/* http://www.rwgrayprojects.com/rbfnotes/maps/graymap6.html
   Slightly modified by jwz for xscreensaver
 */


/**************************************************************/
/*                                                            */
/* This C program is copyrighted by  Robert W. Gray and may   */
/* not be used in ANY for-profit project without written      */
/* permission.                                                */
/*                                                            */
/**************************************************************/

/* (Note: Robert Gray has kindly given me his permission to include
   this code in xscreensaver. -- Jamie Zawinski, Apr 2018.)
 */


/**************************************************************/
/*                                                            */
/* This C program contains the Dymaxion map coordinate        */
/* transformation routines for converting longitude/latitude  */
/* points to (X, Y) points on the Dymaxion map.               */
/*                                                            */
/* This version uses the exact transformation equations.      */
/**************************************************************/

#include <stdio.h>
#include <stdlib.h>
#include <math.h>

#ifdef HAVE_CONFIG_H
# include "config.h"
#endif

#include "dymaxionmap-coords.h"

/************************************************************************/
/* NOTE: in C, array indexing starts with element zero (0).  I choose   */
/*       to start my array indexing with elemennt one (1) so all arrays */
/*       are defined one element longer than they need to be.           */
/************************************************************************/

/************************************************************************/
/* global variables accessable to all procedures                        */
/************************************************************************/

static double v_x[13], v_y[13], v_z[13];
static double center_x[21], center_y[21], center_z[21];
static double garc, gt, gdve, gel;

/********************************************/
/*      function pre-definitions            */
/********************************************/

static double radians(double degrees);
static void rotate(double angle, double *x, double *y);
static void r2(int axis, double alpha, double *x, double *y, double *z);
static void init_stuff(void);
/*static void convert_s_t_p(double lng, double lat, double *x, double *y);*/
static void s_to_c(double theta, double phi, double *x, double *y, double *z);
static void c_to_s(double *theta, double *phi, double x, double y, double z);
static void s_tri_info(double x, double y, double z,
		 int *tri, int *lcd);
static void dymax_point(int tri, int lcd,
		 double x, double y, double z,
		 double *dx, double *dy);
static void conv_ll_t_sc(double lng, double lat, double *theta, double *phi);


/****************************************/
/*      function definitions            */
/****************************************/


void
/* convert_s_t_p */
dymaxion_convert
(double lng, double lat, double *x, double *y)
{
  /***********************************************************/
  /* This is the main control procedure.                     */
  /***********************************************************/

  double theta, phi;
  double hx, hy, hz;
  double px = 0, py = 0;
  int tri, hlcd;

  static int initted = 0;
  if (! initted) {
    init_stuff();
    initted = 1;
  }

  /* Convert the given (long.,lat.) coordinate into spherical */
  /* polar coordinates (r, theta, phi) with radius=1.         */
  /* Angles are given in radians, NOT degrees.                */

  conv_ll_t_sc(lng, lat, &theta, &phi);

  /* convert the spherical polar coordinates into cartesian   */
  /* (x, y, z) coordinates.                                   */

  s_to_c(theta, phi, &hx, &hy, &hz);

  /* determine which of the 20 spherical icosahedron triangles */
  /* the given point is in and the LCD triangle.               */

  s_tri_info(hx, hy, hz, &tri, &hlcd);

  /* Determine the corresponding Fuller map plane (x, y) point */

  dymax_point(tri, hlcd, hx, hy, hz, &px, &py);
  *x = px;
  *y = py;

} /* end convert_s_t_p */


static void conv_ll_t_sc(double lng, double lat, double *theta, double *phi)
{
  /* convert (long., lat.) point into spherical polar coordinates */
  /* with r=radius=1.  Angles are given in radians.               */

  double h_theta, h_phi;

  h_theta = 90.0 - lat ;
  h_phi = lng;
  if (lng < 0.0) {h_phi = lng + 360.0;}
  *theta = radians(h_theta);
  *phi = radians(h_phi);

} /* end conv_ll_t_sc */


static double radians(double degrees)
{
    /* convert angles in degrees into angles in radians */

    double pi2, c1;

    pi2 = 2 * 3.14159265358979323846;
    c1 = pi2 / 360;
    return(c1 * degrees);

} /* end of radians function */


static void init_stuff()
{
   /* initializes the global variables which includes the */
   /* vertix coordinates and mid-face coordinates.        */

   double /* i, */ hold_x, hold_y, hold_z, magn;
   /* double theta, phi; */

   /* Cartesian coordinates for the 12 vertices of icosahedron */

   v_x[1] =    0.420152426708710003;
   v_y[1] =    0.078145249402782959;
   v_z[1] =    0.904082550615019298;
   v_x[2] =    0.995009439436241649 ;
   v_y[2] =   -0.091347795276427931 ;
   v_z[2] =    0.040147175877166645 ;
   v_x[3] =    0.518836730327364437 ;
   v_y[3] =    0.835420380378235850 ;
   v_z[3] =    0.181331837557262454 ;
   v_x[4] =   -0.414682225320335218 ;
   v_y[4] =    0.655962405434800777 ;
   v_z[4] =    0.630675807891475371 ;
   v_x[5] =   -0.515455959944041808 ;
   v_y[5] =   -0.381716898287133011 ;
   v_z[5] =    0.767200992517747538 ;
   v_x[6] =    0.355781402532944713 ;
   v_y[6] =   -0.843580002466178147 ;
   v_z[6] =    0.402234226602925571 ;
   v_x[7] =    0.414682225320335218 ;
   v_y[7] =   -0.655962405434800777 ;
   v_z[7] =   -0.630675807891475371 ;
   v_x[8] =    0.515455959944041808 ;
   v_y[8] =    0.381716898287133011 ;
   v_z[8] =   -0.767200992517747538 ;
   v_x[9] =   -0.355781402532944713 ;
   v_y[9] =    0.843580002466178147 ;
   v_z[9] =   -0.402234226602925571 ;
   v_x[10] =   -0.995009439436241649 ;
   v_y[10] =    0.091347795276427931 ;
   v_z[10] =   -0.040147175877166645 ;
   v_x[11] =   -0.518836730327364437  ;
   v_y[11] =   -0.835420380378235850  ;
   v_z[11] =   -0.181331837557262454  ;
   v_x[12] =   -0.420152426708710003 ;
   v_y[12] =   -0.078145249402782959 ;
   v_z[12] =   -0.904082550615019298 ;

   /* now calculate mid face coordinates             */

   hold_x = (v_x[1] + v_x[2] + v_x[3]) / 3.0 ;
   hold_y = (v_y[1] + v_y[2] + v_y[3]) / 3.0 ;
   hold_z = (v_z[1] + v_z[2] + v_z[3]) / 3.0 ;
   magn = sqrt(hold_x * hold_x + hold_y * hold_y + hold_z * hold_z);
   center_x[1] = hold_x / magn;
   center_y[1] = hold_y / magn;
   center_z[1] = hold_z / magn;

   hold_x = (v_x[1] + v_x[3] + v_x[4]) / 3.0 ;
   hold_y = (v_y[1] + v_y[3] + v_y[4]) / 3.0 ;
   hold_z = (v_z[1] + v_z[3] + v_z[4]) / 3.0 ;
   magn = sqrt(hold_x * hold_x + hold_y * hold_y + hold_z * hold_z);
   center_x[2] = hold_x / magn;
   center_y[2] = hold_y / magn;
   center_z[2] = hold_z / magn;

   hold_x = (v_x[1] + v_x[4] + v_x[5]) / 3.0 ;
   hold_y = (v_y[1] + v_y[4] + v_y[5]) / 3.0 ;
   hold_z = (v_z[1] + v_z[4] + v_z[5]) / 3.0 ;
   magn = sqrt(hold_x * hold_x + hold_y * hold_y + hold_z * hold_z);
   center_x[3] = hold_x / magn;
   center_y[3] = hold_y / magn;
   center_z[3] = hold_z / magn;

   hold_x = (v_x[1] + v_x[5] + v_x[6]) / 3.0 ;
   hold_y = (v_y[1] + v_y[5] + v_y[6]) / 3.0 ;
   hold_z = (v_z[1] + v_z[5] + v_z[6]) / 3.0 ;
   magn = sqrt(hold_x * hold_x + hold_y * hold_y + hold_z * hold_z);
   center_x[4] = hold_x / magn;
   center_y[4] = hold_y / magn;
   center_z[4] = hold_z / magn;

   hold_x = (v_x[1] + v_x[2] + v_x[6]) / 3.0 ;
   hold_y = (v_y[1] + v_y[2] + v_y[6]) / 3.0 ;
   hold_z = (v_z[1] + v_z[2] + v_z[6]) / 3.0 ;
   magn = sqrt(hold_x * hold_x + hold_y * hold_y + hold_z * hold_z);
   center_x[5] = hold_x / magn;
   center_y[5] = hold_y / magn;
   center_z[5] = hold_z / magn;

   hold_x = (v_x[2] + v_x[3] + v_x[8]) / 3.0 ;
   hold_y = (v_y[2] + v_y[3] + v_y[8]) / 3.0 ;
   hold_z = (v_z[2] + v_z[3] + v_z[8]) / 3.0 ;
   magn = sqrt(hold_x * hold_x + hold_y * hold_y + hold_z * hold_z);
   center_x[6] = hold_x / magn;
   center_y[6] = hold_y / magn;
   center_z[6] = hold_z / magn;

   hold_x = (v_x[8] + v_x[3] + v_x[9]) / 3.0 ;
   hold_y = (v_y[8] + v_y[3] + v_y[9]) / 3.0 ;
   hold_z = (v_z[8] + v_z[3] + v_z[9]) / 3.0 ;
   magn = sqrt(hold_x * hold_x + hold_y * hold_y + hold_z * hold_z);
   center_x[7] = hold_x / magn;
   center_y[7] = hold_y / magn;
   center_z[7] = hold_z / magn;

   hold_x = (v_x[9] + v_x[3] + v_x[4]) / 3.0 ;
   hold_y = (v_y[9] + v_y[3] + v_y[4]) / 3.0 ;
   hold_z = (v_z[9] + v_z[3] + v_z[4]) / 3.0 ;
   magn = sqrt(hold_x * hold_x + hold_y * hold_y + hold_z * hold_z);
   center_x[8] = hold_x / magn;
   center_y[8] = hold_y / magn;
   center_z[8] = hold_z / magn;

   hold_x = (v_x[10] + v_x[9] + v_x[4]) / 3.0 ;
   hold_y = (v_y[10] + v_y[9] + v_y[4]) / 3.0 ;
   hold_z = (v_z[10] + v_z[9] + v_z[4]) / 3.0 ;
   magn = sqrt(hold_x * hold_x + hold_y * hold_y + hold_z * hold_z);
   center_x[9] = hold_x / magn;
   center_y[9] = hold_y / magn;
   center_z[9] = hold_z / magn;

   hold_x = (v_x[5] + v_x[10] + v_x[4]) / 3.0 ;
   hold_y = (v_y[5] + v_y[10] + v_y[4]) / 3.0 ;
   hold_z = (v_z[5] + v_z[10] + v_z[4]) / 3.0 ;
   magn = sqrt(hold_x * hold_x + hold_y * hold_y + hold_z * hold_z);
   center_x[10] = hold_x / magn;
   center_y[10] = hold_y / magn;
   center_z[10] = hold_z / magn;

   hold_x = (v_x[5] + v_x[11] + v_x[10]) / 3.0 ;
   hold_y = (v_y[5] + v_y[11] + v_y[10]) / 3.0 ;
   hold_z = (v_z[5] + v_z[11] + v_z[10]) / 3.0 ;
   magn = sqrt(hold_x * hold_x + hold_y * hold_y + hold_z * hold_z);
   center_x[11] = hold_x / magn;
   center_y[11] = hold_y / magn;
   center_z[11] = hold_z / magn;

   hold_x = (v_x[5] + v_x[6] + v_x[11]) / 3.0 ;
   hold_y = (v_y[5] + v_y[6] + v_y[11]) / 3.0 ;
   hold_z = (v_z[5] + v_z[6] + v_z[11]) / 3.0 ;
   magn = sqrt(hold_x * hold_x + hold_y * hold_y + hold_z * hold_z);
   center_x[12] = hold_x / magn;
   center_y[12] = hold_y / magn;
   center_z[12] = hold_z / magn;

   hold_x = (v_x[11] + v_x[6] + v_x[7]) / 3.0 ;
   hold_y = (v_y[11] + v_y[6] + v_y[7]) / 3.0 ;
   hold_z = (v_z[11] + v_z[6] + v_z[7]) / 3.0 ;
   magn = sqrt(hold_x * hold_x + hold_y * hold_y + hold_z * hold_z);
   center_x[13] = hold_x / magn;
   center_y[13] = hold_y / magn;
   center_z[13] = hold_z / magn;

   hold_x = (v_x[7] + v_x[6] + v_x[2]) / 3.0 ;
   hold_y = (v_y[7] + v_y[6] + v_y[2]) / 3.0 ;
   hold_z = (v_z[7] + v_z[6] + v_z[2]) / 3.0 ;
   magn = sqrt(hold_x * hold_x + hold_y * hold_y + hold_z * hold_z);
   center_x[14] = hold_x / magn;
   center_y[14] = hold_y / magn;
   center_z[14] = hold_z / magn;

   hold_x = (v_x[8] + v_x[7] + v_x[2]) / 3.0 ;
   hold_y = (v_y[8] + v_y[7] + v_y[2]) / 3.0 ;
   hold_z = (v_z[8] + v_z[7] + v_z[2]) / 3.0 ;
   magn = sqrt(hold_x * hold_x + hold_y * hold_y + hold_z * hold_z);
   center_x[15] = hold_x / magn;
   center_y[15] = hold_y / magn;
   center_z[15] = hold_z / magn;

   hold_x = (v_x[12] + v_x[9] + v_x[8]) / 3.0 ;
   hold_y = (v_y[12] + v_y[9] + v_y[8]) / 3.0 ;
   hold_z = (v_z[12] + v_z[9] + v_z[8]) / 3.0 ;
   magn = sqrt(hold_x * hold_x + hold_y * hold_y + hold_z * hold_z);
   center_x[16] = hold_x / magn;
   center_y[16] = hold_y / magn;
   center_z[16] = hold_z / magn;

   hold_x = (v_x[12] + v_x[9] + v_x[10]) / 3.0 ;
   hold_y = (v_y[12] + v_y[9] + v_y[10]) / 3.0 ;
   hold_z = (v_z[12] + v_z[9] + v_z[10]) / 3.0 ;
   magn = sqrt(hold_x * hold_x + hold_y * hold_y + hold_z * hold_z);
   center_x[17] = hold_x / magn;
   center_y[17] = hold_y / magn;
   center_z[17] = hold_z / magn;

   hold_x = (v_x[12] + v_x[11] + v_x[10]) / 3.0 ;
   hold_y = (v_y[12] + v_y[11] + v_y[10]) / 3.0 ;
   hold_z = (v_z[12] + v_z[11] + v_z[10]) / 3.0 ;
   magn = sqrt(hold_x * hold_x + hold_y * hold_y + hold_z * hold_z);
   center_x[18] = hold_x / magn;
   center_y[18] = hold_y / magn;
   center_z[18] = hold_z / magn;

   hold_x = (v_x[12] + v_x[11] + v_x[7]) / 3.0 ;
   hold_y = (v_y[12] + v_y[11] + v_y[7]) / 3.0 ;
   hold_z = (v_z[12] + v_z[11] + v_z[7]) / 3.0 ;
   magn = sqrt(hold_x * hold_x + hold_y * hold_y + hold_z * hold_z);
   center_x[19] = hold_x / magn;
   center_y[19] = hold_y / magn;
   center_z[19] = hold_z / magn;

   hold_x = (v_x[12] + v_x[8] + v_x[7]) / 3.0 ;
   hold_y = (v_y[12] + v_y[8] + v_y[7]) / 3.0 ;
   hold_z = (v_z[12] + v_z[8] + v_z[7]) / 3.0 ;
   magn = sqrt(hold_x * hold_x + hold_y * hold_y + hold_z * hold_z);
   center_x[20] = hold_x / magn;
   center_y[20] = hold_y / magn;
   center_z[20] = hold_z / magn;

   garc = 2.0 * asin( sqrt( 5 - sqrt(5)) / sqrt(10) );
   gt = garc / 2.0;

   gdve = sqrt( 3 + sqrt(5) ) / sqrt( 5 + sqrt(5) );
   gel = sqrt(8) / sqrt(5 + sqrt(5));

} /* end of int_stuff procedure */


static void s_to_c(double theta, double phi, double *x, double *y, double *z)
{
    /* Covert spherical polar coordinates to cartesian coordinates. */
    /* The angles are given in radians.                             */

    *x = sin(theta) * cos(phi);
    *y = sin(theta) * sin(phi);
    *z = cos(theta);

 } /* end s_to_c */


static void c_to_s(double *lng, double *lat, double x, double y, double z)
   {
    /* convert cartesian coordinates into spherical polar coordinates. */
    /* The angles are given in radians.                                */

    double a;

    if (x>0.0 && y>0.0){a = radians(0.0);}
    if (x<0.0 && y>0.0){a = radians(180.0);}
    if (x<0.0 && y<0.0){a = radians(180.0);}
    if (x>0.0 && y<0.0){a = radians(360.0);}
    *lat = acos(z);
    if (x==0.0 && y>0.0){*lng = radians(90.0);}
    if (x==0.0 && y<0.0){*lng = radians(270.0);}
    if (x>0.0 && y==0.0){*lng = radians(0.0);}
    if (x<0.0 && y==0.0){*lng = radians(180.0);}
    if (x!=0.0 && y!=0.0){*lng = atan(y/x) + a;}

} /* end c_to_s */


void s_tri_info(double x, double y, double z,
		 int *tri, int *lcd)
{
  /* Determine which triangle and LCD triangle the point is in. */

  double  h_dist1, h_dist2, h_dist3, h1, h2, h3;
  int i, h_tri, h_lcd ;
  int v1 = 0, v2 = 0, v3 = 0;

  h_tri = 0;
  h_dist1 = 9999.0;

  /* Which triangle face center is the closest to the given point */
  /* is the triangle in which the given point is in.              */

  for (i = 1; i <=20; i = i + 1)
   {
     h1 = center_x[i] - x;
     h2 = center_y[i] - y;
     h3 = center_z[i] - z;
     h_dist2 = sqrt(h1 * h1 + h2 * h2 + h3 * h3);
     if (h_dist2 < h_dist1)
      {
        h_tri = i;
        h_dist1 = h_dist2;
      } /* end the if statement */
   }  /* end the for statement */

   *tri = h_tri;

   /* Now the LCD triangle is determined. */

   switch (h_tri)
   {
    case 1:  v1 =  1; v2 =  3; v3 =  2; break;
    case 2:  v1 =  1; v2 =  4; v3 =  3; break;
    case 3:  v1 =  1; v2 =  5; v3 =  4; break;
    case 4:  v1 =  1; v2 =  6; v3 =  5; break;
    case 5:  v1 =  1; v2 =  2; v3 =  6; break;
    case 6:  v1 =  2; v2 =  3; v3 =  8; break;
    case 7:  v1 =  3; v2 =  9; v3 =  8; break;
    case 8:  v1 =  3; v2 =  4; v3 =  9; break;
    case 9:  v1 =  4; v2 = 10; v3 =  9; break;
    case 10: v1 =  4; v2 =  5; v3 = 10; break;
    case 11: v1 =  5; v2 = 11; v3 = 10; break;
    case 12: v1 =  5; v2 =  6; v3 = 11; break;
    case 13: v1 =  6; v2 =  7; v3 = 11; break;
    case 14: v1 =  2; v2 =  7; v3 =  6; break;
    case 15: v1 =  2; v2 =  8; v3 =  7; break;
    case 16: v1 =  8; v2 =  9; v3 = 12; break;
    case 17: v1 =  9; v2 = 10; v3 = 12; break;
    case 18: v1 = 10; v2 = 11; v3 = 12; break;
    case 19: v1 = 11; v2 =  7; v3 = 12; break;
    case 20: v1 =  8; v2 = 12; v3 =  7; break;
   } /* end of switch statement */

   h1 = x - v_x[v1];
   h2 = y - v_y[v1];
   h3 = z - v_z[v1];
   h_dist1 = sqrt(h1 * h1 + h2 * h2 + h3 * h3);

   h1 = x - v_x[v2];
   h2 = y - v_y[v2];
   h3 = z - v_z[v2];
   h_dist2 = sqrt(h1 * h1 + h2 * h2 + h3 * h3);

   h1 = x - v_x[v3];
   h2 = y - v_y[v3];
   h3 = z - v_z[v3];
   h_dist3 = sqrt(h1 * h1 + h2 * h2 + h3 * h3);

   if ( (h_dist1 <= h_dist2) && (h_dist2 <= h_dist3) ) {h_lcd = 1; }
   if ( (h_dist1 <= h_dist3) && (h_dist3 <= h_dist2) ) {h_lcd = 6; }
   if ( (h_dist2 <= h_dist1) && (h_dist1 <= h_dist3) ) {h_lcd = 2; }
   if ( (h_dist2 <= h_dist3) && (h_dist3 <= h_dist1) ) {h_lcd = 3; }
   if ( (h_dist3 <= h_dist1) && (h_dist1 <= h_dist2) ) {h_lcd = 5; }
   if ( (h_dist3 <= h_dist2) && (h_dist2 <= h_dist1) ) {h_lcd = 4; }

   *lcd = h_lcd;

} /* end s_tri_info */


static void dymax_point(int tri, int lcd,
		 double x, double y, double z,
                 double *px, double *py)
{
  int axis, v1 = 0;
  double hlng, hlat, h0x, h0y, h0z, h1x, h1y, h1z;

  double gs;
  double gx, gy, gz, ga1,ga2,ga3,ga1p,ga2p,ga3p,gxp,gyp/*,gzp*/;


  /* In order to rotate the given point into the template spherical */
  /* triangle, we need the spherical polar coordinates of the center */
  /* of the face and one of the face vertices. So set up which vertex */
  /* to use.                                                          */

   switch (tri)
   {
    case 1:  v1 =  1;  break;
    case 2:  v1 =  1;  break;
    case 3:  v1 =  1;  break;
    case 4:  v1 =  1;  break;
    case 5:  v1 =  1;  break;
    case 6:  v1 =  2;  break;
    case 7:  v1 =  3;  break;
    case 8:  v1 =  3;  break;
    case 9:  v1 =  4;  break;
    case 10: v1 =  4;  break;
    case 11: v1 =  5;  break;
    case 12: v1 =  5;  break;
    case 13: v1 =  6;  break;
    case 14: v1 =  2;  break;
    case 15: v1 =  2;  break;
    case 16: v1 =  8;  break;
    case 17: v1 =  9;  break;
    case 18: v1 = 10;  break;
    case 19: v1 = 11;  break;
    case 20: v1 =  8;  break;
   } /* end of switch statement */

   h0x = x;
   h0y = y;
   h0z = z;

   h1x = v_x[v1];
   h1y = v_y[v1];
   h1z = v_z[v1];

   c_to_s(&hlng, &hlat, center_x[tri], center_y[tri], center_z[tri]);

   axis = 3;
   r2(axis,hlng,&h0x,&h0y,&h0z);
   r2(axis,hlng,&h1x,&h1y,&h1z);

   axis = 2;
   r2(axis,hlat,&h0x,&h0y,&h0z);
   r2(axis,hlat,&h1x,&h1y,&h1z);

   c_to_s(&hlng,&hlat,h1x,h1y,h1z);
   hlng = hlng - radians(90.0);

   axis = 3;
   r2(axis,hlng,&h0x,&h0y,&h0z);

   /* exact transformation equations */

   gz = sqrt(1 - h0x * h0x - h0y * h0y);
   gs = sqrt( 5 + 2 * sqrt(5) ) / ( gz * sqrt(15) );

   gxp = h0x * gs ;
   gyp = h0y * gs ;

   ga1p = 2.0 * gyp / sqrt(3.0) + (gel / 3.0) ;
   ga2p = gxp - (gyp / sqrt(3)) +  (gel / 3.0) ;
   ga3p = (gel / 3.0) - gxp - (gyp / sqrt(3));

   ga1 = gt + atan( (ga1p - 0.5 * gel) / gdve);
   ga2 = gt + atan( (ga2p - 0.5 * gel) / gdve);
   ga3 = gt + atan( (ga3p - 0.5 * gel) / gdve);

   gx = 0.5 * (ga2 - ga3) ;

   gy = (1.0 / (2.0 * sqrt(3)) ) * (2 * ga1 - ga2 - ga3);

   /* Re-scale so plane triangle edge length is 1. */

   x = gx / garc;
   y = gy / garc;

  /* rotate and translate to correct position          */

  switch (tri)
   {
     case  1: rotate(240.0,&x, &y);
	      *px = x + 2.0; *py = y + 7.0 / (2.0 * sqrt(3.0)) ; break;
     case  2: rotate(300.0, &x, &y); *px = x + 2.0;
              *py = y + 5.0 / (2.0 * sqrt(3.0)) ; break;
     case  3: rotate(0.0, &x, &y);
             *px = x + 2.5; *py = y + 2.0 / sqrt(3.0); break;
     case  4: rotate(60.0, &x, &y);
              *px = x + 3.0; *py = y + 5.0 / (2.0 * sqrt(3.0)) ; break;
     case  5: rotate(180.0, &x, &y);
	      *px = x + 2.5; *py = y + 4.0 * sqrt(3.0) / 3.0; break;
     case  6: rotate(300.0, &x, &y);
              *px = x + 1.5; *py = y + 4.0 * sqrt(3.0) / 3.0; break;
     case  7: rotate(300.0, &x, &y);
              *px = x + 1.0; *py = y + 5.0 / (2.0 * sqrt(3.0)) ; break;
     case  8: rotate(0.0, &x, &y);
              *px = x + 1.5; *py = y + 2.0 / sqrt(3.0); break;
     case  9: if (lcd > 2)
	      {
	      rotate(300.0, &x, &y);
	      *px = x + 1.5; *py = y + 1.0 / sqrt(3.0);
	      }
	      else
	      {
	      rotate(0.0, &x, &y);
	      *px = x + 2.0; *py = y + 1.0 / (2.0 * sqrt(3.0));
	      }
	      break;

     case 10: rotate(60.0, &x, &y);
              *px = x + 2.5; *py = y + 1.0 / sqrt(3.0); break;
     case 11: rotate(60.0, &x, &y);
              *px = x + 3.5; *py = y + 1.0 / sqrt(3.0); break;
     case 12: rotate(120.0, &x, &y);
              *px = x + 3.5; *py = y + 2.0 / sqrt(3.0); break;
     case 13: rotate(60.0, &x, &y);
              *px = x + 4.0; *py = y + 5.0 / (2.0 * sqrt(3.0)); break;
     case 14: rotate(0.0, &x, &y);
	      *px = x + 4.0; *py = y + 7.0 / (2.0 * sqrt(3.0)) ; break;
     case 15: rotate(0.0, &x, &y);
	      *px = x + 5.0; *py = y + 7.0 / (2.0 * sqrt(3.0)) ; break;
     case 16: if (lcd < 4)
	      {
		rotate(60.0, &x, &y);
		*px = x + 0.5; *py = y + 1.0 / sqrt(3.0);
	       }
	       else
	       {
		rotate(0.0, &x, &y);
		*px = x + 5.5; *py = y + 2.0 / sqrt(3.0);
	       }
	       break;
     case 17: rotate(0.0, &x, &y);
	      *px = x + 1.0; *py = y + 1.0 / (2.0 * sqrt(3.0)); break;
     case 18: rotate(120.0, &x, &y);
              *px = x + 4.0; *py = y + 1.0 / (2.0 * sqrt(3.0)); break;
     case 19: rotate(120.0, &x, &y);
              *px = x + 4.5; *py = y + 2.0 / sqrt(3.0); break;
     case 20: rotate(300.0, &x, &y);
              *px = x + 5.0; *py = y + 5.0 / (2.0 * sqrt(3.0)); break;

   } /* end switch statement */

} /* end of dymax_point */


static void rotate(double angle, double *x, double *y)
{
  /* Rotate the point to correct orientation in XY-plane. */

  double ha, hx, hy ;

  ha = radians(angle);
  hx = *x;
  hy = *y;
  *x = hx * cos(ha) - hy * sin(ha);
  *y = hx * sin(ha) + hy * cos(ha);

} /* end rotate procedure */


static void r2(int axis, double alpha, double *x, double *y, double *z)
{
  /* Rotate a 3-D point about the specified axis.         */

  double a, b, c;

  a = *x;
  b = *y;
  c = *z;
  if (axis == 1)
  {
   *y = b * cos(alpha) + c * sin(alpha);
   *z = c * cos(alpha) - b * sin(alpha);
  }

  if (axis == 2)
  {
   *x = a * cos(alpha) - c * sin(alpha);
   *z = a * sin(alpha) + c * cos(alpha);
  }

  if (axis == 3)
  {
   *x = a * cos(alpha) + b * sin(alpha);
   *y = b * cos(alpha) - a * sin(alpha);
  }

} /* end of r2 */