CrvElementWeights.h

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//  Copyright (c) 2009 Scientific Computing and Imaging Institute,
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#ifndef CORE_BASIS_CRVWEIGHTS_H
#define CORE_BASIS_CRVWEIGHTS_H 1

#include <Core/Basis/share.h>

namespace SCIRun {
namespace Core {
namespace Basis {

class SCISHARE CrvElementWeights {

public:
  template <class VECTOR>
  void get_linear_weights(const VECTOR& coords, double *w) const
  {
    const double x = static_cast<double>(coords[0]);
    w[0] = 1. - x;
    w[1] = x;
  }

  /// get derivative weight factors at parametric coordinate 
  template <class VECTOR>
  void get_linear_derivate_weights(const VECTOR& /*coords*/, double *w) const
  {
    w[0] = -1.0;
    w[1] = 1.0;
  }

  /// get weight factors at parametric coordinate 
  template< class VECTOR>
  void get_quadratic_weights(const VECTOR& coords, double *w) const
  {
    const double x = static_cast<double>(coords[0]);
    w[0] = 1 - 3*x + 2*x*x;
    w[1] = x*(-1 + 2*x);
    w[2] = -4*(-1 + x)*x;
  }

  /// get weight factors of derivative at parametric coordinate 
  template< class VECTOR>
  void get_quadratic_derivate_weights(const VECTOR& coords, double *w) const
  {
    const double x = static_cast<double>(coords[0]);
    w[0] = (-3 + 4*x);
    w[1] = (-1 + 4*x);
    w[2] = (4 - 8*x);
  }

  template <class VECTOR>
  void get_cubic_weights(const VECTOR &coords, double *w) const
  {
    const double x = static_cast<double>(coords[0]);
    w[0] = (x-1)*(x-1)*(1 + 2*x);
    w[1] = (x-1)*(x-1)*x;
    w[2] = (3 - 2*x)*x*x;
    w[3] = (-1+x)*x*x;
  }

  /// get derivative weight factors at parametric coordinate 
  template <class VECTOR>
  void get_cubic_derivate_weights(const VECTOR &coords, double *w) const
  {
    const double x = static_cast<double>(coords[0]);
    w[0] = 6*(-1 + x)*x;
    w[1] = (1 - 4*x + 3*x*x);
    w[2] = -6*(-1 + x)*x;
    w[3] = x*(-2 + 3*x);
  }
  
  inline int num_linear_weights() { return 2; }
  inline int num_quadratic_weights() { return 3; }
  inline int num_cubic_weights() { return 4; }

  inline int num_linear_derivate_weights() { return 2; }
  inline int num_quadratic_derivate_weights() { return 3; }
  inline int num_cubic_derivate_weights() { return 4; }

  inline int num_derivs()  { return 1; }  
  inline int num_hderivs() { return 1; }
};

}}}

#endif