TriLinearLgn.h

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//  Copyright (c) 2009 Scientific Computing and Imaging Institute,
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///   @file    TriLinearLgn.h
///   @author  Martin Cole, Frank B. Sachse
///   @date    Dec 04 2004

#ifndef CORE_BASIS_TRILINEARLGN_H
#define CORE_BASIS_TRILINEARLGN_H 1

#include <float.h>

#include <Core/Basis/CrvLinearLgn.h>
#include <Core/Basis/TriElementWeights.h>
#include <Core/Basis/TriSamplingSchemes.h>

namespace SCIRun {
namespace Core {
namespace Basis {

/// Class for describing unit geometry of TriLinearLgn 
class TriLinearLgnUnitElement {
public:
  /// Parametric coordinates of vertices of unit edge
  static SCISHARE double unit_vertices[3][2];
  /// References to vertices of unit edge 
  static SCISHARE int unit_edges[3][2]; 
  /// References to vertices of unit face
  static SCISHARE int unit_faces[1][3]; 
  /// References to normal of unit face
  static SCISHARE double unit_face_normals[1][3];
  /// The center of the unit element
  static SCISHARE double unit_center[2];

  TriLinearLgnUnitElement() {}
  virtual ~TriLinearLgnUnitElement() {}

  /// return dimension of domain 
  static int domain_dimension() 
    { return 2; } 
  
  /// return size of the domain
  static double domain_size() 
    { return 0.5; }
  
  /// return number of vertices
  static int number_of_vertices() 
    { return 3; }
  
  /// return number of vertices in mesh
  static int number_of_mesh_vertices() 
    { return 3; }
  
  /// return degrees of freedom
  static int dofs() 
    { return 3; }

  /// return number of edges 
  static int number_of_edges() 
    { return 3; } 
  
  /// return number of vertices per face 
  static int vertices_of_face() 
    { return 3; } 
  
  /// return number of faces per cell 
  static int faces_of_cell() 
    { return 1; }

  static inline double length(int edge) 
  { 
    const double *v0 = unit_vertices[unit_edges[edge][0]];
    const double *v1 = unit_vertices[unit_edges[edge][1]];
    const double dx = v1[0] - v0[0];
    const double dy = v1[1] - v0[1];
    return sqrt(dx*dx+dy*dy);
  } 
  
  static double area(int /* face */) { return 0.5; } ///< return area
  static double volume() { return 0.; } ///< return volume
};


/// Class for creating geometrical approximations of Tri meshes
class TriApprox {  
public:
  TriApprox() {}
  virtual ~TriApprox() {}
  
  /// Approximate edge for element by piecewise linear segments
  /// return: coords gives parametric coordinates of the approximation.
  /// Use interpolate with coordinates to get the world coordinates.
  template<class VECTOR>
  void approx_edge(const unsigned edge, 
                   const unsigned div_per_unit, 
                   VECTOR &coords) const
  {
    typedef typename VECTOR::value_type VECTOR2;

    coords.resize(div_per_unit+1);

    const double *v0 = TriLinearLgnUnitElement::unit_vertices[TriLinearLgnUnitElement::unit_edges[edge][0]];
    const double *v1 = TriLinearLgnUnitElement::unit_vertices[TriLinearLgnUnitElement::unit_edges[edge][1]];

    const double &p1x = v0[0];
    const double &p1y = v0[1];
    const double dx = v1[0] - p1x;
    const double dy = v1[1] - p1y;

    for(unsigned i = 0; i <= div_per_unit; i++) {
      const double d = (double)i / (double)div_per_unit;
      typename VECTOR::value_type &tmp = coords[i];
      tmp.resize(2);
      tmp[0] = static_cast<typename VECTOR2::value_type>(p1x + d * dx);
      tmp[1] = static_cast<typename VECTOR2::value_type>(p1y + d * dy);
    }   
  } 
  
   /// Approximate faces for element by piecewise linear elements
  /// return: coords gives parametric coordinates at the approximation point.
  /// Use interpolate with coordinates to get the world coordinates.
  template<class VECTOR>
  void approx_face(const unsigned /* face */, 
                   const unsigned div_per_unit, 
                   VECTOR &coords) const
  {
    typedef typename VECTOR::value_type VECTOR2;
    typedef typename VECTOR2::value_type VECTOR3;
 
    coords.resize(div_per_unit);
    const double d = 1. / div_per_unit;

    for(unsigned j = 0; j < div_per_unit; j++) 
    {
      const double dj = (double)j / (double)div_per_unit;
      unsigned e = 0;
      coords[j].resize((div_per_unit - j) * 2 + 1);
      typename VECTOR2::value_type& tmp = coords[j][e++];
      tmp.resize(2);
      tmp[0] = 0;
      tmp[1] = dj;
      for(unsigned i = 0; i<div_per_unit - j; i++) 
      {
        const double di = (double)i / (double)div_per_unit;
        typename VECTOR2::value_type& tmp1 = coords[j][e++];
        tmp1.resize(2);
        tmp1[0] = static_cast<typename VECTOR3::value_type>(di);
        tmp1[1] = static_cast<typename VECTOR3::value_type>(dj + d);
        typename VECTOR2::value_type& tmp2 = coords[j][e++];
        tmp2.resize(2);
        tmp2[0] = static_cast<typename VECTOR3::value_type>(di + d);
        tmp2[1] = static_cast<typename VECTOR3::value_type>(dj);
      }
    }
  }
};

/// Class for searching of parametric coordinates related to a 
/// value in Tri meshes and fields
template <class ElemBasis>
class TriLocate : public Dim2Locate<ElemBasis> {
public:
  typedef typename ElemBasis::value_type T;

  TriLocate() {}
  virtual ~TriLocate() {}
 
  /// find value in interpolation for given value
  template <class ElemData, class VECTOR>
  bool get_coords(const ElemBasis *pEB, VECTOR &coords, 
          const T& value, const ElemData &cd) const  
  {          
    initial_guess(pEB, value, cd, coords);
    if (this->get_iterative(pEB, coords, value, cd))
      return check_coords(coords);
    return false;
  }

  template<class VECTOR>
  inline bool check_coords(const VECTOR &x) const  
  {  
    if (x[0]>=-Dim2Locate<ElemBasis>::thresholdDist)
      if (x[1]>=-Dim2Locate<ElemBasis>::thresholdDist)
    if (x[0]+x[1]<=Dim2Locate<ElemBasis>::thresholdDist1)
      return true;

    return false;
  }
  
protected:
  /// find a reasonable initial guess 
  template <class ElemData, class VECTOR>
  void initial_guess(const ElemBasis *pElem, const T &val, const ElemData &cd, 
             VECTOR & guess) const
  {
    double dist = DBL_MAX;
    
    VECTOR coord(2);
    StackVector<T,2> derivs;
    guess.resize(2);

    const int end = 3;
    for (int x = 1; x < end; x++) 
    {
      coord[0] = x / (double) end;
      for (int y = 1; y < end; y++) 
      {
        coord[1] = y / (double) end;
        if (coord[0]+coord[1]>Dim2Locate<ElemBasis>::thresholdDist1)
          break;
        double cur_d;
        if (compare_distance(pElem->interpolate(coord, cd), 
                 val, cur_d, dist)) 
        {
          pElem->derivate(coord, cd, derivs);
          if (!check_zero(derivs)) {
            dist = cur_d;
            guess = coord;
          }
        }
      }
    }
  }
};


/// Class with weights and coordinates for 2nd order Gaussian integration
template <class T>
class TriGaussian1 
{
public:
  static int GaussianNum;
  static T GaussianPoints[1][2];
  static T GaussianWeights[1];
};

template <class T>
int TriGaussian1<T>::GaussianNum = 1;

template <class T>
T TriGaussian1<T>::GaussianPoints[1][2] = { {1./3.,1./3.}};

template <class T>
T TriGaussian1<T>::GaussianWeights[1] = {1.0};

/// Class with weights and coordinates for 2nd order Gaussian integration
template <class T>
class TriGaussian2 
{
public:
  static int GaussianNum;
  static T GaussianPoints[3][2];
  static T GaussianWeights[3];
};

template <class T>
int TriGaussian2<T>::GaussianNum = 3;

template <class T>
T TriGaussian2<T>::GaussianPoints[3][2] = {
  {1./6.,1./6.}, {2./3.,1./6.}, {1./6.,2./3.}};

template <class T>
T TriGaussian2<T>::GaussianWeights[3] = {1./3., 1./3., 1./3.};

/// Class with weights and coordinates for 3rd order Gaussian integration
template <class T>
class TriGaussian3 
{
public:
  static int GaussianNum;
  static T GaussianPoints[7][2];
  static T GaussianWeights[7];
};

template <class T>
int TriGaussian3<T>::GaussianNum = 7;

template <class T>
T TriGaussian3<T>::GaussianPoints[7][2] = {
  {0.1012865073, 0.1012865073}, {0.7974269853, 0.1012865073}, {0.1012865073, 0.7974269853},
  {0.4701420641, 0.0597158717}, {0.4701420641, 0.4701420641}, {0.0597158717, 0.4701420641},
  {0.3333333333, 0.3333333333}};

template <class T>
T TriGaussian3<T>::GaussianWeights[7] = 
  {0.1259391805, 0.1259391805, 0.1259391805, 0.1323941527, 0.1323941527, 0.1323941527, 0.225};

#ifdef _WIN32
// force the instantiation of TriGaussian3<double>
template class TriGaussian1<double>;
template class TriGaussian2<double>;
template class TriGaussian3<double>;
#endif


/// Class for handling of element of type triangle with 
/// linear lagrangian interpolation
template <class T>
class TriLinearLgn : 
         public BasisSimple<T>, 
         public TriApprox, 
             public TriGaussian1<double>, 
         public TriSamplingSchemes,
             public TriLinearLgnUnitElement,
         public TriElementWeights
{ 
public:
  typedef T value_type;

  TriLinearLgn() {}
  virtual ~TriLinearLgn() {}
  
  static int polynomial_order() { return 1; }

  template<class VECTOR>
  inline void get_weights(const VECTOR& coords, double *w) const
    { get_linear_weights(coords,w); }

  template<class VECTOR>
  inline void get_derivate_weights(const VECTOR& coords, double *w) const
    { get_linear_derivate_weights(coords,w); }

  /// get value at parametric coordinate
  template <class ElemData, class VECTOR>
  T interpolate(const VECTOR &coords, const ElemData &cd) const
  {
    double w[3];
    get_linear_weights(coords, w); 

    return (T)(w[0] * cd.node0() +
           w[1] * cd.node1() +
           w[2] * cd.node2());
  }

  /// get first derivative at parametric coordinate
  template <class ElemData, class VECTOR1, class VECTOR2>
  void derivate(const VECTOR1& /*coords*/, const ElemData &cd, 
        VECTOR2 &derivs) const
  {
    derivs.resize(2);

    derivs[0] = static_cast<typename VECTOR2::value_type>(-1. * cd.node0() + cd.node1());
    derivs[1] = static_cast<typename VECTOR2::value_type>(-1. * cd.node0() + cd.node2());
  }
    
  /// get the parametric coordinate for value within the element
  template <class ElemData, class VECTOR>
  bool get_coords(VECTOR &coords, const T& value, 
          const ElemData &cd) const  
  {
    TriLocate< TriLinearLgn<T> > CL;
    return CL.get_coords(this, coords, value, cd);
  }
 
  /// get arc length for edge
  template <class ElemData>
  double get_arc_length(const unsigned edge, const ElemData &cd) const  
  {
    return get_arc2d_length<CrvGaussian1<double> >(this, edge, cd);
  }
 
  /// get area
  template <class ElemData>
    double get_area(const unsigned face, const ElemData &cd) const  
  {
    return get_area2<TriGaussian2<double> >(this, face, cd);
  }
 
  /// get volume
  template <class ElemData>
    double get_volume(const ElemData & /* cd */) const  
  {
    return 0.;
  }
  
  template<class VECTOR>
  void approx_edge(const unsigned int edge, 
               const unsigned int div_per_unit,
               VECTOR &coords) const
  {
    typedef typename VECTOR::value_type VECTOR2;

    coords.resize(div_per_unit + 1);

    const double *v0 = TriLinearLgnUnitElement::unit_vertices[TriLinearLgnUnitElement::unit_edges[edge][0]];
    const double *v1 = TriLinearLgnUnitElement::unit_vertices[TriLinearLgnUnitElement::unit_edges[edge][1]];

    const double &p1x = v0[0];
    const double &p1y = v0[1];
    const double dx = v1[0] - p1x;
    const double dy = v1[1] - p1y;

    for(unsigned int i = 0; i <= div_per_unit; i++) {
      const double d = (double)i / (double)div_per_unit;
      typename VECTOR::value_type &tmp = coords[i];
      tmp.resize(2);
      tmp[0] = static_cast<typename VECTOR2::value_type>(p1x + d * dx);
      tmp[1] = static_cast<typename VECTOR2::value_type>(p1y + d * dy);
    }     
  }

  template<class VECTOR>
  void approx_face(const unsigned int /*face*/, 
               const unsigned int div_per_unit,
               VECTOR &coords) const
  {
    typedef typename VECTOR::value_type VECTOR2;
    typedef typename VECTOR2::value_type VECTOR3;
    
    const double *v0 = TriLinearLgnUnitElement::unit_vertices[TriLinearLgnUnitElement::unit_faces[0][0]];
    const double *v1 = TriLinearLgnUnitElement::unit_vertices[TriLinearLgnUnitElement::unit_faces[0][1]];
    const double *v2 = TriLinearLgnUnitElement::unit_vertices[TriLinearLgnUnitElement::unit_faces[0][2]];

    coords.resize(div_per_unit);
    const double d = 1. / div_per_unit;
    for(unsigned int j = 0; j<div_per_unit; j++) 
    {
      const double dj = (double)j / (double)div_per_unit;
      unsigned int e = 0;
      coords[j].resize((div_per_unit - j) * 2 + 1);
      typename VECTOR2::value_type &tmp = coords[j][e++];
      tmp.resize(2);
      tmp[0] = static_cast<typename VECTOR3::value_type>(v0[0] + dj * (v2[0] - v0[0]));
      tmp[1] = static_cast<typename VECTOR3::value_type>(v0[1] + dj * (v2[1] - v0[1]));

      for(unsigned int i = 0; i<div_per_unit - j; i++) 
      {
        const double di = (double)i / (double)div_per_unit;
        typename VECTOR2::value_type &tmp1 = coords[j][e++];
        tmp1.resize(2);
        tmp1[0] = static_cast<typename VECTOR3::value_type>(v0[0] + (dj + d) * (v2[0] - v0[0]) + di * (v1[0] - v0[0]));
        tmp1[1] = static_cast<typename VECTOR3::value_type>(v0[1] + (dj + d) * (v2[1] - v0[1]) + di * (v1[1] - v0[1]));

        typename VECTOR2::value_type &tmp2 = coords[j][e++];
        tmp2.resize(2);
        tmp2[0] = static_cast<typename VECTOR3::value_type>(v0[0] + dj * (v2[0] - v0[0]) + (di + d) * (v1[0] - v0[0]));
        tmp2[1] = static_cast<typename VECTOR3::value_type>(v0[1] + dj * (v2[1] - v0[1]) + (di + d) * (v1[1] - v0[1]));
      }
    }
  }  
  

  static const std::string type_name(int n = -1);


  virtual void io (Piostream& str);

};



template <class T>
const std::string
TriLinearLgn<T>::type_name(int n)
{
  ASSERT((n >= -1) && n <= 1);
  if (n == -1)
  {
    static const std::string name = TypeNameGenerator::make_template_id(type_name(0), type_name(1));
    return name;
  }
  else if (n == 0)
  {
    static const std::string nm("TriLinearLgn");
    return nm;
  } else {
    return find_type_name((T *)0);
  }
}

}}

template <class T>
const TypeDescription* get_type_description(Core::Basis::TriLinearLgn<T> *)
{
  static TypeDescription* td = 0;
  if(!td){
    const TypeDescription *sub = get_type_description((T*)0);
    TypeDescription::td_vec *subs = new TypeDescription::td_vec(1);
    (*subs)[0] = sub;
    td = new TypeDescription("TriLinearLgn", subs, 
      std::string(__FILE__),
      "SCIRun", 
      TypeDescription::BASIS_E);
  }
  return td;
}
  
  const int TRILINEARLGN_VERSION = 1;
  template <class T>
  void
  Core::Basis::TriLinearLgn<T>::io(Piostream &stream)
  {
    stream.begin_class(get_type_description(this)->get_name(),
                       TRILINEARLGN_VERSION);
    stream.end_class();
  }
}

#endif