netgen/libsrc/gprim/geomfuncs.cpp

#include <mystdlib.h>

#include <myadt.hpp>
#include <gprim.hpp>

namespace netgen
{

  /*
  // template <>
inline void CalcInverse (const Mat<2,2> & m, Mat<2,2> & inv)
{
  double det = m(0,0) * m(1,1) - m(0,1) * m(1,0);
  if (det == 0) 
    {
      inv = 0;
      return;
    }

  double idet = 1.0 / det;
  inv(0,0) =  idet * m(1,1);
  inv(0,1) = -idet * m(0,1);
  inv(1,0) = -idet * m(1,0);
  inv(1,1) =  idet * m(0,0);
}
  */



  // template <>
void CalcInverse (const Mat<3,3> & m, Mat<3,3> & inv)
{
  double det = Det (m);
  if (det == 0) 
    {
      inv = 0;
      return;
    }

  double idet = 1.0 / det;
  inv(0,0) =  idet * (m(1,1) * m(2,2) - m(1,2) * m(2,1));
  inv(1,0) = -idet * (m(1,0) * m(2,2) - m(1,2) * m(2,0));
  inv(2,0) =  idet * (m(1,0) * m(2,1) - m(1,1) * m(2,0));

  inv(0,1) = -idet * (m(0,1) * m(2,2) - m(0,2) * m(2,1));
  inv(1,1) =  idet * (m(0,0) * m(2,2) - m(0,2) * m(2,0));
  inv(2,1) = -idet * (m(0,0) * m(2,1) - m(0,1) * m(2,0));

  inv(0,2) =  idet * (m(0,1) * m(1,2) - m(0,2) * m(1,1));
  inv(1,2) = -idet * (m(0,0) * m(1,2) - m(0,2) * m(1,0));
  inv(2,2) =  idet * (m(0,0) * m(1,1) - m(0,1) * m(1,0));
}

/*
// template <>
void CalcInverse (const Mat<2,3> & m, Mat<3,2> & inv)
{
  Mat<2,2> a = m * Trans (m);
  Mat<2,2> ainv;
  CalcInverse (a, ainv);
  inv = Trans (m) * ainv;
}
*/



double Det (const Mat<2,2> & m) 
{
  return  m(0,0) * m(1,1) - m(0,1) * m(1,0);
}

double Det (const Mat<3,3> & m) 
{
  return 
    m(0,0) * m(1,1) * m(2,2)
    + m(1,0) * m(2,1) * m(0,2)
    + m(2,0) * m(0,1) * m(1,2)
    - m(0,0) * m(2,1) * m(1,2)
    - m(1,0) * m(0,1) * m(2,2)
    - m(2,0) * m(1,1) * m(0,2);
}


void EigenValues (const Mat<3,3> & m, Vec<3> & ev)
{
  const double pi = M_PI;
  double a, b, c, d;
  double p, q;
  double arg;

  a = -1.;
  b = m(0,0) + m(1,1) + m(2,2);
  c = -( m(0,0)*m(2,2) + m(1,1)*m(2,2) + m(0,0)*m(1,1) - sqr(m(0,1)) - sqr(m(0,2)) - sqr(m(1,2)) );
  d = Det (m);
  p = 3.*a*c - sqr(b);
  q = 27.*sqr(a)*d - 9.*a*b*c + 2.*sqr(b)*b;


  arg = acos((-q/2)/sqrt(-(p*p*p)));


  ev(0) = (2. * sqrt(-p) * cos(arg/3.) - b) / 3.*a;
  ev(1) = (-2. * sqrt(-p) * cos(arg/3.+pi/3) - b) / 3.*a;
  ev(2) = (-2. * sqrt(-p) * cos(arg/3.-pi/3)- b) / 3.*a;



}


}