QuadBiquadraticLgn.h

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///   @file    QuadBiquadraticLgn.h
///   @author  Marty Cole, Frank B. Sachse
///   @date    30 Nov 2004

#ifndef BASIS_CORE_QUADBIQUADRATICLGN_H
#define BASIS_CORE_QUADBIQUADRATICLGN_H 1

#include <Core/Basis/QuadBilinearLgn.h>

namespace SCIRun {
namespace Core {
namespace Basis {
 
/// Class for describing unit geometry of QuadBiquadraticLgn 
class QuadBiquadraticLgnUnitElement : public QuadBilinearLgnUnitElement {
  
  public: 
  static SCISHARE double unit_vertices[8][2]; ///< Parametric coordinates of vertices of unit edge

  QuadBiquadraticLgnUnitElement() {}
  virtual ~QuadBiquadraticLgnUnitElement() {}
  
  static int number_of_vertices() { return 8; } ///< return number of vertices
  static int dofs() { return 8; } ///< return degrees of freedom
};


/// Class for handling of element of type quad with 
/// biquadratic lagrangian interpolation
template <class T>
class QuadBiquadraticLgn : public BasisAddNodes<T>, 
                           public QuadApprox, 
                           public QuadGaussian3<double>, 
                           public QuadSamplingSchemes, 
                           public QuadBiquadraticLgnUnitElement,
                           public QuadElementWeights
{
public:
  typedef T value_type;

  QuadBiquadraticLgn() {}
  virtual ~QuadBiquadraticLgn() {}
  
  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 first derivative at parametric coordinate 
  template <class ElemData, class VECTOR>
  T interpolate(const VECTOR &coords, const ElemData &cd) const
  {
    double w[8];
    get_quadratic_weights(coords, w); 

    return (T)(w[0] * cd.node0() +
           w[1] * cd.node1() +
           w[2] * cd.node2() +
           w[3] * cd.node3() +
           w[4] * this->nodes_[cd.edge0_index()] +
           w[5] * this->nodes_[cd.edge1_index()] +
           w[6] * this->nodes_[cd.edge2_index()] +
           w[7] * this->nodes_[cd.edge3_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[16];
    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]*cd.node3() +
       w[4]*this->nodes_[cd.edge0_index()] +
         w[5]*this->nodes_[cd.edge1_index()] +
         w[6]*this->nodes_[cd.edge2_index()] +
         w[7]*this->nodes_[cd.edge3_index()]);
    
    derivs[1]=
      static_cast<typename VECTOR2::value_type>(
      w[8]*cd.node0() +
      w[9]*cd.node1() +
        w[10]*cd.node2() +
        w[11]*cd.node3() +
        w[12]*this->nodes_[cd.edge0_index()] +
        w[13]*this->nodes_[cd.edge1_index()] +
        w[14]*this->nodes_[cd.edge2_index()] +
        w[15]*this->nodes_[cd.edge3_index()]);
  }  
  
  /// get parametric coordinate for value within the element
  template <class ElemData, class VECTOR>
  bool get_coords(VECTOR &coords, const T& value, 
          const ElemData &cd) const
  {
    QuadLocate< QuadBiquadraticLgn<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<QuadGaussian2<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
QuadBiquadraticLgn<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("QuadBiquadraticLgn");
    return nm;
  } else {
    return find_type_name((T *)0);
  }
}




}}

template <class T>
const TypeDescription* get_type_description(Core::Basis::QuadBiquadraticLgn<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("QuadBiquadraticLgn", subs, 
      std::string(__FILE__),
      "SCIRun", 
      TypeDescription::BASIS_E);
  }
  return td;
}

const int QUADBIQUADRATICLGN_VERSION = 1;
template <class T>
void
  Core::Basis::QuadBiquadraticLgn<T>::io(Piostream &stream)
{
  stream.begin_class(get_type_description(this)->get_name(),
    QUADBIQUADRATICLGN_VERSION );
  Pio(stream, this->nodes_);
  stream.end_class();
}

}


#endif