Transform.hpp

// This file is part of the imaging2 class library.
//
// University of Innsbruck, Infmath Imaging, 2009.
// http://infmath.uibk.ac.at
//
// All rights reserved.


#ifndef FEM_TRANSFORM_H
#define FEM_TRANSFORM_H

#include <fem/ShapeFunction.hpp>

namespace imaging
{
  template<size_t N_VERTICES, size_t N_FACES, size_t N>
  class Transform
  {
  protected:
    ublas::fixed_vector< ublas::fixed_vector<float_t, N>, N_VERTICES> _vertices;

  public:
    static const size_t n_element_vertices = N_VERTICES;
    
    static const size_t n_element_faces = N_FACES;
    
    static size_t face_vertex(size_t face_index, size_t face_vertex_index);

    void assign(size_t vertex_index, const ublas::fixed_vector<float_t, N> & vertex_coordinates)
    { _vertices(vertex_index) = vertex_coordinates; }

    ublas::fixed_vector<float_t, N> & value(const ublas::fixed_vector<float_t, N> & in, ublas::fixed_vector<float_t, N> & out) const;
    
    ublas::fixed_matrix<float_t, N, N> & derivative(const ublas::fixed_vector<float_t, N> & in, ublas::fixed_matrix<float_t, N, N> & out) const;
    
    ublas::fixed_matrix<float_t, N, N - 1> & boundary_derivative(size_t face_index, const ublas::fixed_vector<float_t, N - 1> & in, ublas::fixed_matrix<float_t, N, N - 1> & out) const;
    
    ublas::fixed_vector<float_t, N> & boundary_normal(size_t face_index, ublas::fixed_vector<float_t, N> & out) const;
    
    ublas::fixed_vector<float_t, N> & boundary2element(size_t face_index, const ublas::fixed_vector<float_t, N - 1> & in, ublas::fixed_vector<float_t, N> & out) const;
  };

  class Square2dTransform : public Transform<4, 4, 2>
  {
  
  public: 
    static size_t face_vertex(size_t face, size_t vertex);

    ublas::fixed_matrix<float_t, 2, 1> & boundary_derivative(size_t face, const ublas::fixed_vector<float_t, 1> & in, ublas::fixed_matrix<float_t, 2, 1> & out) const;

    ublas::fixed_vector<float_t, 2> & value(const ublas::fixed_vector<float_t, 2> & in, ublas::fixed_vector<float_t, 2> & out) const;

    ublas::fixed_matrix<float_t, 2, 2> & derivative(const ublas::fixed_vector<float_t, 2> & in, ublas::fixed_matrix<float_t, 2, 2> & out) const;
    
    ublas::fixed_vector<float_t, 2> & boundary2element(size_t face_index, const ublas::fixed_vector<float_t, 1> & in, ublas::fixed_vector<float_t, 2> & out) const;
    
    ublas::fixed_vector<float_t, 2> & boundary_normal(size_t face, ublas::fixed_vector<float_t, 2> & out) const;
  };

  class Triangle2dTransform : public Transform<3, 3, 2>
  {
    public:
    static size_t face_vertex(size_t face, size_t vertex);

    ublas::fixed_matrix<float_t, 2, 1> & boundary_derivative(size_t face, const ublas::fixed_vector<float_t, 1> & in, ublas::fixed_matrix<float_t, 2, 1> & out) const;

    ublas::fixed_vector<float_t, 2> & value(const ublas::fixed_vector<float_t, 2> & in, ublas::fixed_vector<float_t, 2> & out) const;

    ublas::fixed_matrix<float_t, 2, 2> & derivative(const ublas::fixed_vector<float_t, 2> & in, ublas::fixed_matrix<float_t, 2, 2> & out) const;
    
    ublas::fixed_vector<float_t, 2> & boundary2element(size_t face_index, const ublas::fixed_vector<float_t, 1> & in, ublas::fixed_vector<float_t, 2> & out) const;
    
    ublas::fixed_vector<float_t, 2> & boundary_normal(size_t face, ublas::fixed_vector<float_t, 2> & out) const;
  };

  class Tetrahedra3dTransform : public Transform<4, 4, 3>
  {
    static const size_t face_vertex_matrix[4][3];
    
    public:
    static size_t face_vertex(size_t face, size_t vertex);

    ublas::fixed_matrix<float_t, 3, 2> & boundary_derivative(size_t face, const ublas::fixed_vector<float_t, 2> & in, ublas::fixed_matrix<float_t, 3, 2> & out) const;

    ublas::fixed_vector<float_t, 3> & value(const ublas::fixed_vector<float_t, 3> & in, ublas::fixed_vector<float_t, 3> & out) const;

    ublas::fixed_matrix<float_t, 3, 3> & derivative(const ublas::fixed_vector<float_t, 3> & in, ublas::fixed_matrix<float_t, 3, 3> & out) const;
    
    ublas::fixed_vector<float_t, 3> & boundary2element(size_t face_index, const ublas::fixed_vector<float_t, 2> & in, ublas::fixed_vector<float_t, 3> & out) const;
    
    ublas::fixed_vector<float_t, 3> & boundary_normal(size_t face, ublas::fixed_vector<float_t, 3> & out) const;
  };


   class Cube3dTransform : public Transform<8, 6, 3>
  {
    static const size_t face_vertex_matrix[6][4];
    
    public:
    static size_t face_vertex(size_t face, size_t vertex);

    ublas::fixed_matrix<float_t, 3, 2> & boundary_derivative(size_t face, const ublas::fixed_vector<float_t, 2> & in, ublas::fixed_matrix<float_t, 3, 2> & out) const;

    ublas::fixed_vector<float_t, 3> & value(const ublas::fixed_vector<float_t, 3> & in, ublas::fixed_vector<float_t, 3> & out) const;

    ublas::fixed_matrix<float_t, 3, 3> & derivative(const ublas::fixed_vector<float_t, 3> & in, ublas::fixed_matrix<float_t, 3, 3> & out) const;
    
    ublas::fixed_vector<float_t, 3> & boundary2element(size_t face_index, const ublas::fixed_vector<float_t, 2> & in, ublas::fixed_vector<float_t, 3> & out) const;
    
    ublas::fixed_vector<float_t, 3> & boundary_normal(size_t face, ublas::fixed_vector<float_t, 3> & out) const;
  };


  class Interval1dTransform : public Transform<2, 2, 1>
  {
    public:
    static size_t face_vertex(size_t face, size_t vertex);

    ublas::fixed_matrix<float_t, 1, 0> & boundary_derivative(size_t face, const ublas::fixed_vector<float_t, 0> & in, ublas::fixed_matrix<float_t, 1, 0> & out) const;

    ublas::fixed_vector<float_t, 1> & value(const ublas::fixed_vector<float_t, 1> & in, ublas::fixed_vector<float_t, 1> & out) const;

    ublas::fixed_matrix<float_t, 1, 1> & derivative(const ublas::fixed_vector<float_t, 1> & in, ublas::fixed_matrix<float_t, 1, 1> & out) const;
    
    ublas::fixed_vector<float_t, 1> & boundary2element(size_t face_index, const ublas::fixed_vector<float_t, 0> & in, ublas::fixed_vector<float_t, 1> & out) const;
    
    ublas::fixed_vector<float_t, 1> & boundary_normal(size_t face, ublas::fixed_vector<float_t, 1> & out) const;
  };

}

#endif

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