/* sphereh.c  find coordinates of vertices and edge lengths  */
/*            of Buckminster Fuller sphere                   */

#include <stdio.h>
#include <math.h>
static double pi = 3.141592653589793238462643383279502884197;

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

double dist(point p1, point p2)
{
  return sqrt((p1.x-p2.x)*(p1.x-p2.x)+
              (p1.y-p2.y)*(p1.y-p2.y)+
              (p1.z-p2.z)*(p1.z-p2.z));
}

point norm(point p)
{
  point c;
  double r = sqrt(p.x*p.x+p.y*p.y+p.z*p.z);
  c.x = p.x / r;
  c.y = p.y / r;
  c.z = p.z / r;
  return c;
}

point plus(point a, point b)
{
  point c;
  
  c.x = a.x + b.x;
  c.y = a.y + b.y;
  c.z = a.z + b.z;
  return c;
}


point coord(double phi, double theta)
{
  point c;
  
  c.x = sin(phi)*cos(theta);
  c.y = sin(phi)*sin(theta);
  c.z = cos(phi);             /* down from vertical */
  
  return c;
}

point rotate(point p)
{
  point c;
  double sinp = sin(pi/5.0); /* rotate 36 degrees, pi/5.0 */  
  double cosp = cos(pi/5.0);  
  c.x = p.x*cosp - p.y*sinp; 
  c.y = p.y*cosp + p.x*sinp;
  c.z = -p.z;             /* down from vertical */
  
  return c;
}

int main(int argc, char *argv[])
{
  point vert[100];
  int nvert = 1; /* .dat numbering starts with 1 */
  int i, tvert;

  printf("sphereh.c Buckminster Fuller top half sphere\n");

  vert[nvert].x = 0.0; /* top of sphere */
  vert[nvert].y = 0.0;
  vert[nvert].z = 1.0;  
  nvert++;

                       /* top pentagon */
  vert[nvert] = coord(pi/5.6751, 0.0*pi/5.0);
  nvert++;
  vert[nvert] = coord(pi/5.6751, 2.0*pi/5.0);
  nvert++;
  vert[nvert] = coord(pi/5.6751, 4.0*pi/5.0);
  nvert++;
  vert[nvert] = coord(pi/5.6751, 6.0*pi/5.0);
  nvert++;
  vert[nvert] = coord(pi/5.6751, 8.0*pi/5.0);
  nvert++;

                       /* equator */
  for(i=0; i<10; i++)
  {
    vert[nvert].x = cos(i*pi/5.0 + pi/10.0);
    vert[nvert].y = sin(i*pi/5.0 + pi/10.0);
    vert[nvert].z = 0.0;
    nvert++;
  }

                       /* northern 1/2 */
  vert[nvert] = norm(plus(plus(vert[2],vert[8]),plus(vert[3],vert[7])));
  nvert++;
  vert[nvert] = norm(plus(plus(vert[3],vert[10]),plus(vert[4],vert[9])));
  nvert++;
  vert[nvert] = norm(plus(plus(vert[4],vert[12]),plus(vert[5],vert[11])));
  nvert++;
  vert[nvert] = norm(plus(plus(vert[5],vert[14]),plus(vert[6],vert[13])));
  nvert++;
  vert[nvert] = norm(plus(plus(vert[6],vert[16]),plus(vert[2],vert[15])));
  nvert++;

                       /* northern 2/2 */
  vert[nvert] = norm(plus(plus(plus(vert[2],vert[17]),plus(vert[7],vert[16])),vert[21]));
  nvert++;
  vert[nvert] = norm(plus(plus(plus(vert[3],vert[18]),plus(vert[9],vert[8])),vert[17]));
  nvert++;
  vert[nvert] = norm(plus(plus(plus(vert[4],vert[19]),plus(vert[11],vert[10])),vert[18]));
  nvert++;
  vert[nvert] = norm(plus(plus(plus(vert[5],vert[20]),plus(vert[13],vert[12])),vert[19]));
  nvert++;
  vert[nvert] = norm(plus(plus(plus(vert[6],vert[21]),plus(vert[15],vert[14])),vert[20]));
  nvert++;

  tvert = nvert;
  printf("top vertex number and coordinates \n");
  for(i=1; i<tvert; i++)
  {
    printf("%d  %9.5f  %9.5f  %9.5f \n", i, vert[i].x, vert[i].y, vert[i].z);
  }
  
  printf("\ndistance check \n");
  printf("\nblue branches, groups of five \n");
  printf(" 1  2 %9.6f \n", dist(vert[1],vert[2]));
  printf(" 1  3 %9.6f \n", dist(vert[1],vert[3]));
  printf(" 1  4 %9.6f \n", dist(vert[1],vert[4]));
  printf(" 1  5 %9.6f \n", dist(vert[1],vert[5]));
  printf(" 1  6 %9.6f \n", dist(vert[1],vert[6]));

  printf("22  2 %9.6f \n", dist(vert[22],vert[2]));
  printf("22 17 %9.6f \n", dist(vert[22],vert[17]));
  printf("22  7 %9.6f \n", dist(vert[22],vert[7]));
  printf("22 16 %9.6f \n", dist(vert[22],vert[16]));
  printf("22 21 %9.6f \n", dist(vert[22],vert[21]));

  printf("23  3 %9.6f \n", dist(vert[23],vert[3]));
  printf("23 18 %9.6f \n", dist(vert[23],vert[18]));
  printf("23  9 %9.6f \n", dist(vert[23],vert[9]));
  printf("23  8 %9.6f \n", dist(vert[23],vert[8]));
  printf("23 17 %9.6f \n", dist(vert[23],vert[17]));

  printf("24  4 %9.6f \n", dist(vert[24],vert[4]));
  printf("24 19 %9.6f \n", dist(vert[24],vert[19]));
  printf("24 11 %9.6f \n", dist(vert[24],vert[11]));
  printf("24 10 %9.6f \n", dist(vert[24],vert[10]));
  printf("24 18 %9.6f \n", dist(vert[24],vert[18]));

  printf("25  5 %9.6f \n", dist(vert[25],vert[5]));
  printf("25 20 %9.6f \n", dist(vert[25],vert[20]));
  printf("25 13 %9.6f \n", dist(vert[25],vert[13]));
  printf("25 12 %9.6f \n", dist(vert[25],vert[12]));
  printf("25 19 %9.6f \n", dist(vert[25],vert[19]));

  printf("26  6 %9.6f \n", dist(vert[26],vert[6]));
  printf("26 21 %9.6f \n", dist(vert[26],vert[21]));
  printf("26 15 %9.6f \n", dist(vert[26],vert[15]));
  printf("26 14 %9.6f \n", dist(vert[26],vert[14]));
  printf("26 20 %9.6f \n", dist(vert[26],vert[20]));

  printf("\nyellow  great circles \n");
  printf(" 2  3 %9.6f \n", dist(vert[2],vert[3]));
  printf(" 3  4 %9.6f \n", dist(vert[3],vert[4]));
  printf(" 4  5 %9.6f \n", dist(vert[4],vert[5]));
  printf(" 5  6 %9.6f \n", dist(vert[5],vert[6]));
  printf(" 6  2 %9.6f \n", dist(vert[6],vert[2]));

  printf(" 7  8 %9.6f \n", dist(vert[7],vert[8]));
  printf(" 8  9 %9.6f \n", dist(vert[8],vert[9]));
  printf(" 9 10 %9.6f \n", dist(vert[9],vert[10]));
  printf("10 11 %9.6f \n", dist(vert[10],vert[11]));
  printf("11 12 %9.6f \n", dist(vert[11],vert[12]));
  printf("12 13 %9.6f \n", dist(vert[12],vert[13]));
  printf("13 14 %9.6f \n", dist(vert[13],vert[14]));
  printf("14 15 %9.6f \n", dist(vert[14],vert[15]));
  printf("15 16 %9.6f \n", dist(vert[15],vert[16]));
  printf("16  7 %9.6f \n", dist(vert[16],vert[7]));

  printf(" 2 17 %9.6f \n", dist(vert[2],vert[17]));
  printf(" 3 17 %9.6f \n", dist(vert[3],vert[17]));
  printf(" 3 18 %9.6f \n", dist(vert[3],vert[18]));
  printf(" 4 18 %9.6f \n", dist(vert[4],vert[18]));
  printf(" 4 19 %9.6f \n", dist(vert[4],vert[19]));
  printf(" 5 19 %9.6f \n", dist(vert[5],vert[19]));
  printf(" 5 20 %9.6f \n", dist(vert[5],vert[20]));
  printf(" 6 20 %9.6f \n", dist(vert[6],vert[20]));
  printf(" 6 21 %9.6f \n", dist(vert[6],vert[21]));
  printf(" 2 21 %9.6f \n", dist(vert[2],vert[21]));

  printf(" 7 17 %9.6f \n", dist(vert[7],vert[17]));
  printf(" 8 17 %9.6f \n", dist(vert[8],vert[17]));
  printf(" 9 18 %9.6f \n", dist(vert[9],vert[18]));
  printf("10 18 %9.6f \n", dist(vert[10],vert[18]));
  printf("11 19 %9.6f \n", dist(vert[11],vert[19]));
  printf("12 19 %9.6f \n", dist(vert[12],vert[19]));
  printf("13 20 %9.6f \n", dist(vert[13],vert[20]));
  printf("14 20 %9.6f \n", dist(vert[14],vert[20]));
  printf("15 21 %9.6f \n", dist(vert[15],vert[21]));
  printf("16 21 %9.6f \n", dist(vert[16],vert[21]));
 
  printf("\n");
  printf("triangle cover, CCW looking at outside \n");
  printf("top half including equator \n");
  printf("3  1  3  2 \n");
  printf("3  1  4  3 \n");
  printf("3  1  5  4 \n");
  printf("3  1  6  5 \n");
  printf("3  1  2  6 \n");
  printf("3  2  3 17 \n");
  printf("3  3 23 17 \n");
  printf("3  3 18 23 \n");
  printf("3  3  4 18 \n");
  printf("3  4 24 18 \n");
  printf("3  4 19 24 \n");
  printf("3  4  5 19 \n");
  printf("3  5 25 19 \n");
  printf("3  5 20 25 \n");
  printf("3  5  6 20 \n");
  printf("3  6 26 20 \n");
  printf("3  6 21 26 \n");
  printf("3  6  2 21 \n");
  printf("3  2 22 21 \n");
  printf("3  2 17 22 \n");
  printf("3  7 17  8 \n");
  printf("3  8 17 23 \n");
  printf("3  8 23  9 \n");
  printf("3  9 23 18 \n");
  printf("3  9 18 10 \n");
  printf("3 10 18 24 \n");
  printf("3 10 24 11 \n");
  printf("3 11 24 19 \n");
  printf("3 11 19 12 \n");
  printf("3 12 19 25 \n");
  printf("3 12 25 13 \n");
  printf("3 13 25 20 \n");
  printf("3 13 20 14 \n");
  printf("3 14 20 26 \n");
  printf("3 14 26 15 \n");
  printf("3 15 26 21 \n");
  printf("3 15 21 16 \n");
  printf("3 16 21 22 \n");
  printf("3 16 22  7 \n");
  printf("3  7 22 17 \n");
  printf("3  7 17  8 \n");
  printf("3  8 23  9 \n");
  printf("3  9 18 10 \n");
  printf("3 10 24 11 \n");
  printf("3 11 19 12 \n");
  printf("3 12 25 13 \n");
  printf("3 13 20 14 \n");
  printf("3 14 26 15 \n");
  printf("3 15 21 16 \n");
  printf("3 16 22  7 \n");

  printf("\n");
  printf("bottom up, shift pi/10 circle, 18 degrees \n");

  printf("sphereh.c Buckminster Fuller bottom half sphere\n");

  vert[nvert].x = 0.0; /* top of sphere  27*/
  vert[nvert].y = 0.0;
  vert[nvert].z = -1.0;  
  nvert++;

                       /* bottom pentagon */
  for(i=0; i<5; i++)
  {
    printf("vert %2d being rotated to %2d\n", nvert-26, nvert); 
    vert[nvert] = rotate(vert[nvert-26]);
    nvert++;
  }

  printf("\n");

  printf("not equator, only once, have %d vert \n",nvert);

                       /* southern 1/2 */
  for(i=0; i<5; i++)
  {
    printf("vert %2d being rotated to %2d\n", nvert-16, nvert); 
    vert[nvert] = rotate(vert[nvert-16]);
    nvert++;
  }
                       /* southern 2/2 */
  for(i=0; i<5; i++)
  {
    printf("vert %2d being rotated to %2d\n", nvert-16, nvert); 
    vert[nvert] = rotate(vert[nvert-16]);
    nvert++;
  }

  printf("bottom vertex number and coordinates \n");
  for(i=tvert; i<nvert; i++)
  {
    printf("%d  %9.6f  %9.6f  %9.6f \n", i, vert[i].x, vert[i].y, vert[i].z);
  }

  printf("\ndistance check \n");
  printf("\nblue branches, groups of five \n");
  printf(" 27  28 %9.6f \n", dist(vert[27],vert[28]));
  printf(" 27  29 %9.6f \n", dist(vert[27],vert[29]));
  printf(" 27  30 %9.6f \n", dist(vert[27],vert[30]));
  printf(" 27  31 %9.6f \n", dist(vert[27],vert[31]));
  printf(" 27  32 %9.6f \n", dist(vert[27],vert[32]));

  printf(" 38   7 %9.6f \n", dist(vert[38],vert[ 7]));
  printf(" 38   8 %9.6f \n", dist(vert[38],vert[ 8]));
  printf(" 38  28 %9.6f \n", dist(vert[38],vert[28]));
  printf(" 38  33 %9.6f \n", dist(vert[38],vert[33]));
  printf(" 38  37 %9.6f \n", dist(vert[38],vert[37]));

  printf(" 39   9 %9.6f \n", dist(vert[39],vert[ 9]));
  printf(" 39  10 %9.6f \n", dist(vert[39],vert[10]));
  printf(" 39  29 %9.6f \n", dist(vert[39],vert[29]));
  printf(" 39  33 %9.6f \n", dist(vert[39],vert[33]));
  printf(" 39  34 %9.6f \n", dist(vert[39],vert[34]));

  printf(" 40  11 %9.6f \n", dist(vert[40],vert[11]));
  printf(" 40  12 %9.6f \n", dist(vert[40],vert[12]));
  printf(" 40  30 %9.6f \n", dist(vert[40],vert[30]));
  printf(" 40  34 %9.6f \n", dist(vert[40],vert[34]));
  printf(" 40  35 %9.6f \n", dist(vert[40],vert[35]));

  printf(" 41  13 %9.6f \n", dist(vert[41],vert[13]));
  printf(" 41  14 %9.6f \n", dist(vert[41],vert[14]));
  printf(" 41  31 %9.6f \n", dist(vert[41],vert[31]));
  printf(" 41  35 %9.6f \n", dist(vert[41],vert[35]));
  printf(" 41  36 %9.6f \n", dist(vert[41],vert[36]));

  printf(" 42  15 %9.6f \n", dist(vert[42],vert[15]));
  printf(" 42  16 %9.6f \n", dist(vert[42],vert[16]));
  printf(" 42  32 %9.6f \n", dist(vert[42],vert[32]));
  printf(" 42  36 %9.6f \n", dist(vert[42],vert[36]));
  printf(" 42  37 %9.6f \n", dist(vert[42],vert[37]));

  printf("\nyellow branches \n");
  printf(" 28  29 %9.6f \n", dist(vert[28],vert[29]));
  printf(" 28  37 %9.6f \n", dist(vert[28],vert[37]));
  printf(" 28  32 %9.6f \n", dist(vert[28],vert[32]));
  printf(" 28  33 %9.6f \n", dist(vert[28],vert[33]));
  printf(" 29  28 %9.6f \n", dist(vert[29],vert[28]));
  printf(" 29  30 %9.6f \n", dist(vert[29],vert[30]));
  printf(" 29  33 %9.6f \n", dist(vert[29],vert[33]));
  printf(" 29  34 %9.6f \n", dist(vert[29],vert[34]));
  printf(" 30  29 %9.6f \n", dist(vert[30],vert[29]));
  printf(" 30  31 %9.6f \n", dist(vert[30],vert[31]));
  printf(" 30  34 %9.6f \n", dist(vert[30],vert[34]));
  printf(" 30  35 %9.6f \n", dist(vert[30],vert[35]));
  printf(" 31  32 %9.6f \n", dist(vert[31],vert[32]));
  printf(" 31  36 %9.6f \n", dist(vert[31],vert[36]));
  printf(" 31  35 %9.6f \n", dist(vert[31],vert[35]));
  printf(" 31  36 %9.6f \n", dist(vert[31],vert[36]));
  printf(" 32  36 %9.6f \n", dist(vert[32],vert[36]));
  printf(" 32  37 %9.6f \n", dist(vert[32],vert[37]));
  printf(" 32  31 %9.6f \n", dist(vert[32],vert[31]));
  printf(" 32  28 %9.6f \n", dist(vert[32],vert[28]));
  printf(" 33   8 %9.6f \n", dist(vert[33],vert[ 8]));
  printf(" 33   9 %9.6f \n", dist(vert[33],vert[ 9]));
  printf(" 33  28 %9.6f \n", dist(vert[33],vert[28]));
  printf(" 33  29 %9.6f \n", dist(vert[33],vert[29]));
  printf(" 34  10 %9.6f \n", dist(vert[34],vert[10]));
  printf(" 34  11 %9.6f \n", dist(vert[34],vert[11]));
  printf(" 34  29 %9.6f \n", dist(vert[34],vert[29]));
  printf(" 34  30 %9.6f \n", dist(vert[34],vert[30]));

  printf("\n");
  printf("triangle cover, CCW looking at outside \n");
  printf("bottom half to equator \n");



  printf("3  7 38 37 \n");
  printf("3  8 33 38 \n");
  printf("3  9 39 33 \n");
  printf("3 10 34 39 \n");
  printf("3 11 40 34 \n");
  printf("3 12 35 40 \n");
  printf("3 13 41 35 \n");
  printf("3 14 36 41 \n");
  printf("3 15 42 36 \n");
  printf("3 16 37 42 \n");
  printf("3 27 28 29 \n");
  printf("3 27 29 30 \n");
  printf("3 27 30 31 \n");
  printf("3 27 31 32 \n");
  printf("3 27 32 28 \n");
  printf("3 28 37 38 \n");
  printf("3 28 38 33 \n");
  printf("3 28 33 29 \n");
  printf("3 29 33 39 \n");
  printf("3 29 39 34 \n");
  printf("3 29 34 30 \n");
  printf("3 30 34 40 \n");
  printf("3 30 40 35 \n");
  printf("3 30 35 31 \n");
  printf("3 31 35 41 \n");
  printf("3 31 41 36 \n");
  printf("3 31 36 32 \n");
  printf("3 32 36 42 \n");
  printf("3 32 42 37 \n");
  printf("3 32 37 28 \n");
  printf("3  7 37 16 \n");
  printf("3  7  8 38 \n");
  printf("3  8  9 33 \n");
  printf("3  9 10 39 \n");
  printf("3 10 11 34 \n");
  printf("3 11 12 40 \n");
  printf("3 12 13 35 \n");
  printf("3 13 14 41 \n");
  printf("3 14 15 36 \n");
  printf("3 15 16 42 \n");

  printf("\nend sphereh Buckminster Fuller sphere in bball.dat \n");
  return 0;
}