x_len = x_radius * sqrt(1. - tmp * tmp);

          int x_start = ceil(x - x_len);
          int x_fin = ceil(x + x_len);
          if (x_start < 0)
            {
              x_start = 0;
            }
          if (x_fin > px_width)
            {
              x_fin = px_width;
            }
          for (my_x = x_start; my_x < x_fin; ++my_x)
            {
              /* calculate ray and value */
              point3d_t ray_from = ray_from_init;
              point3d_t ray_dir = ray_dir_init;
              double val;
              int idx;
              pt_mad(&ray_from, my_x, &ray_from_x);
              pt_mad(&ray_dir, my_x, &ray_dir_x);
              pt_mad(&ray_from, my_y, &ray_from_y);
              pt_mad(&ray_dir, my_y, &ray_dir_y);

              val = callback(curr_dt_pt, (const void *)extra_data, &ray_from, &ray_dir);
              if (val < 0)
                {
                  continue;
                }

              idx = my_x + my_y * px_width;

              if (pixels[idx] < 0)
                {
                  pixels[idx] = 0;
                }
              pixels[idx] += val;
            }
        }

      ++curr_dt_pt;
      if (extra_data != NULL) ++extra_data;
    }
  return 0;
}

static point3d_t pt_rev_calc(double *view_inv, double *proj_inv, double x, double y, double z, double w)
{
  /* Reverses coordinates from normalised device space to world space */
  double prj_x = proj_inv[0 * 4 + 0] * x + proj_inv[0 * 4 + 1] * y + proj_inv[0 * 4 + 2] * z + proj_inv[0 * 4 + 3] * w;
  double prj_y = proj_inv[1 * 4 + 0] * x + proj_inv[1 * 4 + 1] * y + proj_inv[1 * 4 + 2] * z + proj_inv[1 * 4 + 3] * w;
  double prj_z = proj_inv[2 * 4 + 0] * x + proj_inv[2 * 4 + 1] * y + proj_inv[2 * 4 + 2] * z + proj_inv[2 * 4 + 3] * w;
  double prj_w = proj_inv[3 * 4 + 0] * x + proj_inv[3 * 4 + 1] * y + proj_inv[3 * 4 + 2] * z + proj_inv[3 * 4 + 3] * w;
  point3d_t ret;
  ret.x = view_inv[0 * 4 + 0] * prj_x + view_inv[0 * 4 + 1] * prj_y + view_inv[0 * 4 + 2] * prj_z +
          view_inv[0 * 4 + 3] * prj_w;
  ret.y = view_inv[1 * 4 + 0] * prj_x + view_inv[1 * 4 + 1] * prj_y + view_inv[1 * 4 + 2] * prj_z +
          view_inv[1 * 4 + 3] * prj_w;
  ret.z = view_inv[2 * 4 + 0] * prj_x + view_inv[2 * 4 + 1] * prj_y + view_inv[2 * 4 + 2] * prj_z +
          view_inv[2 * 4 + 3] * prj_w;
  w = view_inv[3 * 4 + 0] * prj_x + view_inv[3 * 4 + 1] * prj_y + view_inv[3 * 4 + 2] * prj_z +
      view_inv[3 * 4 + 3] * prj_w;
  if (fabs(w) >= 1e-12)
    {
      ret.x /= w;
      ret.y /= w;
      ret.z /= w;
    }
  /* w is now not needed */
  ret.x /= tx.x_axis_scale;
  ret.y /= tx.y_axis_scale;
  ret.z /= tx.z_axis_scale;
  return ret;
}

/*!
 * Draws unstructured volume data using splatting, given volume rendering model and currently set GR colormap.
 *
 * Each data point is only calculated and drawn as far as `radius`/`radius_callback`.
 * The used interpolation method can be given using `callback`
 * `callback` is expected to integrate along a given ray for the given data point.
 * For trilinear interpolation, you can use `gr_volume_interp_tri_linear`.
 * For interpolation using the multivariate gaussian distribution, you can use `gr_volume_interp_gauss`.
 *
 * \param[in]       ndt_pt              Count of data points (`dt_pts`)
 * \param[in]       dt_pts              The data points to draw
 * \param[in]       extra_data          Optional extra data, one for each data point if specified
 * \param[in]       algorithm           Selected algorithm to draw
 * \param[in]       callback            Callback to use to integrate
 * \param[in,out]   dmin_val            if set, will contain lower bound of pixel intensity
 * \param[in,out]   dmax_val            if set, will contain upper bound of pixel intensity
 * \param[in]       radius              the calculation radius of each data point in world coordinates
 * \param[in]       radius_callback     if given, ignores radius and can return the calculation radius per data point
 *
 * \verbatim embed:rst:leading-asterisk
 *
 * The supported volume rendering models are:
 *
 * +---------------------+---+-----------------------------+
 * |GR_VOLUME_EMISSION   |  0|emission model               |
 * +---------------------+---+-----------------------------+
 * |GR_VOLUME_ABSORPTION |  1|absorption model             |
 * +---------------------+---+-----------------------------+
 *
 * \endverbatim
 */
void gr_volume_nogrid(unsigned long ndt_pt, const data_point3d_t *dt_pts, const void *extra_data, int algorithm,
                      kernel_f callback, double *dmin_val, double *dmax_val, double radius, radius_f radius_callback)
{
  point3d_t camera, up;
  point3d_t ray_from_init, ray_from_x, ray_from_y;
  point3d_t ray_dir_init, ray_dir_x, ray_dir_y;
  double aspect, x_factor, y_factor;
  double view_inv[16], proj_inv[16];
  int i, x, y, thread_count;
#ifndef NO_THREADS
  pthread_t *threads;
#endif
  volume_nogrid_data_struct *data_structs;
  double *pixels;

  point3d_t ray_dir;
  camera.x = tx.camera_pos_x;
  camera.y = tx.camera_pos_y;
  camera.z = tx.camera_pos_z;

  up.x = tx.up_x;
  up.y = tx.up_y;
  up.z = tx.up_z;

  ray_dir.x = tx.focus_point_x;
  ray_dir.y = tx.focus_point_y;
  ray_dir.z = tx.focus_point_z;

  pt_sub(&ray_dir, &camera);
  pt_unitize(&ray_dir);

  /* Calculate inverse of view matrice */

  aspect = (vxmax - vxmin) / (vymax - vymin);

  view_inv[0 * 4 + 0] = tx.s_x;
  view_inv[1 * 4 + 0] = tx.s_y;
  view_inv[2 * 4 + 0] = tx.s_z;
  view_inv[3 * 4 + 0] = 0;

  view_inv[0 * 4 + 1] = up.x;
  view_inv[1 * 4 + 1] = up.y;
  view_inv[2 * 4 + 1] = up.z;
  view_inv[3 * 4 + 1] = 0;

  view_inv[0 * 4 + 2] = -ray_dir.x;
  view_inv[1 * 4 + 2] = -ray_dir.y;
  view_inv[2 * 4 + 2] = -ray_dir.z;
  view_inv[3 * 4 + 2] = 0;

  view_inv[0 * 4 + 3] = camera.x;
  view_inv[1 * 4 + 3] = camera.y;
  view_inv[2 * 4 + 3] = camera.z;
  view_inv[3 * 4 + 3] = 1;

  /* Calculate inverse of projection matrice */
  if (gpx.projection_type == GR_PROJECTION_ORTHOGRAPHIC)
    {
      double left = gpx.left, right = gpx.right, bottom = gpx.bottom, top = gpx.top;
      if (aspect > 1)
        {
          right *= aspect;
          left *= aspect;
        }
      else
        {
          top /= aspect;
          bottom /= aspect;
        }

      proj_inv[0 * 4 + 0] = (right - left) / 2;
      proj_inv[1 * 4 + 0] = 0;
      proj_inv[2 * 4 + 0] = 0;
      proj_inv[3 * 4 + 0] = 0;

      proj_inv[0 * 4 + 1] = 0;
      proj_inv[1 * 4 + 1] = (top - bottom) / 2;
      proj_inv[2 * 4 + 1] = 0;
      proj_inv[3 * 4 + 1] = 0;

      proj_inv[0 * 4 + 2] = 0;
      proj_inv[1 * 4 + 2] = 0;
      proj_inv[2 * 4 + 2] = (gpx.far_plane - gpx.near_plane) / -2;
      proj_inv[3 * 4 + 2] = 0;

      proj_inv[0 * 4 + 3] = (left + right) / 2;
      proj_inv[1 * 4 + 3] = (top + bottom) / 2;
      proj_inv[2 * 4 + 3] = (gpx.far_plane + gpx.near_plane) / -2;
      proj_inv[3 * 4 + 3] = 1;
    }
  else if (gpx.projection_type == GR_PROJECTION_PERSPECTIVE)
    {
      double f = cos(gpx.fov * M_PI / 360) / sin(gpx.fov * M_PI / 360); /* cot alpha/2 */
      double c = (gpx.far_plane + gpx.near_plane) / (gpx.near_plane - gpx.far_plane);
      double d_inv = (gpx.near_plane - gpx.far_plane) / (2 * gpx.far_plane * gpx.near_plane);

      if (aspect >= 1)
        {
          proj_inv[0 * 4 + 0] = aspect / f;
        }
      else
        {
          proj_inv[0 * 4 + 0] = 1. / f;
        }
      proj_inv[1 * 4 + 0] = 0;
      proj_inv[2 * 4 + 0] = 0;
      proj_inv[3 * 4 + 0] = 0;

      proj_inv[0 * 4 + 1] = 0;
      if (aspect >= 1)
        {
          proj_inv[1 * 4 + 1] = 1. / f;
        }
      else
        {
          proj_inv[1 * 4 + 1] = 1. / (f * aspect);
        }
      proj_inv[2 * 4 + 1] = 0;
      proj_inv[3 * 4 + 1] = 0;

      proj_inv[0 * 4 + 2] = 0;
      proj_inv[1 * 4 + 2] = 0;
      proj_inv[2 * 4 + 2] = 0;
      proj_inv[3 * 4 + 2] = d_inv;

      proj_inv[0 * 4 + 3] = 0;
      proj_inv[1 * 4 + 3] = 0;
      proj_inv[2 * 4 + 3] = -1;
      proj_inv[3 * 4 + 3] = c * d_inv;
    }

  {
    /* Calculate ray positions and directions */
    double x_start = -1 + 0. / vt.picture_width;
    double x_next = -1 + 2. / vt.picture_width;
    double y_start = 1 - 0. / vt.picture_height;
    double y_next = 1 - 2. / vt.picture_height;

    ray_from_init = pt_rev_calc(view_inv, proj_inv, x_start, y_start, -1, 1);
    ray_from_x = pt_rev_calc(view_inv, proj_inv, x_next, y_start, -1, 1);
    pt_sub(&ray_from_x, &ray_from_init);
    ray_from_y = pt_rev_calc(view_inv, proj_inv, x_start, y_next, -1, 1);
    pt_sub(&ray_from_y, &ray_from_init);

    ray_dir_init = pt_rev_calc(view_inv, proj_inv, x_start, y_start, 1, 1);
    pt_sub(&ray_dir_init, &ray_from_init);
    {
      point3d_t temp = pt_rev_calc(view_inv, proj_inv, x_next, y_start, -1, 1);
      ray_dir_x = pt_rev_calc(view_inv, proj_inv, x_next, y_start, 1, 1);
      pt_sub(&ray_dir_x, &temp);
      pt_sub(&ray_dir_x, &ray_dir_init);
    }

    {
      point3d_t temp = pt_rev_calc(view_inv, proj_inv, x_start, y_next, -1, 1);
      ray_dir_y = pt_rev_calc(view_inv, proj_inv, x_start, y_next, 1, 1);
      pt_sub(&ray_dir_y, &temp);
      pt_sub(&ray_dir_y, &ray_dir_init);
    }
  }

  x_factor = pt_length(&ray_from_x);
  y_factor = pt_length(&ray_from_y);

  pixels = (double *)calloc(vt.picture_width * vt.picture_height, sizeof(double));

#ifndef NO_THREADS
  thread_count = (system_processor_count() - 1) < 256 ? system_processor_count() - 1 : 256;
  if (vt.max_threads > 0)
    {
      thread_count = vt.max_threads;
    }

  if (ndt_pt < (unsigned long)thread_count)
    {
      thread_count = ndt_pt;
    }

  threads = (pthread_t *)calloc(thread_count, sizeof(pthread_t));
#else
  thread_count = 1;
#endif
  data_structs = (volume_nogrid_data_struct *)calloc(thread_count, sizeof(volume_nogrid_data_struct));

  /* Calculate bounds and start threads */

  for (i = 0; i < thread_count; ++i)
    {
      unsigned long start = i * ndt_pt / thread_count;
      unsigned long end = (i + 1) * ndt_pt / thread_count;

      if (i == thread_count - 1)
        {
          end = ndt_pt;
        }

      if (i == 0)
        {
          data_structs[i].pixels = pixels;
        }
      else
        {
          data_structs[i].pixels = (double *)calloc(vt.picture_width * vt.picture_height, sizeof(double));
        }

      data_structs[i].px_width = vt.picture_width;
      data_structs[i].px_height = vt.picture_height;
      data_structs[i].start = dt_pts + start;
      data_structs[i].end = dt_pts + end;
      data_structs[i].callback = callback;
      if (extra_data == NULL)
        {
          data_structs[i].extra_data = NULL;
        }
      else
        {
          data_structs[i].extra_data = (const void **)extra_data + start;
        }
      data_structs[i].radius = radius;
      data_structs[i].radius_callback = radius_callback;
      data_structs[i].ray_dir_init = &ray_dir_init;
      data_structs[i].ray_dir_x = &ray_dir_x;
      data_structs[i].ray_dir_y = &ray_dir_y;
      data_structs[i].ray_from_init = &ray_from_init;
      data_structs[i].ray_from_x = &ray_from_x;
      data_structs[i].ray_from_y = &ray_from_y;
      data_structs[i].x_factor = x_factor;
      data_structs[i].y_factor = y_factor;
#ifndef NO_THREADS
      pthread_create(threads + i, NULL, volume_nogrid_worker, (void *)(data_structs + i));
#else
      volume_nogrid_worker((void *)(data_structs + i));
#endif
    }


#ifndef NO_THREADS
  /* Wait for threads to end and reduce to one image buffer */
  for (i = 0; i < thread_count; ++i)
    {
      pthread_join(threads[i], NULL);

      if (i != 0)
        {
          double *px_t = data_structs[i].pixels;
          for (y = 0; y < vt.picture_height; ++y)
            {
              for (x = 0; x < vt.picture_width; ++x)
                {
                  int idx = x + y * vt.picture_width;

                  double v = px_t[idx];
                  if (v >= 0)
                    {
                      double v2 = pixels[idx];
                      if (v2 < 0)
                        {
                          pixels[idx] = v;
                        }
                      else
                        {
                          pixels[idx] = v2 + v;
                        }
                    }
                }
            }
          free(data_structs[i].pixels);
        }
    }

  free(threads);
#endif
  free(data_structs);

  /* Next Step: convert to absorption model if necessary and calculate min and max */
  {
    double dmin = 1e15;
    double dmax = -1;
    int x, y;
    int *ipixels, *colormap;
    if (algorithm == GR_VOLUME_EMISSION)
      {
        for (y = 0; y < vt.picture_height; ++y)
          {
            for (x = 0; x < vt.picture_width; ++x)
              {
                double v = pixels[x + y * vt.picture_width];
                if (v >= 0)
                  {
                    dmin = min(dmin, v);
                    dmax = max(dmax, v);
                  }
              }
          }
      }
    else
      {
        for (y = 0; y < vt.picture_height; ++y)
          {
            for (x = 0; x < vt.picture_width; ++x)
              {
                double v = pixels[x + y * vt.picture_width];
                if (v >= 0)
                  {
                    v = pixels[x + y * vt.picture_width] = exp(-v);
                    dmin = min(dmin, v);
                    dmax = max(dmax, v);
                  }
              }
          }
      }
    if (dmin_val != NULL)
      {
        *dmin_val = dmin;
      }
    if (dmax_val != NULL)
      {
        *dmax_val = dmax;
      }

    /* Convert double to color according to selected colormap, draw and cleanup */
    ipixels = (int *)gks_malloc(vt.picture_width * vt.picture_height * sizeof(int));

    colormap = (int *)gks_malloc((last_color - first_color + 1) * sizeof(int));
    for (i = first_color; i <= last_color; i++)
      {
        gr_inqcolor(i, colormap + i - first_color);
      }

    for (i = 0; i < vt.picture_width * vt.picture_height; i++)
      {
        if (pixels[i] >= 0)
          {
            if (dmax == 0)
              {
                ipixels[i] = 0;
              }
            else
              {
                ipixels[i] = (255u << 24) + colormap[(int)(pixels[i] / dmax * (last_color - first_color))];
              }
          }
      }
    free(pixels);
    free(colormap);

    drawimage_calculation(lx.xmin, lx.xmax, lx.ymin, lx.ymax, vt.picture_width, vt.picture_height, ipixels, 0);

    free(ipixels);
  }
}

void gr_setmathfont(int font)
{
  check_autoinit;

  math_font = font;

  if (flag_stream) gr_writestream("<setmathfont font=\"%d\"/>\n", font);
}

void gr_inqmathfont(int *font)
{
  check_autoinit;

  *font = math_font;
}
