quad3d.hpp

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# ifndef _QUADTD_HPP
# define _QUADTD_HPP
 
/*
 
  1) Classes implementing some (most used) quadrature formulas on tetrahedra
  
  2) This implementation does not require any specific mesh structures, but
  only arrays of coordinates of triangles vertices given as double[].
 
*/
 
#include <cassert>
#include <cmath>
 
#include <algorithm>
#include <array>
#include <iostream>
#include <vector>
 
#include <tetra_quad.hpp>
 
 
/*
  
  cq0[0..nqn-1],  barycentric coordinates of tetrahedron's vertices V0,V1,V2,V3
  cq1[0..nqn-1],
  cq2[0..nqn-1],
  cq3[0..nqn-1],
 
  cqw[0..nqn-1],  weights
  
*/
 
namespace HArDCore3D {
 
class QuadRuleTetra {
protected:
  static constexpr size_t num_rules = 15;
 
  const size_t rule;
  const size_t nqn;
 
  double vol_T;
 
  std::vector<double> xV, yV, zV;
  std::vector<double> cq0, cq1, cq2, cq3, cwq;
 
  void init();
 
 
  size_t required_rule(size_t doe) const;
 
public:
 
 
  QuadRuleTetra(size_t doe, bool warn);
 
  QuadRuleTetra(size_t _rule = 0);
 
  inline size_t nq() const;
 
  inline double xq(int iq) const;
 
  inline double yq(int iq) const;
 
  inline double zq(int iq) const;
 
  inline double wq(int iq) const;
 
 
  void setup(double (&_xV)[4], double (&_yV)[4], double (&_zV)[4]);
 
  void get_quadrule(int iq, double &_xq, double &_yq, double &_zq, double &_wq) const;
 
};
// -------------------------------------------------------------------------------------------- 
 
inline size_t QuadRuleTetra::nq() const { return nqn; }
 
inline double QuadRuleTetra::xq(int iq) const { return cq0[iq] * xV[0] + cq1[iq] * xV[1] + cq2[iq] * xV[2] + cq3[iq] * xV[3]; }
 
inline double QuadRuleTetra::yq(int iq) const { return cq0[iq] * yV[0] + cq1[iq] * yV[1] + cq2[iq] * yV[2] + cq3[iq] * yV[3]; }
 
inline double QuadRuleTetra::zq(int iq) const { return cq0[iq] * zV[0] + cq1[iq] * zV[1] + cq2[iq] * zV[2] + cq3[iq] * zV[3]; }
 
inline double QuadRuleTetra::wq(int iq) const { return cwq[iq] * vol_T; }
 
} // end of namespace HArDCore3D
 
#endif // end of _QUADTD_HPP