text: #pragma once
  
  #ifndef MARCHING_CUBES_H
  #define MARCHING_CUBES_H
  
  #include "SimpleMesh.h"
  #include "Volume.h"
  
  struct MC_Triangle {
  	EIGEN_MAKE_ALIGNED_OPERATOR_NEW
  	Vector3d p[3];
  };
  
  struct MC_Gridcell {
  	EIGEN_MAKE_ALIGNED_OPERATOR_NEW
  	Vector3d p[8];
  	double val[8];
  };
  
  struct MC_Gridcell_2 {
  	EIGEN_MAKE_ALIGNED_OPERATOR_NEW
  	Vector3d p[8];
  	double val[8];
  	Vector3d ev0[8];
  };
  
  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
  };
  
  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 }
  };
  
  
  //****************************************************************************************************************
  /*
  Linearly interpolate the position where an isosurface cuts
  an edge between two vertices, each with their own scalar value
  */
  Vector3d VertexInterp(double isolevel, const Vector3d& p1, const Vector3d& p2, double valp1, double valp2)
  {
  
  	// TODO: implement the linear interpolant
  	// Assume that the function value at 'p1' is 'valp1' and the function value at 'p2' is 'valp2'.
  	// Further assume that the function is linear between 'p1' and 'p2'. Compute and return the
  	// point 'p' on the line from 'p1' to 'p2' where the function takes on the value 'isolevel'
  	//
  	//       f(p2) = valp2
  	//       x
  	//      /
  	//     x f(p) = isolevel
  	//    /
  	//   /
  	//  /
  	// x
  	// f(p1) = valp1
  	double totalDiff = valp2 - valp1;
  	double pDiff = isolevel - valp1;
  
  	return p1 + (p2 - p1)* pDiff / totalDiff;
  
  	//return (p1+p2)/2; // replace me
  }
  
  /*
  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
  or totally below the isolevel.
  */
  int Polygonise(MC_Gridcell grid, double isolevel, MC_Triangle* triangles) {
  
  	int ntriang;
  	int cubeindex;
  	Vector3d vertlist[12];
  
  	cubeindex = 0;
  	if (grid.val[0] < isolevel) cubeindex |= 1;
  	if (grid.val[1] < isolevel) cubeindex |= 2;
  	if (grid.val[2] < isolevel) cubeindex |= 4;
  	if (grid.val[3] < isolevel) cubeindex |= 8;
  	if (grid.val[4] < isolevel) cubeindex |= 16;
  	if (grid.val[5] < isolevel) cubeindex |= 32;
  	if (grid.val[6] < isolevel) cubeindex |= 64;
  	if (grid.val[7] < isolevel) 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(isolevel, grid.p[0], grid.p[1], grid.val[0], grid.val[1]);
  	if (edgeTable[cubeindex] & 2)
  		vertlist[1] = VertexInterp(isolevel, grid.p[1], grid.p[2], grid.val[1], grid.val[2]);
  	if (edgeTable[cubeindex] & 4)
  		vertlist[2] = VertexInterp(isolevel, grid.p[2], grid.p[3], grid.val[2], grid.val[3]);
  	if (edgeTable[cubeindex] & 8)
  		vertlist[3] = VertexInterp(isolevel, grid.p[3], grid.p[0], grid.val[3], grid.val[0]);
  	if (edgeTable[cubeindex] & 16)
  		vertlist[4] = VertexInterp(isolevel, grid.p[4], grid.p[5], grid.val[4], grid.val[5]);
  	if (edgeTable[cubeindex] & 32)
  		vertlist[5] = VertexInterp(isolevel, grid.p[5], grid.p[6], grid.val[5], grid.val[6]);
  	if (edgeTable[cubeindex] & 64)
  		vertlist[6] = VertexInterp(isolevel, grid.p[6], grid.p[7], grid.val[6], grid.val[7]);
  	if (edgeTable[cubeindex] & 128)
  		vertlist[7] = VertexInterp(isolevel, grid.p[7], grid.p[4], grid.val[7], grid.val[4]);
  	if (edgeTable[cubeindex] & 256)
  		vertlist[8] = VertexInterp(isolevel, grid.p[0], grid.p[4], grid.val[0], grid.val[4]);
  	if (edgeTable[cubeindex] & 512)
  		vertlist[9] = VertexInterp(isolevel, grid.p[1], grid.p[5], grid.val[1], grid.val[5]);
  	if (edgeTable[cubeindex] & 1024)
  		vertlist[10] = VertexInterp(isolevel, grid.p[2], grid.p[6], grid.val[2], grid.val[6]);
  	if (edgeTable[cubeindex] & 2048)
  		vertlist[11] = VertexInterp(isolevel, grid.p[3], grid.p[7], grid.val[3], grid.val[7]);
  
  	/* Create the triangle */
  	ntriang = 0;
  	for (int 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]];
  		ntriang++;
  	}
  
  	return ntriang;
  }
  
  
  bool ProcessVolumeCell(Volume* vol, int x, int y, int z, double iso, SimpleMesh* mesh)
  {
  	MC_Gridcell cell;
  
  	Vector3d tmp;
  
  	// cell corners
  	tmp = vol->pos(x + 1, y, z);
  	cell.p[0] = Vector3d(tmp[0], tmp[1], tmp[2]);
  	tmp = vol->pos(x, y, z);
  	cell.p[1] = Vector3d(tmp[0], tmp[1], tmp[2]);
  	tmp = vol->pos(x, y + 1, z);
  	cell.p[2] = Vector3d(tmp[0], tmp[1], tmp[2]);
  	tmp = vol->pos(x + 1, y + 1, z);
  	cell.p[3] = Vector3d(tmp[0], tmp[1], tmp[2]);
  	tmp = vol->pos(x + 1, y, z + 1);
  	cell.p[4] = Vector3d(tmp[0], tmp[1], tmp[2]);
  	tmp = vol->pos(x, y, z + 1);
  	cell.p[5] = Vector3d(tmp[0], tmp[1], tmp[2]);
  	tmp = vol->pos(x, y + 1, z + 1);
  	cell.p[6] = Vector3d(tmp[0], tmp[1], tmp[2]);
  	tmp = vol->pos(x + 1, y + 1, z + 1);
  	cell.p[7] = Vector3d(tmp[0], tmp[1], tmp[2]);
  
  	// cell corner values
  	cell.val[0] = (double)vol->get(x + 1, y, z);
  	cell.val[1] = (double)vol->get(x, y, z);
  	cell.val[2] = (double)vol->get(x, y + 1, z);
  	cell.val[3] = (double)vol->get(x + 1, y + 1, z);
  	cell.val[4] = (double)vol->get(x + 1, y, z + 1);
  	cell.val[5] = (double)vol->get(x, y, z + 1);
  	cell.val[6] = (double)vol->get(x, y + 1, z + 1);
  	cell.val[7] = (double)vol->get(x + 1, y + 1, z + 1);
  
  	MC_Triangle tris[6];
  	int numTris = Polygonise(cell, iso, tris);
  
  	if (numTris == 0)
  		return false;
  
  	for (int i1 = 0; i1 < numTris; i1++)
  	{
  		Vertex v0((float)tris[i1].p[0][0], (float)tris[i1].p[0][1], (float)tris[i1].p[0][2]);
  		Vertex v1((float)tris[i1].p[1][0], (float)tris[i1].p[1][1], (float)tris[i1].p[1][2]);
  		Vertex v2((float)tris[i1].p[2][0], (float)tris[i1].p[2][1], (float)tris[i1].p[2][2]);
  
  		unsigned int vhandle[3];
  		vhandle[0] = mesh->AddVertex(v0);
  		vhandle[1] = mesh->AddVertex(v1);
  		vhandle[2] = mesh->AddVertex(v2);
  
  		mesh->AddFace(vhandle[0], vhandle[1], vhandle[2]);
  	}
  
  	return true;
  }
  
  #endif // MARCHING_CUBES_H
  