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MarchingCubes.cpp
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//
// Created by s132054 on 18-6-2017.
//
// source: http://paulbourke.net/geometry/polygonise/ (with minor changes to work with our codebase)
//
#include "System.h"
#include <random>
#include <string>
#include "MarchingCubes.h"
#if defined(__CYGWIN__) || defined(WIN32)
#include <GL/glut.h>
#else
#include <GLUT/glut.h>
#endif
const int edgeTable[256] = {
0x0, 0x109, 0x203, 0x30a, 0x406, 0x50f, 0x605, 0x70c,
0x80c, 0x905, 0xa0f, 0xb06, 0xc0a, 0xd03, 0xe09, 0xf00,
0x190, 0x99, 0x393, 0x29a, 0x596, 0x49f, 0x795, 0x69c,
0x99c, 0x895, 0xb9f, 0xa96, 0xd9a, 0xc93, 0xf99, 0xe90,
0x230, 0x339, 0x33, 0x13a, 0x636, 0x73f, 0x435, 0x53c,
0xa3c, 0xb35, 0x83f, 0x936, 0xe3a, 0xf33, 0xc39, 0xd30,
0x3a0, 0x2a9, 0x1a3, 0xaa, 0x7a6, 0x6af, 0x5a5, 0x4ac,
0xbac, 0xaa5, 0x9af, 0x8a6, 0xfaa, 0xea3, 0xda9, 0xca0,
0x460, 0x569, 0x663, 0x76a, 0x66, 0x16f, 0x265, 0x36c,
0xc6c, 0xd65, 0xe6f, 0xf66, 0x86a, 0x963, 0xa69, 0xb60,
0x5f0, 0x4f9, 0x7f3, 0x6fa, 0x1f6, 0xff, 0x3f5, 0x2fc,
0xdfc, 0xcf5, 0xfff, 0xef6, 0x9fa, 0x8f3, 0xbf9, 0xaf0,
0x650, 0x759, 0x453, 0x55a, 0x256, 0x35f, 0x55, 0x15c,
0xe5c, 0xf55, 0xc5f, 0xd56, 0xa5a, 0xb53, 0x859, 0x950,
0x7c0, 0x6c9, 0x5c3, 0x4ca, 0x3c6, 0x2cf, 0x1c5, 0xcc,
0xfcc, 0xec5, 0xdcf, 0xcc6, 0xbca, 0xac3, 0x9c9, 0x8c0,
0x8c0, 0x9c9, 0xac3, 0xbca, 0xcc6, 0xdcf, 0xec5, 0xfcc,
0xcc, 0x1c5, 0x2cf, 0x3c6, 0x4ca, 0x5c3, 0x6c9, 0x7c0,
0x950, 0x859, 0xb53, 0xa5a, 0xd56, 0xc5f, 0xf55, 0xe5c,
0x15c, 0x55, 0x35f, 0x256, 0x55a, 0x453, 0x759, 0x650,
0xaf0, 0xbf9, 0x8f3, 0x9fa, 0xef6, 0xfff, 0xcf5, 0xdfc,
0x2fc, 0x3f5, 0xff, 0x1f6, 0x6fa, 0x7f3, 0x4f9, 0x5f0,
0xb60, 0xa69, 0x963, 0x86a, 0xf66, 0xe6f, 0xd65, 0xc6c,
0x36c, 0x265, 0x16f, 0x66, 0x76a, 0x663, 0x569, 0x460,
0xca0, 0xda9, 0xea3, 0xfaa, 0x8a6, 0x9af, 0xaa5, 0xbac,
0x4ac, 0x5a5, 0x6af, 0x7a6, 0xaa, 0x1a3, 0x2a9, 0x3a0,
0xd30, 0xc39, 0xf33, 0xe3a, 0x936, 0x83f, 0xb35, 0xa3c,
0x53c, 0x435, 0x73f, 0x636, 0x13a, 0x33, 0x339, 0x230,
0xe90, 0xf99, 0xc93, 0xd9a, 0xa96, 0xb9f, 0x895, 0x99c,
0x69c, 0x795, 0x49f, 0x596, 0x29a, 0x393, 0x99, 0x190,
0xf00, 0xe09, 0xd03, 0xc0a, 0xb06, 0xa0f, 0x905, 0x80c,
0x70c, 0x605, 0x50f, 0x406, 0x30a, 0x203, 0x109, 0x0};
const int triTable[256][16] =
{{-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{0, 8, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{0, 1, 9, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{1, 8, 3, 9, 8, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{1, 2, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{0, 8, 3, 1, 2, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{9, 2, 10, 0, 2, 9, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{2, 8, 3, 2, 10, 8, 10, 9, 8, -1, -1, -1, -1, -1, -1, -1},
{3, 11, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{0, 11, 2, 8, 11, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{1, 9, 0, 2, 3, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{1, 11, 2, 1, 9, 11, 9, 8, 11, -1, -1, -1, -1, -1, -1, -1},
{3, 10, 1, 11, 10, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{0, 10, 1, 0, 8, 10, 8, 11, 10, -1, -1, -1, -1, -1, -1, -1},
{3, 9, 0, 3, 11, 9, 11, 10, 9, -1, -1, -1, -1, -1, -1, -1},
{9, 8, 10, 10, 8, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{4, 7, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{4, 3, 0, 7, 3, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{0, 1, 9, 8, 4, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{4, 1, 9, 4, 7, 1, 7, 3, 1, -1, -1, -1, -1, -1, -1, -1},
{1, 2, 10, 8, 4, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{3, 4, 7, 3, 0, 4, 1, 2, 10, -1, -1, -1, -1, -1, -1, -1},
{9, 2, 10, 9, 0, 2, 8, 4, 7, -1, -1, -1, -1, -1, -1, -1},
{2, 10, 9, 2, 9, 7, 2, 7, 3, 7, 9, 4, -1, -1, -1, -1},
{8, 4, 7, 3, 11, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{11, 4, 7, 11, 2, 4, 2, 0, 4, -1, -1, -1, -1, -1, -1, -1},
{9, 0, 1, 8, 4, 7, 2, 3, 11, -1, -1, -1, -1, -1, -1, -1},
{4, 7, 11, 9, 4, 11, 9, 11, 2, 9, 2, 1, -1, -1, -1, -1},
{3, 10, 1, 3, 11, 10, 7, 8, 4, -1, -1, -1, -1, -1, -1, -1},
{1, 11, 10, 1, 4, 11, 1, 0, 4, 7, 11, 4, -1, -1, -1, -1},
{4, 7, 8, 9, 0, 11, 9, 11, 10, 11, 0, 3, -1, -1, -1, -1},
{4, 7, 11, 4, 11, 9, 9, 11, 10, -1, -1, -1, -1, -1, -1, -1},
{9, 5, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{9, 5, 4, 0, 8, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{0, 5, 4, 1, 5, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{8, 5, 4, 8, 3, 5, 3, 1, 5, -1, -1, -1, -1, -1, -1, -1},
{1, 2, 10, 9, 5, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{3, 0, 8, 1, 2, 10, 4, 9, 5, -1, -1, -1, -1, -1, -1, -1},
{5, 2, 10, 5, 4, 2, 4, 0, 2, -1, -1, -1, -1, -1, -1, -1},
{2, 10, 5, 3, 2, 5, 3, 5, 4, 3, 4, 8, -1, -1, -1, -1},
{9, 5, 4, 2, 3, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{0, 11, 2, 0, 8, 11, 4, 9, 5, -1, -1, -1, -1, -1, -1, -1},
{0, 5, 4, 0, 1, 5, 2, 3, 11, -1, -1, -1, -1, -1, -1, -1},
{2, 1, 5, 2, 5, 8, 2, 8, 11, 4, 8, 5, -1, -1, -1, -1},
{10, 3, 11, 10, 1, 3, 9, 5, 4, -1, -1, -1, -1, -1, -1, -1},
{4, 9, 5, 0, 8, 1, 8, 10, 1, 8, 11, 10, -1, -1, -1, -1},
{5, 4, 0, 5, 0, 11, 5, 11, 10, 11, 0, 3, -1, -1, -1, -1},
{5, 4, 8, 5, 8, 10, 10, 8, 11, -1, -1, -1, -1, -1, -1, -1},
{9, 7, 8, 5, 7, 9, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{9, 3, 0, 9, 5, 3, 5, 7, 3, -1, -1, -1, -1, -1, -1, -1},
{0, 7, 8, 0, 1, 7, 1, 5, 7, -1, -1, -1, -1, -1, -1, -1},
{1, 5, 3, 3, 5, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{9, 7, 8, 9, 5, 7, 10, 1, 2, -1, -1, -1, -1, -1, -1, -1},
{10, 1, 2, 9, 5, 0, 5, 3, 0, 5, 7, 3, -1, -1, -1, -1},
{8, 0, 2, 8, 2, 5, 8, 5, 7, 10, 5, 2, -1, -1, -1, -1},
{2, 10, 5, 2, 5, 3, 3, 5, 7, -1, -1, -1, -1, -1, -1, -1},
{7, 9, 5, 7, 8, 9, 3, 11, 2, -1, -1, -1, -1, -1, -1, -1},
{9, 5, 7, 9, 7, 2, 9, 2, 0, 2, 7, 11, -1, -1, -1, -1},
{2, 3, 11, 0, 1, 8, 1, 7, 8, 1, 5, 7, -1, -1, -1, -1},
{11, 2, 1, 11, 1, 7, 7, 1, 5, -1, -1, -1, -1, -1, -1, -1},
{9, 5, 8, 8, 5, 7, 10, 1, 3, 10, 3, 11, -1, -1, -1, -1},
{5, 7, 0, 5, 0, 9, 7, 11, 0, 1, 0, 10, 11, 10, 0, -1},
{11, 10, 0, 11, 0, 3, 10, 5, 0, 8, 0, 7, 5, 7, 0, -1},
{11, 10, 5, 7, 11, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{10, 6, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{0, 8, 3, 5, 10, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{9, 0, 1, 5, 10, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{1, 8, 3, 1, 9, 8, 5, 10, 6, -1, -1, -1, -1, -1, -1, -1},
{1, 6, 5, 2, 6, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{1, 6, 5, 1, 2, 6, 3, 0, 8, -1, -1, -1, -1, -1, -1, -1},
{9, 6, 5, 9, 0, 6, 0, 2, 6, -1, -1, -1, -1, -1, -1, -1},
{5, 9, 8, 5, 8, 2, 5, 2, 6, 3, 2, 8, -1, -1, -1, -1},
{2, 3, 11, 10, 6, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{11, 0, 8, 11, 2, 0, 10, 6, 5, -1, -1, -1, -1, -1, -1, -1},
{0, 1, 9, 2, 3, 11, 5, 10, 6, -1, -1, -1, -1, -1, -1, -1},
{5, 10, 6, 1, 9, 2, 9, 11, 2, 9, 8, 11, -1, -1, -1, -1},
{6, 3, 11, 6, 5, 3, 5, 1, 3, -1, -1, -1, -1, -1, -1, -1},
{0, 8, 11, 0, 11, 5, 0, 5, 1, 5, 11, 6, -1, -1, -1, -1},
{3, 11, 6, 0, 3, 6, 0, 6, 5, 0, 5, 9, -1, -1, -1, -1},
{6, 5, 9, 6, 9, 11, 11, 9, 8, -1, -1, -1, -1, -1, -1, -1},
{5, 10, 6, 4, 7, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{4, 3, 0, 4, 7, 3, 6, 5, 10, -1, -1, -1, -1, -1, -1, -1},
{1, 9, 0, 5, 10, 6, 8, 4, 7, -1, -1, -1, -1, -1, -1, -1},
{10, 6, 5, 1, 9, 7, 1, 7, 3, 7, 9, 4, -1, -1, -1, -1},
{6, 1, 2, 6, 5, 1, 4, 7, 8, -1, -1, -1, -1, -1, -1, -1},
{1, 2, 5, 5, 2, 6, 3, 0, 4, 3, 4, 7, -1, -1, -1, -1},
{8, 4, 7, 9, 0, 5, 0, 6, 5, 0, 2, 6, -1, -1, -1, -1},
{7, 3, 9, 7, 9, 4, 3, 2, 9, 5, 9, 6, 2, 6, 9, -1},
{3, 11, 2, 7, 8, 4, 10, 6, 5, -1, -1, -1, -1, -1, -1, -1},
{5, 10, 6, 4, 7, 2, 4, 2, 0, 2, 7, 11, -1, -1, -1, -1},
{0, 1, 9, 4, 7, 8, 2, 3, 11, 5, 10, 6, -1, -1, -1, -1},
{9, 2, 1, 9, 11, 2, 9, 4, 11, 7, 11, 4, 5, 10, 6, -1},
{8, 4, 7, 3, 11, 5, 3, 5, 1, 5, 11, 6, -1, -1, -1, -1},
{5, 1, 11, 5, 11, 6, 1, 0, 11, 7, 11, 4, 0, 4, 11, -1},
{0, 5, 9, 0, 6, 5, 0, 3, 6, 11, 6, 3, 8, 4, 7, -1},
{6, 5, 9, 6, 9, 11, 4, 7, 9, 7, 11, 9, -1, -1, -1, -1},
{10, 4, 9, 6, 4, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{4, 10, 6, 4, 9, 10, 0, 8, 3, -1, -1, -1, -1, -1, -1, -1},
{10, 0, 1, 10, 6, 0, 6, 4, 0, -1, -1, -1, -1, -1, -1, -1},
{8, 3, 1, 8, 1, 6, 8, 6, 4, 6, 1, 10, -1, -1, -1, -1},
{1, 4, 9, 1, 2, 4, 2, 6, 4, -1, -1, -1, -1, -1, -1, -1},
{3, 0, 8, 1, 2, 9, 2, 4, 9, 2, 6, 4, -1, -1, -1, -1},
{0, 2, 4, 4, 2, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{8, 3, 2, 8, 2, 4, 4, 2, 6, -1, -1, -1, -1, -1, -1, -1},
{10, 4, 9, 10, 6, 4, 11, 2, 3, -1, -1, -1, -1, -1, -1, -1},
{0, 8, 2, 2, 8, 11, 4, 9, 10, 4, 10, 6, -1, -1, -1, -1},
{3, 11, 2, 0, 1, 6, 0, 6, 4, 6, 1, 10, -1, -1, -1, -1},
{6, 4, 1, 6, 1, 10, 4, 8, 1, 2, 1, 11, 8, 11, 1, -1},
{9, 6, 4, 9, 3, 6, 9, 1, 3, 11, 6, 3, -1, -1, -1, -1},
{8, 11, 1, 8, 1, 0, 11, 6, 1, 9, 1, 4, 6, 4, 1, -1},
{3, 11, 6, 3, 6, 0, 0, 6, 4, -1, -1, -1, -1, -1, -1, -1},
{6, 4, 8, 11, 6, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{7, 10, 6, 7, 8, 10, 8, 9, 10, -1, -1, -1, -1, -1, -1, -1},
{0, 7, 3, 0, 10, 7, 0, 9, 10, 6, 7, 10, -1, -1, -1, -1},
{10, 6, 7, 1, 10, 7, 1, 7, 8, 1, 8, 0, -1, -1, -1, -1},
{10, 6, 7, 10, 7, 1, 1, 7, 3, -1, -1, -1, -1, -1, -1, -1},
{1, 2, 6, 1, 6, 8, 1, 8, 9, 8, 6, 7, -1, -1, -1, -1},
{2, 6, 9, 2, 9, 1, 6, 7, 9, 0, 9, 3, 7, 3, 9, -1},
{7, 8, 0, 7, 0, 6, 6, 0, 2, -1, -1, -1, -1, -1, -1, -1},
{7, 3, 2, 6, 7, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{2, 3, 11, 10, 6, 8, 10, 8, 9, 8, 6, 7, -1, -1, -1, -1},
{2, 0, 7, 2, 7, 11, 0, 9, 7, 6, 7, 10, 9, 10, 7, -1},
{1, 8, 0, 1, 7, 8, 1, 10, 7, 6, 7, 10, 2, 3, 11, -1},
{11, 2, 1, 11, 1, 7, 10, 6, 1, 6, 7, 1, -1, -1, -1, -1},
{8, 9, 6, 8, 6, 7, 9, 1, 6, 11, 6, 3, 1, 3, 6, -1},
{0, 9, 1, 11, 6, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{7, 8, 0, 7, 0, 6, 3, 11, 0, 11, 6, 0, -1, -1, -1, -1},
{7, 11, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{7, 6, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{3, 0, 8, 11, 7, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{0, 1, 9, 11, 7, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{8, 1, 9, 8, 3, 1, 11, 7, 6, -1, -1, -1, -1, -1, -1, -1},
{10, 1, 2, 6, 11, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{1, 2, 10, 3, 0, 8, 6, 11, 7, -1, -1, -1, -1, -1, -1, -1},
{2, 9, 0, 2, 10, 9, 6, 11, 7, -1, -1, -1, -1, -1, -1, -1},
{6, 11, 7, 2, 10, 3, 10, 8, 3, 10, 9, 8, -1, -1, -1, -1},
{7, 2, 3, 6, 2, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{7, 0, 8, 7, 6, 0, 6, 2, 0, -1, -1, -1, -1, -1, -1, -1},
{2, 7, 6, 2, 3, 7, 0, 1, 9, -1, -1, -1, -1, -1, -1, -1},
{1, 6, 2, 1, 8, 6, 1, 9, 8, 8, 7, 6, -1, -1, -1, -1},
{10, 7, 6, 10, 1, 7, 1, 3, 7, -1, -1, -1, -1, -1, -1, -1},
{10, 7, 6, 1, 7, 10, 1, 8, 7, 1, 0, 8, -1, -1, -1, -1},
{0, 3, 7, 0, 7, 10, 0, 10, 9, 6, 10, 7, -1, -1, -1, -1},
{7, 6, 10, 7, 10, 8, 8, 10, 9, -1, -1, -1, -1, -1, -1, -1},
{6, 8, 4, 11, 8, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{3, 6, 11, 3, 0, 6, 0, 4, 6, -1, -1, -1, -1, -1, -1, -1},
{8, 6, 11, 8, 4, 6, 9, 0, 1, -1, -1, -1, -1, -1, -1, -1},
{9, 4, 6, 9, 6, 3, 9, 3, 1, 11, 3, 6, -1, -1, -1, -1},
{6, 8, 4, 6, 11, 8, 2, 10, 1, -1, -1, -1, -1, -1, -1, -1},
{1, 2, 10, 3, 0, 11, 0, 6, 11, 0, 4, 6, -1, -1, -1, -1},
{4, 11, 8, 4, 6, 11, 0, 2, 9, 2, 10, 9, -1, -1, -1, -1},
{10, 9, 3, 10, 3, 2, 9, 4, 3, 11, 3, 6, 4, 6, 3, -1},
{8, 2, 3, 8, 4, 2, 4, 6, 2, -1, -1, -1, -1, -1, -1, -1},
{0, 4, 2, 4, 6, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{1, 9, 0, 2, 3, 4, 2, 4, 6, 4, 3, 8, -1, -1, -1, -1},
{1, 9, 4, 1, 4, 2, 2, 4, 6, -1, -1, -1, -1, -1, -1, -1},
{8, 1, 3, 8, 6, 1, 8, 4, 6, 6, 10, 1, -1, -1, -1, -1},
{10, 1, 0, 10, 0, 6, 6, 0, 4, -1, -1, -1, -1, -1, -1, -1},
{4, 6, 3, 4, 3, 8, 6, 10, 3, 0, 3, 9, 10, 9, 3, -1},
{10, 9, 4, 6, 10, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{4, 9, 5, 7, 6, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{0, 8, 3, 4, 9, 5, 11, 7, 6, -1, -1, -1, -1, -1, -1, -1},
{5, 0, 1, 5, 4, 0, 7, 6, 11, -1, -1, -1, -1, -1, -1, -1},
{11, 7, 6, 8, 3, 4, 3, 5, 4, 3, 1, 5, -1, -1, -1, -1},
{9, 5, 4, 10, 1, 2, 7, 6, 11, -1, -1, -1, -1, -1, -1, -1},
{6, 11, 7, 1, 2, 10, 0, 8, 3, 4, 9, 5, -1, -1, -1, -1},
{7, 6, 11, 5, 4, 10, 4, 2, 10, 4, 0, 2, -1, -1, -1, -1},
{3, 4, 8, 3, 5, 4, 3, 2, 5, 10, 5, 2, 11, 7, 6, -1},
{7, 2, 3, 7, 6, 2, 5, 4, 9, -1, -1, -1, -1, -1, -1, -1},
{9, 5, 4, 0, 8, 6, 0, 6, 2, 6, 8, 7, -1, -1, -1, -1},
{3, 6, 2, 3, 7, 6, 1, 5, 0, 5, 4, 0, -1, -1, -1, -1},
{6, 2, 8, 6, 8, 7, 2, 1, 8, 4, 8, 5, 1, 5, 8, -1},
{9, 5, 4, 10, 1, 6, 1, 7, 6, 1, 3, 7, -1, -1, -1, -1},
{1, 6, 10, 1, 7, 6, 1, 0, 7, 8, 7, 0, 9, 5, 4, -1},
{4, 0, 10, 4, 10, 5, 0, 3, 10, 6, 10, 7, 3, 7, 10, -1},
{7, 6, 10, 7, 10, 8, 5, 4, 10, 4, 8, 10, -1, -1, -1, -1},
{6, 9, 5, 6, 11, 9, 11, 8, 9, -1, -1, -1, -1, -1, -1, -1},
{3, 6, 11, 0, 6, 3, 0, 5, 6, 0, 9, 5, -1, -1, -1, -1},
{0, 11, 8, 0, 5, 11, 0, 1, 5, 5, 6, 11, -1, -1, -1, -1},
{6, 11, 3, 6, 3, 5, 5, 3, 1, -1, -1, -1, -1, -1, -1, -1},
{1, 2, 10, 9, 5, 11, 9, 11, 8, 11, 5, 6, -1, -1, -1, -1},
{0, 11, 3, 0, 6, 11, 0, 9, 6, 5, 6, 9, 1, 2, 10, -1},
{11, 8, 5, 11, 5, 6, 8, 0, 5, 10, 5, 2, 0, 2, 5, -1},
{6, 11, 3, 6, 3, 5, 2, 10, 3, 10, 5, 3, -1, -1, -1, -1},
{5, 8, 9, 5, 2, 8, 5, 6, 2, 3, 8, 2, -1, -1, -1, -1},
{9, 5, 6, 9, 6, 0, 0, 6, 2, -1, -1, -1, -1, -1, -1, -1},
{1, 5, 8, 1, 8, 0, 5, 6, 8, 3, 8, 2, 6, 2, 8, -1},
{1, 5, 6, 2, 1, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{1, 3, 6, 1, 6, 10, 3, 8, 6, 5, 6, 9, 8, 9, 6, -1},
{10, 1, 0, 10, 0, 6, 9, 5, 0, 5, 6, 0, -1, -1, -1, -1},
{0, 3, 8, 5, 6, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{10, 5, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{11, 5, 10, 7, 5, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{11, 5, 10, 11, 7, 5, 8, 3, 0, -1, -1, -1, -1, -1, -1, -1},
{5, 11, 7, 5, 10, 11, 1, 9, 0, -1, -1, -1, -1, -1, -1, -1},
{10, 7, 5, 10, 11, 7, 9, 8, 1, 8, 3, 1, -1, -1, -1, -1},
{11, 1, 2, 11, 7, 1, 7, 5, 1, -1, -1, -1, -1, -1, -1, -1},
{0, 8, 3, 1, 2, 7, 1, 7, 5, 7, 2, 11, -1, -1, -1, -1},
{9, 7, 5, 9, 2, 7, 9, 0, 2, 2, 11, 7, -1, -1, -1, -1},
{7, 5, 2, 7, 2, 11, 5, 9, 2, 3, 2, 8, 9, 8, 2, -1},
{2, 5, 10, 2, 3, 5, 3, 7, 5, -1, -1, -1, -1, -1, -1, -1},
{8, 2, 0, 8, 5, 2, 8, 7, 5, 10, 2, 5, -1, -1, -1, -1},
{9, 0, 1, 5, 10, 3, 5, 3, 7, 3, 10, 2, -1, -1, -1, -1},
{9, 8, 2, 9, 2, 1, 8, 7, 2, 10, 2, 5, 7, 5, 2, -1},
{1, 3, 5, 3, 7, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{0, 8, 7, 0, 7, 1, 1, 7, 5, -1, -1, -1, -1, -1, -1, -1},
{9, 0, 3, 9, 3, 5, 5, 3, 7, -1, -1, -1, -1, -1, -1, -1},
{9, 8, 7, 5, 9, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{5, 8, 4, 5, 10, 8, 10, 11, 8, -1, -1, -1, -1, -1, -1, -1},
{5, 0, 4, 5, 11, 0, 5, 10, 11, 11, 3, 0, -1, -1, -1, -1},
{0, 1, 9, 8, 4, 10, 8, 10, 11, 10, 4, 5, -1, -1, -1, -1},
{10, 11, 4, 10, 4, 5, 11, 3, 4, 9, 4, 1, 3, 1, 4, -1},
{2, 5, 1, 2, 8, 5, 2, 11, 8, 4, 5, 8, -1, -1, -1, -1},
{0, 4, 11, 0, 11, 3, 4, 5, 11, 2, 11, 1, 5, 1, 11, -1},
{0, 2, 5, 0, 5, 9, 2, 11, 5, 4, 5, 8, 11, 8, 5, -1},
{9, 4, 5, 2, 11, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{2, 5, 10, 3, 5, 2, 3, 4, 5, 3, 8, 4, -1, -1, -1, -1},
{5, 10, 2, 5, 2, 4, 4, 2, 0, -1, -1, -1, -1, -1, -1, -1},
{3, 10, 2, 3, 5, 10, 3, 8, 5, 4, 5, 8, 0, 1, 9, -1},
{5, 10, 2, 5, 2, 4, 1, 9, 2, 9, 4, 2, -1, -1, -1, -1},
{8, 4, 5, 8, 5, 3, 3, 5, 1, -1, -1, -1, -1, -1, -1, -1},
{0, 4, 5, 1, 0, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{8, 4, 5, 8, 5, 3, 9, 0, 5, 0, 3, 5, -1, -1, -1, -1},
{9, 4, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{4, 11, 7, 4, 9, 11, 9, 10, 11, -1, -1, -1, -1, -1, -1, -1},
{0, 8, 3, 4, 9, 7, 9, 11, 7, 9, 10, 11, -1, -1, -1, -1},
{1, 10, 11, 1, 11, 4, 1, 4, 0, 7, 4, 11, -1, -1, -1, -1},
{3, 1, 4, 3, 4, 8, 1, 10, 4, 7, 4, 11, 10, 11, 4, -1},
{4, 11, 7, 9, 11, 4, 9, 2, 11, 9, 1, 2, -1, -1, -1, -1},
{9, 7, 4, 9, 11, 7, 9, 1, 11, 2, 11, 1, 0, 8, 3, -1},
{11, 7, 4, 11, 4, 2, 2, 4, 0, -1, -1, -1, -1, -1, -1, -1},
{11, 7, 4, 11, 4, 2, 8, 3, 4, 3, 2, 4, -1, -1, -1, -1},
{2, 9, 10, 2, 7, 9, 2, 3, 7, 7, 4, 9, -1, -1, -1, -1},
{9, 10, 7, 9, 7, 4, 10, 2, 7, 8, 7, 0, 2, 0, 7, -1},
{3, 7, 10, 3, 10, 2, 7, 4, 10, 1, 10, 0, 4, 0, 10, -1},
{1, 10, 2, 8, 7, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{4, 9, 1, 4, 1, 7, 7, 1, 3, -1, -1, -1, -1, -1, -1, -1},
{4, 9, 1, 4, 1, 7, 0, 8, 1, 8, 7, 1, -1, -1, -1, -1},
{4, 0, 3, 7, 4, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{4, 8, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{9, 10, 8, 10, 11, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{3, 0, 9, 3, 9, 11, 11, 9, 10, -1, -1, -1, -1, -1, -1, -1},
{0, 1, 10, 0, 10, 8, 8, 10, 11, -1, -1, -1, -1, -1, -1, -1},
{3, 1, 10, 11, 3, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{1, 2, 11, 1, 11, 9, 9, 11, 8, -1, -1, -1, -1, -1, -1, -1},
{3, 0, 9, 3, 9, 11, 1, 2, 9, 2, 11, 9, -1, -1, -1, -1},
{0, 2, 11, 8, 0, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{3, 2, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{2, 3, 8, 2, 8, 10, 10, 8, 9, -1, -1, -1, -1, -1, -1, -1},
{9, 10, 2, 0, 9, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{2, 3, 8, 2, 8, 10, 0, 1, 8, 1, 10, 8, -1, -1, -1, -1},
{1, 10, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{1, 3, 8, 9, 1, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{0, 9, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{0, 3, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}};
/*
Given a grid cell and an isolevel, calculate the triangular
facets required to represent the isosurface through the cell.
Return the number of triangular facets, the array "triangles"
will be loaded up with the vertices at most 5 triangular facets.
0 will be returned if the grid cell is either totally above
of totally below the isolevel.
*/
int MarchingCubes::Polygonise(GRIDCELL &grid, TRIANGLE *triangles) {
int i, ntriang;
int cubeindex;
XYZ vertlist[12];
XYZ normlist[12];
/*
Determine the index into the edge table which
tells us which vertices are inside of the surface
*/
cubeindex = 0;
if (grid.p[0].a < iso) cubeindex |= 1;
if (grid.p[1].a < iso) cubeindex |= 2;
if (grid.p[2].a < iso) cubeindex |= 4;
if (grid.p[3].a < iso) cubeindex |= 8;
if (grid.p[4].a < iso) cubeindex |= 16;
if (grid.p[5].a < iso) cubeindex |= 32;
if (grid.p[6].a < iso) cubeindex |= 64;
if (grid.p[7].a < iso) cubeindex |= 128;
/* Cube is entirely in/out of the surface */
if (edgeTable[cubeindex] == 0)
return (0);
/* Find the vertices where the surface intersects the cube */
if (edgeTable[cubeindex] & 1) {
vertlist[0] =
VertexInterp(iso, grid.p[0].v, grid.p[1].v, grid.p[0].a, grid.p[1].a);
normlist[0] =
VertexInterpNormal(iso, grid.n[0], grid.n[1], grid.p[0].a, grid.p[1].a);
}
if (edgeTable[cubeindex] & 2) {
vertlist[1] =
VertexInterp(iso, grid.p[1].v, grid.p[2].v, grid.p[1].a, grid.p[2].a);
normlist[1] =
VertexInterpNormal(iso, grid.n[1], grid.n[2], grid.p[1].a, grid.p[2].a);
}
if (edgeTable[cubeindex] & 4) {
vertlist[2] =
VertexInterp(iso, grid.p[2].v, grid.p[3].v, grid.p[2].a, grid.p[3].a);
normlist[2] =
VertexInterpNormal(iso, grid.n[2], grid.n[3], grid.p[2].a, grid.p[3].a);
}
if (edgeTable[cubeindex] & 8) {
vertlist[3] =
VertexInterp(iso, grid.p[3].v, grid.p[0].v, grid.p[3].a, grid.p[0].a);
normlist[3] =
VertexInterpNormal(iso, grid.n[3], grid.n[0], grid.p[3].a, grid.p[0].a);
}
if (edgeTable[cubeindex] & 16) {
vertlist[4] =
VertexInterp(iso, grid.p[4].v, grid.p[5].v, grid.p[4].a, grid.p[5].a);
normlist[4] =
VertexInterpNormal(iso, grid.n[4], grid.n[5], grid.p[4].a, grid.p[5].a);
}
if (edgeTable[cubeindex] & 32) {
vertlist[5] =
VertexInterp(iso, grid.p[5].v, grid.p[6].v, grid.p[5].a, grid.p[6].a);
normlist[5] =
VertexInterpNormal(iso, grid.n[5], grid.n[6], grid.p[5].a, grid.p[6].a);
}
if (edgeTable[cubeindex] & 64) {
vertlist[6] =
VertexInterp(iso, grid.p[6].v, grid.p[7].v, grid.p[6].a, grid.p[7].a);
normlist[6] =
VertexInterpNormal(iso, grid.n[6], grid.n[7], grid.p[6].a, grid.p[7].a);
}
if (edgeTable[cubeindex] & 128) {
vertlist[7] =
VertexInterp(iso, grid.p[7].v, grid.p[4].v, grid.p[7].a, grid.p[4].a);
normlist[7] =
VertexInterpNormal(iso, grid.n[7], grid.n[4], grid.p[7].a, grid.p[4].a);
}
if (edgeTable[cubeindex] & 256) {
vertlist[8] =
VertexInterp(iso, grid.p[0].v, grid.p[4].v, grid.p[0].a, grid.p[4].a);
normlist[8] =
VertexInterpNormal(iso, grid.n[0], grid.n[4], grid.p[0].a, grid.p[4].a);
}
if (edgeTable[cubeindex] & 512) {
vertlist[9] =
VertexInterp(iso, grid.p[1].v, grid.p[5].v, grid.p[1].a, grid.p[5].a);
normlist[9] =
VertexInterpNormal(iso, grid.n[1], grid.n[5], grid.p[1].a, grid.p[5].a);
}
if (edgeTable[cubeindex] & 1024) {
vertlist[10] =
VertexInterp(iso, grid.p[2].v, grid.p[6].v, grid.p[2].a, grid.p[6].a);
normlist[10] =
VertexInterpNormal(iso, grid.n[2], grid.n[6], grid.p[2].a, grid.p[6].a);
}
if (edgeTable[cubeindex] & 2048) {
vertlist[11] =
VertexInterp(iso, grid.p[3].v, grid.p[7].v, grid.p[3].a, grid.p[7].a);
normlist[11] =
VertexInterpNormal(iso, grid.n[3], grid.n[7], grid.p[3].a, grid.p[7].a);
}
/* Create the triangle */
ntriang = 0;
for (i = 0; triTable[cubeindex][i] != -1; i += 3) {
triangles[ntriang].p[0] = vertlist[triTable[cubeindex][i]];
triangles[ntriang].p[1] = vertlist[triTable[cubeindex][i + 1]];
triangles[ntriang].p[2] = vertlist[triTable[cubeindex][i + 2]];
triangles[ntriang].n[0] = normlist[triTable[cubeindex][i]];
triangles[ntriang].n[1] = normlist[triTable[cubeindex][i + 1]];
triangles[ntriang].n[2] = normlist[triTable[cubeindex][i + 2]];
ntriang++;
}
return (ntriang);
}
bool operator<(const Vector3f &left, const Vector3f &right) {
if (left[0] < right[0])
return true;
else if (left[0] > right[0])
return false;
if (left[1] < right[1])
return true;
else if (left[1] > right[1])
return false;
if (left[2] < right[2])
return true;
else if (left[2] > right[2])
return false;
return false;
}
/*
Linearly interpolate the position where an isosurface cuts
an edge between two vertices, each with their own scalar value
*/
MarchingCubes::XYZ MarchingCubes::VertexInterp(float isolevel, MarchingCubes::XYZ &p1, MarchingCubes::XYZ &p2,
float valp1, float valp2) {
float mu;
XYZ p;
if (fabs(isolevel - valp1) < 0.00001)
return (p1);
if (fabs(isolevel - valp2) < 0.00001)
return (p2);
if (fabs(valp1 - valp2) < 0.00001)
return (p1);
mu = (isolevel - valp1) / (valp2 - valp1);
p = p1 + (p2 - p1).mult(mu);
return p;
}
MarchingCubes::XYZ MarchingCubes::VertexInterpNormal(float isolevel, MarchingCubes::XYZ &np1, MarchingCubes::XYZ &np2,
float valp1, float valp2) {
float mu;
XYZ p;
if (fabs(isolevel - valp1) < 0.00001)
return (np1);
if (fabs(isolevel - valp2) < 0.00001)
return (np2);
if (fabs(valp1 - valp2) < 0.00001)
return (np1);
mu = (isolevel - valp1) / (valp2 - valp1);
p = np1.mult(1.f - mu) + np2.mult(mu);
return p;
}
/* DEPRECATED
void MarchingCubes::updateGradient(int index) {
//only update normals if center index is within cube grid
if (0 <= index && index < size) {
//for each neighbouring grid cell
for (int x = -1; x <= 1; x++) {
for (int y = -1; y <= 1; y++) {
for (int z = -1; z <= 1; z++) {
// only neighbouring cells though, not the cell itself
if (abs(x) + abs(y) + abs(z) == 1) {
//calculate grid cell index
int centerIndex = index + x + cubeCornerDim[0] * (y + cubeCornerDim[1] * z);
//only update normals if grid cell is within cube grid
if (0 <= centerIndex && centerIndex < size) {
//get all the indices of grid cell-neighbouring cells, setting them to the cell
// itself when they are outside the cube grid
int plusXIndex = index + 1;
plusXIndex = plusXIndex < size ? plusXIndex : index;
int minusXIndex = index - 1;
minusXIndex = minusXIndex >= 0 ? minusXIndex : index;
int plusYIndex = index + cubeCornerDim[0];
plusYIndex = plusYIndex < size ? plusYIndex : index;
int minusYIndex = index - cubeCornerDim[0];
minusYIndex = minusYIndex >= 0 ? minusYIndex : index;
int plusZIndex = index + cubeCornerDim[0] * cubeCornerDim[1];
plusZIndex = plusZIndex < size ? plusZIndex : index;
int minusZIndex = index - cubeCornerDim[0] * cubeCornerDim[1];
minusZIndex = minusZIndex >= 0 ? minusZIndex : index;
//calculate gradient from neighbouring cell difference
float dx = cubeCorners[plusXIndex] - cubeCorners[minusXIndex];
float dy = cubeCorners[plusYIndex] - cubeCorners[minusYIndex];
float dz = cubeCorners[plusZIndex] - cubeCorners[minusZIndex];
//save gradient
gradientCorners[index] = XYZ{dx, dy, dz};
}
}
}
}
}
}
}
*/
/* DEPRECATED
MarchingCubes::XYZ MarchingCubes::getEdgeNormal(MarchingCubes::XYZ edgePoint) {
XYZ edgeStart = XYZ{floorf(edgePoint[0] / cubeStep) * cubeStep,
floorf(edgePoint[1] / cubeStep) * cubeStep,
floorf(edgePoint[2] / cubeStep) * cubeStep};
XYZ edgeEnd = XYZ{ceilf(edgePoint[0] / cubeStep) * cubeStep,
ceilf(edgePoint[1] / cubeStep) * cubeStep,
ceilf(edgePoint[2] / cubeStep) * cubeStep};
//edge should fall inside of grid
if (cubeStart < edgeStart && edgeStart < cubeEnd
&& cubeStart < edgeEnd && edgeEnd < cubeEnd) {
// get normal at edge start
XYZ relEdgeStart = edgeStart - cubeStart;
int edgeStartGridPos[3] = {(int) lroundf(relEdgeStart[0] / cubeStep),
(int) lroundf(relEdgeStart[1] / cubeStep),
(int) lroundf(relEdgeStart[2] / cubeStep)};
int edgeStartIndex = edgeStartGridPos[0] + cubeCornerDim[0] * (edgeStartGridPos[1] + (cubeCornerDim[1] * edgeStartGridPos[2]));
XYZ startNormal = gradientCorners[edgeStartIndex];
// get normal at edge end
XYZ relEdgeEnd = edgeEnd - cubeStart;
int edgeEndGridPos[3] = {(int) lroundf(relEdgeEnd[0] / cubeStep),
(int) lroundf(relEdgeEnd[1] / cubeStep),
(int) lroundf(relEdgeEnd[2] / cubeStep)};
int edgeEndIndex = edgeEndGridPos[0] + cubeCornerDim[0] * (edgeEndGridPos[1] + (cubeCornerDim[1] * edgeEndGridPos[2]));
XYZ endNormal = gradientCorners[edgeEndIndex];
// return average of start end end normal
XYZ normal = (startNormal + endNormal).div(2.f);
normal.normalize();
return normal;
} else {
return XYZ{0.f, 0.f, 0.f};
}
}
*/
void MarchingCubes::drawMarching() {
for (int i = 0; i < size; i++) {
cubeCorners[i] = XYZA{XYZ{.0f, .0f, .0f}, .0f};
//gradientCorners[i] = XYZ{0.f,0.f,0.f};
}
for (Particle *p: system->particles) {
if (!p->movable) continue;
Vector3f vecPos = p->position;
XYZ pos = {vecPos[0], vecPos[1], vecPos[2]};
// only apply marching cube to particle when it is inside the rendering volume
if (pos[0] > cubeStart[0] && pos[1] > cubeStart[1] && pos[2] > cubeStart[2]
&& pos[0] < cubeEnd[0] && pos[1] < cubeEnd[1] && pos[2] < cubeEnd[2]) {
// add the distance between the point and each of the 8 corners of its surrounding gridcube
// to the grid values
// lower corner [0, 0, 0] of gridcube
XYZ lowerGridPos = XYZ{floor(pos[0] / cubeStep) * cubeStep,
floor(pos[1] / cubeStep) * cubeStep,
floor(pos[2] / cubeStep) * cubeStep};
int lowerCubePos = (int) (floor(pos[0] / cubeStep) + -cubeStartInt[0] +
cubeCornerDim[0] * (floor(pos[1] / cubeStep) + -cubeStartInt[1]
+ (cubeCornerDim[1] *
(floor(pos[2] / cubeStep) + -cubeStartInt[2]))));
//fill in all the gridcube values
int steps = (int) ceilf(particleRange / cubeStep);
for (int x = -steps; x <= steps + 1; x++) {
for (int y = -steps; y <= steps + 1; y++) {
for (int z = -steps; z <= steps + 1; z++) {
XYZ gridPos = lowerGridPos + XYZ{x * cubeStep, y * cubeStep, z * cubeStep};
int cubePos = lowerCubePos + x + (cubeCornerDim[0] * (y + cubeCornerDim[1] * z));
if (cubePos < cubeCornerDim[0] * cubeCornerDim[1] * cubeCornerDim[0] && cubePos >= 0) {
XYZ relPos = pos - gridPos;
float relDist = relPos.size();
cubeCorners[cubePos].a = min(
cubeCorners[cubePos].a +
max(particleRange - relDist, 0.f) / particleRange, 1.f);
cubeCorners[cubePos].v += relPos.normalize().mult(max(particleRange - relDist, 0.f) / -particleRange);
// update gradients based on change in grid
// updateGradient(cubePos);
}
}
}
}
}
}
triangles.clear();
//normals.clear();
for (int x = cubeStartInt[0]; x < cubeEndInt[0] - 1; x++) {
for (int y = cubeStartInt[1]; y < cubeEndInt[1] - 1; y++) {
for (int z = cubeStartInt[2]; z < cubeEndInt[2] - 1; z++) {
int cubePos0 =
x + -cubeStartInt[0] + cubeCornerDim[0] * (y + -cubeStartInt[1] +
(cubeCornerDim[1] * (z + -cubeStartInt[2])));
int cubePos1 = cubePos0 + 1; // [1,0,0]
int cubePos2 = cubePos0 + 1 + cubeCornerDim[0]; // [1,1,0]
int cubePos3 = cubePos0 + cubeCornerDim[0]; // [0,1,0]
int cubePos4 = cubePos0 + cubeCornerDim[0] * cubeCornerDim[1]; // [0,0,1]
int cubePos5 = cubePos0 + 1 + cubeCornerDim[0] * cubeCornerDim[1]; // [1,0,1]
int cubePos6 = cubePos0 + 1 + cubeCornerDim[0] + cubeCornerDim[0] * cubeCornerDim[1]; // [1,1,1]
int cubePos7 = cubePos0 + cubeCornerDim[0] + cubeCornerDim[0] * cubeCornerDim[1]; // [0,1,1]
GRIDCELL cell = {
{
XYZA{XYZ{x * cubeStep, y * cubeStep, z * cubeStep}, cubeCorners[cubePos0].a}, //[0,0,0]
XYZA{XYZ{x * cubeStep + cubeStep, y * cubeStep, z * cubeStep},
cubeCorners[cubePos1].a}, //[1,0,0]
XYZA{XYZ{x * cubeStep + cubeStep, y * cubeStep + cubeStep, z * cubeStep},
cubeCorners[cubePos2].a}, //[1,1,0]
XYZA{XYZ{x * cubeStep, y * cubeStep + cubeStep, z * cubeStep},
cubeCorners[cubePos3].a}, //[0,1,0]
XYZA{XYZ{x * cubeStep, y * cubeStep, z * cubeStep + cubeStep},
cubeCorners[cubePos4].a}, //[0,0,1]
XYZA{XYZ{x * cubeStep + cubeStep, y * cubeStep, z * cubeStep + cubeStep},
cubeCorners[cubePos5].a}, //[1,0,1]
XYZA{XYZ{x * cubeStep + cubeStep, y * cubeStep + cubeStep, z * cubeStep + cubeStep},
cubeCorners[cubePos6].a}, //[1,1,1]
XYZA{XYZ{x * cubeStep, y * cubeStep + cubeStep, z * cubeStep + cubeStep},
cubeCorners[cubePos7].a} //[0,1,1]
}, {
cubeCorners[cubePos0].v,
cubeCorners[cubePos1].v,
cubeCorners[cubePos2].v,
cubeCorners[cubePos3].v,
cubeCorners[cubePos4].v,
cubeCorners[cubePos5].v,
cubeCorners[cubePos6].v,
cubeCorners[cubePos7].v,
}
};
double cellsum = 0;
cellsum += cubeCorners[cubePos0].a;
cellsum += cubeCorners[cubePos1].a;
cellsum += cubeCorners[cubePos2].a;
cellsum += cubeCorners[cubePos3].a;
cellsum += cubeCorners[cubePos4].a;
cellsum += cubeCorners[cubePos5].a;
cellsum += cubeCorners[cubePos6].a;
cellsum += cubeCorners[cubePos7].a;
if (cellsum > 0) {
TRIANGLE tris[5] = {};
int n = Polygonise(cell, tris);
if (n > 0) {
for (int i = 0; i < n; i++) {
TRIANGLE tri = tris[i];
triangles.push_back(tri);
/* add normal to combined normals of each point in triangle. (per-vertex normals) DEPRECATED
XYZ a = tri.p[0];
XYZ b = tri.p[1];
XYZ c = tri.p[2];
XYZ norm = (b - a)^(c - b);
long akey = a.toLongHash();
if (!normals.emplace(akey, norm).second) {
normals[akey] += norm;
}
long bkey = b.toLongHash();
if (!normals.emplace(bkey, norm).second) {
normals[bkey] += norm;
}
long ckey = c.toLongHash();
if (!normals.emplace(ckey, norm).second) {
normals[ckey] += norm;
}
//*/
}
}
}
/* draw each grid cell DEBUG
if (cubeCorners[cubePos0] > 0.f) {
glColor3f(cubeCorners[cubePos0], 0.f, 0.f);
glPushMatrix();
glTranslated(x*cubeStep, y*cubeStep, z*cubeStep);
glBegin(GL_POINTS);
glVertex3f(0.f, 0.f, 0.f);
glEnd();
glPopMatrix();
}
//*/
}
}
}
//// draw triangles
if (system->type == SystemBuilder::SMOKE)
glColor4f(0.9f, 0.9f, 0.9f, 0.2f);
else
glColor4f(0.1f, 0.9f, 0.9f, 1.0f);
glBegin(GL_TRIANGLES);
for (int i = 0; i < triangles.size(); i++) {
TRIANGLE triangle = triangles[i];
XYZ a = triangle.p[0];
XYZ b = triangle.p[1];
XYZ c = triangle.p[2];
//*/// per vertex normals
XYZ anorm = triangle.n[0].normalize();
XYZ bnorm = triangle.n[1].normalize();
XYZ cnorm = triangle.n[2].normalize();
/*/// per-face normals
XYZ norm = (b - a)^(c - b);
norm.normalize();
XYZ anorm = norm;
XYZ bnorm = norm;
XYZ cnorm = norm;
/* /// per vertex normals
XYZ anorm = normals[a.toLongHash()];
XYZ bnorm = normals[b.toLongHash()];
XYZ cnorm = normals[c.toLongHash()];
anorm.normalize();
bnorm.normalize();
cnorm.normalize();
///
/* per vertex normals 2 DEPRECATED
XYZ anorm = getEdgeNormal(a).mult(-1.f);
XYZ bnorm = getEdgeNormal(b).mult(-1.f);
XYZ cnorm = getEdgeNormal(c).mult(-1.f);
//*/
glNormal3f(anorm[0], anorm[1], anorm[2]);
glVertex3f(a[0], a[1], a[2]);
glNormal3f(bnorm[0], bnorm[1], bnorm[2]);
glVertex3f(b[0], b[1], b[2]);
glNormal3f(cnorm[0], cnorm[1], cnorm[2]);
glVertex3f(c[0], c[1], c[2]);
}
glEnd();
//*/
}
MarchingCubes::MarchingCubes(System *system) : system(system) {
cubeStart = XYZ{-1.1f, -1.1f, -1.1f};
cubeEnd = XYZ{1.1f, 1.1f, 1.1f};
cubeStep = .0125f; // a whole number of steps should fit into interval
cubeStartInt = new int[3];
cubeEndInt = new int[3];
cubeCornerDim = new int[3];
for (int i = 0; i < 3; i++) {
cubeStartInt[i] = (int) roundf(cubeStart[i] / cubeStep);
cubeEndInt[i] = (int) roundf(cubeEnd[i] / cubeStep);
cubeCornerDim[i] = cubeEndInt[0] - cubeStartInt[0] + 1;
}
size = cubeCornerDim[0] * cubeCornerDim[1] * cubeCornerDim[2];
cubeCorners = new XYZA[size];
//gradientCorners = new XYZ[size];
for (int i = 0; i < size; i++) {
cubeCorners[i] = XYZA{XYZ{0.f, 0.f, 0.f},0.f};
//gradientCorners[i] = XYZ{0.f, 0.f, 0.f};
}
particleRange = .1f;
iso = .3f;
triangles = {};
//normals = {};
}
MarchingCubes::~MarchingCubes() {
delete cubeCorners;
//delete gradientCorners;
delete[] cubeStartInt;
delete[] cubeEndInt;
delete[] cubeCornerDim;
}