QuadBilinearLgn.h

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

#ifndef CORE_BASIS_QUADBILINEARLGN_H
#define CORE_BASIS_QUADBILINEARLGN_H 1

#include <float.h>

#include <Core/Basis/CrvLinearLgn.h>
#include <Core/Basis/QuadElementWeights.h>
#include <Core/Basis/QuadSamplingSchemes.h>

namespace SCIRun {
namespace Core {
namespace Basis {

/// Class for describing unit geometry of QuadBilinearLgn 
class QuadBilinearLgnUnitElement {
public: 
  /// Parametric coordinates of vertices of unit edge
  static SCISHARE double unit_vertices[4][2];
  /// References to vertices of unit edge  
  static SCISHARE int unit_edges[4][2]; 
  /// References to vertices of unit face 
  static SCISHARE int unit_faces[1][4]; 
  /// References to normal of unit face
  static SCISHARE double unit_face_normals[1][3];
  /// Center of the unit element
  static SCISHARE double unit_center[2];

  QuadBilinearLgnUnitElement() {}
  virtual ~QuadBilinearLgnUnitElement() {}
  /// return dimension of domain 
  static int domain_dimension() 
    { return 2; }
  
  /// return size of the domain
  static double domain_size() 
    { return 1.0; }
  
  /// return number of vertices
  static int number_of_vertices() 
    { return 4; }
  
  /// return number of vertices in mesh
  static int number_of_mesh_vertices() 
    { return 4; }
  
  /// return degrees of freedom
  static int dofs() 
    { return 4; } 

  /// return number of edges
  static int number_of_edges() 
    { return 4; }
  
  /// return number of vertices per face 
  static int vertices_of_face() 
    { return 4; }
  
  /// return number of faces per cell 
  static int faces_of_cell() 
    { return 1; }

  static inline double length(int edge) 
  { ///< return length
    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 1; } ///< return area
  static double volume() { return 0.; } ///< return volume
};


/// Class for creating geometrical approximations of Quad meshes
class QuadApprox {  
public:
  QuadApprox() {}
  virtual ~QuadApprox() {}
   
  /// 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 p1x = QuadBilinearLgnUnitElement::unit_vertices[QuadBilinearLgnUnitElement::unit_edges[edge][0]][0];
    const double p1y = QuadBilinearLgnUnitElement::unit_vertices[QuadBilinearLgnUnitElement::unit_edges[edge][0]][1];
    const double dx = QuadBilinearLgnUnitElement::unit_vertices[QuadBilinearLgnUnitElement::unit_edges[edge][1]][0] - p1x;
    const double dy = QuadBilinearLgnUnitElement::unit_vertices[QuadBilinearLgnUnitElement::unit_edges[edge][1]][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);
    double d = 1. / div_per_unit;
    for(unsigned j = 0; j < div_per_unit; j++) 
    {
      coords[j].resize(2 * (div_per_unit + 1));
      unsigned e = 0;
      for(unsigned i = 0; i <= div_per_unit; i++) 
      {
        typename VECTOR2::value_type &e1 = coords[j][e++];
        e1.resize(2);
        e1[0] = static_cast<typename VECTOR3::value_type>((double)i / (double)div_per_unit);
        e1[1] = static_cast<typename VECTOR3::value_type>((double)j / (double)div_per_unit);
        typename VECTOR2::value_type &e2 = coords[j][e++];
        e2.resize(2);
        e2[0] = e1[0];
        e2[1] = static_cast<typename VECTOR3::value_type>((double)j / (double)div_per_unit + d);
      }
    }
  }
};
 
/// Class for searching of parametric coordinates related to a 
/// value in Quad meshes and fields
/// to do
template <class ElemBasis>
class QuadLocate : public Dim2Locate<ElemBasis> {
public:
  typedef typename ElemBasis::value_type T;

  QuadLocate() {}
  virtual ~QuadLocate() {}
 
  /// 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 && 
      x[0]<=Dim2Locate<ElemBasis>::thresholdDist1)
      if (x[1]>=-Dim2Locate<ElemBasis>::thresholdDist && 
        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;
        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 QuadGaussian1
{
public:
  static int GaussianNum;
  static T GaussianPoints[1][2];
  static T GaussianWeights[1];
};

template <class T>
int QuadGaussian1<T>::GaussianNum = 1;

template <class T>
T QuadGaussian1<T>::GaussianPoints[1][2] = {
  {0.5, 0.5}};

template <class T>
T QuadGaussian1<T>::GaussianWeights[1] = {1.0};


/// Class with weights and coordinates for 2nd order Gaussian integration
template <class T>
class QuadGaussian2 
{
public:
  static int GaussianNum;
  static T GaussianPoints[4][2];
  static T GaussianWeights[4];
};

template <class T>
int QuadGaussian2<T>::GaussianNum = 4;

template <class T>
T QuadGaussian2<T>::GaussianPoints[4][2] = {
  {0.211324865405, 0.211324865405},
  {0.788675134595, 0.211324865405},
  {0.788675134595, 0.788675134595},
  {0.211324865405, 0.788675134595}};

template <class T>
T QuadGaussian2<T>::GaussianWeights[4] = {.25, .25, .25, .25};

/// Class with weights and coordinates for 3rd order Gaussian integration
template <class T>
class QuadGaussian3 
{
public:
  static int GaussianNum;
  static T GaussianPoints[9][2];
  static T GaussianWeights[9];
};

template <class T>
int QuadGaussian3<T>::GaussianNum = 9;

template <class T>
T QuadGaussian3<T>::GaussianPoints[9][2] = {
  {0.11270166537950, 0.11270166537950}, {0.5, 0.11270166537950}, {0.88729833462050, 0.11270166537950},
  {0.11270166537950, 0.5}, {0.5, 0.5}, {0.88729833462050, 0.5},
  {0.11270166537950, 0.88729833462050}, {0.5, 0.88729833462050}, {0.88729833462050, 0.88729833462050}
};
  
template <class T>
T QuadGaussian3<T>::GaussianWeights[9] = {
  0.07716049378395,   0.12345679007654,   0.07716049378395,
  0.12345679007654,   0.19753086415802,   0.12345679007654,
  0.07716049378395,   0.12345679007654,   0.07716049378395
};


/// Class for handling of element of type quad with 
/// bilinear lagrangian interpolation
template <class T>
class QuadBilinearLgn : 
      public BasisSimple<T>, 
      public QuadApprox, 
            public QuadGaussian3<double>, 
            public QuadSamplingSchemes, 
            public QuadBilinearLgnUnitElement,
      public QuadElementWeights 
{
public:
  typedef T value_type;

  QuadBilinearLgn() {}
  virtual ~QuadBilinearLgn() {}
  
  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[4];
    get_linear_weights(coords, w); 

    return (T)(w[0] * cd.node0() +
           w[1] * cd.node1() +
           w[2] * cd.node2() +
           w[3] * cd.node3());
  }


  /// 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_linear_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());
         
    derivs[1] = static_cast<typename VECTOR2::value_type>(
         w[4] * cd.node0() +
           w[5] * cd.node1() +
           w[6] * cd.node2() +
           w[7] * cd.node3());
  }  

  /// 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< QuadBilinearLgn<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<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
QuadBilinearLgn<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("QuadBilinearLgn");
    return nm;
  } else {
    return find_type_name((T *)0);
  }
}




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

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

#endif