TriSamplingSchemes.h

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/*
   For more information, please see: http://software.sci.utah.edu

   The MIT License

   Copyright (c) 2009 Scientific Computing and Imaging Institute,
   University of Utah.

   
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/// @todo Documentation Core/Basis/TriSamplingSchemes.h

#ifndef CORE_BASIS_TRISAMPLINGSCHEMES_H
#define CORE_BASIS_TRISAMPLINGSCHEMES_H 1

#include <vector>
#include <Core/Utils/Legacy/Assert.h>

#include <Core/Basis/share.h>

namespace SCIRun {
namespace Core {
namespace Basis {

class SCISHARE TriSamplingSchemes
{
  public:
  
  template <class ARRAY1, class ARRAY2>
  void get_gaussian_scheme(ARRAY1& coords, ARRAY2& weights, int order)
  {
    typedef typename ARRAY1::value_type coords_type;

    if (order == 1 || order == 0)
    {
      const double gaussian_weights[1] = { 1.0};
      const double gaussian_coords[1][2] = {{1./3.,1./3.}};
      const unsigned int num_coords = 2;
      const unsigned int num_points = 1;
      
      coords.resize(num_points);
      weights.resize(num_points);
      for (unsigned int i=0; i<num_points; i++)
      {
        coords[i].resize(num_coords);
        for (unsigned int j=0; j<num_coords; j++)
          coords[i][j] = static_cast<typename coords_type::value_type>(gaussian_coords[i][j]);
        weights[i] = static_cast<typename ARRAY2::value_type>(gaussian_weights[i]);
      }
    }
    else if (order == 2)
    { 
      const double gaussian_weights[3] = 
        {1./3., 1./3., 1./3.};
      const double gaussian_coords[3][2] = 
        {{1./6.,1./6.}, {2./3.,1./6.}, {1./6.,2./3.}};
      const unsigned int num_coords = 2;
      const unsigned int num_points = 3;
      
      coords.resize(num_points);
      weights.resize(num_points);
      for (unsigned int i=0; i<num_points; i++)
      {
        coords[i].resize(num_coords);
        for (unsigned int j=0; j<num_coords; j++)
          coords[i][j] = static_cast<typename coords_type::value_type>(gaussian_coords[i][j]);
        weights[i] = static_cast<typename ARRAY2::value_type>(gaussian_weights[i]);
      }
    }
    else if (order == 3)
    {
      const double gaussian_weights[7] =   
        { 0.1259391805, 0.1259391805, 0.1259391805, 0.1323941527, 
          0.1323941527, 0.1323941527, 0.225};
      const double gaussian_coords[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}};
      const unsigned int num_coords = 2;
      const unsigned int num_points = 7;
      
      coords.resize(num_points);
      weights.resize(num_points);
      for (unsigned int i=0; i<num_points; i++)
      {
        coords[i].resize(num_coords);
        for (unsigned int j=0; j<num_coords; j++)
          coords[i][j] = static_cast<typename coords_type::value_type>(gaussian_coords[i][j]);
        weights[i] = static_cast<typename ARRAY2::value_type>(gaussian_weights[i]);
      }
    }
    else
    {
      REPORT_NOT_IMPLEMENTED("Only Gaussian scheme 1, 2, and 3 are implemented");
    }
  }
  
  template <class ARRAY1, class ARRAY2>
  void get_regular_scheme(ARRAY1& coords,ARRAY2& weights, int order)
  {
    typedef typename ARRAY1::value_type coords_type;

    int m = 0;
    for (int j=0; j<order;j++) m += (2*j+1);
    coords.resize(m);
    
    weights.resize(m);
    for (int p=0; p<m;p++) weights[p] = static_cast<typename ARRAY2::value_type>(1.0/static_cast<double>(m)); 
        
    int k= 0;
    for (int p=0;p<order;p++)
    {
      int r=0;   
      for (; r<p; r++)
      {
        coords[k].resize(2);
        coords[k][1] = static_cast<typename coords_type::value_type>((static_cast<double>(order-1-p)+1.0/3.0)/static_cast<double>(order));
        coords[k][0] = static_cast<typename coords_type::value_type>((static_cast<double>(r)+1.0/3.0)/static_cast<double>(order));
        k++;
        coords[k].resize(2);
        coords[k][1] = static_cast<typename coords_type::value_type>((static_cast<double>(order-1-p)+2.0/3.0)/static_cast<double>(order));
        coords[k][0] = static_cast<typename coords_type::value_type>((static_cast<double>(r)+2.0/3.0)/static_cast<double>(order));
        k++;
      }       
      coords[k].resize(2);
      coords[k][1] = static_cast<typename coords_type::value_type>((static_cast<double>(order-1-p)+1.0/3.0)/static_cast<double>(order));
      coords[k][0] = static_cast<typename coords_type::value_type>((static_cast<double>(r)+1.0/3.0)/static_cast<double>(order));
      k++;
    }
  }
};

}}}

#endif