mat.hpp

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/*
Copyright (c) 2007, Michael Kazhdan
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are permitted provided that the following conditions are met:

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*/
// MinimalAreaTriangulation //

namespace pcl
{
  namespace poisson
  {

    template <class Real>
    MinimalAreaTriangulation<Real>::MinimalAreaTriangulation(void)
    {
      bestTriangulation=NULL;
      midPoint=NULL;
    }
    template <class Real>
    MinimalAreaTriangulation<Real>::~MinimalAreaTriangulation(void)
    {
      if(bestTriangulation)
        delete[] bestTriangulation;
      bestTriangulation=NULL;
      if(midPoint)
        delete[] midPoint;
      midPoint=NULL;
    }
    template <class Real>
    void MinimalAreaTriangulation<Real>::GetTriangulation(const std::vector<Point3D<Real> >& vertices,std::vector<TriangleIndex>& triangles)
    {
      if(vertices.size()==3)
      {
        triangles.resize(1);
        triangles[0].idx[0]=0;
        triangles[0].idx[1]=1;
        triangles[0].idx[2]=2;
        return;
      }
      else if(vertices.size()==4)
      {
        TriangleIndex tIndex[2][2];
        Real area[2];

        area[0]=area[1]=0;
        triangles.resize(2);

        tIndex[0][0].idx[0]=0;
        tIndex[0][0].idx[1]=1;
        tIndex[0][0].idx[2]=2;
        tIndex[0][1].idx[0]=2;
        tIndex[0][1].idx[1]=3;
        tIndex[0][1].idx[2]=0;

        tIndex[1][0].idx[0]=0;
        tIndex[1][0].idx[1]=1;
        tIndex[1][0].idx[2]=3;
        tIndex[1][1].idx[0]=3;
        tIndex[1][1].idx[1]=1;
        tIndex[1][1].idx[2]=2;

        Point3D<Real> n,p1,p2;
        for(int i=0;i<2;i++)
          for(int j=0;j<2;j++)
          {
            p1=vertices[tIndex[i][j].idx[1]]-vertices[tIndex[i][j].idx[0]];
            p2=vertices[tIndex[i][j].idx[2]]-vertices[tIndex[i][j].idx[0]];
            CrossProduct(p1,p2,n);
            area[i] += Real( Length(n) );
          }
        if(area[0]>area[1])
        {
          triangles[0]=tIndex[1][0];
          triangles[1]=tIndex[1][1];
        }
        else
        {
          triangles[0]=tIndex[0][0];
          triangles[1]=tIndex[0][1];
        }
        return;
      }
      if(bestTriangulation)
        delete[] bestTriangulation;
      if(midPoint)
        delete[] midPoint;
      bestTriangulation=NULL;
      midPoint=NULL;
      size_t eCount=vertices.size();
      bestTriangulation=new Real[eCount*eCount];
      midPoint=new int[eCount*eCount];
      for(size_t i=0;i<eCount*eCount;i++)
        bestTriangulation[i]=-1;
      memset(midPoint,-1,sizeof(int)*eCount*eCount);
      GetArea(0,1,vertices);
      triangles.clear();
      GetTriangulation(0,1,vertices,triangles);
    }
    template <class Real>
    Real MinimalAreaTriangulation<Real>::GetArea(const std::vector<Point3D<Real> >& vertices)
    {
      if(bestTriangulation)
        delete[] bestTriangulation;
      if(midPoint)
        delete[] midPoint;
      bestTriangulation=NULL;
      midPoint=NULL;
      int eCount=vertices.size();
      bestTriangulation=new double[eCount*eCount];
      midPoint=new int[eCount*eCount];
      for(int i=0;i<eCount*eCount;i++)
        bestTriangulation[i]=-1;
      memset(midPoint,-1,sizeof(int)*eCount*eCount);
      return GetArea(0,1,vertices);
    }
    template<class Real>
    void MinimalAreaTriangulation<Real>::GetTriangulation(const size_t& i,const size_t& j,const std::vector<Point3D<Real> >& vertices,std::vector<TriangleIndex>& triangles)
    {
      TriangleIndex tIndex;
      size_t eCount=vertices.size();
      size_t ii=i;
      if(i<j)
        ii+=eCount;
      if(j+1>=ii)
        return;
      ii=midPoint[i*eCount+j];
      if(ii>=0)
      {
        tIndex.idx[0] = int( i );
        tIndex.idx[1] = int( j );
        tIndex.idx[2] = int( ii );
        triangles.push_back(tIndex);
        GetTriangulation(i,ii,vertices,triangles);
        GetTriangulation(ii,j,vertices,triangles);
      }
    }

    template<class Real>
    Real MinimalAreaTriangulation<Real>::GetArea(const size_t& i,const size_t& j,const std::vector<Point3D<Real> >& vertices)
    {
      Real a=FLT_MAX,temp;
      size_t eCount=vertices.size();
      size_t idx=i*eCount+j;
      size_t ii=i;
      if(i<j)
        ii+=eCount;
      if(j+1>=ii)
      {
        bestTriangulation[idx]=0;
        return 0;
      }
      if(midPoint[idx]!=-1)
        return bestTriangulation[idx];
      int mid=-1;
      for(size_t r=j+1;r<ii;r++)
      {
        size_t rr=r%eCount;
        size_t idx1=i*eCount+rr,idx2=rr*eCount+j;
        Point3D<Real> p,p1,p2;
        p1=vertices[i]-vertices[rr];
        p2=vertices[j]-vertices[rr];
        CrossProduct(p1,p2,p);
        temp = Real( Length(p) );
        if(bestTriangulation[idx1]>=0)
        {
          temp+=bestTriangulation[idx1];
          if(temp>a)
            continue;
          if(bestTriangulation[idx2]>0)
            temp+=bestTriangulation[idx2];
          else
            temp+=GetArea(rr,j,vertices);
        }
        else
        {
          if(bestTriangulation[idx2]>=0)
            temp+=bestTriangulation[idx2];
          else
            temp+=GetArea(rr,j,vertices);
          if(temp>a)
            continue;
          temp+=GetArea(i,rr,vertices);
        }

        if(temp<a)
        {
          a=temp;
          mid=int(rr);
        }
      }
      bestTriangulation[idx]=a;
      midPoint[idx]=mid;

      return a;
    }


  }
}