/* 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 */