// File Name: CIsoSurface.cpp
// Last Modified: 5/8/2000
// Author: Raghavendra Chandrashekara (based on source code provided
// by Paul Bourke and Cory Gene Bloyd)
// Email: rc99@doc.ic.ac.uk, rchandrashekara@hotmail.com
//
// Description: This is the implementation file for the CIsoSurface class.

#include <cmath>
#include <limits>
#include <cstdlib>
#include "CIsoSurface.h"

// disable the warning  "conversion from 'int' to 'const unsigned int'"
#pragma warning( disable : 4245 ) 

template <class T> const unsigned int CIsoSurface<T>::m_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 unsigned int minus_1 = std::numeric_limits<unsigned int>::max();

template <class T> const unsigned int CIsoSurface<T>::m_triTable[256][16] = {
	{minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{0, 8, 3, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{0, 1, 9, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{1, 8, 3, 9, 8, 1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{1, 2, 10, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{0, 8, 3, 1, 2, 10, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{9, 2, 10, 0, 2, 9, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{2, 8, 3, 2, 10, 8, 10, 9, 8, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{3, 11, 2, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{0, 11, 2, 8, 11, 0, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{1, 9, 0, 2, 3, 11, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{1, 11, 2, 1, 9, 11, 9, 8, 11, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{3, 10, 1, 11, 10, 3, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{0, 10, 1, 0, 8, 10, 8, 11, 10, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{3, 9, 0, 3, 11, 9, 11, 10, 9, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{9, 8, 10, 10, 8, 11, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{4, 7, 8, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{4, 3, 0, 7, 3, 4, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{0, 1, 9, 8, 4, 7, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{4, 1, 9, 4, 7, 1, 7, 3, 1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{1, 2, 10, 8, 4, 7, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{3, 4, 7, 3, 0, 4, 1, 2, 10, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{9, 2, 10, 9, 0, 2, 8, 4, 7, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{2, 10, 9, 2, 9, 7, 2, 7, 3, 7, 9, 4, minus_1, minus_1, minus_1, minus_1},
	{8, 4, 7, 3, 11, 2, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{11, 4, 7, 11, 2, 4, 2, 0, 4, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{9, 0, 1, 8, 4, 7, 2, 3, 11, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{4, 7, 11, 9, 4, 11, 9, 11, 2, 9, 2, 1, minus_1, minus_1, minus_1, minus_1},
	{3, 10, 1, 3, 11, 10, 7, 8, 4, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{1, 11, 10, 1, 4, 11, 1, 0, 4, 7, 11, 4, minus_1, minus_1, minus_1, minus_1},
	{4, 7, 8, 9, 0, 11, 9, 11, 10, 11, 0, 3, minus_1, minus_1, minus_1, minus_1},
	{4, 7, 11, 4, 11, 9, 9, 11, 10, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{9, 5, 4, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{9, 5, 4, 0, 8, 3, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{0, 5, 4, 1, 5, 0, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{8, 5, 4, 8, 3, 5, 3, 1, 5, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{1, 2, 10, 9, 5, 4, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{3, 0, 8, 1, 2, 10, 4, 9, 5, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{5, 2, 10, 5, 4, 2, 4, 0, 2, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{2, 10, 5, 3, 2, 5, 3, 5, 4, 3, 4, 8, minus_1, minus_1, minus_1, minus_1},
	{9, 5, 4, 2, 3, 11, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{0, 11, 2, 0, 8, 11, 4, 9, 5, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{0, 5, 4, 0, 1, 5, 2, 3, 11, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{2, 1, 5, 2, 5, 8, 2, 8, 11, 4, 8, 5, minus_1, minus_1, minus_1, minus_1},
	{10, 3, 11, 10, 1, 3, 9, 5, 4, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{4, 9, 5, 0, 8, 1, 8, 10, 1, 8, 11, 10, minus_1, minus_1, minus_1, minus_1},
	{5, 4, 0, 5, 0, 11, 5, 11, 10, 11, 0, 3, minus_1, minus_1, minus_1, minus_1},
	{5, 4, 8, 5, 8, 10, 10, 8, 11, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{9, 7, 8, 5, 7, 9, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{9, 3, 0, 9, 5, 3, 5, 7, 3, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{0, 7, 8, 0, 1, 7, 1, 5, 7, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{1, 5, 3, 3, 5, 7, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{9, 7, 8, 9, 5, 7, 10, 1, 2, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{10, 1, 2, 9, 5, 0, 5, 3, 0, 5, 7, 3, minus_1, minus_1, minus_1, minus_1},
	{8, 0, 2, 8, 2, 5, 8, 5, 7, 10, 5, 2, minus_1, minus_1, minus_1, minus_1},
	{2, 10, 5, 2, 5, 3, 3, 5, 7, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{7, 9, 5, 7, 8, 9, 3, 11, 2, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{9, 5, 7, 9, 7, 2, 9, 2, 0, 2, 7, 11, minus_1, minus_1, minus_1, minus_1},
	{2, 3, 11, 0, 1, 8, 1, 7, 8, 1, 5, 7, minus_1, minus_1, minus_1, minus_1},
	{11, 2, 1, 11, 1, 7, 7, 1, 5, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{9, 5, 8, 8, 5, 7, 10, 1, 3, 10, 3, 11, minus_1, minus_1, minus_1, minus_1},
	{5, 7, 0, 5, 0, 9, 7, 11, 0, 1, 0, 10, 11, 10, 0, minus_1},
	{11, 10, 0, 11, 0, 3, 10, 5, 0, 8, 0, 7, 5, 7, 0, minus_1},
	{11, 10, 5, 7, 11, 5, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{10, 6, 5, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{0, 8, 3, 5, 10, 6, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{9, 0, 1, 5, 10, 6, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{1, 8, 3, 1, 9, 8, 5, 10, 6, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{1, 6, 5, 2, 6, 1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{1, 6, 5, 1, 2, 6, 3, 0, 8, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{9, 6, 5, 9, 0, 6, 0, 2, 6, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{5, 9, 8, 5, 8, 2, 5, 2, 6, 3, 2, 8, minus_1, minus_1, minus_1, minus_1},
	{2, 3, 11, 10, 6, 5, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{11, 0, 8, 11, 2, 0, 10, 6, 5, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{0, 1, 9, 2, 3, 11, 5, 10, 6, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{5, 10, 6, 1, 9, 2, 9, 11, 2, 9, 8, 11, minus_1, minus_1, minus_1, minus_1},
	{6, 3, 11, 6, 5, 3, 5, 1, 3, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{0, 8, 11, 0, 11, 5, 0, 5, 1, 5, 11, 6, minus_1, minus_1, minus_1, minus_1},
	{3, 11, 6, 0, 3, 6, 0, 6, 5, 0, 5, 9, minus_1, minus_1, minus_1, minus_1},
	{6, 5, 9, 6, 9, 11, 11, 9, 8, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{5, 10, 6, 4, 7, 8, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{4, 3, 0, 4, 7, 3, 6, 5, 10, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{1, 9, 0, 5, 10, 6, 8, 4, 7, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{10, 6, 5, 1, 9, 7, 1, 7, 3, 7, 9, 4, minus_1, minus_1, minus_1, minus_1},
	{6, 1, 2, 6, 5, 1, 4, 7, 8, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{1, 2, 5, 5, 2, 6, 3, 0, 4, 3, 4, 7, minus_1, minus_1, minus_1, minus_1},
	{8, 4, 7, 9, 0, 5, 0, 6, 5, 0, 2, 6, minus_1, minus_1, minus_1, minus_1},
	{7, 3, 9, 7, 9, 4, 3, 2, 9, 5, 9, 6, 2, 6, 9, minus_1},
	{3, 11, 2, 7, 8, 4, 10, 6, 5, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{5, 10, 6, 4, 7, 2, 4, 2, 0, 2, 7, 11, minus_1, minus_1, minus_1, minus_1},
	{0, 1, 9, 4, 7, 8, 2, 3, 11, 5, 10, 6, minus_1, minus_1, minus_1, minus_1},
	{9, 2, 1, 9, 11, 2, 9, 4, 11, 7, 11, 4, 5, 10, 6, minus_1},
	{8, 4, 7, 3, 11, 5, 3, 5, 1, 5, 11, 6, minus_1, minus_1, minus_1, minus_1},
	{5, 1, 11, 5, 11, 6, 1, 0, 11, 7, 11, 4, 0, 4, 11, minus_1},
	{0, 5, 9, 0, 6, 5, 0, 3, 6, 11, 6, 3, 8, 4, 7, minus_1},
	{6, 5, 9, 6, 9, 11, 4, 7, 9, 7, 11, 9, minus_1, minus_1, minus_1, minus_1},
	{10, 4, 9, 6, 4, 10, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{4, 10, 6, 4, 9, 10, 0, 8, 3, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{10, 0, 1, 10, 6, 0, 6, 4, 0, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{8, 3, 1, 8, 1, 6, 8, 6, 4, 6, 1, 10, minus_1, minus_1, minus_1, minus_1},
	{1, 4, 9, 1, 2, 4, 2, 6, 4, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{3, 0, 8, 1, 2, 9, 2, 4, 9, 2, 6, 4, minus_1, minus_1, minus_1, minus_1},
	{0, 2, 4, 4, 2, 6, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{8, 3, 2, 8, 2, 4, 4, 2, 6, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{10, 4, 9, 10, 6, 4, 11, 2, 3, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{0, 8, 2, 2, 8, 11, 4, 9, 10, 4, 10, 6, minus_1, minus_1, minus_1, minus_1},
	{3, 11, 2, 0, 1, 6, 0, 6, 4, 6, 1, 10, minus_1, minus_1, minus_1, minus_1},
	{6, 4, 1, 6, 1, 10, 4, 8, 1, 2, 1, 11, 8, 11, 1, minus_1},
	{9, 6, 4, 9, 3, 6, 9, 1, 3, 11, 6, 3, minus_1, minus_1, minus_1, minus_1},
	{8, 11, 1, 8, 1, 0, 11, 6, 1, 9, 1, 4, 6, 4, 1, minus_1},
	{3, 11, 6, 3, 6, 0, 0, 6, 4, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{6, 4, 8, 11, 6, 8, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{7, 10, 6, 7, 8, 10, 8, 9, 10, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{0, 7, 3, 0, 10, 7, 0, 9, 10, 6, 7, 10, minus_1, minus_1, minus_1, minus_1},
	{10, 6, 7, 1, 10, 7, 1, 7, 8, 1, 8, 0, minus_1, minus_1, minus_1, minus_1},
	{10, 6, 7, 10, 7, 1, 1, 7, 3, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{1, 2, 6, 1, 6, 8, 1, 8, 9, 8, 6, 7, minus_1, minus_1, minus_1, minus_1},
	{2, 6, 9, 2, 9, 1, 6, 7, 9, 0, 9, 3, 7, 3, 9, minus_1},
	{7, 8, 0, 7, 0, 6, 6, 0, 2, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{7, 3, 2, 6, 7, 2, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{2, 3, 11, 10, 6, 8, 10, 8, 9, 8, 6, 7, minus_1, minus_1, minus_1, minus_1},
	{2, 0, 7, 2, 7, 11, 0, 9, 7, 6, 7, 10, 9, 10, 7, minus_1},
	{1, 8, 0, 1, 7, 8, 1, 10, 7, 6, 7, 10, 2, 3, 11, minus_1},
	{11, 2, 1, 11, 1, 7, 10, 6, 1, 6, 7, 1, minus_1, minus_1, minus_1, minus_1},
	{8, 9, 6, 8, 6, 7, 9, 1, 6, 11, 6, 3, 1, 3, 6, minus_1},
	{0, 9, 1, 11, 6, 7, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{7, 8, 0, 7, 0, 6, 3, 11, 0, 11, 6, 0, minus_1, minus_1, minus_1, minus_1},
	{7, 11, 6, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{7, 6, 11, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{3, 0, 8, 11, 7, 6, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{0, 1, 9, 11, 7, 6, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{8, 1, 9, 8, 3, 1, 11, 7, 6, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{10, 1, 2, 6, 11, 7, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{1, 2, 10, 3, 0, 8, 6, 11, 7, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{2, 9, 0, 2, 10, 9, 6, 11, 7, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{6, 11, 7, 2, 10, 3, 10, 8, 3, 10, 9, 8, minus_1, minus_1, minus_1, minus_1},
	{7, 2, 3, 6, 2, 7, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{7, 0, 8, 7, 6, 0, 6, 2, 0, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{2, 7, 6, 2, 3, 7, 0, 1, 9, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{1, 6, 2, 1, 8, 6, 1, 9, 8, 8, 7, 6, minus_1, minus_1, minus_1, minus_1},
	{10, 7, 6, 10, 1, 7, 1, 3, 7, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{10, 7, 6, 1, 7, 10, 1, 8, 7, 1, 0, 8, minus_1, minus_1, minus_1, minus_1},
	{0, 3, 7, 0, 7, 10, 0, 10, 9, 6, 10, 7, minus_1, minus_1, minus_1, minus_1},
	{7, 6, 10, 7, 10, 8, 8, 10, 9, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{6, 8, 4, 11, 8, 6, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{3, 6, 11, 3, 0, 6, 0, 4, 6, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{8, 6, 11, 8, 4, 6, 9, 0, 1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{9, 4, 6, 9, 6, 3, 9, 3, 1, 11, 3, 6, minus_1, minus_1, minus_1, minus_1},
	{6, 8, 4, 6, 11, 8, 2, 10, 1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{1, 2, 10, 3, 0, 11, 0, 6, 11, 0, 4, 6, minus_1, minus_1, minus_1, minus_1},
	{4, 11, 8, 4, 6, 11, 0, 2, 9, 2, 10, 9, minus_1, minus_1, minus_1, minus_1},
	{10, 9, 3, 10, 3, 2, 9, 4, 3, 11, 3, 6, 4, 6, 3, minus_1},
	{8, 2, 3, 8, 4, 2, 4, 6, 2, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{0, 4, 2, 4, 6, 2, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{1, 9, 0, 2, 3, 4, 2, 4, 6, 4, 3, 8, minus_1, minus_1, minus_1, minus_1},
	{1, 9, 4, 1, 4, 2, 2, 4, 6, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{8, 1, 3, 8, 6, 1, 8, 4, 6, 6, 10, 1, minus_1, minus_1, minus_1, minus_1},
	{10, 1, 0, 10, 0, 6, 6, 0, 4, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{4, 6, 3, 4, 3, 8, 6, 10, 3, 0, 3, 9, 10, 9, 3, minus_1},
	{10, 9, 4, 6, 10, 4, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{4, 9, 5, 7, 6, 11, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{0, 8, 3, 4, 9, 5, 11, 7, 6, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{5, 0, 1, 5, 4, 0, 7, 6, 11, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{11, 7, 6, 8, 3, 4, 3, 5, 4, 3, 1, 5, minus_1, minus_1, minus_1, minus_1},
	{9, 5, 4, 10, 1, 2, 7, 6, 11, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{6, 11, 7, 1, 2, 10, 0, 8, 3, 4, 9, 5, minus_1, minus_1, minus_1, minus_1},
	{7, 6, 11, 5, 4, 10, 4, 2, 10, 4, 0, 2, minus_1, minus_1, minus_1, minus_1},
	{3, 4, 8, 3, 5, 4, 3, 2, 5, 10, 5, 2, 11, 7, 6, minus_1},
	{7, 2, 3, 7, 6, 2, 5, 4, 9, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{9, 5, 4, 0, 8, 6, 0, 6, 2, 6, 8, 7, minus_1, minus_1, minus_1, minus_1},
	{3, 6, 2, 3, 7, 6, 1, 5, 0, 5, 4, 0, minus_1, minus_1, minus_1, minus_1},
	{6, 2, 8, 6, 8, 7, 2, 1, 8, 4, 8, 5, 1, 5, 8, minus_1},
	{9, 5, 4, 10, 1, 6, 1, 7, 6, 1, 3, 7, minus_1, minus_1, minus_1, minus_1},
	{1, 6, 10, 1, 7, 6, 1, 0, 7, 8, 7, 0, 9, 5, 4, minus_1},
	{4, 0, 10, 4, 10, 5, 0, 3, 10, 6, 10, 7, 3, 7, 10, minus_1},
	{7, 6, 10, 7, 10, 8, 5, 4, 10, 4, 8, 10, minus_1, minus_1, minus_1, minus_1},
	{6, 9, 5, 6, 11, 9, 11, 8, 9, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{3, 6, 11, 0, 6, 3, 0, 5, 6, 0, 9, 5, minus_1, minus_1, minus_1, minus_1},
	{0, 11, 8, 0, 5, 11, 0, 1, 5, 5, 6, 11, minus_1, minus_1, minus_1, minus_1},
	{6, 11, 3, 6, 3, 5, 5, 3, 1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{1, 2, 10, 9, 5, 11, 9, 11, 8, 11, 5, 6, minus_1, minus_1, minus_1, minus_1},
	{0, 11, 3, 0, 6, 11, 0, 9, 6, 5, 6, 9, 1, 2, 10, minus_1},
	{11, 8, 5, 11, 5, 6, 8, 0, 5, 10, 5, 2, 0, 2, 5, minus_1},
	{6, 11, 3, 6, 3, 5, 2, 10, 3, 10, 5, 3, minus_1, minus_1, minus_1, minus_1},
	{5, 8, 9, 5, 2, 8, 5, 6, 2, 3, 8, 2, minus_1, minus_1, minus_1, minus_1},
	{9, 5, 6, 9, 6, 0, 0, 6, 2, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{1, 5, 8, 1, 8, 0, 5, 6, 8, 3, 8, 2, 6, 2, 8, minus_1},
	{1, 5, 6, 2, 1, 6, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{1, 3, 6, 1, 6, 10, 3, 8, 6, 5, 6, 9, 8, 9, 6, minus_1},
	{10, 1, 0, 10, 0, 6, 9, 5, 0, 5, 6, 0, minus_1, minus_1, minus_1, minus_1},
	{0, 3, 8, 5, 6, 10, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{10, 5, 6, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{11, 5, 10, 7, 5, 11, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{11, 5, 10, 11, 7, 5, 8, 3, 0, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{5, 11, 7, 5, 10, 11, 1, 9, 0, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{10, 7, 5, 10, 11, 7, 9, 8, 1, 8, 3, 1, minus_1, minus_1, minus_1, minus_1},
	{11, 1, 2, 11, 7, 1, 7, 5, 1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{0, 8, 3, 1, 2, 7, 1, 7, 5, 7, 2, 11, minus_1, minus_1, minus_1, minus_1},
	{9, 7, 5, 9, 2, 7, 9, 0, 2, 2, 11, 7, minus_1, minus_1, minus_1, minus_1},
	{7, 5, 2, 7, 2, 11, 5, 9, 2, 3, 2, 8, 9, 8, 2, minus_1},
	{2, 5, 10, 2, 3, 5, 3, 7, 5, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{8, 2, 0, 8, 5, 2, 8, 7, 5, 10, 2, 5, minus_1, minus_1, minus_1, minus_1},
	{9, 0, 1, 5, 10, 3, 5, 3, 7, 3, 10, 2, minus_1, minus_1, minus_1, minus_1},
	{9, 8, 2, 9, 2, 1, 8, 7, 2, 10, 2, 5, 7, 5, 2, minus_1},
	{1, 3, 5, 3, 7, 5, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{0, 8, 7, 0, 7, 1, 1, 7, 5, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{9, 0, 3, 9, 3, 5, 5, 3, 7, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{9, 8, 7, 5, 9, 7, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{5, 8, 4, 5, 10, 8, 10, 11, 8, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{5, 0, 4, 5, 11, 0, 5, 10, 11, 11, 3, 0, minus_1, minus_1, minus_1, minus_1},
	{0, 1, 9, 8, 4, 10, 8, 10, 11, 10, 4, 5, minus_1, minus_1, minus_1, minus_1},
	{10, 11, 4, 10, 4, 5, 11, 3, 4, 9, 4, 1, 3, 1, 4, minus_1},
	{2, 5, 1, 2, 8, 5, 2, 11, 8, 4, 5, 8, minus_1, minus_1, minus_1, minus_1},
	{0, 4, 11, 0, 11, 3, 4, 5, 11, 2, 11, 1, 5, 1, 11, minus_1},
	{0, 2, 5, 0, 5, 9, 2, 11, 5, 4, 5, 8, 11, 8, 5, minus_1},
	{9, 4, 5, 2, 11, 3, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{2, 5, 10, 3, 5, 2, 3, 4, 5, 3, 8, 4, minus_1, minus_1, minus_1, minus_1},
	{5, 10, 2, 5, 2, 4, 4, 2, 0, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{3, 10, 2, 3, 5, 10, 3, 8, 5, 4, 5, 8, 0, 1, 9, minus_1},
	{5, 10, 2, 5, 2, 4, 1, 9, 2, 9, 4, 2, minus_1, minus_1, minus_1, minus_1},
	{8, 4, 5, 8, 5, 3, 3, 5, 1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{0, 4, 5, 1, 0, 5, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{8, 4, 5, 8, 5, 3, 9, 0, 5, 0, 3, 5, minus_1, minus_1, minus_1, minus_1},
	{9, 4, 5, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{4, 11, 7, 4, 9, 11, 9, 10, 11, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{0, 8, 3, 4, 9, 7, 9, 11, 7, 9, 10, 11, minus_1, minus_1, minus_1, minus_1},
	{1, 10, 11, 1, 11, 4, 1, 4, 0, 7, 4, 11, minus_1, minus_1, minus_1, minus_1},
	{3, 1, 4, 3, 4, 8, 1, 10, 4, 7, 4, 11, 10, 11, 4, minus_1},
	{4, 11, 7, 9, 11, 4, 9, 2, 11, 9, 1, 2, minus_1, minus_1, minus_1, minus_1},
	{9, 7, 4, 9, 11, 7, 9, 1, 11, 2, 11, 1, 0, 8, 3, minus_1},
	{11, 7, 4, 11, 4, 2, 2, 4, 0, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{11, 7, 4, 11, 4, 2, 8, 3, 4, 3, 2, 4, minus_1, minus_1, minus_1, minus_1},
	{2, 9, 10, 2, 7, 9, 2, 3, 7, 7, 4, 9, minus_1, minus_1, minus_1, minus_1},
	{9, 10, 7, 9, 7, 4, 10, 2, 7, 8, 7, 0, 2, 0, 7, minus_1},
	{3, 7, 10, 3, 10, 2, 7, 4, 10, 1, 10, 0, 4, 0, 10, minus_1},
	{1, 10, 2, 8, 7, 4, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{4, 9, 1, 4, 1, 7, 7, 1, 3, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{4, 9, 1, 4, 1, 7, 0, 8, 1, 8, 7, 1, minus_1, minus_1, minus_1, minus_1},
	{4, 0, 3, 7, 4, 3, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{4, 8, 7, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{9, 10, 8, 10, 11, 8, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{3, 0, 9, 3, 9, 11, 11, 9, 10, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{0, 1, 10, 0, 10, 8, 8, 10, 11, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{3, 1, 10, 11, 3, 10, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{1, 2, 11, 1, 11, 9, 9, 11, 8, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{3, 0, 9, 3, 9, 11, 1, 2, 9, 2, 11, 9, minus_1, minus_1, minus_1, minus_1},
	{0, 2, 11, 8, 0, 11, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{3, 2, 11, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{2, 3, 8, 2, 8, 10, 10, 8, 9, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{9, 10, 2, 0, 9, 2, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{2, 3, 8, 2, 8, 10, 0, 1, 8, 1, 10, 8, minus_1, minus_1, minus_1, minus_1},
	{1, 10, 2, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{1, 3, 8, 9, 1, 8, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{0, 9, 1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{0, 3, 8, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1},
	{minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1, minus_1}
};

template <class T> CIsoSurface<T>::CIsoSurface()
{
	m_fCellLengthX = 0;
	m_fCellLengthY = 0;
	m_fCellLengthZ = 0;
	m_nCellsX = 0;
	m_nCellsY = 0;
	m_nCellsZ = 0;
	m_nTriangles = 0;
	m_nNormals = 0;
	m_nVertices = 0;
	m_ppt3dVertices = NULL;
	m_piTriangleIndices = NULL;
	m_pvec3dNormals = NULL;
	m_ptScalarField = NULL;
	m_tIsoLevel = 0;
	m_bValidSurface = false;
}

template <class T> CIsoSurface<T>::~CIsoSurface()
{
	DeleteSurface();
}

template <class T> void CIsoSurface<T>::GenerateSurface(const T* ptScalarField, T tIsoLevel, unsigned int nCellsX, unsigned int nCellsY, unsigned int nCellsZ, T fCellLengthX, T fCellLengthY, T fCellLengthZ)
{
	if (m_bValidSurface)
		DeleteSurface();

	m_tIsoLevel = tIsoLevel;
	m_nCellsX = nCellsX;
	m_nCellsY = nCellsY;
	m_nCellsZ = nCellsZ;
	m_fCellLengthX = fCellLengthX;
	m_fCellLengthY = fCellLengthY;
	m_fCellLengthZ = fCellLengthZ;
	m_ptScalarField = ptScalarField;

	unsigned int nPointsInXDirection = (m_nCellsX + 1);
	unsigned int nPointsInSlice = nPointsInXDirection*(m_nCellsY + 1);

	// Generate isosurface.
	for (unsigned int z = 0; z < m_nCellsZ; z++)
		for (unsigned int y = 0; y < m_nCellsY; y++)
			for (unsigned int x = 0; x < m_nCellsX; x++) {
				// Calculate table lookup index from those
				// vertices which are below the isolevel.
				unsigned int tableIndex = 0;
				if (m_ptScalarField[z*nPointsInSlice + y*nPointsInXDirection + x] < m_tIsoLevel)
					tableIndex |= 1;
				if (m_ptScalarField[z*nPointsInSlice + (y+1)*nPointsInXDirection + x] < m_tIsoLevel)
					tableIndex |= 2;
				if (m_ptScalarField[z*nPointsInSlice + (y+1)*nPointsInXDirection + (x+1)] < m_tIsoLevel)
					tableIndex |= 4;
				if (m_ptScalarField[z*nPointsInSlice + y*nPointsInXDirection + (x+1)] < m_tIsoLevel)
					tableIndex |= 8;
				if (m_ptScalarField[(z+1)*nPointsInSlice + y*nPointsInXDirection + x] < m_tIsoLevel)
					tableIndex |= 16;
				if (m_ptScalarField[(z+1)*nPointsInSlice + (y+1)*nPointsInXDirection + x] < m_tIsoLevel)
					tableIndex |= 32;
				if (m_ptScalarField[(z+1)*nPointsInSlice + (y+1)*nPointsInXDirection + (x+1)] < m_tIsoLevel)
					tableIndex |= 64;
				if (m_ptScalarField[(z+1)*nPointsInSlice + y*nPointsInXDirection + (x+1)] < m_tIsoLevel)
					tableIndex |= 128;

				// Now create a triangulation of the isosurface in this
				// cell.
				if (m_edgeTable[tableIndex] != 0) {
					if (m_edgeTable[tableIndex] & 8) {
						POINT3DID pt = CalculateIntersection(x, y, z, 3);
						unsigned int id = GetEdgeID(x, y, z, 3);
						m_i2pt3idVertices.insert(ID2POINT3DID::value_type(id, pt));
					}
					if (m_edgeTable[tableIndex] & 1) {
						POINT3DID pt = CalculateIntersection(x, y, z, 0);
						unsigned int id = GetEdgeID(x, y, z, 0);
						m_i2pt3idVertices.insert(ID2POINT3DID::value_type(id, pt));
					}
					if (m_edgeTable[tableIndex] & 256) {
						POINT3DID pt = CalculateIntersection(x, y, z, 8);
						unsigned int id = GetEdgeID(x, y, z, 8);
						m_i2pt3idVertices.insert(ID2POINT3DID::value_type(id, pt));
					}
					
					if (x == m_nCellsX - 1) {
						if (m_edgeTable[tableIndex] & 4) {
							POINT3DID pt = CalculateIntersection(x, y, z, 2);
							unsigned int id = GetEdgeID(x, y, z, 2);
							m_i2pt3idVertices.insert(ID2POINT3DID::value_type(id, pt));
						}
						if (m_edgeTable[tableIndex] & 2048) {
							POINT3DID pt = CalculateIntersection(x, y, z, 11);
							unsigned int id = GetEdgeID(x, y, z, 11);
							m_i2pt3idVertices.insert(ID2POINT3DID::value_type(id, pt));
						}
					}
					if (y == m_nCellsY - 1) {
						if (m_edgeTable[tableIndex] & 2) {
							POINT3DID pt = CalculateIntersection(x, y, z, 1);
							unsigned int id = GetEdgeID(x, y, z, 1);
							m_i2pt3idVertices.insert(ID2POINT3DID::value_type(id, pt));
						}
						if (m_edgeTable[tableIndex] & 512) {
							POINT3DID pt = CalculateIntersection(x, y, z, 9);
							unsigned int id = GetEdgeID(x, y, z, 9);
							m_i2pt3idVertices.insert(ID2POINT3DID::value_type(id, pt));
						}
					}
					if (z == m_nCellsZ - 1) {
						if (m_edgeTable[tableIndex] & 16) {
							POINT3DID pt = CalculateIntersection(x, y, z, 4);
							unsigned int id = GetEdgeID(x, y, z, 4);
							m_i2pt3idVertices.insert(ID2POINT3DID::value_type(id, pt));
						}
						if (m_edgeTable[tableIndex] & 128) {
							POINT3DID pt = CalculateIntersection(x, y, z, 7);
							unsigned int id = GetEdgeID(x, y, z, 7);
							m_i2pt3idVertices.insert(ID2POINT3DID::value_type(id, pt));
						}
					}
					if ((x==m_nCellsX - 1) && (y==m_nCellsY - 1))
						if (m_edgeTable[tableIndex] & 1024) {
							POINT3DID pt = CalculateIntersection(x, y, z, 10);
							unsigned int id = GetEdgeID(x, y, z, 10);
							m_i2pt3idVertices.insert(ID2POINT3DID::value_type(id, pt));
						}
					if ((x==m_nCellsX - 1) && (z==m_nCellsZ - 1))
						if (m_edgeTable[tableIndex] & 64) {
							POINT3DID pt = CalculateIntersection(x, y, z, 6);
							unsigned int id = GetEdgeID(x, y, z, 6);
							m_i2pt3idVertices.insert(ID2POINT3DID::value_type(id, pt));
						}
					if ((y==m_nCellsY - 1) && (z==m_nCellsZ - 1))
						if (m_edgeTable[tableIndex] & 32) {
							POINT3DID pt = CalculateIntersection(x, y, z, 5);
							unsigned int id = GetEdgeID(x, y, z, 5);
							m_i2pt3idVertices.insert(ID2POINT3DID::value_type(id, pt));
						}
					
					for (unsigned int i = 0; m_triTable[tableIndex][i] != -1; i += 3) {
						TRIANGLE triangle;
						unsigned int pointID0, pointID1, pointID2;
						pointID0 = GetEdgeID(x, y, z, m_triTable[tableIndex][i]);
						pointID1 = GetEdgeID(x, y, z, m_triTable[tableIndex][i+1]);
						pointID2 = GetEdgeID(x, y, z, m_triTable[tableIndex][i+2]);
						triangle.pointID[0] = pointID0;
						triangle.pointID[1] = pointID1;
						triangle.pointID[2] = pointID2;
						m_trivecTriangles.push_back(triangle);
					}
				}
			}
	
	RenameVerticesAndTriangles();
	CalculateNormals();
	m_bValidSurface = true;
}

template <class T> bool CIsoSurface<T>::IsSurfaceValid()
{
	return m_bValidSurface;
}

template <class T> void CIsoSurface<T>::DeleteSurface()
{
	m_fCellLengthX = 0;
	m_fCellLengthY = 0;
	m_fCellLengthZ = 0;
	m_nCellsX = 0;
	m_nCellsY = 0;
	m_nCellsZ = 0;
	m_nTriangles = 0;
	m_nNormals = 0;
	m_nVertices = 0;
	if (m_ppt3dVertices != NULL) {
		delete[] m_ppt3dVertices;
		m_ppt3dVertices = NULL;
	}
	if (m_piTriangleIndices != NULL) {
		delete[] m_piTriangleIndices;
		m_piTriangleIndices = NULL;
	}
	if (m_pvec3dNormals != NULL) {
		delete[] m_pvec3dNormals;
		m_pvec3dNormals = NULL;
	}
	m_ptScalarField = NULL;
	m_tIsoLevel = 0;
	m_bValidSurface = false;
}

template <class T> int CIsoSurface<T>::GetVolumeLengths(T& fVolLengthX, T& fVolLengthY, T& fVolLengthZ)
{
	if (IsSurfaceValid()) {
		fVolLengthX = m_fCellLengthX*m_nCellsX;
		fVolLengthY = m_fCellLengthY*m_nCellsY;
		fVolLengthZ = m_fCellLengthZ*m_nCellsZ;
		return 1;
	}
	else
		return -1;
}

template <class T> unsigned int CIsoSurface<T>::GetEdgeID(unsigned int nX, unsigned int nY, unsigned int nZ, unsigned int nEdgeNo)
{
	switch (nEdgeNo) {
	case 0:
		return GetVertexID(nX, nY, nZ) + 1;
	case 1:
		return GetVertexID(nX, nY + 1, nZ);
	case 2:
		return GetVertexID(nX + 1, nY, nZ) + 1;
	case 3:
		return GetVertexID(nX, nY, nZ);
	case 4:
		return GetVertexID(nX, nY, nZ + 1) + 1;
	case 5:
		return GetVertexID(nX, nY + 1, nZ + 1);
	case 6:
		return GetVertexID(nX + 1, nY, nZ + 1) + 1;
	case 7:
		return GetVertexID(nX, nY, nZ + 1);
	case 8:
		return GetVertexID(nX, nY, nZ) + 2;
	case 9:
		return GetVertexID(nX, nY + 1, nZ) + 2;
	case 10:
		return GetVertexID(nX + 1, nY + 1, nZ) + 2;
	case 11:
		return GetVertexID(nX + 1, nY, nZ) + 2;
	default:
		// Invalid edge no.
		return (unsigned int)-1;
	}
}

template <class T> unsigned int CIsoSurface<T>::GetVertexID(unsigned int nX, unsigned int nY, unsigned int nZ)
{
	return 3*(nZ*(m_nCellsY + 1)*(m_nCellsX + 1) + nY*(m_nCellsX + 1) + nX);
}

template <class T> POINT3DID CIsoSurface<T>::CalculateIntersection(unsigned int nX, unsigned int nY, unsigned int nZ, unsigned int nEdgeNo)
{
	T x1, y1, z1, x2, y2, z2;
	unsigned int v1x = nX, v1y = nY, v1z = nZ;
	unsigned int v2x = nX, v2y = nY, v2z = nZ;
	
	switch (nEdgeNo)
	{
	case 0:
		v2y += 1;
		break;
	case 1:
		v1y += 1;
		v2x += 1;
		v2y += 1;
		break;
	case 2:
		v1x += 1;
		v1y += 1;
		v2x += 1;
		break;
	case 3:
		v1x += 1;
		break;
	case 4:
		v1z += 1;
		v2y += 1;
		v2z += 1;
		break;
	case 5:
		v1y += 1;
		v1z += 1;
		v2x += 1;
		v2y += 1;
		v2z += 1;
		break;
	case 6:
		v1x += 1;
		v1y += 1;
		v1z += 1;
		v2x += 1;
		v2z += 1;
		break;
	case 7:
		v1x += 1;
		v1z += 1;
		v2z += 1;
		break;
	case 8:
		v2z += 1;
		break;
	case 9:
		v1y += 1;
		v2y += 1;
		v2z += 1;
		break;
	case 10:
		v1x += 1;
		v1y += 1;
		v2x += 1;
		v2y += 1;
		v2z += 1;
		break;
	case 11:
		v1x += 1;
		v2x += 1;
		v2z += 1;
		break;
	}

	x1 = v1x*m_fCellLengthX;
	y1 = v1y*m_fCellLengthY;
	z1 = v1z*m_fCellLengthZ;
	x2 = v2x*m_fCellLengthX;
	y2 = v2y*m_fCellLengthY;
	z2 = v2z*m_fCellLengthZ;

	unsigned int nPointsInXDirection = (m_nCellsX + 1);
	unsigned int nPointsInSlice = nPointsInXDirection*(m_nCellsY + 1);
	T val1 = m_ptScalarField[v1z*nPointsInSlice + v1y*nPointsInXDirection + v1x];
	T val2 = m_ptScalarField[v2z*nPointsInSlice + v2y*nPointsInXDirection + v2x];
	POINT3DID intersection = Interpolate(x1, y1, z1, x2, y2, z2, val1, val2);
	
	return intersection;
}

template <class T> POINT3DID CIsoSurface<T>::Interpolate(T fX1, T fY1, T fZ1, T fX2, T fY2, T fZ2, T tVal1, T tVal2)
{
	POINT3DID interpolation;
	T mu;

	mu = T((m_tIsoLevel - tVal1))/(tVal2 - tVal1);
	interpolation.x = fX1 + mu*(fX2 - fX1);
	interpolation.y = fY1 + mu*(fY2 - fY1);
	interpolation.z = fZ1 + mu*(fZ2 - fZ1);

	return interpolation;
}

template <class T> void CIsoSurface<T>::RenameVerticesAndTriangles()
{
	unsigned int nextID = 0;
	ID2POINT3DID::iterator mapIterator = m_i2pt3idVertices.begin();
	TRIANGLEVECTOR::iterator vecIterator = m_trivecTriangles.begin();

	// Rename vertices.
	while (mapIterator != m_i2pt3idVertices.end()) {
		(*mapIterator).second.newID = nextID;
		nextID++;
		mapIterator++;
	}

	// Now rename triangles.
	while (vecIterator != m_trivecTriangles.end()) {
		for (unsigned int i = 0; i < 3; i++) {
			unsigned int newID = m_i2pt3idVertices[(*vecIterator).pointID[i]].newID;
			(*vecIterator).pointID[i] = newID;
		}
		vecIterator++;
	}

	// Copy all the vertices and triangles into two arrays so that they
	// can be efficiently accessed.
	// Copy vertices.
	mapIterator = m_i2pt3idVertices.begin();
	m_nVertices = (unsigned int)m_i2pt3idVertices.size();
	m_ppt3dVertices = new POINT3D[m_nVertices];
	for (unsigned int i = 0; i < m_nVertices; i++, mapIterator++) {
		m_ppt3dVertices[i][0] = (*mapIterator).second.x;
		m_ppt3dVertices[i][1] = (*mapIterator).second.y;
		m_ppt3dVertices[i][2] = (*mapIterator).second.z;
	}
	// Copy vertex indices which make triangles.
	vecIterator = m_trivecTriangles.begin();
	m_nTriangles = (unsigned int)m_trivecTriangles.size();
	m_piTriangleIndices = new unsigned int[m_nTriangles*3];
	for (unsigned int i = 0; i < m_nTriangles; i++, vecIterator++) {
		m_piTriangleIndices[i*3] = (*vecIterator).pointID[0];
		m_piTriangleIndices[i*3+1] = (*vecIterator).pointID[1];
		m_piTriangleIndices[i*3+2] = (*vecIterator).pointID[2];
	}

	m_i2pt3idVertices.clear();
	m_trivecTriangles.clear();
}

template <class T> void CIsoSurface<T>::CalculateNormals()
{
	m_nNormals = m_nVertices;
	m_pvec3dNormals = new VECTOR3D[m_nNormals];
	
	// Set all normals to 0.
	for (unsigned int i = 0; i < m_nNormals; i++) {
		m_pvec3dNormals[i][0] = 0;
		m_pvec3dNormals[i][1] = 0;
		m_pvec3dNormals[i][2] = 0;
	}

	// Calculate normals.
	for (unsigned int i = 0; i < m_nTriangles; i++) {
		VECTOR3D vec1, vec2, normal;
		unsigned int id0, id1, id2;
		id0 = m_piTriangleIndices[i*3];
		id1 = m_piTriangleIndices[i*3+1];
		id2 = m_piTriangleIndices[i*3+2];
		vec1[0] = m_ppt3dVertices[id1][0] - m_ppt3dVertices[id0][0];
		vec1[1] = m_ppt3dVertices[id1][1] - m_ppt3dVertices[id0][1];
		vec1[2] = m_ppt3dVertices[id1][2] - m_ppt3dVertices[id0][2];
		vec2[0] = m_ppt3dVertices[id2][0] - m_ppt3dVertices[id0][0];
		vec2[1] = m_ppt3dVertices[id2][1] - m_ppt3dVertices[id0][1];
		vec2[2] = m_ppt3dVertices[id2][2] - m_ppt3dVertices[id0][2];
		normal[0] = vec1[2]*vec2[1] - vec1[1]*vec2[2];
		normal[1] = vec1[0]*vec2[2] - vec1[2]*vec2[0];
		normal[2] = vec1[1]*vec2[0] - vec1[0]*vec2[1];
		m_pvec3dNormals[id0][0] += normal[0];
		m_pvec3dNormals[id0][1] += normal[1];
		m_pvec3dNormals[id0][2] += normal[2];
		m_pvec3dNormals[id1][0] += normal[0];
		m_pvec3dNormals[id1][1] += normal[1];
		m_pvec3dNormals[id1][2] += normal[2];
		m_pvec3dNormals[id2][0] += normal[0];
		m_pvec3dNormals[id2][1] += normal[1];
		m_pvec3dNormals[id2][2] += normal[2];
	}

	// Normalize normals.
	for (unsigned int i = 0; i < m_nNormals; i++) {
		T length = sqrt(m_pvec3dNormals[i][0]*m_pvec3dNormals[i][0] + m_pvec3dNormals[i][1]*m_pvec3dNormals[i][1] + m_pvec3dNormals[i][2]*m_pvec3dNormals[i][2]);
		m_pvec3dNormals[i][0] /= length;
		m_pvec3dNormals[i][1] /= length;
		m_pvec3dNormals[i][2] /= length;
	}
}

template class CIsoSurface<float>;