mayakraft/Platonic Solids

## Platonic Solids
// the 5 platonic solids
//
//  + point coordinates
//  + the related drawing functions
//  + a rotate in 3D function, around the origin
//
// written for Processing (processing.org)

  int xCenter =  // center of polyhedra
  int yCenter =  // center of polyhedra
  int r =  // radius of polyhedra(approximately in pixels)

  float phi = (float)(1+Math.sqrt(5))/2;
  float sqrt3 = (float)Math.sqrt(3);

  tetrahedronX[0] =  1/sqrt3;    tetrahedronY[0] =  1/sqrt3;    tetrahedronZ[0] =  1/sqrt3;
  tetrahedronX[1] = -1/sqrt3;    tetrahedronY[1] =  1/sqrt3;    tetrahedronZ[1] = -1/sqrt3;
  tetrahedronX[2] = -1/sqrt3;    tetrahedronY[2] = -1/sqrt3;    tetrahedronZ[2] =  1/sqrt3;
  tetrahedronX[3] =  1/sqrt3;    tetrahedronY[3] = -1/sqrt3;    tetrahedronZ[3] = -1/sqrt3;

  octahedronX[0] =  0;    octahedronY[0] =  1;    octahedronZ[0] =  0;
  octahedronX[1] =  1;    octahedronY[1] =  0;    octahedronZ[1] =  0;
  octahedronX[2] =  0;    octahedronY[2] =  0;    octahedronZ[2] =  1;
  octahedronX[3] = -1;    octahedronY[3] =  0;    octahedronZ[3] =  0;
  octahedronX[4] =  0;    octahedronY[4] =  0;    octahedronZ[4] = -1;
  octahedronX[5] =  0;    octahedronY[5] = -1;    octahedronZ[5] =  0;

  hexahedronX[0] =  1/sqrt3;    hexahedronY[0] =  1/sqrt3;    hexahedronZ[0] =  1/sqrt3;
  hexahedronX[1] = -1/sqrt3;    hexahedronY[1] =  1/sqrt3;    hexahedronZ[1] =  1/sqrt3;
  hexahedronX[2] =  1/sqrt3;    hexahedronY[2] =  1/sqrt3;    hexahedronZ[2] = -1/sqrt3;
  hexahedronX[3] = -1/sqrt3;    hexahedronY[3] =  1/sqrt3;    hexahedronZ[3] = -1/sqrt3;
  hexahedronX[4] =  1/sqrt3;    hexahedronY[4] = -1/sqrt3;    hexahedronZ[4] =  1/sqrt3;
  hexahedronX[5] = -1/sqrt3;    hexahedronY[5] = -1/sqrt3;    hexahedronZ[5] =  1/sqrt3;
  hexahedronX[6] =  1/sqrt3;    hexahedronY[6] = -1/sqrt3;    hexahedronZ[6] = -1/sqrt3;
  hexahedronX[7] = -1/sqrt3;    hexahedronY[7] = -1/sqrt3;    hexahedronZ[7] = -1/sqrt3;

  icosahedronX[0] = (float)(-1/Math.sqrt(phi*phi+1));      icosahedronY[0] =  (float)(1*phi/Math.sqrt(phi*phi+1));  icosahedronZ[0] = 0;
  icosahedronX[1] =  (float)(1/Math.sqrt(phi*phi+1));      icosahedronY[1] =  (float)(1*phi/Math.sqrt(phi*phi+1));  icosahedronZ[1] = 0;
  icosahedronX[2] = (float)(-1/Math.sqrt(phi*phi+1));      icosahedronY[2] = (float)(-1*phi/Math.sqrt(phi*phi+1));  icosahedronZ[2] = 0;
  icosahedronX[3] =  (float)(1/Math.sqrt(phi*phi+1));      icosahedronY[3] = (float)(-1*phi/Math.sqrt(phi*phi+1));  icosahedronZ[3] = 0;
  icosahedronX[4] = 0;                                     icosahedronY[4] =  (float)(1/Math.sqrt(phi*phi+1));      icosahedronZ[4] =   (float)(1*phi/Math.sqrt(phi*phi+1));
  icosahedronX[5] = 0;                                     icosahedronY[5] = (float)(-1/Math.sqrt(phi*phi+1));      icosahedronZ[5] =   (float)(1*phi/Math.sqrt(phi*phi+1));
  icosahedronX[6] = 0;                                     icosahedronY[6] =  (float)(1/Math.sqrt(phi*phi+1));      icosahedronZ[6] =  (float)(-1*phi/Math.sqrt(phi*phi+1));
  icosahedronX[7] = 0;                                     icosahedronY[7] = (float)(-1/Math.sqrt(phi*phi+1));      icosahedronZ[7] =  (float)(-1*phi/Math.sqrt(phi*phi+1));
  icosahedronX[8] =   (float)(1*phi/Math.sqrt(phi*phi+1)); icosahedronY[8] = 0;                                     icosahedronZ[8] =   (float)(1/Math.sqrt(phi*phi+1));
  icosahedronX[9] =   (float)(1*phi/Math.sqrt(phi*phi+1)); icosahedronY[9] = 0;                                     icosahedronZ[9] =  (float)(-1/Math.sqrt(phi*phi+1));
  icosahedronX[10] = (float)(-1*phi/Math.sqrt(phi*phi+1)); icosahedronY[10] = 0;                                    icosahedronZ[10] =  (float)(1/Math.sqrt(phi*phi+1));
  icosahedronX[11] = (float)(-1*phi/Math.sqrt(phi*phi+1)); icosahedronY[11] = 0;                                    icosahedronZ[11] = (float)(-1/Math.sqrt(phi*phi+1));

  dodecahedronX[0] = 1/sqrt3;          dodecahedronY[0] = 1/sqrt3;          dodecahedronZ[0] = 1/sqrt3;
  dodecahedronX[1] = 1/sqrt3;          dodecahedronY[1] = 1/sqrt3;          dodecahedronZ[1] = -1/sqrt3;
  dodecahedronX[2] = 1/sqrt3;          dodecahedronY[2] = -1/sqrt3;         dodecahedronZ[2] = 1/sqrt3;
  dodecahedronX[3] = 1/sqrt3;          dodecahedronY[3] = -1/sqrt3;         dodecahedronZ[3] = -1/sqrt3;
  dodecahedronX[4] = -1/sqrt3;         dodecahedronY[4] = 1/sqrt3;          dodecahedronZ[4] = 1/sqrt3;
  dodecahedronX[5] = -1/sqrt3;         dodecahedronY[5] = 1/sqrt3;          dodecahedronZ[5] = -1/sqrt3;
  dodecahedronX[6] = -1/sqrt3;         dodecahedronY[6] = -1/sqrt3;         dodecahedronZ[6] = 1/sqrt3;
  dodecahedronX[7] = -1/sqrt3;         dodecahedronY[7] = -1/sqrt3;         dodecahedronZ[7] = -1/sqrt3;
  dodecahedronX[8] = 0;                dodecahedronY[8] = 1/(phi*sqrt3);    dodecahedronZ[8] = phi/sqrt3;
  dodecahedronX[9] = 0;                dodecahedronY[9] = 1/(phi*sqrt3);    dodecahedronZ[9] = -phi/sqrt3;
  dodecahedronX[10] = 0;               dodecahedronY[10] = -1/(phi*sqrt3);  dodecahedronZ[10] = phi/sqrt3;
  dodecahedronX[11] = 0;               dodecahedronY[11] = -1/(phi*sqrt3);  dodecahedronZ[11] = -phi/sqrt3;
  dodecahedronX[12] = phi/sqrt3;       dodecahedronY[12] = 0;               dodecahedronZ[12] = 1/(phi*sqrt3);
  dodecahedronX[13] = phi/sqrt3;       dodecahedronY[13] = 0;               dodecahedronZ[13] = -1/(phi*sqrt3);
  dodecahedronX[14] = -phi/sqrt3;      dodecahedronY[14] = 0;               dodecahedronZ[14] = 1/(phi*sqrt3);
  dodecahedronX[15] = -phi/sqrt3;      dodecahedronY[15] = 0;               dodecahedronZ[15] = -1/(phi*sqrt3);
  dodecahedronX[16] = 1/(phi*sqrt3);   dodecahedronY[16] = phi/sqrt3;       dodecahedronZ[16] = 0;
  dodecahedronX[17] = 1/(phi*sqrt3);   dodecahedronY[17] = -phi/sqrt3;      dodecahedronZ[17] = 0;
  dodecahedronX[18] = -1/(phi*sqrt3);  dodecahedronY[18] = phi/sqrt3;       dodecahedronZ[18] = 0;
  dodecahedronX[19] = -1/(phi*sqrt3);  dodecahedronY[19] = -phi/sqrt3;      dodecahedronZ[19] = 0;


void drawTetrahedron(){
  line(xCenter+r*tetrahedronX[0],yCenter+r*tetrahedronY[0], xCenter+r*tetrahedronX[1],yCenter+r*tetrahedronY[1]);
  line(xCenter+r*tetrahedronX[1],yCenter+r*tetrahedronY[1], xCenter+r*tetrahedronX[2],yCenter+r*tetrahedronY[2]);
  line(xCenter+r*tetrahedronX[2],yCenter+r*tetrahedronY[2], xCenter+r*tetrahedronX[0],yCenter+r*tetrahedronY[0]);
  line(xCenter+r*tetrahedronX[0],yCenter+r*tetrahedronY[0], xCenter+r*tetrahedronX[3],yCenter+r*tetrahedronY[3]);
  line(xCenter+r*tetrahedronX[3],yCenter+r*tetrahedronY[3], xCenter+r*tetrahedronX[1],yCenter+r*tetrahedronY[1]);
  line(xCenter+r*tetrahedronX[2],yCenter+r*tetrahedronY[2], xCenter+r*tetrahedronX[3],yCenter+r*tetrahedronY[3]);
}

void drawOctahedron(){
  line(xCenter+r*octahedronX[0],yCenter+r*octahedronY[0], xCenter+r*octahedronX[1],yCenter+r*octahedronY[1]);
  line(xCenter+r*octahedronX[1],yCenter+r*octahedronY[1], xCenter+r*octahedronX[2],yCenter+r*octahedronY[2]);
  line(xCenter+r*octahedronX[2],yCenter+r*octahedronY[2], xCenter+r*octahedronX[0],yCenter+r*octahedronY[0]);
  line(xCenter+r*octahedronX[0],yCenter+r*octahedronY[0], xCenter+r*octahedronX[3],yCenter+r*octahedronY[3]);
  line(xCenter+r*octahedronX[3],yCenter+r*octahedronY[3], xCenter+r*octahedronX[4],yCenter+r*octahedronY[4]);
  line(xCenter+r*octahedronX[4],yCenter+r*octahedronY[4], xCenter+r*octahedronX[0],yCenter+r*octahedronY[0]);
  line(xCenter+r*octahedronX[5],yCenter+r*octahedronY[5], xCenter+r*octahedronX[4],yCenter+r*octahedronY[4]);
  line(xCenter+r*octahedronX[4],yCenter+r*octahedronY[4], xCenter+r*octahedronX[1],yCenter+r*octahedronY[1]);
  line(xCenter+r*octahedronX[1],yCenter+r*octahedronY[1], xCenter+r*octahedronX[5],yCenter+r*octahedronY[5]);
  line(xCenter+r*octahedronX[5],yCenter+r*octahedronY[5], xCenter+r*octahedronX[2],yCenter+r*octahedronY[2]);
  line(xCenter+r*octahedronX[2],yCenter+r*octahedronY[2], xCenter+r*octahedronX[3],yCenter+r*octahedronY[3]);
  line(xCenter+r*octahedronX[3],yCenter+r*octahedronY[3], xCenter+r*octahedronX[5],yCenter+r*octahedronY[5]);
}

void drawHexahedron(){
  line(xCenter+r*hexahedronX[0],yCenter+r*hexahedronY[0], xCenter+r*hexahedronX[1],yCenter+r*hexahedronY[1]);
  line(xCenter+r*hexahedronX[1],yCenter+r*hexahedronY[1], xCenter+r*hexahedronX[3],yCenter+r*hexahedronY[3]);
  line(xCenter+r*hexahedronX[3],yCenter+r*hexahedronY[3], xCenter+r*hexahedronX[2],yCenter+r*hexahedronY[2]);
  line(xCenter+r*hexahedronX[2],yCenter+r*hexahedronY[2], xCenter+r*hexahedronX[0],yCenter+r*hexahedronY[0]);
  line(xCenter+r*hexahedronX[0],yCenter+r*hexahedronY[0], xCenter+r*hexahedronX[4],yCenter+r*hexahedronY[4]);
  line(xCenter+r*hexahedronX[4],yCenter+r*hexahedronY[4], xCenter+r*hexahedronX[5],yCenter+r*hexahedronY[5]);
  line(xCenter+r*hexahedronX[5],yCenter+r*hexahedronY[5], xCenter+r*hexahedronX[7],yCenter+r*hexahedronY[7]);
  line(xCenter+r*hexahedronX[7],yCenter+r*hexahedronY[7], xCenter+r*hexahedronX[6],yCenter+r*hexahedronY[6]);
  line(xCenter+r*hexahedronX[6],yCenter+r*hexahedronY[6], xCenter+r*hexahedronX[4],yCenter+r*hexahedronY[4]);
  line(xCenter+r*hexahedronX[1],yCenter+r*hexahedronY[1], xCenter+r*hexahedronX[5],yCenter+r*hexahedronY[5]);
  line(xCenter+r*hexahedronX[3],yCenter+r*hexahedronY[3], xCenter+r*hexahedronX[7],yCenter+r*hexahedronY[7]);
  line(xCenter+r*hexahedronX[2],yCenter+r*hexahedronY[2], xCenter+r*hexahedronX[6],yCenter+r*hexahedronY[6]);
}

void drawIcosahedron(){
  line(xCenter+r*icosahedronX[1],yCenter+r*icosahedronY[1], xCenter+r*icosahedronX[8],yCenter+r*icosahedronY[8]);
  line(xCenter+r*icosahedronX[8],yCenter+r*icosahedronY[8], xCenter+r*icosahedronX[4],yCenter+r*icosahedronY[4]);
  line(xCenter+r*icosahedronX[4],yCenter+r*icosahedronY[4], xCenter+r*icosahedronX[5],yCenter+r*icosahedronY[5]);
  line(xCenter+r*icosahedronX[5],yCenter+r*icosahedronY[5], xCenter+r*icosahedronX[10],yCenter+r*icosahedronY[10]);
  line(xCenter+r*icosahedronX[10],yCenter+r*icosahedronY[10], xCenter+r*icosahedronX[2],yCenter+r*icosahedronY[2]);
  line(xCenter+r*icosahedronX[2],yCenter+r*icosahedronY[2], xCenter+r*icosahedronX[11],yCenter+r*icosahedronY[11]);
  line(xCenter+r*icosahedronX[11],yCenter+r*icosahedronY[11], xCenter+r*icosahedronX[7],yCenter+r*icosahedronY[7]);
  line(xCenter+r*icosahedronX[7],yCenter+r*icosahedronY[7], xCenter+r*icosahedronX[6],yCenter+r*icosahedronY[6]);
  line(xCenter+r*icosahedronX[6],yCenter+r*icosahedronY[6], xCenter+r*icosahedronX[9],yCenter+r*icosahedronY[9]);
  line(xCenter+r*icosahedronX[9],yCenter+r*icosahedronY[9], xCenter+r*icosahedronX[1],yCenter+r*icosahedronY[1]);
  line(xCenter+r*icosahedronX[1],yCenter+r*icosahedronY[1], xCenter+r*icosahedronX[4],yCenter+r*icosahedronY[4]);
  line(xCenter+r*icosahedronX[4],yCenter+r*icosahedronY[4], xCenter+r*icosahedronX[10],yCenter+r*icosahedronY[10]);
  line(xCenter+r*icosahedronX[10],yCenter+r*icosahedronY[10], xCenter+r*icosahedronX[11],yCenter+r*icosahedronY[11]);
  line(xCenter+r*icosahedronX[11],yCenter+r*icosahedronY[11], xCenter+r*icosahedronX[6],yCenter+r*icosahedronY[6]);
  line(xCenter+r*icosahedronX[6],yCenter+r*icosahedronY[6], xCenter+r*icosahedronX[1],yCenter+r*icosahedronY[1]);
  line(xCenter+r*icosahedronX[1],yCenter+r*icosahedronY[1], xCenter+r*icosahedronX[0],yCenter+r*icosahedronY[0]);
  line(xCenter+r*icosahedronX[0],yCenter+r*icosahedronY[0], xCenter+r*icosahedronX[4],yCenter+r*icosahedronY[4]);
  line(xCenter+r*icosahedronX[10],yCenter+r*icosahedronY[10], xCenter+r*icosahedronX[0],yCenter+r*icosahedronY[0]);
  line(xCenter+r*icosahedronX[0],yCenter+r*icosahedronY[0], xCenter+r*icosahedronX[11],yCenter+r*icosahedronY[11]);
  line(xCenter+r*icosahedronX[6],yCenter+r*icosahedronY[6], xCenter+r*icosahedronX[0],yCenter+r*icosahedronY[0]);
  line(xCenter+r*icosahedronX[8],yCenter+r*icosahedronY[8], xCenter+r*icosahedronX[5],yCenter+r*icosahedronY[5]);
  line(xCenter+r*icosahedronX[5],yCenter+r*icosahedronY[5], xCenter+r*icosahedronX[2],yCenter+r*icosahedronY[2]);
  line(xCenter+r*icosahedronX[2],yCenter+r*icosahedronY[2], xCenter+r*icosahedronX[7],yCenter+r*icosahedronY[7]);
  line(xCenter+r*icosahedronX[7],yCenter+r*icosahedronY[7], xCenter+r*icosahedronX[9],yCenter+r*icosahedronY[9]);
  line(xCenter+r*icosahedronX[9],yCenter+r*icosahedronY[9], xCenter+r*icosahedronX[8],yCenter+r*icosahedronY[8]);
  line(xCenter+r*icosahedronX[8],yCenter+r*icosahedronY[8], xCenter+r*icosahedronX[3],yCenter+r*icosahedronY[3]);
  line(xCenter+r*icosahedronX[3],yCenter+r*icosahedronY[3], xCenter+r*icosahedronX[5],yCenter+r*icosahedronY[5]);
  line(xCenter+r*icosahedronX[2],yCenter+r*icosahedronY[2], xCenter+r*icosahedronX[3],yCenter+r*icosahedronY[3]);
  line(xCenter+r*icosahedronX[3],yCenter+r*icosahedronY[3], xCenter+r*icosahedronX[7],yCenter+r*icosahedronY[7]);
  line(xCenter+r*icosahedronX[9],yCenter+r*icosahedronY[9], xCenter+r*icosahedronX[3],yCenter+r*icosahedronY[3]);
  line(xCenter+r*icosahedronX[3],yCenter+r*icosahedronY[3], xCenter+r*icosahedronX[8],yCenter+r*icosahedronY[8]);
}

void drawDodecahedron(){
  line(xCenter+r*dodecahedronX[0],yCenter+r*dodecahedronY[0], xCenter+r*dodecahedronX[12],yCenter+r*dodecahedronY[12]);
  line(xCenter+r*dodecahedronX[12],yCenter+r*dodecahedronY[12], xCenter+r*dodecahedronX[13],yCenter+r*dodecahedronY[13]);
  line(xCenter+r*dodecahedronX[13],yCenter+r*dodecahedronY[13], xCenter+r*dodecahedronX[1],yCenter+r*dodecahedronY[1]);
  line(xCenter+r*dodecahedronX[1],yCenter+r*dodecahedronY[1], xCenter+r*dodecahedronX[16],yCenter+r*dodecahedronY[16]);
  line(xCenter+r*dodecahedronX[16],yCenter+r*dodecahedronY[16], xCenter+r*dodecahedronX[0],yCenter+r*dodecahedronY[0]);
  line(xCenter+r*dodecahedronX[16],yCenter+r*dodecahedronY[16], xCenter+r*dodecahedronX[18],yCenter+r*dodecahedronY[18]);
  line(xCenter+r*dodecahedronX[18],yCenter+r*dodecahedronY[18], xCenter+r*dodecahedronX[4],yCenter+r*dodecahedronY[4]);
  line(xCenter+r*dodecahedronX[4],yCenter+r*dodecahedronY[4], xCenter+r*dodecahedronX[8],yCenter+r*dodecahedronY[8]);
  line(xCenter+r*dodecahedronX[12],yCenter+r*dodecahedronY[12], xCenter+r*dodecahedronX[2],yCenter+r*dodecahedronY[2]);
  line(xCenter+r*dodecahedronX[2],yCenter+r*dodecahedronY[2], xCenter+r*dodecahedronX[17],yCenter+r*dodecahedronY[17]);
  line(xCenter+r*dodecahedronX[17],yCenter+r*dodecahedronY[17], xCenter+r*dodecahedronX[3],yCenter+r*dodecahedronY[3]);
  line(xCenter+r*dodecahedronX[3],yCenter+r*dodecahedronY[3], xCenter+r*dodecahedronX[13],yCenter+r*dodecahedronY[13]);
  line(xCenter+r*dodecahedronX[0],yCenter+r*dodecahedronY[0], xCenter+r*dodecahedronX[8],yCenter+r*dodecahedronY[8]);
  line(xCenter+r*dodecahedronX[8],yCenter+r*dodecahedronY[8], xCenter+r*dodecahedronX[10],yCenter+r*dodecahedronY[10]);
  line(xCenter+r*dodecahedronX[10],yCenter+r*dodecahedronY[10], xCenter+r*dodecahedronX[2],yCenter+r*dodecahedronY[2]);
  line(xCenter+r*dodecahedronX[1],yCenter+r*dodecahedronY[1], xCenter+r*dodecahedronX[9],yCenter+r*dodecahedronY[9]);
  line(xCenter+r*dodecahedronX[9],yCenter+r*dodecahedronY[9], xCenter+r*dodecahedronX[11],yCenter+r*dodecahedronY[11]);
  line(xCenter+r*dodecahedronX[11],yCenter+r*dodecahedronY[11], xCenter+r*dodecahedronX[3],yCenter+r*dodecahedronY[3]);
  line(xCenter+r*dodecahedronX[11],yCenter+r*dodecahedronY[11], xCenter+r*dodecahedronX[7],yCenter+r*dodecahedronY[7]);
  line(xCenter+r*dodecahedronX[7],yCenter+r*dodecahedronY[7], xCenter+r*dodecahedronX[19],yCenter+r*dodecahedronY[19]);
  line(xCenter+r*dodecahedronX[10],yCenter+r*dodecahedronY[10], xCenter+r*dodecahedronX[6],yCenter+r*dodecahedronY[6]);
  line(xCenter+r*dodecahedronX[6],yCenter+r*dodecahedronY[6], xCenter+r*dodecahedronX[19],yCenter+r*dodecahedronY[19]);
  line(xCenter+r*dodecahedronX[19],yCenter+r*dodecahedronY[19], xCenter+r*dodecahedronX[17],yCenter+r*dodecahedronY[17]);
  line(xCenter+r*dodecahedronX[18],yCenter+r*dodecahedronY[18], xCenter+r*dodecahedronX[5],yCenter+r*dodecahedronY[5]);
  line(xCenter+r*dodecahedronX[5],yCenter+r*dodecahedronY[5], xCenter+r*dodecahedronX[9],yCenter+r*dodecahedronY[9]);
  line(xCenter+r*dodecahedronX[5],yCenter+r*dodecahedronY[5], xCenter+r*dodecahedronX[15],yCenter+r*dodecahedronY[15]);
  line(xCenter+r*dodecahedronX[15],yCenter+r*dodecahedronY[15], xCenter+r*dodecahedronX[7],yCenter+r*dodecahedronY[7]);
  line(xCenter+r*dodecahedronX[15],yCenter+r*dodecahedronY[15], xCenter+r*dodecahedronX[14],yCenter+r*dodecahedronY[14]);
  line(xCenter+r*dodecahedronX[14],yCenter+r*dodecahedronY[14], xCenter+r*dodecahedronX[4],yCenter+r*dodecahedronY[4]);
  line(xCenter+r*dodecahedronX[14],yCenter+r*dodecahedronY[14], xCenter+r*dodecahedronX[6],yCenter+r*dodecahedronY[6]);
}

void rotatePoints(float[] pointsX, //
                  float[] pointsY, // 3 arrays of coordinates: X, Y, and Z
                  float[] pointsZ, //
                  float increment, // angle of rotation (in radians)
                  char axis)       //axis: x=0,y=1,z=2
{
  float angle;
  float rad;
  if(axis=='X' || axis == 'x'){
    for(j=0;j<pointsX.length;j++){
      rad = (float)Math.sqrt(pointsZ[j]*pointsZ[j]+pointsY[j]*pointsY[j]);
      angle=(float)Math.atan2(pointsZ[j],pointsY[j]);
      angle+=increment;
      pointsZ[j] = (float)( rad*Math.sin(angle) );
      pointsY[j] = (float)( rad*Math.cos(angle) );
    }
  }
  else if(axis=='Y' || axis=='y'){
    for(j=0;j<pointsY.length;j++){
      rad = (float)Math.sqrt(pointsZ[j]*pointsZ[j]+pointsX[j]*pointsX[j]);
      angle=(float)Math.atan2(pointsZ[j],pointsX[j]);
      angle+=increment;
      pointsZ[j] = (float)( rad*Math.sin(angle) );
      pointsX[j] = (float)( rad*Math.cos(angle) );
    }
  }
  else if(axis=='Z' || axis == 'z'){
    for(j=0;j<pointsZ.length;j++){
      rad = (float)Math.sqrt(pointsX[j]*pointsX[j]+pointsY[j]*pointsY[j]);
      angle=(float)Math.atan2(pointsY[j],pointsX[j]);
      angle+=increment;
      pointsY[j] = (float)( rad*Math.sin(angle) );
      pointsX[j] = (float)( rad*Math.cos(angle) );
    }
  }
}
	// the 5 platonic solids
	//
	// + point coordinates
	// + the related drawing functions
	// + a rotate in 3D function, around the origin
	//
	// written for Processing (processing.org)

	int xCenter = // center of polyhedra
	int yCenter = // center of polyhedra
	int r = // radius of polyhedra(approximately in pixels)

	float phi = (float)(1+Math.sqrt(5))/2;
	float sqrt3 = (float)Math.sqrt(3);

	tetrahedronX[0] = 1/sqrt3; tetrahedronY[0] = 1/sqrt3; tetrahedronZ[0] = 1/sqrt3;
	tetrahedronX[1] = -1/sqrt3; tetrahedronY[1] = 1/sqrt3; tetrahedronZ[1] = -1/sqrt3;
	tetrahedronX[2] = -1/sqrt3; tetrahedronY[2] = -1/sqrt3; tetrahedronZ[2] = 1/sqrt3;
	tetrahedronX[3] = 1/sqrt3; tetrahedronY[3] = -1/sqrt3; tetrahedronZ[3] = -1/sqrt3;

	octahedronX[0] = 0; octahedronY[0] = 1; octahedronZ[0] = 0;
	octahedronX[1] = 1; octahedronY[1] = 0; octahedronZ[1] = 0;
	octahedronX[2] = 0; octahedronY[2] = 0; octahedronZ[2] = 1;
	octahedronX[3] = -1; octahedronY[3] = 0; octahedronZ[3] = 0;
	octahedronX[4] = 0; octahedronY[4] = 0; octahedronZ[4] = -1;
	octahedronX[5] = 0; octahedronY[5] = -1; octahedronZ[5] = 0;

	hexahedronX[0] = 1/sqrt3; hexahedronY[0] = 1/sqrt3; hexahedronZ[0] = 1/sqrt3;
	hexahedronX[1] = -1/sqrt3; hexahedronY[1] = 1/sqrt3; hexahedronZ[1] = 1/sqrt3;
	hexahedronX[2] = 1/sqrt3; hexahedronY[2] = 1/sqrt3; hexahedronZ[2] = -1/sqrt3;
	hexahedronX[3] = -1/sqrt3; hexahedronY[3] = 1/sqrt3; hexahedronZ[3] = -1/sqrt3;
	hexahedronX[4] = 1/sqrt3; hexahedronY[4] = -1/sqrt3; hexahedronZ[4] = 1/sqrt3;
	hexahedronX[5] = -1/sqrt3; hexahedronY[5] = -1/sqrt3; hexahedronZ[5] = 1/sqrt3;
	hexahedronX[6] = 1/sqrt3; hexahedronY[6] = -1/sqrt3; hexahedronZ[6] = -1/sqrt3;
	hexahedronX[7] = -1/sqrt3; hexahedronY[7] = -1/sqrt3; hexahedronZ[7] = -1/sqrt3;

	icosahedronX[0] = (float)(-1/Math.sqrt(phiphi+1)); icosahedronY[0] = (float)(1phi/Math.sqrt(phi*phi+1)); icosahedronZ[0] = 0;
	icosahedronX[1] = (float)(1/Math.sqrt(phiphi+1)); icosahedronY[1] = (float)(1phi/Math.sqrt(phi*phi+1)); icosahedronZ[1] = 0;
	icosahedronX[2] = (float)(-1/Math.sqrt(phiphi+1)); icosahedronY[2] = (float)(-1phi/Math.sqrt(phi*phi+1)); icosahedronZ[2] = 0;
	icosahedronX[3] = (float)(1/Math.sqrt(phiphi+1)); icosahedronY[3] = (float)(-1phi/Math.sqrt(phi*phi+1)); icosahedronZ[3] = 0;
	icosahedronX[4] = 0; icosahedronY[4] = (float)(1/Math.sqrt(phiphi+1)); icosahedronZ[4] = (float)(1phi/Math.sqrt(phi*phi+1));
	icosahedronX[5] = 0; icosahedronY[5] = (float)(-1/Math.sqrt(phiphi+1)); icosahedronZ[5] = (float)(1phi/Math.sqrt(phi*phi+1));
	icosahedronX[6] = 0; icosahedronY[6] = (float)(1/Math.sqrt(phiphi+1)); icosahedronZ[6] = (float)(-1phi/Math.sqrt(phi*phi+1));
	icosahedronX[7] = 0; icosahedronY[7] = (float)(-1/Math.sqrt(phiphi+1)); icosahedronZ[7] = (float)(-1phi/Math.sqrt(phi*phi+1));
	icosahedronX[8] = (float)(1phi/Math.sqrt(phiphi+1)); icosahedronY[8] = 0; icosahedronZ[8] = (float)(1/Math.sqrt(phi*phi+1));
	icosahedronX[9] = (float)(1phi/Math.sqrt(phiphi+1)); icosahedronY[9] = 0; icosahedronZ[9] = (float)(-1/Math.sqrt(phi*phi+1));
	icosahedronX[10] = (float)(-1phi/Math.sqrt(phiphi+1)); icosahedronY[10] = 0; icosahedronZ[10] = (float)(1/Math.sqrt(phi*phi+1));
	icosahedronX[11] = (float)(-1phi/Math.sqrt(phiphi+1)); icosahedronY[11] = 0; icosahedronZ[11] = (float)(-1/Math.sqrt(phi*phi+1));

	dodecahedronX[0] = 1/sqrt3; dodecahedronY[0] = 1/sqrt3; dodecahedronZ[0] = 1/sqrt3;
	dodecahedronX[1] = 1/sqrt3; dodecahedronY[1] = 1/sqrt3; dodecahedronZ[1] = -1/sqrt3;
	dodecahedronX[2] = 1/sqrt3; dodecahedronY[2] = -1/sqrt3; dodecahedronZ[2] = 1/sqrt3;
	dodecahedronX[3] = 1/sqrt3; dodecahedronY[3] = -1/sqrt3; dodecahedronZ[3] = -1/sqrt3;
	dodecahedronX[4] = -1/sqrt3; dodecahedronY[4] = 1/sqrt3; dodecahedronZ[4] = 1/sqrt3;
	dodecahedronX[5] = -1/sqrt3; dodecahedronY[5] = 1/sqrt3; dodecahedronZ[5] = -1/sqrt3;
	dodecahedronX[6] = -1/sqrt3; dodecahedronY[6] = -1/sqrt3; dodecahedronZ[6] = 1/sqrt3;
	dodecahedronX[7] = -1/sqrt3; dodecahedronY[7] = -1/sqrt3; dodecahedronZ[7] = -1/sqrt3;
	dodecahedronX[8] = 0; dodecahedronY[8] = 1/(phi*sqrt3); dodecahedronZ[8] = phi/sqrt3;
	dodecahedronX[9] = 0; dodecahedronY[9] = 1/(phi*sqrt3); dodecahedronZ[9] = -phi/sqrt3;
	dodecahedronX[10] = 0; dodecahedronY[10] = -1/(phi*sqrt3); dodecahedronZ[10] = phi/sqrt3;
	dodecahedronX[11] = 0; dodecahedronY[11] = -1/(phi*sqrt3); dodecahedronZ[11] = -phi/sqrt3;
	dodecahedronX[12] = phi/sqrt3; dodecahedronY[12] = 0; dodecahedronZ[12] = 1/(phi*sqrt3);
	dodecahedronX[13] = phi/sqrt3; dodecahedronY[13] = 0; dodecahedronZ[13] = -1/(phi*sqrt3);
	dodecahedronX[14] = -phi/sqrt3; dodecahedronY[14] = 0; dodecahedronZ[14] = 1/(phi*sqrt3);
	dodecahedronX[15] = -phi/sqrt3; dodecahedronY[15] = 0; dodecahedronZ[15] = -1/(phi*sqrt3);
	dodecahedronX[16] = 1/(phi*sqrt3); dodecahedronY[16] = phi/sqrt3; dodecahedronZ[16] = 0;
	dodecahedronX[17] = 1/(phi*sqrt3); dodecahedronY[17] = -phi/sqrt3; dodecahedronZ[17] = 0;
	dodecahedronX[18] = -1/(phi*sqrt3); dodecahedronY[18] = phi/sqrt3; dodecahedronZ[18] = 0;
	dodecahedronX[19] = -1/(phi*sqrt3); dodecahedronY[19] = -phi/sqrt3; dodecahedronZ[19] = 0;


	void drawTetrahedron(){
	line(xCenter+rtetrahedronX[0],yCenter+rtetrahedronY[0], xCenter+rtetrahedronX[1],yCenter+rtetrahedronY[1]);
	line(xCenter+rtetrahedronX[1],yCenter+rtetrahedronY[1], xCenter+rtetrahedronX[2],yCenter+rtetrahedronY[2]);
	line(xCenter+rtetrahedronX[2],yCenter+rtetrahedronY[2], xCenter+rtetrahedronX[0],yCenter+rtetrahedronY[0]);
	line(xCenter+rtetrahedronX[0],yCenter+rtetrahedronY[0], xCenter+rtetrahedronX[3],yCenter+rtetrahedronY[3]);
	line(xCenter+rtetrahedronX[3],yCenter+rtetrahedronY[3], xCenter+rtetrahedronX[1],yCenter+rtetrahedronY[1]);
	line(xCenter+rtetrahedronX[2],yCenter+rtetrahedronY[2], xCenter+rtetrahedronX[3],yCenter+rtetrahedronY[3]);
	}

	void drawOctahedron(){
	line(xCenter+roctahedronX[0],yCenter+roctahedronY[0], xCenter+roctahedronX[1],yCenter+roctahedronY[1]);
	line(xCenter+roctahedronX[1],yCenter+roctahedronY[1], xCenter+roctahedronX[2],yCenter+roctahedronY[2]);
	line(xCenter+roctahedronX[2],yCenter+roctahedronY[2], xCenter+roctahedronX[0],yCenter+roctahedronY[0]);
	line(xCenter+roctahedronX[0],yCenter+roctahedronY[0], xCenter+roctahedronX[3],yCenter+roctahedronY[3]);
	line(xCenter+roctahedronX[3],yCenter+roctahedronY[3], xCenter+roctahedronX[4],yCenter+roctahedronY[4]);
	line(xCenter+roctahedronX[4],yCenter+roctahedronY[4], xCenter+roctahedronX[0],yCenter+roctahedronY[0]);
	line(xCenter+roctahedronX[5],yCenter+roctahedronY[5], xCenter+roctahedronX[4],yCenter+roctahedronY[4]);
	line(xCenter+roctahedronX[4],yCenter+roctahedronY[4], xCenter+roctahedronX[1],yCenter+roctahedronY[1]);
	line(xCenter+roctahedronX[1],yCenter+roctahedronY[1], xCenter+roctahedronX[5],yCenter+roctahedronY[5]);
	line(xCenter+roctahedronX[5],yCenter+roctahedronY[5], xCenter+roctahedronX[2],yCenter+roctahedronY[2]);
	line(xCenter+roctahedronX[2],yCenter+roctahedronY[2], xCenter+roctahedronX[3],yCenter+roctahedronY[3]);
	line(xCenter+roctahedronX[3],yCenter+roctahedronY[3], xCenter+roctahedronX[5],yCenter+roctahedronY[5]);
	}

	void drawHexahedron(){
	line(xCenter+rhexahedronX[0],yCenter+rhexahedronY[0], xCenter+rhexahedronX[1],yCenter+rhexahedronY[1]);
	line(xCenter+rhexahedronX[1],yCenter+rhexahedronY[1], xCenter+rhexahedronX[3],yCenter+rhexahedronY[3]);
	line(xCenter+rhexahedronX[3],yCenter+rhexahedronY[3], xCenter+rhexahedronX[2],yCenter+rhexahedronY[2]);
	line(xCenter+rhexahedronX[2],yCenter+rhexahedronY[2], xCenter+rhexahedronX[0],yCenter+rhexahedronY[0]);
	line(xCenter+rhexahedronX[0],yCenter+rhexahedronY[0], xCenter+rhexahedronX[4],yCenter+rhexahedronY[4]);
	line(xCenter+rhexahedronX[4],yCenter+rhexahedronY[4], xCenter+rhexahedronX[5],yCenter+rhexahedronY[5]);
	line(xCenter+rhexahedronX[5],yCenter+rhexahedronY[5], xCenter+rhexahedronX[7],yCenter+rhexahedronY[7]);
	line(xCenter+rhexahedronX[7],yCenter+rhexahedronY[7], xCenter+rhexahedronX[6],yCenter+rhexahedronY[6]);
	line(xCenter+rhexahedronX[6],yCenter+rhexahedronY[6], xCenter+rhexahedronX[4],yCenter+rhexahedronY[4]);
	line(xCenter+rhexahedronX[1],yCenter+rhexahedronY[1], xCenter+rhexahedronX[5],yCenter+rhexahedronY[5]);
	line(xCenter+rhexahedronX[3],yCenter+rhexahedronY[3], xCenter+rhexahedronX[7],yCenter+rhexahedronY[7]);
	line(xCenter+rhexahedronX[2],yCenter+rhexahedronY[2], xCenter+rhexahedronX[6],yCenter+rhexahedronY[6]);
	}

	void drawIcosahedron(){
	line(xCenter+ricosahedronX[1],yCenter+ricosahedronY[1], xCenter+ricosahedronX[8],yCenter+ricosahedronY[8]);
	line(xCenter+ricosahedronX[8],yCenter+ricosahedronY[8], xCenter+ricosahedronX[4],yCenter+ricosahedronY[4]);
	line(xCenter+ricosahedronX[4],yCenter+ricosahedronY[4], xCenter+ricosahedronX[5],yCenter+ricosahedronY[5]);
	line(xCenter+ricosahedronX[5],yCenter+ricosahedronY[5], xCenter+ricosahedronX[10],yCenter+ricosahedronY[10]);
	line(xCenter+ricosahedronX[10],yCenter+ricosahedronY[10], xCenter+ricosahedronX[2],yCenter+ricosahedronY[2]);
	line(xCenter+ricosahedronX[2],yCenter+ricosahedronY[2], xCenter+ricosahedronX[11],yCenter+ricosahedronY[11]);
	line(xCenter+ricosahedronX[11],yCenter+ricosahedronY[11], xCenter+ricosahedronX[7],yCenter+ricosahedronY[7]);
	line(xCenter+ricosahedronX[7],yCenter+ricosahedronY[7], xCenter+ricosahedronX[6],yCenter+ricosahedronY[6]);
	line(xCenter+ricosahedronX[6],yCenter+ricosahedronY[6], xCenter+ricosahedronX[9],yCenter+ricosahedronY[9]);
	line(xCenter+ricosahedronX[9],yCenter+ricosahedronY[9], xCenter+ricosahedronX[1],yCenter+ricosahedronY[1]);
	line(xCenter+ricosahedronX[1],yCenter+ricosahedronY[1], xCenter+ricosahedronX[4],yCenter+ricosahedronY[4]);
	line(xCenter+ricosahedronX[4],yCenter+ricosahedronY[4], xCenter+ricosahedronX[10],yCenter+ricosahedronY[10]);
	line(xCenter+ricosahedronX[10],yCenter+ricosahedronY[10], xCenter+ricosahedronX[11],yCenter+ricosahedronY[11]);
	line(xCenter+ricosahedronX[11],yCenter+ricosahedronY[11], xCenter+ricosahedronX[6],yCenter+ricosahedronY[6]);
	line(xCenter+ricosahedronX[6],yCenter+ricosahedronY[6], xCenter+ricosahedronX[1],yCenter+ricosahedronY[1]);
	line(xCenter+ricosahedronX[1],yCenter+ricosahedronY[1], xCenter+ricosahedronX[0],yCenter+ricosahedronY[0]);
	line(xCenter+ricosahedronX[0],yCenter+ricosahedronY[0], xCenter+ricosahedronX[4],yCenter+ricosahedronY[4]);
	line(xCenter+ricosahedronX[10],yCenter+ricosahedronY[10], xCenter+ricosahedronX[0],yCenter+ricosahedronY[0]);
	line(xCenter+ricosahedronX[0],yCenter+ricosahedronY[0], xCenter+ricosahedronX[11],yCenter+ricosahedronY[11]);
	line(xCenter+ricosahedronX[6],yCenter+ricosahedronY[6], xCenter+ricosahedronX[0],yCenter+ricosahedronY[0]);
	line(xCenter+ricosahedronX[8],yCenter+ricosahedronY[8], xCenter+ricosahedronX[5],yCenter+ricosahedronY[5]);
	line(xCenter+ricosahedronX[5],yCenter+ricosahedronY[5], xCenter+ricosahedronX[2],yCenter+ricosahedronY[2]);
	line(xCenter+ricosahedronX[2],yCenter+ricosahedronY[2], xCenter+ricosahedronX[7],yCenter+ricosahedronY[7]);
	line(xCenter+ricosahedronX[7],yCenter+ricosahedronY[7], xCenter+ricosahedronX[9],yCenter+ricosahedronY[9]);
	line(xCenter+ricosahedronX[9],yCenter+ricosahedronY[9], xCenter+ricosahedronX[8],yCenter+ricosahedronY[8]);
	line(xCenter+ricosahedronX[8],yCenter+ricosahedronY[8], xCenter+ricosahedronX[3],yCenter+ricosahedronY[3]);
	line(xCenter+ricosahedronX[3],yCenter+ricosahedronY[3], xCenter+ricosahedronX[5],yCenter+ricosahedronY[5]);
	line(xCenter+ricosahedronX[2],yCenter+ricosahedronY[2], xCenter+ricosahedronX[3],yCenter+ricosahedronY[3]);
	line(xCenter+ricosahedronX[3],yCenter+ricosahedronY[3], xCenter+ricosahedronX[7],yCenter+ricosahedronY[7]);
	line(xCenter+ricosahedronX[9],yCenter+ricosahedronY[9], xCenter+ricosahedronX[3],yCenter+ricosahedronY[3]);
	line(xCenter+ricosahedronX[3],yCenter+ricosahedronY[3], xCenter+ricosahedronX[8],yCenter+ricosahedronY[8]);
	}

	void drawDodecahedron(){
	line(xCenter+rdodecahedronX[0],yCenter+rdodecahedronY[0], xCenter+rdodecahedronX[12],yCenter+rdodecahedronY[12]);
	line(xCenter+rdodecahedronX[12],yCenter+rdodecahedronY[12], xCenter+rdodecahedronX[13],yCenter+rdodecahedronY[13]);
	line(xCenter+rdodecahedronX[13],yCenter+rdodecahedronY[13], xCenter+rdodecahedronX[1],yCenter+rdodecahedronY[1]);
	line(xCenter+rdodecahedronX[1],yCenter+rdodecahedronY[1], xCenter+rdodecahedronX[16],yCenter+rdodecahedronY[16]);
	line(xCenter+rdodecahedronX[16],yCenter+rdodecahedronY[16], xCenter+rdodecahedronX[0],yCenter+rdodecahedronY[0]);
	line(xCenter+rdodecahedronX[16],yCenter+rdodecahedronY[16], xCenter+rdodecahedronX[18],yCenter+rdodecahedronY[18]);
	line(xCenter+rdodecahedronX[18],yCenter+rdodecahedronY[18], xCenter+rdodecahedronX[4],yCenter+rdodecahedronY[4]);
	line(xCenter+rdodecahedronX[4],yCenter+rdodecahedronY[4], xCenter+rdodecahedronX[8],yCenter+rdodecahedronY[8]);
	line(xCenter+rdodecahedronX[12],yCenter+rdodecahedronY[12], xCenter+rdodecahedronX[2],yCenter+rdodecahedronY[2]);
	line(xCenter+rdodecahedronX[2],yCenter+rdodecahedronY[2], xCenter+rdodecahedronX[17],yCenter+rdodecahedronY[17]);
	line(xCenter+rdodecahedronX[17],yCenter+rdodecahedronY[17], xCenter+rdodecahedronX[3],yCenter+rdodecahedronY[3]);
	line(xCenter+rdodecahedronX[3],yCenter+rdodecahedronY[3], xCenter+rdodecahedronX[13],yCenter+rdodecahedronY[13]);
	line(xCenter+rdodecahedronX[0],yCenter+rdodecahedronY[0], xCenter+rdodecahedronX[8],yCenter+rdodecahedronY[8]);
	line(xCenter+rdodecahedronX[8],yCenter+rdodecahedronY[8], xCenter+rdodecahedronX[10],yCenter+rdodecahedronY[10]);
	line(xCenter+rdodecahedronX[10],yCenter+rdodecahedronY[10], xCenter+rdodecahedronX[2],yCenter+rdodecahedronY[2]);
	line(xCenter+rdodecahedronX[1],yCenter+rdodecahedronY[1], xCenter+rdodecahedronX[9],yCenter+rdodecahedronY[9]);
	line(xCenter+rdodecahedronX[9],yCenter+rdodecahedronY[9], xCenter+rdodecahedronX[11],yCenter+rdodecahedronY[11]);
	line(xCenter+rdodecahedronX[11],yCenter+rdodecahedronY[11], xCenter+rdodecahedronX[3],yCenter+rdodecahedronY[3]);
	line(xCenter+rdodecahedronX[11],yCenter+rdodecahedronY[11], xCenter+rdodecahedronX[7],yCenter+rdodecahedronY[7]);
	line(xCenter+rdodecahedronX[7],yCenter+rdodecahedronY[7], xCenter+rdodecahedronX[19],yCenter+rdodecahedronY[19]);
	line(xCenter+rdodecahedronX[10],yCenter+rdodecahedronY[10], xCenter+rdodecahedronX[6],yCenter+rdodecahedronY[6]);
	line(xCenter+rdodecahedronX[6],yCenter+rdodecahedronY[6], xCenter+rdodecahedronX[19],yCenter+rdodecahedronY[19]);
	line(xCenter+rdodecahedronX[19],yCenter+rdodecahedronY[19], xCenter+rdodecahedronX[17],yCenter+rdodecahedronY[17]);
	line(xCenter+rdodecahedronX[18],yCenter+rdodecahedronY[18], xCenter+rdodecahedronX[5],yCenter+rdodecahedronY[5]);
	line(xCenter+rdodecahedronX[5],yCenter+rdodecahedronY[5], xCenter+rdodecahedronX[9],yCenter+rdodecahedronY[9]);
	line(xCenter+rdodecahedronX[5],yCenter+rdodecahedronY[5], xCenter+rdodecahedronX[15],yCenter+rdodecahedronY[15]);
	line(xCenter+rdodecahedronX[15],yCenter+rdodecahedronY[15], xCenter+rdodecahedronX[7],yCenter+rdodecahedronY[7]);
	line(xCenter+rdodecahedronX[15],yCenter+rdodecahedronY[15], xCenter+rdodecahedronX[14],yCenter+rdodecahedronY[14]);
	line(xCenter+rdodecahedronX[14],yCenter+rdodecahedronY[14], xCenter+rdodecahedronX[4],yCenter+rdodecahedronY[4]);
	line(xCenter+rdodecahedronX[14],yCenter+rdodecahedronY[14], xCenter+rdodecahedronX[6],yCenter+rdodecahedronY[6]);
	}

	void rotatePoints(float[] pointsX, //
	float[] pointsY, // 3 arrays of coordinates: X, Y, and Z
	float[] pointsZ, //
	float increment, // angle of rotation (in radians)
	char axis) //axis: x=0,y=1,z=2
	{
	float angle;
	float rad;
	if(axis=='X' \|\| axis == 'x'){
	for(j=0;j<pointsX.length;j++){
	rad = (float)Math.sqrt(pointsZ[j]pointsZ[j]+pointsY[j]pointsY[j]);
	angle=(float)Math.atan2(pointsZ[j],pointsY[j]);
	angle+=increment;
	pointsZ[j] = (float)( rad*Math.sin(angle) );
	pointsY[j] = (float)( rad*Math.cos(angle) );
	}
	}
	else if(axis=='Y' \|\| axis=='y'){
	for(j=0;j<pointsY.length;j++){
	rad = (float)Math.sqrt(pointsZ[j]pointsZ[j]+pointsX[j]pointsX[j]);
	angle=(float)Math.atan2(pointsZ[j],pointsX[j]);
	angle+=increment;
	pointsZ[j] = (float)( rad*Math.sin(angle) );
	pointsX[j] = (float)( rad*Math.cos(angle) );
	}
	}
	else if(axis=='Z' \|\| axis == 'z'){
	for(j=0;j<pointsZ.length;j++){
	rad = (float)Math.sqrt(pointsX[j]pointsX[j]+pointsY[j]pointsY[j]);
	angle=(float)Math.atan2(pointsY[j],pointsX[j]);
	angle+=increment;
	pointsY[j] = (float)( rad*Math.sin(angle) );
	pointsX[j] = (float)( rad*Math.cos(angle) );
	}
	}
	}