platonic.h

////////////////////////////////////////////////////////////////////
//                        PLATONIC SOLIDS                         //
//           centered at origin          radius = 1               //
//                                                                //
//         TETRA               OCTA              ICOSA            //
//             one point aligned along the +X axis                //
//                                                                //
//                   HEXA                DODECA                   //
//          aligned as duals to the octa / icosahedron            //
//                   faces in place of points                     //
//         (one face normal aligned along the +X axis)            //
//                                                                //
//                     + + + + + + + + + + +                      //
//                                                                //
//     even possible to cross-reference indices across duals      //
//                                                                //
//  eg:                                                           //
//   octa's 6 point indices correlate to hexa's 6 face indices    //
//       and octa's point[0] is along hexa's face[0] normal       //
//                                                                //
//      this means: a solid's face normal is that same index      //
//                  in its dual's point array                     //
//                                                                //
////////////////////////////////////////////////////////////////////

// for higher precision replace occurrences of "float" with "double" or "long double"

#define TETRAHEDRON_POINT_COUNT 4
#define TETRAHEDRON_LINE_COUNT 6
#define TETRAHEDRON_FACE_COUNT 4

#define OCTAHEDRON_POINT_COUNT 6
#define OCTAHEDRON_LINE_COUNT 12
#define OCTAHEDRON_FACE_COUNT 8

#define HEXAHEDRON_POINT_COUNT 8
#define HEXAHEDRON_LINE_COUNT 12
#define HEXAHEDRON_FACE_COUNT 6
#define HEXAHEDRON_TRIANGLE_FACE_COUNT 12  // OpenGL ES can only render triangles

#define ICOSAHEDRON_POINT_COUNT 12
#define ICOSAHEDRON_LINE_COUNT 30
#define ICOSAHEDRON_FACE_COUNT 20

#define DODECAHEDRON_POINT_COUNT 20
#define DODECAHEDRON_LINE_COUNT 30
#define DODECAHEDRON_FACE_COUNT 12
#define DODECAHEDRON_TRIANGLE_FACE_COUNT 36

// dihedral angle is the angle between two adjacent faces,
//  circling under and running perpendicular to the edge dividing the faces
#define TETRAHEDRON_DIHEDRAL_ANGLE   70.52877936550930863075400066
#define OCTAHEDRON_DIHEDRAL_ANGLE   109.47122063449069136924599934
#define HEXAHEDRON_DIHEDRAL_ANGLE    90
#define ICOSAHEDRON_DIHEDRAL_ANGLE  138.189685104221401934142083269
#define DODECAHEDRON_DIHEDRAL_ANGLE 116.56505117707798935157219372

// inradius, the inscribed sphere, distance from center to midpoint of a face
#define TETRAHEDRON_INRADIUS    0.333333333333333333333333333333
#define OCTAHEDRON_INRADIUS     0.577350269189625764509148780502
#define HEXAHEDRON_INRADIUS     0.5773502691896257645091487805
#define ICOSAHEDRON_INRADIUS    0.794654472291766122955530928331
#define DODECAHEDRON_INRADIUS   0.794654472291766122955530928327

#define TETRAHEDRON_MIDRADIUS   0.577350269189625764509148780501
#define OCTAHEDRON_MIDRADIUS    0.707106781186547524400844362104
#define HEXAHEDRON_MIDRADIUS    0.816496580927726032732428024901
#define ICOSAHEDRON_MIDRADIUS   0.8506508083520399321815404970630
#define DODECAHEDRON_MIDRADIUS  0.9341723589627156964511186235480

#define TETRAHEDRON_SIDE_LENGTH   1.6329931618554520654648560498
#define OCTAHEDRON_SIDE_LENGTH    1.41421356237309504880168872421
#define HEXAHEDRON_SIDE_LENGTH    1.154700538379251529018297561
#define ICOSAHEDRON_SIDE_LENGTH   1.0514622242382672120513381697
#define DODECAHEDRON_SIDE_LENGTH  0.713644179546179863883939686092

#define TETRAHEDRON_VOLUME    0.513200239279667346230354471554
#define OCTAHEDRON_VOLUME     1.33333333333333333333333333333
#define HEXAHEDRON_VOLUME     1.53960071783900203869106341466
#define ICOSAHEDRON_VOLUME    2.53615071012040952564383822238
#define DODECAHEDRON_VOLUME   2.78516386312262296729255491273

const float _tetrahedron_points[TETRAHEDRON_POINT_COUNT*3] = { 
	1.0,                 0.0,               0.0,               
	-0.333333333333333, -0.942809041582063, 0.0,               
	-0.333333333333333,  0.471404520791032, 0.816496580927726, 
	-0.333333333333333,  0.471404520791032, -0.816496580927726};
const unsigned short _tetrahedron_lines[TETRAHEDRON_LINE_COUNT*2] = {
	2, 3, 2, 0, 2, 1, 3, 0, 3, 1, 0, 1};
const unsigned short _tetrahedron_faces[TETRAHEDRON_FACE_COUNT*3] = {
	2, 1, 3,  
	2, 3, 0,  
	2, 0, 1,  
	3, 1, 0};
const float _tetrahedron_dual_points[TETRAHEDRON_POINT_COUNT*3] = { 
	-1.0,               0.0,               0.0,               
	0.333333333333333,  0.942809041582063, 0.0,               
	0.333333333333333,  -0.471404520791032, 0.816496580927726, 
	0.333333333333333,  -0.471404520791032, -0.816496580927726};
const unsigned short _tetrahedron_dual_lines[TETRAHEDRON_LINE_COUNT*2] = {
	2, 3, 2, 0, 2, 1, 3, 0, 3, 1, 0, 1};
const unsigned short _tetrahedron_dual_faces[TETRAHEDRON_FACE_COUNT*3] = {
	2, 1, 3,  
	2, 3, 0,  
	2, 0, 1,  
	3, 1, 0};
const float _octahedron_points[OCTAHEDRON_POINT_COUNT*3] = {
	1.0, 0.0, 0.0,
	0.0, 1.0, 0.0,
	0.0, 0.0, 1.0,
	-1.0, 0.0, 0.0,
	0.0, -1.0, 0.0,
	0.0, 0.0, -1.0};
const unsigned short _octahedron_lines[OCTAHEDRON_LINE_COUNT*2] = {
	1, 0, 1, 2, 1, 5, 1, 3, 3, 2, 2, 0, 0, 5, 5, 3, 4, 2, 4, 3, 4, 5, 4, 0};
const unsigned short _octahedron_faces[OCTAHEDRON_FACE_COUNT*3] = { 
	1, 0, 2, 
	1, 5, 0, 
	4, 0, 5,
	4, 2, 0, 
	1, 2, 3, 
	1, 3, 5, 
	4, 5, 3, 
	4, 3, 2};
const float _hexahedron_points[HEXAHEDRON_POINT_COUNT*3] = { 
	0.57735026918963, 0.57735026918963, 0.57735026918963,
	0.57735026918963, 0.57735026918963, -0.57735026918963,
	0.57735026918963, -0.57735026918963, -0.57735026918963,
	0.57735026918963, -0.57735026918963, 0.57735026918963,
	-0.57735026918963, 0.57735026918963, 0.57735026918963,
	-0.57735026918963, 0.57735026918963, -0.57735026918963,
	-0.57735026918963, -0.57735026918963, -0.57735026918963,
	-0.57735026918963, -0.57735026918963, 0.57735026918963};
const unsigned short _hexahedron_lines[HEXAHEDRON_LINE_COUNT*2] = {
	0, 1, 1, 2, 2, 3, 3, 0, 0, 4, 1, 5, 2, 6, 3, 7, 4, 5, 5, 6, 6, 7, 7, 4};
const unsigned short _hexahedron_faces[HEXAHEDRON_FACE_COUNT*4] = {
// these are being stored as squares, not triangles
	0, 3, 2, 1,
	4, 0, 1, 5,
	0, 3, 7, 4,
	7, 4, 5, 6,
	3, 7, 6, 2,
	1, 5, 6, 2};
const unsigned short _hexahedron_triangle_faces[HEXAHEDRON_TRIANGLE_FACE_COUNT*3] = {
	0, 2, 3,
	2, 0, 1,
	4, 1, 0,
	1, 4, 5,
	0, 3, 7,
	7, 4, 0,
	7, 5, 4,
	5, 7, 6,
	3, 6, 7,
	6, 3, 2,
	1, 5, 6,
	6, 2, 1};
const float _icosahedron_points[ICOSAHEDRON_POINT_COUNT*3] = {
	0.447213595499958, -0.276393202250021, 0.850650808352040,
	-0.447213595499958, 0.276393202250021, 0.850650808352040,
	-0.447213595499958, 0.276393202250021, -0.850650808352040,
	0.447213595499958, -0.276393202250021, -0.850650808352040,
	-0.447213595499958, -0.723606797749979, 0.525731112119134,
	0.447213595499958, 0.723606797749979, 0.525731112119134,
	0.447213595499958, 0.723606797749979, -0.525731112119134,
	-0.447213595499958, -0.723606797749979, -0.525731112119134,
	0.447213595499958, -0.894427190999916, 0.0,
	1.0,                0.0,               0.0,
	-0.447213595499958, 0.894427190999916, 0.0,
	-1.0,               0.0,               0.0};
const unsigned short _icosahedron_lines[ICOSAHEDRON_LINE_COUNT*2] = {
	0, 8, 0, 9, 0, 1, 0, 4, 0, 5, 8, 3, 8, 9, 8, 7, 8, 4, 9, 3, 
	9, 6, 9, 5, 7, 4, 7, 3, 7, 2, 7, 11, 2, 10, 2, 11, 2, 3, 2, 6,
	10, 11, 10, 5, 10, 6, 10, 1, 11, 1, 11, 4, 4, 1, 5, 1, 5, 6, 6, 3};
const unsigned short _icosahedron_faces[ICOSAHEDRON_FACE_COUNT*3] = { 
	8, 7, 4, 
	7, 8, 3,    // pair 2 
	8, 4, 0, 
	8, 0, 9, 
	9, 3, 8, 
	9, 0, 5, 
	9, 5, 6, 
	9, 6, 3, 
	3, 2, 7,   // pair 2
	3, 6, 2, 
	0, 4, 1, 
	0, 1, 5, 
	11, 4, 7, 
	11, 7, 2, 
	11, 2, 10, 
	1, 11, 10,    // pair 1
	11, 1, 4, 
	10, 6, 5, 
	10, 5, 1,     // pair 1
	10, 2, 6};
const float _dodecahedron_points[DODECAHEDRON_POINT_COUNT * 3] = {
	-0.794655, 0.491123, 0.356822,
	-0.187593, 0.794654, -0.577350,
	-0.794655, 0.491123, -0.356822,
	-0.794654, -0.187593, -0.577350,
	0.187592, 0.303531, -0.934172,
	0.187592, 0.982247, 0.000000,
	0.187593, -0.794654, -0.577350,
	-0.187592, -0.303531, -0.934172,
	-0.187592, -0.982247, 0.000000,
	-0.794654, -0.607062, 0.000000,
	0.794655, -0.491123, -0.356822,
	0.187593, -0.794654, 0.577350,
	-0.187592, -0.303531, 0.934172,
	-0.794654, -0.187593, 0.577350,
	0.794655, -0.491123, 0.356822,
	-0.187593, 0.794654, 0.577350,
	0.187592, 0.303531, 0.934172,
	0.794654, 0.187593, 0.577350,
	0.794654, 0.607062, 0.000000,
	0.794654, 0.187593, -0.577350 };
const unsigned short _dodecahedron_lines[DODECAHEDRON_LINE_COUNT * 2] = {
	19, 18,
	18, 17,
	17, 14,
	14, 10,
	10, 19,
	14, 11,
	11, 8,
	8, 6,
	6, 10,
	19, 4,
	4, 1,
	1, 5,
	5, 18,
	9, 3,
	3, 7,
	7, 6,
	8, 9,
	13, 9,
	3, 2,
	2, 0,
	0, 13,
	12, 11,
	12, 13,
	1, 2,
	5, 15,
	15, 0,
	15, 16,
	16, 17,
	16, 12,
	4, 7 };
const unsigned short _dodecahedron_triangle_faces[DODECAHEDRON_TRIANGLE_FACE_COUNT * 3] = {
	5, 2, 1,
	15, 0, 5,
	2, 5, 0,

	9, 2, 13,
	2, 0, 13,
	3, 2, 9,

	10, 17, 19,
	18, 19, 17,
	14, 17, 10,

	19, 1,  4,
	6, 9, 8,   
	1, 18, 5, 

	11, 14, 8, 
	18, 1, 19,
	8, 9, 11,

	10, 8, 14,
	8, 10, 6, 
	6, 7, 9,

	9, 7, 3,
	13, 12, 9,
	12, 11, 9,

	18, 15, 5,
	17, 15, 18,
	15, 17, 16,

	11, 12, 14,
	14, 12, 17,
	17, 12, 16,

	12, 13, 16,
	13, 0, 16,
	0,  15, 16,

	7, 2, 3,
	2, 7, 1,
	1, 7, 4,

	4, 7,  19,
	19, 7, 10,
	6, 10, 7 };