isoSurface.cpp

Go to the documentation of this file.

/*
 *  IsoSurface.cpp - Isosurface interface generation
 *  Copyright (C) 2018, D Haley 

 *  This program is free software: you can redistribute it and/or modify
 *  it under the terms of the GNU General Public License as published by
 *  the Free Software Foundation, either version 3 of the License, or
 *  (at your option) any later version.

 *  This program is distributed in the hope that it will be useful,
 *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 *  GNU General Public License for more details.

 *  You should have received a copy of the GNU General Public License
 *  along with this program.  If not, see <http://www.gnu.org/licenses/>.
*/
#include "atomprobe/algorithm/isoSurface.h"
#include "atomprobe/helper/aptAssert.h"
#include <map>
#include <list>
#include <vector>


using std::list;
using std::map;
using std::vector;
using std::pair;
using std::make_pair;


#ifdef DEBUG
#include "atomprobe/primitives/mesh.h"
#endif

namespace AtomProbe
{



#ifdef DEBUG
template<class T1, class T2>
bool mapUnique(const std::map<T1,T2> &m) 
{
    vector<T2> vec;
    vec.reserve(m.size());

    for(typename std::map<T1,T2>::const_iterator it = m.begin(); it!=m.end(); ++it)
    {
        if(std::find(vec.begin(),vec.end(),it->second) != vec.end())
            return false;

        vec.push_back(it->second);

    }

    return true;
}
#endif


//input vector "vec" must be sorted and unique
template<class T>
void removeElements( const std::vector<size_t> &elems,std::vector<T> &vec)
{
    if(vec.empty() || elems.empty())
        return;

    if(vec.size() == elems.size())
    {
        vec.clear();
        return;
    }

    size_t offset=vec.size()-1; 
    //Run backwards, swapping out 
    for(size_t ui=elems.size();ui--;)
    {
        ASSERT(ui <= offset);
        std::swap(vec[elems[ui]],vec[offset]);
        offset--;
    }
    vec.resize(offset+1);
}




void TriangleWithVertexNorm::computeACWNormal(Point3D &n) const
{
    Point3D a,b;

    a = p[0]-p[1];
    b = p[0]-p[2];

    n=a.crossProd(b);
    n.normalise();
}

void TriangleWithVertexNorm::safeComputeACWNormal(Point3D &n) const
{
    Point3D a,b;

    a = p[0]-p[1];
    b = p[0]-p[2];

    n=a.crossProd(b);
    if(n.sqrMag() < sqrt(std::numeric_limits<float>::epsilon()) )
        n=Point3D(0,0,1);   
    else
        n.normalise();



}

float TriangleWithVertexNorm::computeArea() const
{
    Point3D a,b;

    a = p[0]-p[1];
    b = p[0]-p[2];

    return  a.crossProd(b).sqrMag();

}

bool TriangleWithVertexNorm::isDegenerate() const
{
    return (p[0].sqrDist(p[1]) < std::numeric_limits<float>::epsilon() ||
    p[0].sqrDist(p[2]) < std::numeric_limits<float>::epsilon() ||
    p[2].sqrDist(p[1]) < std::numeric_limits<float>::epsilon());
}

void TriangleWithVertexNorm::getCentroid(Point3D &c) const
{
    c=p[0];
        c+=p[1];
    c+=p[2];

    c*=1.0f/3.0f;
}

//This code is a modified version of the following:
//==============
// Marching Cubes Example Program 
// by Cory Bloyd (corysama@yahoo.com)
//
// A simple, portable and complete implementation of the Marching Cubes
// and Marching Tetrahedrons algorithms in a single source file.
// There are many ways that this code could be made faster, but the 
// intent is for the code to be easy to understand.
//
// For a description of the algorithm go to
// http://astronomy.swin.edu.au/pbourke/modelling/polygonise/
//
// The original code is public domain, and is used here under the GNU General Public Licence, V3 or later.
// =========

// For any edge, if one vertex is inside of the surface and the other is outside of the surface
//  then the edge intersects the surface
// For each of the 8 vertices of the cube can be two possible states : either inside or outside of the surface
// For any cube the are 2^8=256 possible sets of vertex states
// This table lists the edges intersected by the surface for all 256 possible vertex states
// There are 12 edges.  For each entry in the table, if edge #n is intersected, then bit #n is set to 1
int aiCubeEdgeFlags[256]=
{
        0x000, 0x109, 0x203, 0x30a, 0x406, 0x50f, 0x605, 0x70c, 0x80c, 0x905, 0xa0f, 0xb06, 0xc0a, 0xd03, 0xe09, 0xf00, 
        0x190, 0x099, 0x393, 0x29a, 0x596, 0x49f, 0x795, 0x69c, 0x99c, 0x895, 0xb9f, 0xa96, 0xd9a, 0xc93, 0xf99, 0xe90, 
        0x230, 0x339, 0x033, 0x13a, 0x636, 0x73f, 0x435, 0x53c, 0xa3c, 0xb35, 0x83f, 0x936, 0xe3a, 0xf33, 0xc39, 0xd30, 
        0x3a0, 0x2a9, 0x1a3, 0x0aa, 0x7a6, 0x6af, 0x5a5, 0x4ac, 0xbac, 0xaa5, 0x9af, 0x8a6, 0xfaa, 0xea3, 0xda9, 0xca0, 
        0x460, 0x569, 0x663, 0x76a, 0x066, 0x16f, 0x265, 0x36c, 0xc6c, 0xd65, 0xe6f, 0xf66, 0x86a, 0x963, 0xa69, 0xb60, 
        0x5f0, 0x4f9, 0x7f3, 0x6fa, 0x1f6, 0x0ff, 0x3f5, 0x2fc, 0xdfc, 0xcf5, 0xfff, 0xef6, 0x9fa, 0x8f3, 0xbf9, 0xaf0, 
        0x650, 0x759, 0x453, 0x55a, 0x256, 0x35f, 0x055, 0x15c, 0xe5c, 0xf55, 0xc5f, 0xd56, 0xa5a, 0xb53, 0x859, 0x950, 
        0x7c0, 0x6c9, 0x5c3, 0x4ca, 0x3c6, 0x2cf, 0x1c5, 0x0cc, 0xfcc, 0xec5, 0xdcf, 0xcc6, 0xbca, 0xac3, 0x9c9, 0x8c0, 
        0x8c0, 0x9c9, 0xac3, 0xbca, 0xcc6, 0xdcf, 0xec5, 0xfcc, 0x0cc, 0x1c5, 0x2cf, 0x3c6, 0x4ca, 0x5c3, 0x6c9, 0x7c0, 
        0x950, 0x859, 0xb53, 0xa5a, 0xd56, 0xc5f, 0xf55, 0xe5c, 0x15c, 0x055, 0x35f, 0x256, 0x55a, 0x453, 0x759, 0x650, 
        0xaf0, 0xbf9, 0x8f3, 0x9fa, 0xef6, 0xfff, 0xcf5, 0xdfc, 0x2fc, 0x3f5, 0x0ff, 0x1f6, 0x6fa, 0x7f3, 0x4f9, 0x5f0, 
        0xb60, 0xa69, 0x963, 0x86a, 0xf66, 0xe6f, 0xd65, 0xc6c, 0x36c, 0x265, 0x16f, 0x066, 0x76a, 0x663, 0x569, 0x460, 
        0xca0, 0xda9, 0xea3, 0xfaa, 0x8a6, 0x9af, 0xaa5, 0xbac, 0x4ac, 0x5a5, 0x6af, 0x7a6, 0x0aa, 0x1a3, 0x2a9, 0x3a0, 
        0xd30, 0xc39, 0xf33, 0xe3a, 0x936, 0x83f, 0xb35, 0xa3c, 0x53c, 0x435, 0x73f, 0x636, 0x13a, 0x033, 0x339, 0x230, 
        0xe90, 0xf99, 0xc93, 0xd9a, 0xa96, 0xb9f, 0x895, 0x99c, 0x69c, 0x795, 0x49f, 0x596, 0x29a, 0x393, 0x099, 0x190, 
        0xf00, 0xe09, 0xd03, 0xc0a, 0xb06, 0xa0f, 0x905, 0x80c, 0x70c, 0x605, 0x50f, 0x406, 0x30a, 0x203, 0x109, 0x000
};

//  For each of the possible vertex states listed in aiCubeEdgeFlags there is a specific triangulation
//  of the edge intersection points.  a2iTriangleConnectionTable lists all of them in the form of
//  0-5 edge triples with the list terminated by the invalid value -1.
//  For example: a2iTriangleConnectionTable[3] list the 2 triangles formed when corner[0] 
//  and corner[1] are inside of the surface, but the rest of the cube is not.
//
//  I found this table in an example program someone wrote long ago.  It was probably generated by hand

int a2iTriangleConnectionTable[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}
};

//a2fVertexOffset lists the positions, relative to vertex0, of each of the 8 vertices of a cube
/*static const float a2fVertexOffset[8][3] =
{
        {0.0, 0.0, 0.0},{1.0, 0.0, 0.0},{1.0, 1.0, 0.0},{0.0, 1.0, 0.0},
        {0.0, 0.0, 1.0},{1.0, 0.0, 1.0},{1.0, 1.0, 1.0},{0.0, 1.0, 1.0}
};*/

//The deltas for the vertex offsets.  This is the int version of a2fVertexOffset
const unsigned int VERTEX_OFFSET[8][3] = 
{
        {0, 0, 0},{1, 0, 0},{1, 1, 0},{0, 1, 0},
        {0, 0, 1},{1, 0, 1},{1, 1, 1},{0, 1, 1}
};

//a2iEdgeConnection lists the index of the endpoint vertices for each of the 12 edges of the cube
/*
static const int a2iEdgeConnection[12][2] = 
{
        {0,1}, {1,2}, {2,3}, {3,0},
        {4,5}, {5,6}, {6,7}, {7,4},
        {0,4}, {1,5}, {2,6}, {3,7}
};

//a2fEdgeDirection lists the direction vector (vertex1-vertex0) for each edge in the cube
static const float a2fEdgeDirection[12][3] =
{
        {1.0, 0.0, 0.0},{0.0, 1.0, 0.0},{-1.0, 0.0, 0.0},{0.0, -1.0, 0.0},
        {1.0, 0.0, 0.0},{0.0, 1.0, 0.0},{-1.0, 0.0, 0.0},{0.0, -1.0, 0.0},
        {0.0, 0.0, 1.0},{0.0, 0.0, 1.0},{ 0.0, 0.0, 1.0},{0.0,  0.0, 1.0}
};
*/

//Mapping between edges as defined in a2iEdgeConenction, (and thus implicitly in edge table)
//and the voxels.h definition
int edgeRemap[12]  ={ 0,6,1,4,
              2,7,3,5,
              8,10,11,9};


//vMarchingCubes iterates over the entire dataset, calling vMarchCube on each cube
void marchingCubes(const Voxels<float> &v,float isoValue, vector<TriangleWithVertexNorm> &tVec)
{
    size_t nx,ny,nz;
    v.getSize(nx,ny,nz);

    ASSERT(nx > 1 && ny>1 && nz>1);

    //Don't try to isosurface a any volume with a unitary dimension.
    if(nx ==1 || ny ==1 || nz == 1)
        return;

    Point3D gridSpacing;
    gridSpacing=v.getPitch();

#ifdef DEBUG
    BoundCube boundC;
    boundC.setBounds(v.getMinBounds(),v.getMaxBounds());
#endif

    vector<TriangleWithIndexedVertices> indexedTriVec;

    //Loop over the vertexs, with the mesh such that the 
    //nominally cube centres are now on a grid that is dual
    //to the original grid (excluding the external boundary of course)
#pragma omp parallel for
        for(size_t iX = 0; iX < nx-1; iX++)
    {
        int iEdgeFlags,iFlagIndex;  
        for(size_t iY = 0; iY < ny-1; iY++)
        {
        for(size_t iZ = 0; iZ < nz-1; iZ++)
        {
            iFlagIndex=0;

            //Find which vertices are inside of the surface and which are outside
            for(int iVertexTest = 0; iVertexTest < 8; iVertexTest++)
            {
                float f;
                f=v.getData(iX+VERTEX_OFFSET[iVertexTest][0],
                        iY+VERTEX_OFFSET[iVertexTest][1],
                        iZ+VERTEX_OFFSET[iVertexTest][2]);

                //Compute position in triangle and edge connection
                //tables
                if(f <= isoValue) 
                    iFlagIndex |= 1<<iVertexTest;
            }
            //Find which edges are intersected by the surface
            iEdgeFlags = aiCubeEdgeFlags[iFlagIndex];
            if(!iEdgeFlags) 
                continue;


            //Find the point of intersection of the surface with each edge
            //Then find the normal to the surface at those points
            size_t asEdgeVertex[12];
            for(int iEdge = 0; iEdge < 12; iEdge++)
            {
                //if there is an intersection on this edge
                if(iEdgeFlags & (1<<iEdge))
                {
                    //Store a  reference to the vertex position
                    asEdgeVertex[iEdge] = v.deprecatedGetEdgeUniqueIndex(iX,iY,iZ,edgeRemap[iEdge]);
                }
            }

        
            //Store the triangles that were found.  There can be up to five per cube; 
            //these are listed as triplets in the connection table
            for(int iTriangle = 0; iTriangle < 5; iTriangle++)
            {
                //Check to see if this triplet is a valid triangle
                if(a2iTriangleConnectionTable[iFlagIndex][3*iTriangle] < 0)
                    break;

                TriangleWithIndexedVertices t;
                for(int iCorner = 0; iCorner < 3; iCorner++)
                {
                    int iVertex;
                    iVertex = a2iTriangleConnectionTable[iFlagIndex][3*iTriangle+iCorner];
                    //we should only be accessing an edge if the edge was set.
                    ASSERT((1 << iVertex) & iEdgeFlags);




                    t.p[iCorner] = asEdgeVertex[iVertex];
                }
#pragma omp critical
                indexedTriVec.push_back(t);
            }
        }
        }
    }

    //---------

    //OK, so we set up a network of triangle vertices which consist of edge numbers
    //and a list of triangles which are the triplets of those numbers.
    //Convert this into a 

    //Map that contains a list of triangles in the vector  "indexedTriVec"
    // which share a particular edge (or rather, position along that edge)
    // First element is the edge index. Second element is the list of triangles
    // who share this edge.
    //
    // We will need this when we do the vertex normals.
    std::map<size_t,list<size_t> > edgeTriMap;
#pragma omp parallel for 
    for(size_t ui=0;ui<indexedTriVec.size(); ui++)  
    {
        for(size_t uj=0;uj<3;uj++)
        {
            map<size_t,list<size_t> >::iterator it;
            it = edgeTriMap.find(indexedTriVec[ui].p[uj]); 
            if(it == edgeTriMap.end())
            {

                list<size_t> seedList;
                seedList.push_back(ui);
#pragma omp critical
                edgeTriMap.insert(
                    make_pair(indexedTriVec[ui].p[uj],seedList));
                        
            }
            else
            {
                it->second.push_back(ui);
            }
        }

    }


    //Generate the position points for each edge
    map<size_t,Point3D> pointMap;
    for(map<size_t,list<size_t> >::iterator it=edgeTriMap.begin();
        it!=edgeTriMap.end(); ++it)
    {
        Point3D low,high,voxelFrameIntersection; 
        float lowF,highF;

        if(pointMap.find((it->first)) != pointMap.end())
            continue;

        //Low/high sides of edge's scalar values
        v.getEdgeEndApproxVals(it->first,lowF,highF);


        //Get the edge's low and high end node positions
        v.getEdgeEnds(it->first,low,high);


        
        //OK, now we have that, lets use the values to "lever" the 
        //solution point note node locations for isosurface 
        if(fabs(highF-lowF) < sqrt(std::numeric_limits<float>::epsilon()))
        {
            //Prevent divide by zero
            voxelFrameIntersection=(low+high)*0.5;
        }
        else
        {
            //interpolate
            float alpha;
            alpha= (isoValue- lowF) / (highF- lowF);
            voxelFrameIntersection=low + (high-low)*alpha;
        }

        voxelFrameIntersection+=gridSpacing*0.5;


            
        pointMap.insert(make_pair(it->first,voxelFrameIntersection));

    }   


    tVec.resize(indexedTriVec.size());
    vector<size_t> popTris;
    //Set all triangle vertices
    #pragma omp parallel for
    for(size_t ui=0;ui<tVec.size();ui++)
    {
    
        //Do a lookup of the edge point locations
        // by mapping the edge indices to the edge points 
        for(int uj=0;uj<3;uj++)
            tVec[ui].p[uj] = pointMap.at((indexedTriVec[ui].p[uj]));

        if(tVec[ui].isDegenerate())
        {
#pragma omp critical
            popTris.push_back(ui);
        }
    }
    

    //Remove any degenerate triangles from both indexed and real maps
    removeElements(popTris,tVec);
    removeElements(popTris,indexedTriVec);

    if(tVec.empty())
        return;
    
    //set all triangle edge normals by inverse face area weighting.
    // The idea is that big triangles don't affect the normal at the point
    // as they are quite delocalised. Little triangles affect it more.
    // This is entirely empirical
    // ----
    
    vector<Point3D> origNormal;
    origNormal.resize(indexedTriVec.size());
    #pragma omp parallel for
    for(size_t ui=0;ui<indexedTriVec.size();ui++)
        tVec[ui].safeComputeACWNormal(origNormal[ui]);


    //Loop over all vertices again, then assign a weighted
    //normal in place of the original normal. Lets cheat and
    //re-use "pointmap".
    // --
    for(map<size_t,Point3D>::iterator it=pointMap.begin(); 
                    it!=pointMap.end();++it)
        it->second=Point3D(0,0,0);

    //Construct the shared normals
    float smallNum=sqrt(std::numeric_limits<float>::epsilon());
    for(size_t ui=0;ui<indexedTriVec.size();ui++)
    {
        //For each vertex in our current triangle
        //update the weight mapping
        float weight;
        weight=tVec[ui].computeArea();

        if(weight > smallNum)
        {
            for(int uj=0;uj<3;uj++)
                pointMap.at((indexedTriVec[ui].p[uj]))+=origNormal[ui]*weight;
        }
    }


    //re-normalise normals
    for(map<size_t,Point3D>::iterator it=pointMap.begin(); 
                    it!=pointMap.end();++it)
    {
        if(it->second.sqrMag() > smallNum)
            it->second.normalise();
        else
            it->second=Point3D(0,0,1);
    }

    //assign these normals to the vertices of each triangle
    #pragma omp parallel for
    for(size_t ui=0;ui<indexedTriVec.size();ui++)
    {
        for(unsigned int uj=0;uj<3;uj++)
            tVec[ui].normal[uj] = pointMap.at((indexedTriVec[ui].p[uj]));
    }   
    // --
    
    // ----



}

#ifdef DEBUG
bool testIsoSurface()
{
    Voxels<float> data;

    data.resize(4,4,4);
    data.fill(0);
    data.setData(1,1,1,1.0);


    vector<TriangleWithVertexNorm> tVec;
    marchingCubes(data,0.5,tVec);

    TEST(!tVec.empty(),"isosurface exists");

    

    //Should be 2 rect. pyramids back to back, with no bases
    TEST(tVec.size() == 8, "isosurf. triangle count"); 
    //Ensure that all the points are contained within the original data bounding box

    Point3D pMin,pMax;
    data.getBounds(pMin,pMax);
    BoundCube b;
    b.setBounds(pMin,pMax);

    for(size_t ui=0;ui<tVec.size();ui++)
    {
        for(size_t uj=0;uj<3;uj++)
        {
            TEST(b.containsPt(tVec[ui].p[uj]),"Mesh contained in voxel bounds");
        }
    }

    //Convert the triangle soup into a mesh
    Mesh debugMesh;
    TRIANGLE t;
    t.physGroup=0;
    for(size_t ui=0;ui<tVec.size();ui++)
    {

        for(size_t uj=0;uj<3;uj++)
        {
            t.p[uj] = debugMesh.nodes.size();
            debugMesh.nodes.push_back(tVec[ui].p[uj]);
        }
        
        debugMesh.triangles.push_back(t);   
    }   
    ASSERT(debugMesh.isSane())

    debugMesh.saveGmshMesh("debug-isosurf.msh");

    //Convert all duplicate vertices into single blob 
    debugMesh.mergeDuplicateVertices(0.0001);
    ASSERT(debugMesh.isSane())
    return true;
}
#endif
}