curv.h

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#ifndef AIMS_MESH_MESHCURVATURE_H
#define AIMS_MESH_MESHCURVATURE_H

#include <aims/mesh/texture.h>
#include <aims/mesh/surface.h>
#include <aims/data/data.h>
#include <list>

inline float fsign(float x);
inline Point3df cross(Point3df a, Point3df b); 


TimeTexture<float> AimsMeshCurvature( const AimsSurface<3,Void> & mesh);

//Estimation of the time step dt for the diffusion equation.
float AimsMeshFiniteElementDt( const Texture<float> &tex,
                               const Texture<float> &lapl,
                               float tmax);

//Estimation of the curvature. Boix method
Texture<float> AimsMeshBoixCurvature( const AimsSurface<3,Void> & mesh,
                                      const std::vector<float> & ALPHA,
                                      const std::vector<float> & BETA,
                                      const std::vector<std::list<float> > & SURFACE);

//Regularization of a texture map. 
//Definition of the Outliers from the histogram
Texture<float> AimsRegularizeTexture( const Texture<float> &tex,
                                      const AimsSurface<3,Void> & mesh, 
                                      float alpha ); 

Texture<float> AimsRegularizeTexture(const Texture<float> & tex,
                                     float ratio );
//Estimation of the curvature (finite element method)
Texture<float> AimsMeshFiniteElementCurvature( const AimsSurface<3,Void> & mesh,
                                                   const std::vector< std::list<unsigned> > & neighbourso,
                                                   const std::vector< std::list<float> > & PHI,
                                                   const std::vector< std::list<float> > & THETA,
                                                   const std::vector< std::list<float> > & SURFACE,
                                                   const std::vector< std::list<float> > & DOT);

//Eequired for the curvature and the laplacian estimation (finite element method).
std::vector< std::list<float> > AimsMeshFiniteElementPhi( const AimsSurface<3,Void> & mesh,
                                                const std::vector< std::list<unsigned> > & neighbourso,
                                                const std::vector< std::list<float> > & surf);

//Eequired for the curvature and the laplacian estimation (finite element method).
std::vector< std::list<float> > AimsMeshFiniteElementTheta( const AimsSurface<3,Void> & mesh,
                                                  const std::vector< std::list<unsigned> > & neighbourso,
                                                  const std::vector< std::list<float> > & surf);
//Eequired for the curvature and the laplacian estimation (finite element method).
std::vector<float> AimsMeshFiniteElementAlpha( const AimsSurface<3,Void> & mesh,
                                          const std::vector< std::list<unsigned> > & neighbourso);

//Eequired for the curvature  estimation (boix method).
std::vector<float>  AimsMeshFiniteElementBeta( const AimsSurface<3,Void> & mesh,
                                          const std::vector< std::list<unsigned> > & neighbourso);

//Required for the curvature and the laplacian estimation (finite element and boix method).
//The first list element for each coordinate i of the vector
//Correspond to the total surface of the patch surrounding the node i.
std::vector< std::list<float> > AimsMeshFiniteElementSurface( const AimsSurface<3,Void> & mesh,
                                                    const std::vector< std::list<unsigned> > & neighbourso);

//Eequired for the curvature and the laplacian estimation (finite element method).
std::vector< std::list<float> > AimsMeshFiniteElementDot( const AimsSurface<3,Void> & mesh,
                                                const std::vector< std::list<unsigned> > & neighbourso);


//Give for each node the clockwise ordered list of neighbours nodes
std::vector< std::list<unsigned> > AimsMeshOrderNode(const AimsSurface<3,Void> & mesh);

//Give for each node the clockwise ordered list of neighbours triangles.
std::vector< std::list<unsigned> > AimsMeshOrderTriangle(const AimsSurface<3,Void> & mesh);

//Estimation of the laplacian of a texture map; (finite element method).

Texture<float> AimsMeshLaplacian( const Texture<float> &inittex, 
                                  const std::map<unsigned, 
                                  std::set< std::pair<unsigned,
                                  float> > > &lapl);

template <typename T>
void AimsMeshLaplacian( const std::vector<T> &inittex,
                        std::vector<T> & outtex,
                        const std::map<unsigned,
                          std::set< std::pair<unsigned,float> > > &lapl);


std::map<unsigned, std::set< std::pair<unsigned,float> > >  AimsMeshWeightFiniteElementLaplacian( const AimsSurface<3,Void> & mesh, 
                                               const float Wmax);

namespace aims
{
  typedef std::map<unsigned, std::set< std::pair<unsigned,float> > >
    LaplacianWeights;

  void makeLaplacianMatrix( const LaplacianWeights & weights,
                            LaplacianWeights & lmat, float dt );

  LaplacianWeights* sparseMult( const LaplacianWeights & in1,
                                const LaplacianWeights & in2,
                                float sparseThresh=0 );

  template <typename T>
  void applyLaplacianMatrix( const std::vector<T> &inittex,
                             std::vector<T> & outtex,
                             const LaplacianWeights &lapl );

  void laplacianMatrixThreshold( LaplacianWeights & lmat, float threshold );

  LaplacianWeights* makeLaplacianSmoothingCoefficients(
    const LaplacianWeights & weights, unsigned niter, float dt,
    float sparseThresh=0 );

}

#endif