clean up and add root finding interface

include/igl/copyleft/marching_cubes.cpp

@@ -157,6 +157,64 @@ public:
     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,
@@ -229,6 +287,78 @@ public:
     }
   };
 
+  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,
@@ -249,21 +379,71 @@ public:
     // 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;
 
+    edge2vertex[EdgeKey(i0, i1)] = num_vertices-1;
     return num_vertices-1;
   }
 
@@ -288,6 +468,29 @@ IGL_INLINE void igl::copyleft::marching_cubes(
           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,

include/igl/copyleft/marching_cubes.h

@@ -49,6 +49,21 @@ namespace igl
         const double isovalue,
         Eigen::PlainObjectBase<DerivedVertices> &vertices,
         Eigen::PlainObjectBase<DerivedFaces> &faces);
+    template <
+      typename DerivedValue, 
+      typename DerivedPoint,
+      typename DerivedPoints, 
+      typename DerivedVertices, 
+      typename DerivedFaces>
+    IGL_INLINE void 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);
 
     // Overload of the above function where the isovalue defaults to 0.0
     template <typename DerivedValues, typename DerivedPoints, typename DerivedVertices, typename DerivedFaces>