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* *
* IsoEx *
* Copyright (C) 2002 by Computer Graphics Group, RWTH Aachen *
* www.rwth-graphics.de *
* *
*---------------------------------------------------------------------------*
* *
* License *
* *
* This library is free software; you can redistribute it and/or modify it *
* under the terms of the GNU Library General Public License as published *
* by the Free Software Foundation, version 2. *
* *
* This library 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 *
* Library General Public License for more details. *
* *
* You should have received a copy of the GNU Library General Public *
* License along with this library; if not, write to the Free Software *
* Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA. *
* *
\*===========================================================================*/
#include "marching_cubes.h"
#include "marching_cubes_tables.h"
#include <unordered_map>
extern const int edgeTable[256];
extern const int triTable[256][2][17];
extern const int polyTable[8][16];
template <typename DerivedValues, typename DerivedPoints, typename DerivedVertices, typename DerivedIndices, typename DerivedFaces>
class MarchingCubes
{
struct EdgeKey
{
EdgeKey(unsigned i0, unsigned i1) : i0_(i0), i1_(i1) {}
bool operator==(const EdgeKey& _rhs) const
{
return i0_ == _rhs.i0_ && i1_ == _rhs.i1_;
}
unsigned i0_, i1_;
};
struct EdgeHash
{
std::size_t operator()(const EdgeKey& key) const {
std::size_t seed = 0;
seed ^= key.i0_ + 0x9e3779b9 + (seed<<6) + (seed>>2); // Copied from boost::hash_combine
seed ^= key.i1_ + 0x9e3779b9 + (seed<<6) + (seed>>2);
return std::hash<std::size_t>()(seed);
}
};
typedef std::unordered_map<EdgeKey, unsigned, EdgeHash> MyMap;
typedef typename MyMap::const_iterator MyMapIterator;
public:
// Dense index grid version
MarchingCubes(const Eigen::MatrixBase<DerivedValues> &values,
const Eigen::MatrixBase<DerivedPoints> &points,
const unsigned x_res,
const unsigned y_res,
const unsigned z_res,
const double isovalue,
Eigen::PlainObjectBase<DerivedVertices> &vertices,
Eigen::PlainObjectBase<DerivedFaces> &faces)
{
assert(values.cols() == 1);
assert(points.cols() == 3);
if(x_res <2 || y_res<2 ||z_res<2)
return;
faces.resize(10000,3);
int num_faces = 0;
vertices.resize(10000,3);
int num_vertices = 0;
unsigned n_cubes = (x_res-1) * (y_res-1) * (z_res-1);
assert(unsigned(points.rows()) == x_res * y_res * z_res);
unsigned int offsets_[8];
offsets_[0] = 0;
offsets_[1] = 1;
offsets_[2] = 1 + x_res;
offsets_[3] = x_res;
offsets_[4] = x_res*y_res;
offsets_[5] = 1 + x_res*y_res;
offsets_[6] = 1 + x_res + x_res*y_res;
offsets_[7] = x_res + x_res*y_res;
for (unsigned cube_it =0 ; cube_it < n_cubes; ++cube_it)
{
unsigned corner[8];
// get point indices of corner vertices
for (int i=0; i<8; ++i)
{
// get cube coordinates
unsigned int _idx = cube_it;
unsigned int X(x_res-1), Y(y_res-1);
unsigned int x = _idx % X; _idx /= X;
unsigned int y = _idx % Y; _idx /= Y;
unsigned int z = _idx;
// transform to point coordinates
_idx = x + y*x_res + z*x_res*y_res;
// add offset
corner[i] = _idx + offsets_[i];
}
add_cube(values,points,isovalue,corner,vertices,num_vertices,faces,num_faces,edge2vertex);
}
vertices.conservativeResize(num_vertices, Eigen::NoChange);
faces.conservativeResize(num_faces, Eigen::NoChange);
}
// Sparse index grid version
MarchingCubes(const Eigen::MatrixBase<DerivedValues> &values,
const Eigen::MatrixBase<DerivedPoints> &points,
const Eigen::MatrixBase<DerivedIndices> &cubes,
const double isovalue,
Eigen::PlainObjectBase<DerivedVertices> &vertices,
Eigen::PlainObjectBase<DerivedFaces> &faces)
{
assert(values.cols() == 1);
assert(points.cols() == 3);
assert(cubes.cols() == 8);
if(cubes.rows() == 0)
{
return;
}
faces.resize(10000,3);
int num_faces = 0;
vertices.resize(10000,3);
int num_vertices = 0;
unsigned n_cubes = cubes.rows();
for (unsigned cube_it =0 ; cube_it < n_cubes; ++cube_it)
{
typedef Eigen::Matrix<typename DerivedIndices::Scalar, 1, 8> CubeIndexVector;
CubeIndexVector corner = cubes.row(cube_it);
add_cube(values,points,isovalue,corner.data(),vertices,num_vertices,faces,num_faces,edge2vertex);
}
vertices.conservativeResize(num_vertices, Eigen::NoChange);
faces.conservativeResize(num_faces, Eigen::NoChange);
}
// Dense index grid function version
template <typename DerivedValue, typename DerivedPoint>
MarchingCubes(
const std::function< DerivedValue(const DerivedPoint & ) > & value_fun,
const Eigen::MatrixBase<DerivedPoints> &points,
const unsigned x_res,
const unsigned y_res,
const unsigned z_res,
const double isovalue,
Eigen::PlainObjectBase<DerivedVertices> &vertices,
Eigen::PlainObjectBase<DerivedFaces> &faces)
{
assert(points.cols() == 3);
if(x_res <2 || y_res<2 ||z_res<2)
return;
faces.resize(10000,3);
int num_faces = 0;
vertices.resize(10000,3);
int num_vertices = 0;
unsigned n_cubes = (x_res-1) * (y_res-1) * (z_res-1);
assert(unsigned(points.rows()) == x_res * y_res * z_res);
unsigned int offsets_[8];
offsets_[0] = 0;
offsets_[1] = 1;
offsets_[2] = 1 + x_res;
offsets_[3] = x_res;
offsets_[4] = x_res*y_res;
offsets_[5] = 1 + x_res*y_res;
offsets_[6] = 1 + x_res + x_res*y_res;
offsets_[7] = x_res + x_res*y_res;
for (unsigned cube_it =0 ; cube_it < n_cubes; ++cube_it)
{
unsigned corner[8];
// get point indices of corner vertices
for (int i=0; i<8; ++i)
{
// get cube coordinates
unsigned int _idx = cube_it;
unsigned int X(x_res-1), Y(y_res-1);
unsigned int x = _idx % X; _idx /= X;
unsigned int y = _idx % Y; _idx /= Y;
unsigned int z = _idx;
// transform to point coordinates
_idx = x + y*x_res + z*x_res*y_res;
// add offset
corner[i] = _idx + offsets_[i];
}
add_cube(value_fun,points,isovalue,corner,vertices,num_vertices,faces,num_faces,edge2vertex);
}
vertices.conservativeResize(num_vertices, Eigen::NoChange);
faces.conservativeResize(num_faces, Eigen::NoChange);
}
template <typename CubeIndexType>
static void add_cube(
const Eigen::MatrixBase<DerivedValues> &values,
const Eigen::MatrixBase<DerivedPoints> &points,
const double isovalue,
const CubeIndexType corner[],
Eigen::PlainObjectBase<DerivedVertices> &vertices,
int &num_vertices,
Eigen::PlainObjectBase<DerivedFaces> &faces,
int & num_faces,
MyMap &edge2vertex)
{
typedef typename DerivedFaces::Scalar SampleScalar;
SampleScalar samples[12];
unsigned char cubetype(0);
// determine cube type
for (int i=0; i<8; ++i)
{
if (values(corner[i]) > isovalue)
{
cubetype |= (1<<i);
}
}
// trivial reject ?
if (cubetype == 0 || cubetype == 255)
{
return;
}
// compute samples on cube's edges
if (edgeTable[cubetype]&1)
samples[0] = add_vertex(values, points, isovalue, corner[0], corner[1], vertices, num_vertices, edge2vertex);
if (edgeTable[cubetype]&2)
samples[1] = add_vertex(values, points, isovalue, corner[1], corner[2], vertices, num_vertices, edge2vertex);
if (edgeTable[cubetype]&4)
samples[2] = add_vertex(values, points, isovalue, corner[3], corner[2], vertices, num_vertices, edge2vertex);
if (edgeTable[cubetype]&8)
samples[3] = add_vertex(values, points, isovalue, corner[0], corner[3], vertices, num_vertices, edge2vertex);
if (edgeTable[cubetype]&16)
samples[4] = add_vertex(values, points, isovalue, corner[4], corner[5], vertices, num_vertices, edge2vertex);
if (edgeTable[cubetype]&32)
samples[5] = add_vertex(values, points, isovalue, corner[5], corner[6], vertices, num_vertices, edge2vertex);
if (edgeTable[cubetype]&64)
samples[6] = add_vertex(values, points, isovalue, corner[7], corner[6], vertices, num_vertices, edge2vertex);
if (edgeTable[cubetype]&128)
samples[7] = add_vertex(values, points, isovalue, corner[4], corner[7], vertices, num_vertices, edge2vertex);
if (edgeTable[cubetype]&256)
samples[8] = add_vertex(values, points, isovalue, corner[0], corner[4], vertices, num_vertices, edge2vertex);
if (edgeTable[cubetype]&512)
samples[9] = add_vertex(values, points, isovalue, corner[1], corner[5], vertices, num_vertices, edge2vertex);
if (edgeTable[cubetype]&1024)
samples[10] = add_vertex(values, points, isovalue, corner[2], corner[6], vertices, num_vertices, edge2vertex);
if (edgeTable[cubetype]&2048)
samples[11] = add_vertex(values, points, isovalue, corner[3], corner[7], vertices, num_vertices, edge2vertex);
// connect samples by triangles
for (int i=0; triTable[cubetype][0][i] != -1; i+=3 )
{
num_faces++;
if (num_faces > faces.rows())
{
faces.conservativeResize(faces.rows()+10000, Eigen::NoChange);
}
faces.row(num_faces-1) <<
samples[triTable[cubetype][0][i ]],
samples[triTable[cubetype][0][i+1]],
samples[triTable[cubetype][0][i+2]];
}
};
template <typename DerivedValue, typename DerivedPoint, typename CubeIndexType>
static void add_cube(
const std::function< DerivedValue(const DerivedPoint & ) > & value_fun,
const Eigen::MatrixBase<DerivedPoints> &points,
const double isovalue,
const CubeIndexType corner[],
Eigen::PlainObjectBase<DerivedVertices> &vertices,
int &num_vertices,
Eigen::PlainObjectBase<DerivedFaces> &faces,
int & num_faces,
MyMap &edge2vertex)
{
typedef typename DerivedFaces::Scalar SampleScalar;
SampleScalar samples[12];
unsigned char cubetype(0);
// determine cube type
for (int i=0; i<8; ++i)
{
if (value_fun(points.row(corner[i])) > isovalue)
{
cubetype |= (1<<i);
}
}
// trivial reject ?
if (cubetype == 0 || cubetype == 255)
{
return;
}
// compute samples on cube's edges
if (edgeTable[cubetype]&1)
samples[0] = add_vertex(value_fun, points, isovalue, corner[0], corner[1], vertices, num_vertices, edge2vertex);
if (edgeTable[cubetype]&2)
samples[1] = add_vertex(value_fun, points, isovalue, corner[1], corner[2], vertices, num_vertices, edge2vertex);
if (edgeTable[cubetype]&4)
samples[2] = add_vertex(value_fun, points, isovalue, corner[3], corner[2], vertices, num_vertices, edge2vertex);
if (edgeTable[cubetype]&8)
samples[3] = add_vertex(value_fun, points, isovalue, corner[0], corner[3], vertices, num_vertices, edge2vertex);
if (edgeTable[cubetype]&16)
samples[4] = add_vertex(value_fun, points, isovalue, corner[4], corner[5], vertices, num_vertices, edge2vertex);
if (edgeTable[cubetype]&32)
samples[5] = add_vertex(value_fun, points, isovalue, corner[5], corner[6], vertices, num_vertices, edge2vertex);
if (edgeTable[cubetype]&64)
samples[6] = add_vertex(value_fun, points, isovalue, corner[7], corner[6], vertices, num_vertices, edge2vertex);
if (edgeTable[cubetype]&128)
samples[7] = add_vertex(value_fun, points, isovalue, corner[4], corner[7], vertices, num_vertices, edge2vertex);
if (edgeTable[cubetype]&256)
samples[8] = add_vertex(value_fun, points, isovalue, corner[0], corner[4], vertices, num_vertices, edge2vertex);
if (edgeTable[cubetype]&512)
samples[9] = add_vertex(value_fun, points, isovalue, corner[1], corner[5], vertices, num_vertices, edge2vertex);
if (edgeTable[cubetype]&1024)
samples[10] = add_vertex(value_fun, points, isovalue, corner[2], corner[6], vertices, num_vertices, edge2vertex);
if (edgeTable[cubetype]&2048)
samples[11] = add_vertex(value_fun, points, isovalue, corner[3], corner[7], vertices, num_vertices, edge2vertex);
// connect samples by triangles
for (int i=0; triTable[cubetype][0][i] != -1; i+=3 )
{
num_faces++;
if (num_faces > faces.rows())
{
faces.conservativeResize(faces.rows()+10000, Eigen::NoChange);
}
faces.row(num_faces-1) <<
samples[triTable[cubetype][0][i ]],
samples[triTable[cubetype][0][i+1]],
samples[triTable[cubetype][0][i+2]];
}
};
static typename DerivedFaces::Scalar add_vertex(
const Eigen::MatrixBase<DerivedValues> &values,
const Eigen::MatrixBase<DerivedPoints> &points,
const double isovalue,
unsigned int i0,
unsigned int i1,
Eigen::PlainObjectBase<DerivedVertices> &vertices,
int &num_vertices,
MyMap &edge2vertex)
{
// find vertex if it has been computed already
MyMapIterator it = edge2vertex.find(EdgeKey(i0, i1));
if (it != edge2vertex.end())
{
return it->second;
}
// generate new vertex
const Eigen::Matrix<typename DerivedPoints::Scalar, 1, 3> & p0 = points.row(i0);
const Eigen::Matrix<typename DerivedPoints::Scalar, 1, 3> & p1 = points.row(i1);
typename DerivedValues::Scalar s0 = fabs(values(i0)-isovalue);
typename DerivedValues::Scalar s1 = fabs(values(i1)-isovalue);
typename DerivedValues::Scalar t = s0 / (s0+s1);
num_vertices++;
if (num_vertices > vertices.rows())
{
vertices.conservativeResize(vertices.rows()+10000, Eigen::NoChange);
}
//
// Linear interpolation based on linearly interpolating values
vertices.row(num_vertices-1) = ((1.0f-t)*p0 + t*p1).template cast<typename DerivedVertices::Scalar>();
edge2vertex[EdgeKey(i0, i1)] = num_vertices-1;
return num_vertices-1;
}
template <typename DerivedValue, typename DerivedPoint>
static typename DerivedFaces::Scalar add_vertex(
const std::function< DerivedValue(const DerivedPoint & ) > & value_fun,
const Eigen::MatrixBase<DerivedPoints> &points,
const double isovalue,
unsigned int i0,
unsigned int i1,
Eigen::PlainObjectBase<DerivedVertices> &vertices,
int &num_vertices,
MyMap &edge2vertex)
{
// find vertex if it has been computed already
MyMapIterator it = edge2vertex.find(EdgeKey(i0, i1));
if (it != edge2vertex.end())
{
return it->second;
}
num_vertices++;
if (num_vertices > vertices.rows())
{
vertices.conservativeResize(vertices.rows()+10000, Eigen::NoChange);
}
// generate new vertex
typedef Eigen::Matrix<typename DerivedPoints::Scalar, 1, 3> RowVector3S;
const RowVector3S & p0 = points.row(i0);
const RowVector3S & p1 = points.row(i1);
// Linear interpolation based on linearly interpolating values
//typename DerivedValues::Scalar s0 = fabs(value_fun(points.row(i0))-isovalue);
//typename DerivedValues::Scalar s1 = fabs(value_fun(points.row(i1))-isovalue);
//typename DerivedValues::Scalar t = s0 / (s0+s1);
const DerivedValue v1 = value_fun(p1);
double t0 = (v1>isovalue)?0:1;
double t1 = (v1>isovalue)?1:0;
double t;
for(int j = 0;j<10;j++)
{
t = 0.5*(t0+t1);
const double val = value_fun( ((1.0f-t)*p0 + t*p1) );
if( val > isovalue )
{
t1 = t;
}else
{
t0 = t;
}
}
vertices.row(num_vertices-1) = ((1.0f-t)*p0 + t*p1).template cast<typename DerivedVertices::Scalar>();
edge2vertex[EdgeKey(i0, i1)] = num_vertices-1;
return num_vertices-1;
}
// maps an edge to the sample vertex generated on it
MyMap edge2vertex;
};
template <typename DerivedValues, typename DerivedPoints, typename DerivedVertices, typename DerivedFaces>
IGL_INLINE void igl::copyleft::marching_cubes(
const Eigen::MatrixBase<DerivedValues> &values,
const Eigen::MatrixBase<DerivedPoints> &points,
const unsigned x_res,
const unsigned y_res,
const unsigned z_res,
const double isovalue,
Eigen::PlainObjectBase<DerivedVertices> &vertices,
Eigen::PlainObjectBase<DerivedFaces> &faces)
{
typedef Eigen::MatrixXi Shim; /* DerivedIndices shim type is unused in this instantiation*/
MarchingCubes<DerivedValues, DerivedPoints, DerivedVertices, Shim, DerivedFaces>
mc(values, points, x_res, y_res, z_res, isovalue, vertices, faces);
}
template <
typename DerivedValue,
typename DerivedPoint,
typename DerivedPoints,
typename DerivedVertices,
typename DerivedFaces>
IGL_INLINE void igl::copyleft::marching_cubes(
const std::function< DerivedValue(const DerivedPoint & ) > & value_fun,
const Eigen::MatrixBase<DerivedPoints> &points,
const unsigned x_res,
const unsigned y_res,
const unsigned z_res,
const double isovalue,
Eigen::PlainObjectBase<DerivedVertices> &vertices,
Eigen::PlainObjectBase<DerivedFaces> &faces)
{
MarchingCubes<
Eigen::Matrix<DerivedValue,Eigen::Dynamic,1>, /* unnecessary */
DerivedPoints, DerivedVertices,
Eigen::Matrix<int,Eigen::Dynamic,1>, /* unnecessary */
DerivedFaces> mc(value_fun, points, x_res, y_res, z_res, isovalue, vertices, faces);
}
template <typename DerivedValues, typename DerivedPoints, typename DerivedVertices, typename DerivedFaces>
IGL_INLINE void igl::copyleft::marching_cubes(
const Eigen::MatrixBase<DerivedValues> &values,
const Eigen::MatrixBase<DerivedPoints> &points,
const unsigned x_res,
const unsigned y_res,
const unsigned z_res,
Eigen::PlainObjectBase<DerivedVertices> &vertices,
Eigen::PlainObjectBase<DerivedFaces> &faces)
{
typedef Eigen::MatrixXi Shim; /* DerivedIndices shim type is unused in this instantiation*/
MarchingCubes<DerivedValues, DerivedPoints, DerivedVertices, Shim, DerivedFaces>
mc(values, points, x_res, y_res, z_res, 0.0 /*isovalue*/, vertices, faces);
}
template <typename DerivedValues, typename DerivedPoints, typename DerivedVertices, typename DerivedIndices, typename DerivedFaces>
IGL_INLINE void igl::copyleft::marching_cubes(
const Eigen::MatrixBase<DerivedValues>& values,
const Eigen::MatrixBase<DerivedPoints>& points,
const Eigen::MatrixBase<DerivedIndices>& indices,
const double isovalue,
Eigen::PlainObjectBase<DerivedVertices>& vertices,
Eigen::PlainObjectBase<DerivedFaces> &faces)
{
MarchingCubes<DerivedValues, DerivedPoints, DerivedVertices, DerivedIndices, DerivedFaces> mc(values, points, indices, isovalue, vertices, faces);
}
template <typename DerivedValues, typename DerivedPoints, typename DerivedVertices, typename DerivedIndices, typename DerivedFaces>
IGL_INLINE void igl::copyleft::marching_cubes(
const Eigen::MatrixBase<DerivedValues> &values,
const Eigen::MatrixBase<DerivedPoints> &points,
const Eigen::MatrixBase<DerivedIndices> & indices,
Eigen::PlainObjectBase<DerivedVertices> &vertices,
Eigen::PlainObjectBase<DerivedFaces> &faces)
{
MarchingCubes<DerivedValues, DerivedPoints, DerivedVertices, DerivedIndices, DerivedFaces> mc(values, points, indices, 0.0 /*isovalue*/, vertices, faces);
}
#ifdef IGL_STATIC_LIBRARY
// Explicit template instantiation
// generated by autoexplicit.sh
template void igl::copyleft::marching_cubes<Eigen::Matrix<double, -1, 1, 0, -1, 1>, Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, 3, 1, -1, 3>, Eigen::Matrix<int, -1, 3, 1, -1, 3> >(Eigen::MatrixBase<Eigen::Matrix<double, -1, 1, 0, -1, 1> > const&, Eigen::MatrixBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, unsigned int, unsigned int, unsigned int, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, 3, 1, -1, 3> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 3, 1, -1, 3> >&);
template void igl::copyleft::marching_cubes<Eigen::Matrix<float, -1, 1, 0, -1, 1>, Eigen::Matrix<float, -1, 3, 0, -1, 3>, Eigen::Matrix<float, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, 3, 0, -1, 3> >(Eigen::MatrixBase<Eigen::Matrix<float, -1, 1, 0, -1, 1> > const&, Eigen::MatrixBase<Eigen::Matrix<float, -1, 3, 0, -1, 3> > const&, unsigned int, unsigned int, unsigned int, Eigen::PlainObjectBase<Eigen::Matrix<float, -1, 3, 0, -1, 3> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 3, 0, -1, 3> >&);
template void igl::copyleft::marching_cubes<Eigen::Matrix<float, -1, 1, 0, -1, 1>, Eigen::Matrix<float, -1, 3, 1, -1, 3>, Eigen::Matrix<float, -1, 3, 1, -1, 3>, Eigen::Matrix<int, -1, 3, 1, -1, 3> >(Eigen::MatrixBase<Eigen::Matrix<float, -1, 1, 0, -1, 1> > const&, Eigen::MatrixBase<Eigen::Matrix<float, -1, 3, 1, -1, 3> > const&, unsigned int, unsigned int, unsigned int, Eigen::PlainObjectBase<Eigen::Matrix<float, -1, 3, 1, -1, 3> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 3, 1, -1, 3> >&);
template void igl::copyleft::marching_cubes<Eigen::Matrix<float, -1, 1, 0, -1, 1>, Eigen::Matrix<float, -1, -1, 0, -1, -1>, Eigen::Matrix<float, -1, 3, 1, -1, 3>, Eigen::Matrix<int, -1, 3, 1, -1, 3> >(Eigen::MatrixBase<Eigen::Matrix<float, -1, 1, 0, -1, 1> > const&, Eigen::MatrixBase<Eigen::Matrix<float, -1, -1, 0, -1, -1> > const&, unsigned int, unsigned int, unsigned int, Eigen::PlainObjectBase<Eigen::Matrix<float, -1, 3, 1, -1, 3> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 3, 1, -1, 3> >&);
template void igl::copyleft::marching_cubes<Eigen::Matrix<double, -1, 1, 0, -1, 1>, Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<float, -1, 3, 1, -1, 3>, Eigen::Matrix<int, -1, 3, 1, -1, 3> >(Eigen::MatrixBase<Eigen::Matrix<double, -1, 1, 0, -1, 1> > const&, Eigen::MatrixBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, unsigned int, unsigned int, unsigned int, Eigen::PlainObjectBase<Eigen::Matrix<float, -1, 3, 1, -1, 3> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 3, 1, -1, 3> >&);
template void igl::copyleft::marching_cubes<Eigen::Matrix<double, -1, 1, 0, -1, 1>, Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1> >(Eigen::MatrixBase<Eigen::Matrix<double, -1, 1, 0, -1, 1> > const&, Eigen::MatrixBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, unsigned int, unsigned int, unsigned int, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> >&);
template void igl::copyleft::marching_cubes<Eigen::Matrix<double, -1, 1, 0, -1, 1>, Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1> >(const Eigen::MatrixBase<Eigen::Matrix<double, -1, 1, 0, -1, 1> >&, const Eigen::MatrixBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> >&, const Eigen::MatrixBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> >&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> >&);
template void igl::copyleft::marching_cubes<Eigen::Matrix<double, -1, 1, 0, -1, 1>, Eigen::Matrix<double, -1, 3, 0, -1, 3>, Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1> >(const Eigen::MatrixBase<Eigen::Matrix<double, -1, 1, 0, -1, 1> >&, const Eigen::MatrixBase<Eigen::Matrix<double, -1, 3, 0, -1, 3> >&, const Eigen::MatrixBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> >&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> >&);
template void igl::copyleft::marching_cubes<Eigen::Matrix<double, -1, 1, 0, -1, 1>, Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1> >(const Eigen::MatrixBase<Eigen::Matrix<double, -1, 1, 0, -1, 1> >&, const Eigen::MatrixBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> >&, const Eigen::MatrixBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> >&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, 3, 0, -1, 3> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> >&);
template void igl::copyleft::marching_cubes<Eigen::Matrix<double, -1, 1, 0, -1, 1>, Eigen::Matrix<double, -1, 3, 0, -1, 3>, Eigen::Matrix<double, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1> >(const Eigen::MatrixBase<Eigen::Matrix<double, -1, 1, 0, -1, 1> >&, const Eigen::MatrixBase<Eigen::Matrix<double, -1, 3, 0, -1, 3> >&, const Eigen::MatrixBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> >&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, 3, 0, -1, 3> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> >&);
template void igl::copyleft::marching_cubes<Eigen::Matrix<double, -1, 1, 0, -1, 1>, Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, 8, 0, -1, 8>, Eigen::Matrix<int, -1, -1, 0, -1, -1> >(const Eigen::MatrixBase<Eigen::Matrix<double, -1, 1, 0, -1, 1> >&, const Eigen::MatrixBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> >&, const Eigen::MatrixBase<Eigen::Matrix<int, -1, 8, 0, -1, 8> >&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> >&);
template void igl::copyleft::marching_cubes<Eigen::Matrix<double, -1, 1, 0, -1, 1>,Eigen::Matrix<double, -1, -1, 0, -1, -1>,Eigen::Matrix<double, -1, -1, 0, -1, -1>,Eigen::Matrix<int, -1, -1, 0, -1, -1>,Eigen::Matrix<int, -1, 3, 0, -1, 3> >(const Eigen::MatrixBase<Eigen::Matrix<double, -1, 1, 0, -1, 1> >&,const Eigen::MatrixBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> >&,const Eigen::MatrixBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> >&,Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> >&,Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 3, 0, -1, 3> >&);
template void igl::copyleft::marching_cubes<Eigen::Matrix<double, -1, 1, 0, -1, 1>,Eigen::Matrix<double, -1, -1, 0, -1, -1>,Eigen::Matrix<double, -1, -1, 0, -1, -1>,Eigen::Matrix<int, -1, 8, 0, -1, 8>,Eigen::Matrix<int, -1, 3, 0, -1, 3> >(const Eigen::MatrixBase<Eigen::Matrix<double, -1, 1, 0, -1, 1> >&,const Eigen::MatrixBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> >&,const Eigen::MatrixBase<Eigen::Matrix<int, -1, 8, 0, -1, 8> >&,Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> >&,Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 3, 0, -1, 3> >&);
template void igl::copyleft::marching_cubes<Eigen::Matrix<double, -1, 1, 0, -1, 1>,Eigen::Matrix<double, -1, 3, 0, -1, 3>,Eigen::Matrix<double, -1, 3, 0, -1, 3>,Eigen::Matrix<int, -1, 8, 0, -1, 8>,Eigen::Matrix<int, -1, 3, 0, -1, 3> >(const Eigen::MatrixBase<Eigen::Matrix<double, -1, 1, 0, -1, 1> >&,const Eigen::MatrixBase<Eigen::Matrix<double, -1, 3, 0, -1, 3> >&,const Eigen::MatrixBase<Eigen::Matrix<int, -1, 8, 0, -1, 8> >&,Eigen::PlainObjectBase<Eigen::Matrix<double, -1, 3, 0, -1, 3> >&,Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 3, 0, -1, 3> >&);
template void igl::copyleft::marching_cubes<Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1> >(Eigen::MatrixBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::MatrixBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> >&);
template void igl::copyleft::marching_cubes<Eigen::Matrix<double, -1, 1, 0, -1, 1>, Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1> >(Eigen::MatrixBase<Eigen::Matrix<double, -1, 1, 0, -1, 1> > const&, Eigen::MatrixBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, unsigned int, unsigned int, unsigned int, double, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> >&);
#endif
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