findip.cpp

// find inner point

#include <mystdlib.h>
#include "meshing.hpp"

namespace netgen
{


template <typename POINTARRAY, typename FACEARRAY>
int FindInnerPoint (POINTARRAY & points,
		    FACEARRAY & faces,
		    Point3d & p)
{
  int i, j;
  ARRAY<Vec3d> a;
  ARRAY<double> c;
  Point3d p1, pmin;
  int i1, i2, i3, i4;
  int nf;
  DenseMatrix m(3), inv(3);
  Vector rs(3), x(3);
  double f, fmin, hd, hmax;

  nf = faces.Size();

  //  testout << "#faces  = " << faces.Size() << endl;
  //  testout << "#points = " << points.Size() << endl;

  a.SetSize (nf);
  c.SetSize (nf);

  for (i = 1; i <= nf; i++)
    {
      p1 = points.Get(faces.Get(i).PNum(1));
      a.Elem(i) = Cross (points.Get(faces.Get(i).PNum(2)) - points.Get(faces.Get(i).PNum(1)),
		    points.Get(faces.Get(i).PNum(3)) - points.Get(faces.Get(i).PNum(1)));
      a.Elem(i) /= a.Get(i).Length();
      c.Elem(i) = - (a.Get(i).X() * p1.X() + a.Get(i).Y() * p1.Y() + a.Get(i).Z() * p1.Z());
    }


  hmax = 0;
  for (i = 1; i <= nf; i++)
    {
      const Element2d & el = faces.Get(i);
      for (j = 1; j <= 3; j++)
	{
	  double hi = Dist (points.Get(el.PNumMod(j)),
			    points.Get(el.PNumMod(j+1)));
	  if (hi > hmax) hmax = hi;
	}
    }


  fmin = 100;
  pmin = Point3d (0, 0, 0);

  for (i1 = 1; i1 <= nf; i1++)
    for (i2 = i1+1; i2 <= nf; i2++)
      for (i3 = i2+1; i3 <= nf; i3++)
        for (i4 = i3+1; i4 <= nf; i4++)
          {
	    m.Elem(1, 1) = a.Get(i1).X() - a.Get(i2).X();
	    m.Elem(1, 2) = a.Get(i1).Y() - a.Get(i2).Y();
	    m.Elem(1, 3) = a.Get(i1).Z() - a.Get(i2).Z();
	    rs.Elem(1) = c.Get(i2) - c.Get(i1);

	    m.Elem(2, 1) = a.Get(i1).X() - a.Get(i3).X();
	    m.Elem(2, 2) = a.Get(i1).Y() - a.Get(i3).Y();
	    m.Elem(2, 3) = a.Get(i1).Z() - a.Get(i3).Z();
	    rs.Elem(2) = c.Get(i3) - c.Get(i1);

	    m.Elem(3, 1) = a.Get(i1).X() - a.Get(i4).X();
	    m.Elem(3, 2) = a.Get(i1).Y() - a.Get(i4).Y();
	    m.Elem(3, 3) = a.Get(i1).Z() - a.Get(i4).Z();
	    rs.Elem(3) = c.Get(i4) - c.Get(i1);


	    if (fabs (m.Det()) > 1e-10)
	      {
		CalcInverse (m, inv);
		inv.Mult (rs, x);

		//            testout << "x = " << x << endl;


		f = -1e10;
		for (i = 1; i <= nf; i++)
		  {
		    hd = x.Elem(1) * a.Get(i).X()
		      + x.Elem(2) * a.Get(i).Y()
		      + x.Elem(3) * a.Get(i).Z()
		      + c.Get(i);
		    if (hd > f) f = hd;
		  }

		if (f < fmin)
		  {
		    fmin = f;
		    pmin.X() = x.Elem(1);
		    pmin.Y() = x.Elem(2);
		    pmin.Z() = x.Elem(3);
		  }
	      }
          }

  //  testout << "fmin = " << fmin << endl;
  //  testout << "pmin = " << pmin << endl;

  p = pmin;
  return (fmin < -1e-3 * hmax) ? 1 : 0;
  //  return (fmin < 0) ? 1 : 0;
}
}