contourSurface.h

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// -*- Mode: C++; tab-width: 2; -*-
// vi: set ts=2:
//

#ifndef BALL_DATATYPE_CONTOURSURFACE_H
#define BALL_DATATYPE_CONTOURSURFACE_H

#ifndef BALL_COMMON_H
# include <BALL/common.h>
#endif

#ifndef BALL_DATATYPE_REGULARDATA3D_H
# include <BALL/DATATYPE/regularData3D.h>
#endif

#ifndef BALL_MATHS_SURFACE_H
# include <BALL/MATHS/surface.h>
#endif

#ifndef BALL_DATATYPE_HASHMAP_H
# include <BALL/DATATYPE/hashMap.h>
#endif

#include <vector>
#include <math.h>

#ifdef BALL_HAS_HASH_MAP
namespace BALL_MAP_NAMESPACE
{
  template<>
  struct hash<std::pair<BALL::Position, BALL::Position> >
  {
    size_t operator () (const std::pair<BALL::Position, BALL::Position>& p) const
    {return (size_t)(p.first + p.second);}
  };
}
#endif

namespace BALL
{
  template<>
  BALL_EXPORT HashIndex Hash(const std::pair<Position, Position>& p);

  // 
  typedef Index FacetArray[256][12];

  // function defined in contourSurface.C to precompute some tables.
  BALL_EXPORT extern const FacetArray& getContourSurfaceFacetData(double threshold);

  template <typename T>  
  class TContourSurface 
    : public Surface
  {
    public:

    
    typedef std::pair<Position, Position> KeyType;

    typedef Vector3 PointType;
    
    typedef std::vector<std::pair<PointType, std::pair<Position, Position> > > VectorType;


    TContourSurface();

    TContourSurface(T threshold);

    TContourSurface(const TContourSurface& surface);

    TContourSurface(const TRegularData3D<T>& data, T threshold = 0.0);

    virtual ~TContourSurface();

    
    const TContourSurface& operator = (const TContourSurface<T>& surface);

    const TContourSurface<T>& operator << (const TRegularData3D<T>& data);

    virtual void clear();


    bool operator == (const TContourSurface<T>& surface) const;


    
    protected:

    class Cube
    { 
      public:

      Cube(const TRegularData3D<T>& grid)
        : grid_(&grid),
          current_position_(0),
          ptr_(0),
          spacing_(grid.getSpacing().x, grid.getSpacing().y, grid.getSpacing().z)
      {
        // Retrieve the number of points in the grid along the x- and y-axes.
        Size nx = grid.getSize().x;
        Size ny = grid.getSize().y;

        // Compute the offsets in the grid for the eight 
        // corners of the cube (in absolute grid indices).
        grid_offset_[0] = nx * ny;
        grid_offset_[1] = 0;
        grid_offset_[2] = 1;
        grid_offset_[3] = 1 + nx * ny;
        grid_offset_[4] = nx * ny + nx;
        grid_offset_[5] = nx;
        grid_offset_[6] = nx + 1;
        grid_offset_[7] = nx * ny + nx + 1;
      }

      void setTo(Position p) 
      {
        current_position_ = p;

        ptr_ = &(const_cast<TRegularData3D<T>*>(grid_)->getData(current_position_));
        for (Position i = 0; i < 8; i++)
        {
          values[i] = *(ptr_ + grid_offset_[i]);
        }
      }

      inline Vector3 getOrigin() const
      {
        return grid_->getCoordinates(current_position_);
      }

      inline const Vector3& getSpacing() const
      {
        return spacing_;
      }

      inline Vector3 getCoordinates(Position index) const
      {
        return grid_->getCoordinates(index);
      }

      inline Position getIndex(Position corner) const
      {
        return current_position_ + grid_offset_[corner];
      }

      void shift() 
      {
        // Shift the cube by one along the x-axis.
        current_position_++;
        ptr_++;
        
        // Keep the four old values for x = 1.
        values[0] = values[3];
        values[1] = values[2];
        values[4] = values[7];
        values[5] = values[6];
        
        // Retrieve the four new values.
        values[3] = *(ptr_ + grid_offset_[3]);
        values[2] = *(ptr_ + grid_offset_[2]);
        values[7] = *(ptr_ + grid_offset_[7]);
        values[6] = *(ptr_ + grid_offset_[6]);
      }

      Position computeTopology(double threshold)  
      {
        static const Position topology_modifier[8] = {1, 2, 4, 8, 16, 32, 64, 128};

        // The topology is a bitvector constructed by ORing the
        // bits corresponding to each of the inside/outside status of
        // of each individual corner.
        Position topology = 0;
        for (Position i = 0; i < 8; i++)
        {
          topology |= ((values[i] > threshold) ? topology_modifier[i] : 0);
        }
        
        return topology;
      }

      // The values at the eight corners of the cube.
      double                    values[8];

      protected:

      // A pointer to the grid.
      const TRegularData3D<T>*  grid_;

      // The current position of the cube as an absolute index into the grid.
      Position                  current_position_;

      // The gridd offsets: what to add to current_index_ to get to the correct
      // grid coordinate.
      Position                  grid_offset_[8];

      // A pointer into (nasty hack!) the grid itself. For speed's sake.
      const T*                  ptr_;
    
      // The spacing of the grid.
      Vector3 spacing_;
    };


    void addTriangles_(Cube& cube, const FacetArray& facet_data);

    void computeTriangles(Size topology, const TRegularData3D<T>& data);

    T threshold_;

    //
    HashMap<std::pair<Position, Position>, Position> cut_hash_map_;
  };

  typedef TContourSurface<float> ContourSurface;

  template <typename T>
  TContourSurface<T>::TContourSurface()
    : threshold_(0.0)
  {
  }

  template <typename T>
  TContourSurface<T>::TContourSurface(T threshold)
    : threshold_(threshold)
  {
  }
   
  template <typename T>
  TContourSurface<T>::TContourSurface(const TRegularData3D<T>& data, T threshold)
    : threshold_(threshold)
  {
    this->operator << (data);
  }
   
  template <typename T>
  TContourSurface<T>::~TContourSurface()  
  {
  }

  template <typename T>
  TContourSurface<T>::TContourSurface(const TContourSurface<T>& from)
    : threshold_(from.threshold_)
  {
  }

  template <typename T>
  void TContourSurface<T>::clear()
  {
    Surface::clear();
    cut_hash_map_.clear();
  }

  template <typename T>
  const TContourSurface<T>& TContourSurface<T>::operator = (const TContourSurface<T>& data)
  {
    // Avoid self-assignment
    if (&data != this)
    {
      threshold_ = data.threshold_;
    }

    return *this;
  }

  template <typename T>
  bool TContourSurface<T>:: operator == (const TContourSurface<T>& data) const
  {
    return ((threshold_    == data.threshold_)
             && Surface::operator == (data.data_));
  }

  template <typename T>
  const TContourSurface<T>& TContourSurface<T>::operator << (const TRegularData3D<T>& data)
  {
    // Clear the old stuff:
    clear();
    
    
    // Marching cube algorithm: construct a contour surface from
    // a volume data set.

    // Get the dimensions of the volume data set.
    Vector3 origin = data.getOrigin();
    Size number_of_cells_x = (Size)data.getSize().x;
    Size number_of_cells_y = (Size)data.getSize().y;
    Size number_of_cells_z = (Size)data.getSize().z;

    // Precompute the facet data. This depends on the threshold!
    const FacetArray& facet_data = getContourSurfaceFacetData(threshold_);

    // We start in the left-front-bottom-most corner of the grid.
    Position current_index = 0;
    Cube cube(data);
    for (Position curr_cell_z = 0; curr_cell_z < (number_of_cells_z - 1); curr_cell_z++)
    { 
      // Determine the start position in the current XY plane.
      current_index = curr_cell_z * number_of_cells_y * number_of_cells_x;

      // Walk along the y-axis....
      for (Position curr_cell_y = 0; curr_cell_y < (number_of_cells_y - 1); curr_cell_y++)
      {
        // Retrieve the cube from the current grid position (the first position along
        // along the x-axis).
        cube.setTo(current_index);

        // Walk along the x-axis....
        for (Position curr_cell_x = 0; (curr_cell_x < (number_of_cells_x - 2)); )
        {
          // Compute topology, triangles, and add those triangles to the surface.
          addTriangles_(cube, facet_data);
            
          // Done. cube.shift() will now shift the cube
          // along the x-axis and efficently retrieve the four new values.
          curr_cell_x++;
          cube.shift();
        }

        // Add the triangles from the last cube position.
        addTriangles_(cube, facet_data);
  
        // Shift the cube by one along the y-axis.
        current_index += number_of_cells_x;
      }
    }

    // Normalize the vertex normals.
    for (Position i = 0; i < normal.size(); i++)
    {
      try
      {
        normal[i].normalize();
      }
      catch (...)
      {
      }
    }

    // Return this (stream operator, for command chaining...)
    return *this;
  }

  template <typename T>
  void TContourSurface<T>::addTriangles_
    (typename TContourSurface<T>::Cube& cube, const FacetArray& facet_data)
  { 
    // Some static variables we need below -- since we will
    // call this rather often, we would rather want to avoid
    // to many ctor/dtor calls.
    static Triangle t;
    static std::pair<Position, Position> key;
    static std::pair<Position, Position> indices;

    // The indices of the corners of a cube's twelve edges.
    static const Position edge_indices[12][2] 
      = {{1, 0}, {1, 2}, {2, 3}, {0, 3}, {5, 4}, {5, 6},
         {6, 7}, {4, 7}, {0, 4}, {1, 5}, {2, 6}, {3, 7}
        };

    // The index (into Vector3) of the axis along which the
    // current edged runs (0: x, 1: y, 2: z).
    static const Position edge_axis[12] 
      = {2, 0, 2, 0, 2, 0, 2, 0, 1, 1, 1, 1};

    // Retrieve some basic grid properties.
    const Vector3& spacing = cube.getSpacing();

    // The indices (into Surface::vertex) of the triangle
    // under construction.
    TVector3<Position> triangle_vertices;

    // A counter for the number of vertices already in triangle_vertices
    Size vertex_counter = 0;
    
    // Compute the cube's topology
    Position topology = cube.computeTopology(threshold_);
    if (topology == 0)
    {
      return;
    }

    // Iterate over all 12 edges and determine whether
    // there's a cut. 
    for (Position i = 0; i < 12; i++) 
    { 
      // facet_data_ defines whether there's a cut for
      // a given topology and a given edge.
      Index facet_index = facet_data[topology][i];

      // There's a cut only for values larger than -1
      if (facet_index != -1)
      { 
        // There is a cut -- determine its position along the edge.

        // The axis: x = 0, y = 1, z = 2 -- used as in index into Vector3.
        Position edge = edge_axis[facet_index];

        indices.first = edge_indices[facet_index][0];
        indices.second = edge_indices[facet_index][1];
        key.first = cube.getIndex(indices.first);
        key.second = cube.getIndex(indices.second);

        // Check whether we computed this cut already.
        if (!cut_hash_map_.has(key))
        {
          // Compute the position of the cut.
          
          // Get the position of the d1 point
          Vector3 pos = cube.getCoordinates(key.first);

          // Compute the position of the cut along the edge.
          const double& d1 = cube.values[indices.first];
          const double& d2 = cube.values[indices.second];
          pos[edge] += ((double)threshold_ - d1) / (d2 - d1) * spacing[edge];
          
          // Store it as a triangle vertex.
          triangle_vertices[vertex_counter++] = vertex.size();

          // Store the index of the vertex in the hash map under the
          // indices of its grid points.
          cut_hash_map_.insert(std::pair<std::pair<Position, Position>, Position>(key, (Size)vertex.size()));

          // Create a vertex and a normal (the normal reamins empty for now).
          vertex.push_back(pos);
          static Vector3 null_normal(0.0, 0.0, 0.0);
          normal.push_back(null_normal);
        }
        else
        {
          // This one we know already! Retrieve it from the hash map.
          triangle_vertices[vertex_counter++] = cut_hash_map_[key];
        }
        
        // For every three vertices, create a new triangle.
        if (vertex_counter == 3)
        {
          // Create a new triangle.
          t.v1 = triangle_vertices.x;
          t.v2 = triangle_vertices.y;
          t.v3 = triangle_vertices.z;
          triangle.push_back(t);

          // We can start with the next one.
          vertex_counter = 0;

          // Compute the normals: add the triangle
          // normals to each of the triangle vertices.
          // We will average them out to the correct normals later.
          Vector3 h1(vertex[t.v1] - vertex[t.v2]);
          Vector3 h2(vertex[t.v3] - vertex[t.v2]);
          Vector3 current_normal(h1.y * h2.z - h1.z * h2.y,
                                 h1.z * h2.x - h2.z * h1.x,
                                 h1.x * h2.y - h1.y * h2.x);
          normal[t.v1] += current_normal;
          normal[t.v2] += current_normal;
          normal[t.v3] += current_normal;
        }
      }
    }
  }
}
#endif