QuadSamplingSchemes.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/QuadSamplingSchemes.h
#ifndef CORE_BASIS_QUADSAMPLINGSCHEMES_H
#define CORE_BASIS_QUADSAMPLINGSCHEMES_H 1

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

#include <Core/Basis/share.h>

namespace SCIRun {
namespace Core {
namespace Basis {

class SCISHARE QuadSamplingSchemes
{
  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] = {{.5,.5}};
      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[4] = {.25, .25, .25, .25};
      const double gaussian_coords[4][2] = {
        {0.211324865405, 0.211324865405},
        {0.788675134595, 0.211324865405},
        {0.788675134595, 0.788675134595},
        {0.211324865405, 0.788675134595}};
      const unsigned int num_coords = 2;
      const unsigned int num_points = 4;
      
      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[9] = {
        0.07716049378395,   0.12345679007654,   0.07716049378395,
        0.12345679007654,   0.19753086415802,   0.12345679007654,
        0.07716049378395,   0.12345679007654,   0.07716049378395 };
      const double gaussian_coords[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}};
      const unsigned int num_coords = 2;
      const unsigned int num_points = 9;
      
      coords.resize(num_points);
      weights.resize(num_points);
      for (unsigned int i=0; i<num_coords; i++)
      {
        coords[i].resize(num_points);
        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;

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

}}}

#endif