TriQuadraticLgn.h

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///   @file    TriQuadraticLgn.h
///   @author  Martin Cole, Frank Sachse
///   @date    Dec 04 2004
 
#ifndef CORE_BASIS_TRIQUADRATICLGN_H
#define CORE_BASIS_TRIQUADRATICLGN_H 1

#include <Core/Persistent/PersistentSTL.h>
#include <Core/Basis/TriLinearLgn.h>

namespace SCIRun {
namespace Core {
namespace Basis {

/// Class for describing unit geometry of TriQuadraticLgn 
  class TriQuadraticLgnUnitElement : public TriLinearLgnUnitElement {
public: 
  static SCISHARE double unit_vertices[6][2]; ///< Parametric coordinates of vertices of unit edge
  
  TriQuadraticLgnUnitElement() {}
  virtual ~TriQuadraticLgnUnitElement() {}
    
  static int number_of_vertices() { return 6; } ///< return number of vertices
  static int dofs() { return 6; } ///< return degrees of freedom
};
  
  
/// Class for handling of element of type triangle with 
/// linear quadratic interpolation
template <class T>
class TriQuadraticLgn : public BasisAddNodes<T>, 
                        public TriApprox, 
            public TriGaussian3<double>, 
      public TriSamplingSchemes,
            public TriQuadraticLgnUnitElement,
      public TriElementWeights 
{
public:
  typedef T value_type;
    
  TriQuadraticLgn() {}
  virtual ~TriQuadraticLgn() {}

  static int polynomial_order() { return 2; }

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

  template<class VECTOR>
  inline void get_derivate_weights(const VECTOR& coords, double *w) const
    { get_quadratic_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[6];
    get_quadratic_weights(coords, w); 

    return (T)(
         w[0] * cd.node0() +
           w[1] * cd.node1() +
           w[2] * cd.node2() +
           w[3] * this->nodes_[cd.edge0_index()] +
           w[4] * this->nodes_[cd.edge1_index()] +
           w[5] * this->nodes_[cd.edge2_index()]);
  }

  /// get first derivative at parametric coordinate
  template <class ElemData, class VECTOR1, class VECTOR2>
  void derivate(const VECTOR1 &coords, const ElemData &cd, 
        VECTOR2 &derivs) const
  {
    double w[12];
    get_quadratic_derivate_weights(coords, w);

    derivs.resize(2);

    derivs[0]=static_cast<typename VECTOR2::value_type>(
      w[0]*cd.node0() 
      + w[1]*cd.node1()
      + w[2]*cd.node2() 
      + w[3]*this->nodes_[cd.edge0_index()] 
      + w[4]*this->nodes_[cd.edge1_index()] 
      + w[5]*this->nodes_[cd.edge2_index()]);

    derivs[1]=static_cast<typename VECTOR2::value_type>(
      w[6]*cd.node0()
        + w[7]*cd.node1() 
    + w[8]*cd.node2() 
    + w[9]*this->nodes_[cd.edge0_index()] 
    + w[10]*this->nodes_[cd.edge1_index()] 
    + w[11] *this->nodes_[cd.edge2_index()]);
  }

  /// 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< TriQuadraticLgn<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<CrvGaussian2<double> >(this, edge, cd);
  }
 
  /// get area
  template <class ElemData>
    double get_area(const unsigned face, const ElemData &cd) const  
  {
    return get_area2<TriGaussian3<double> >(this, face, cd);
  }
 
  /// get volume
  template <class ElemData>
    double get_volume(const ElemData & /* cd */) const  
  {
    return 0.;
  }
  

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


  virtual void io (Piostream& str);

};





template <class T>
const std::string
TriQuadraticLgn<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("TriQuadraticLgn");
    return nm;
  } else {
    return find_type_name((T *)0);
  }
}

}}

template <class T>
const TypeDescription* get_type_description(Core::Basis::TriQuadraticLgn<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("TriQuadraticLgn", subs, 
      std::string(__FILE__),
      "SCIRun", 
      TypeDescription::BASIS_E);
  }
  return td;
}
  
  const int TRIQUADRATICLGN_VERSION = 1;
  template <class T>
  void
  Core::Basis::TriQuadraticLgn<T>::io(Piostream &stream)
  {
    stream.begin_class(get_type_description(this)->get_name(),
                       TRIQUADRATICLGN_VERSION);
    Pio(stream, this->nodes_);
    stream.end_class();
  }
}

#endif