netgen/libsrc/meshing/bisect.cpp

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

#define noDEBUG


namespace netgen
{
  //#include "../interface/writeuser.hpp"
  class MarkedTet;
  class MarkedPrism;
  class MarkedIdentification;
  class MarkedTri;
  class MarkedQuad;
  
  typedef MoveableArray<MarkedTet> T_MTETS;
  typedef MoveableArray<MarkedPrism> T_MPRISMS;
  typedef MoveableArray<MarkedIdentification> T_MIDS;
  typedef MoveableArray<MarkedTri> T_MTRIS;
  typedef MoveableArray<MarkedQuad> T_MQUADS;

  
  
  class MarkedTet
  {
  public:
    /// pnums of tet
    PointIndex pnums[4];
    /// material number
    int matindex;
    /// element marked for refinement
    /// marked = 1: marked by element marker, marked = 2 due to closure
    unsigned int marked:2;
    /// flag of Arnold-Mukherjee algorithm
    unsigned int flagged:1;
    /// tetedge (local coordinates 0..3)
    unsigned int tetedge1:3;
    unsigned int tetedge2:3;
    // marked edge of faces
    // face_j : face without node j,
    // mark_k : edge without node k
    
    char faceedges[4];
    // unsigned char faceedges[4];
    bool incorder;
    unsigned int order:6;

    MarkedTet()
    { 
      for (int i = 0; i < 4; i++) { faceedges[i] = 255; }
    }
  };

  ostream & operator<< (ostream & ost, const MarkedTet & mt)
  {
    for(int i=0; i<4; i++)
      ost << mt.pnums[i] << " ";

    ost << mt.matindex << " " << int(mt.marked) << " " << int(mt.flagged) << " " << int(mt.tetedge1) << " " << int(mt.tetedge2) << " ";
    
    ost << "faceedges = ";
    for(int i=0; i<4; i++)
      ost << int(mt.faceedges[i]) << " ";

    ost << " order = ";
    ost << mt.incorder << " " << int(mt.order) << "\n";
    return ost;
  }
  istream & operator>> (istream & ost, MarkedTet & mt)
  {
    for(int i=0; i<4; i++)
      ost >> mt.pnums[i];

    ost >> mt.matindex;

    int auxint;
    ost >> auxint;
    mt.marked = auxint;
    ost >> auxint;
    mt.flagged = auxint;
    ost >> auxint;
    mt.tetedge1 = auxint;
    ost >> auxint;
    mt.tetedge2 = auxint;
    
    char auxchar;

    for(int i=0; i<4; i++)
      {
	ost >> auxchar;
	mt.faceedges[i] = auxchar;
      }

    ost >> mt.incorder;
    ost >> auxint;
    mt.order = auxint;
    return ost;
  }

  class MarkedPrism
  {
  public:
    /// 6 point numbers
    PointIndex pnums[6];
    /// material number
    int matindex;
    /// marked for refinement
    int marked;
    /// edge without node k (0,1,2)
    int markededge;

    bool incorder;
    unsigned int order:6;
  };

  
  ostream & operator<< (ostream & ost, const MarkedPrism & mp)
  {
    for(int i=0; i<6; i++)
      ost << mp.pnums[i] << " ";

    ost << mp.matindex << " " << mp.marked << " " << mp.markededge << " " << mp.incorder << " " << int(mp.order) << "\n";
    return ost;
  }
  istream & operator>> (istream & ist, MarkedPrism & mp)
  {
    for(int i=0; i<6; i++)
      ist >> mp.pnums[i];

    ist >> mp.matindex >> mp.marked >> mp.markededge >> mp.incorder;
    int auxint;
    ist >> auxint;
    mp.order = auxint;
    return ist;
  }


  class MarkedIdentification
  {
  public:
    // number of points of one face (3 or 4)
    int np;
    /// 6 or 8 point numbers
    PointIndex pnums[8];
    /// marked for refinement
    int marked;
    /// edge starting with node k (0,1,2, or 3)
    int markededge;

    bool incorder;
    unsigned int order:6;
  };
    
  
  ostream & operator<< (ostream & ost, const MarkedIdentification & mi)
  {
    ost << mi.np << " ";
    for(int i=0; i<2*mi.np; i++)
      ost << mi.pnums[i] << " ";
    ost << mi.marked << " " << mi.markededge << " " << mi.incorder << " " << int(mi.order) << "\n";
    return ost;
  }
  istream & operator>> (istream & ist, MarkedIdentification & mi)
  {
    ist >> mi.np;
    for(int i=0; i<2*mi.np; i++)
      ist >> mi.pnums[i];
    ist >> mi.marked >> mi.markededge >> mi.incorder;
    int auxint;
    ist >> auxint;
    mi.order = auxint;
    return ist;
  }
  




  class MarkedTri
  {
  public:
    /// three point numbers
    PointIndex pnums[3];
    /// three geominfos
    PointGeomInfo pgeominfo[3];
    /// marked for refinement
    int marked;
    /// edge without node k
    int markededge;
    /// surface id
    int surfid;

    bool incorder;
    unsigned int order:6;
  };
  
  ostream & operator<< (ostream & ost, const MarkedTri & mt)
  {
    for(int i=0; i<3; i++)
      ost << mt.pnums[i] << " ";
    for(int i=0; i<3; i++)
      ost << mt.pgeominfo[i] << " ";
    ost << mt.marked << " " << mt.markededge << " " << mt.surfid << " " << mt.incorder << " " << int(mt.order) << "\n";
    return ost;
  } 
  istream & operator>> (istream & ist, MarkedTri & mt)
  {
    for(int i=0; i<3; i++)
      ist >> mt.pnums[i];
    for(int i=0; i<3; i++)
      ist >> mt.pgeominfo[i];
    ist >> mt.marked >> mt.markededge >> mt.surfid >> mt.incorder;
    int auxint;
    ist >> auxint;
    mt.order = auxint;
    return ist;
  }
    


  class MarkedQuad
  {
  public:
    /// point numbers
    PointIndex pnums[4];
    ///
    PointGeomInfo pgeominfo[4];
    /// marked for refinement
    int marked;
    /// marked edge: 0/2 = vertical, 1/3 = horizontal
    int markededge;
    /// surface id
    int surfid;

    bool incorder;
    unsigned int order:6;
  };

  ostream & operator<< (ostream & ost, const MarkedQuad & mt)
  {
    for(int i=0; i<4; i++)
      ost << mt.pnums[i] << " ";
    for(int i=0; i<4; i++)
      ost << mt.pgeominfo[i] << " ";
    ost << mt.marked << " " << mt.markededge << " " << mt.surfid << " " << mt.incorder << " " << int(mt.order) << "\n";
    return ost;
  } 
  istream & operator>> (istream & ist, MarkedQuad & mt)
  {
    for(int i=0; i<4; i++)
      ist >> mt.pnums[i];
    for(int i=0; i<4; i++)
      ist >> mt.pgeominfo[i];
    ist >> mt.marked >> mt.markededge >> mt.surfid >> mt.incorder;
    int auxint;
    ist >> auxint;
    mt.order = auxint;
    return ist;
  }




  void PrettyPrint(ostream & ost, const MarkedTet & mt)
  {
    int te1 = mt.tetedge1;
    int te2 = mt.tetedge2;
    int order = mt.order;

    ost << "MT: " << mt.pnums[0] << " - " << mt.pnums[1] << " - " 
	<< mt.pnums[2] << " - " << mt.pnums[3] << endl
	<< "marked edge: " << te1 << " - " << te2
	<< ", order = " << order << endl;
    //for (int k = 0; k < 4; k++)
    //  ost << int(mt.faceedges[k]) << "  ";
    for (int k = 0; k < 4; k++)
      {
	ost << "face";
	for (int j=0; j<4; j++)
	  if(j != k)
	    ost << " " << mt.pnums[j];
	for(int i=0; i<3; i++)
	  for(int j=i+1; j<4; j++)
	    if(i != k && j != k && int(mt.faceedges[k]) == 6-k-i-j)
	      ost << " marked edge " << mt.pnums[i] << " " << mt.pnums[j] << endl;
      }
    ost << endl;
  }




  int BTSortEdges (const Mesh & mesh,
		   const Array< Array<int,PointIndex::BASE>* > & idmaps,
		   INDEX_2_CLOSED_HASHTABLE<int> & edgenumber)
  {
    PrintMessage(4,"sorting ... ");

    //  if (mesh.PureTetMesh())
    if (1)
      {
	// new, fast version
      
	Array<INDEX_2> edges;
	Array<int> eclasses;
      
	int i, j, k;
	int cntedges = 0;
	int go_on;
	int ned(0);
      
	// enumerate edges:
	for (i = 1; i <= mesh.GetNE(); i++)
	  {
	    const Element & el = mesh.VolumeElement (i);
	    static int tetedges[6][2] =
	      { { 1, 2 },
		{ 1, 3 },
		{ 1, 4 },
		{ 2, 3 },
		{ 2, 4 },
		{ 3, 4 } } ;
	    static int prismedges[9][2] =
	      { { 1, 2 },
		{ 1, 3 },
		{ 2, 3 },
		{ 4, 5 },
		{ 4, 6 },
		{ 5, 6 },
		{ 1, 4 },
		{ 2, 5 },
		{ 3, 6 } };
	    int pyramidedges[6][2] =
	      { { 1, 2 },
		{ 3, 4 },
		{ 1, 5 },
		{ 2, 5 },
		{ 3, 5 },
		{ 4, 5 } };
	  
	    int (*tip)[2] = NULL;
	  
	    switch (el.GetType())
	      {
	      case TET:
	      case TET10:
		{
		  tip = tetedges;
		  ned = 6;
		  break;
		}
	      case PRISM:
	      case PRISM12:
		{
		  tip = prismedges;
		  ned = 6;
		  break;
		}
	      case PYRAMID:
		{
		  tip = pyramidedges;
		  ned = 6;
		  break;
		}
              default:
                throw NgException("Bisect, element type not handled in switch");
	      }
	      
	    for (j = 0; j < ned; j++)
	      {
		INDEX_2 i2(el.PNum(tip[j][0]), el.PNum(tip[j][1]));
		i2.Sort();
		//(*testout) << "edge " << i2 << endl;
		if (!edgenumber.Used(i2))
		  {
		    cntedges++;
		    edges.Append (i2);
		    edgenumber.Set(i2, cntedges);
		  }
	      }
	  }
      
	// additional surface edges:
	for (i = 1; i <= mesh.GetNSE(); i++)
	  {
	    const Element2d & el = mesh.SurfaceElement (i);
	    static int trigedges[3][2] =
	      { { 1, 2 },
		{ 2, 3 },
		{ 3, 1 } };

	    static int quadedges[4][2] =
	      { { 1, 2 },
		{ 2, 3 },
		{ 3, 4 },
		{ 4, 1 } };


	    int (*tip)[2] = NULL;
	  
	    switch (el.GetType())
	      {
	      case TRIG:
	      case TRIG6:
		{
		  tip = trigedges;
		  ned = 3;
		  break;
		}
	      case QUAD:
	      case QUAD6:
		{
		  tip = quadedges;
		  ned = 4;
		  break;
		}
	      default:
		{
		  cerr << "Error: Sort for Bisect, SE has " << el.GetNP() << " points" << endl;
		  ned = 0;
		}
	      }
	      
	    for (j = 0; j < ned; j++)
	      {
		INDEX_2 i2(el.PNum(tip[j][0]), el.PNum(tip[j][1]));
		i2.Sort();
		if (!edgenumber.Used(i2))
		  {
		    cntedges++;
		    edges.Append (i2);
		    edgenumber.Set(i2, cntedges);
		  }
	      }
	  }





	eclasses.SetSize (cntedges);
	for (i = 1; i <= cntedges; i++)
	  eclasses.Elem(i) = i;

	// identify edges in element stack
	do
	  {
	    go_on = 0;
	    for (i = 1; i <= mesh.GetNE(); i++)
	      {
		const Element & el = mesh.VolumeElement (i);	     
	      
		if (el.GetType() != PRISM &&
		    el.GetType() != PRISM12 &&
		    el.GetType() != PYRAMID)
		  continue;

		int prismpairs[3][4] =
		  { { 1, 2, 4, 5 },
		    { 2, 3, 5, 6 },
		    { 1, 3, 4, 6 } };
	      
		int pyramidpairs[3][4] =
		  { { 1, 2, 4, 3 },
		    { 1, 5, 4, 5 },
		    { 2, 5, 3, 5 } };
                
		int (*pairs)[4] = NULL;
		switch (el.GetType())
		  {
		  case PRISM:
		  case PRISM12:
		    {
		      pairs = prismpairs;
		      break;
		    }
		  case PYRAMID:
		    {
		      pairs = pyramidpairs;
		      break;
		    }
                  default:
                    throw NgException("Bisect, element type not handled in switch, 2");
		  }

		for (j = 0; j < 3; j++)
		  {
		    INDEX_2 e1 (el.PNum(pairs[j][0]), 
				el.PNum(pairs[j][1]));
		    INDEX_2 e2 (el.PNum(pairs[j][2]), 
				el.PNum(pairs[j][3]));
		    e1.Sort();
		    e2.Sort();
		      
		    int eclass1 = edgenumber.Get (e1);
		    int eclass2 = edgenumber.Get (e2);

		    //		  (*testout) << "identify edges " << eclass1 << "-" << eclass2 << endl;

		    if (eclasses.Get(eclass1) >
			eclasses.Get(eclass2))
		      {
			eclasses.Elem(eclass1) = 
			  eclasses.Get(eclass2);
			go_on = 1;
		      }
		    else if (eclasses.Get(eclass2) >
			     eclasses.Get(eclass1))
		      {
			eclasses.Elem(eclass2) = 
			  eclasses.Get(eclass1);
			go_on = 1;
		      }
		  }
	      }

	    for(SurfaceElementIndex sei = 0; sei < mesh.GetNSE(); sei++)
	      {
		const Element2d & el2d = mesh[sei];

		for(i = 0; i < el2d.GetNP(); i++)
		  {
		    INDEX_2 e1(el2d[i], el2d[(i+1) % el2d.GetNP()]);
		    e1.Sort();
		    INDEX_2 e2;
		    
		    for(k = 0; k < idmaps.Size(); k++)
		      {
			e2.I1() = (*idmaps[k])[e1.I1()];
			e2.I2() = (*idmaps[k])[e1.I2()];
			
			if(e2.I1() == 0 || e2.I2() == 0 ||
			   e1.I1() == e2.I1() || e1.I2() == e2.I2())
			  continue;
			
			e2.Sort();
			if(!edgenumber.Used(e2))
			  continue;
			

			int eclass1 = edgenumber.Get (e1);
			int eclass2 = edgenumber.Get (e2);
			
			if (eclasses.Get(eclass1) >
			    eclasses.Get(eclass2))
			  {
			    eclasses.Elem(eclass1) = 
			      eclasses.Get(eclass2);


			    go_on = 1;
			  }
			else if (eclasses.Get(eclass2) >
				 eclasses.Get(eclass1))
			  {
			    eclasses.Elem(eclass2) = 
			      eclasses.Get(eclass1);
			    go_on = 1;
			  }
		      }		      
		  }
		
	      }

	  }
	while (go_on);

// 	for (i = 1; i <= cntedges; i++)
// 	  {
// 	    (*testout) << "edge " << i << ": " 
// 		       << edges.Get(i).I1() << "-" << edges.Get(i).I2()
// 		       << ", class = " << eclasses.Get(i) << endl;
// 	  }
	
	// compute classlength:
	Array<double> edgelength(cntedges);

	/*
	for (i = 1; i <= cntedges; i++)
	  edgelength.Elem(i) = 1e20;
	*/

	for (i = 1; i <= cntedges; i++)
	  {
	    INDEX_2 edge = edges.Get(i);
	    double elen = Dist (mesh.Point(edge.I1()),
				mesh.Point(edge.I2()));
	    edgelength.Elem (i) = elen;
	  }

	/*
	  for (i = 1; i <= mesh.GetNE(); i++)
	  {
	  const Element & el = mesh.VolumeElement (i);
	  
	  if (el.GetType() == TET)
	  {
	  for (j = 1; j <= 3; j++)
	  for (k = j+1; k <= 4; k++)
	  {
	  INDEX_2 i2(el.PNum(j), el.PNum(k));
	  i2.Sort();
		    
	  int enr = edgenumber.Get(i2);
	  double elen = Dist (mesh.Point (i2.I1()), mesh.Point (i2.I2()));
	  if (elen < edgelength.Get(enr))
	  edgelength.Set (enr, elen);
	  }
	  }
	  else if (el.GetType() == PRISM)
	  {
	  for (j = 1; j <= 3; j++)
	  {
	  k = (j % 3) + 1;
		  
	  INDEX_2 i2(el.PNum(j), el.PNum(k));
	  i2.Sort();
		  
	  int enr = edgenumber.Get(i2);
	  double elen = Dist (mesh.Point (i2.I1()), mesh.Point (i2.I2()));
	  if (elen < edgelength.Get(enr))
	  edgelength.Set (enr, elen);
		  
	  i2 = INDEX_2(el.PNum(j+3), el.PNum(k+3));
	  i2.Sort();
		  
	  enr = edgenumber.Get(i2);
	  elen = Dist (mesh.Point (i2.I1()), mesh.Point (i2.I2()));
	  if (elen < edgelength.Get(enr))
	  edgelength.Set (enr, elen);
		  
	  if (!edgenumber.Used(i2))
	  {
	  cntedges++;
	  edgenumber.Set(i2, cntedges);
	  }
	  i2 = INDEX_2(el.PNum(j), el.PNum(j+3));
	  i2.Sort();
		  
	  enr = edgenumber.Get(i2);
	  elen = Dist (mesh.Point (i2.I1()), mesh.Point (i2.I2()));
	  if (elen < edgelength.Get(enr))
	  edgelength.Set (enr, elen);
	  }
	  }
	  }
	*/

      
	for (i = 1; i <= cntedges; i++)
	  {
	    if (eclasses.Get(i) != i)
	      {
		if (edgelength.Get(i) < edgelength.Get(eclasses.Get(i)))
		  edgelength.Elem(eclasses.Get(i)) = edgelength.Get(i);
		edgelength.Elem(i) = 1e20;
	      }
	  }


	TABLE<int> eclasstab(cntedges);
	for (i = 1; i <= cntedges; i++)
	  eclasstab.Add1 (eclasses.Get(i), i);


	// sort edges:
	Array<int> sorted(cntedges);
      
	QuickSort (edgelength, sorted);
      
	int cnt = 0;
	for (i = 1; i <= cntedges; i++)
	  {
	    int ii = sorted.Get(i);
	    for (j = 1; j <= eclasstab.EntrySize(ii); j++)
	      {
		cnt++;
		edgenumber.Set (edges.Get(eclasstab.Get(ii, j)), cnt); 
	      }
	  }
	return cnt;
      }

    else
    
      {
	// old version
      
	int i, j;
	int cnt = 0;
	int found;
	double len2, maxlen2;
	INDEX_2 ep;
      
	// sort edges by length, parallel edges (on prisms)
	// are added in blocks
      
	do
	  {
	    found = 0;
	    maxlen2 = 1e30;
	  
	    for (i = 1; i <= mesh.GetNE(); i++)
	      {
		const Element & el = mesh.VolumeElement (i);
		int ned;
		int tetedges[6][2] =
		  { { 1, 2 },
		    { 1, 3 },
		    { 1, 4 },
		    { 2, 3 },
		    { 2, 4 },
		    { 3, 4 } };
		int prismedges[6][2] =
		  { { 1, 2 },
		    { 1, 3 },
		    { 2, 4 },
		    { 4, 5 },
		    { 4, 6 },
		    { 5, 6 } };
		int pyramidedges[6][2] =
		  { { 1, 2 },
		    { 3, 4 },
		    { 1, 5 },
		    { 2, 5 },
		    { 3, 5 },
		    { 4, 5 } };

		int (*tip)[2];

		switch (el.GetType())
		  {
		  case TET:
		    {
		      tip = tetedges;
		      ned = 6;
		      break;
		    }
		  case PRISM:
		    {
		      tip = prismedges;
		      ned = 6;
		      break;
		    }
		  case PYRAMID:
		    {
		      tip = pyramidedges;
		      ned = 6;
		      break;
		    }
                  default:
                    throw NgException("Bisect, element type not handled in switch, 3");
		  }
	      
		for (j = 0; j < ned; j++)
		  {
		    INDEX_2 i2(el.PNum(tip[j][0]), el.PNum(tip[j][1]));
		    i2.Sort();
		    if (!edgenumber.Used(i2))
		      {
			len2 = Dist (mesh.Point (i2.I1()),
				     mesh.Point (i2.I2()));
			if (len2 < maxlen2)
			  {
			    maxlen2 = len2;
			    ep = i2;
			    found = 1;
			  }
		      }
		  }
	      }
	    if (found)
	      {
		cnt++;
		edgenumber.Set (ep, cnt);
	      
	      
		// find connected edges:
		int go_on = 0;
		do
		  {
		    go_on = 0;
		    for (i = 1; i <= mesh.GetNE(); i++)
		      {
			const Element & el = mesh.VolumeElement (i);	      
			if (el.GetNP() != 6) continue;

			int prismpairs[3][4] =
			  { { 1, 2, 4, 5 },
			    { 2, 3, 5, 6 },
			    { 1, 3, 4, 6 } };

			int pyramidpairs[3][4] =
			  { { 1, 2, 4, 3 },
			    { 1, 5, 4, 5 },
			    { 2, 5, 3, 5 } };
		      
			int (*pairs)[4];
			switch (el.GetType())
			  {
			  case PRISM:
			    {
			      pairs = prismpairs;
			      break;
			    }
			  case PYRAMID:
			    {
			      pairs = pyramidpairs;
			      break;
			    }
                          default:
                            throw NgException("Bisect, element type not handled in switch, 3a");
			  }

			for (j = 0; j < 3; j++)
			  {
			    INDEX_2 e1 (el.PNum(pairs[j][0]), 
					el.PNum(pairs[j][1]));
			    INDEX_2 e2 (el.PNum(pairs[j][2]), 
					el.PNum(pairs[j][3]));
			    e1.Sort();
			    e2.Sort();
			  
			    int used1 = edgenumber.Used (e1);
			    int used2 = edgenumber.Used (e2);
			  
			    if (used1 && !used2)
			      {
				cnt++;
				edgenumber.Set (e2, cnt);
				go_on = 1;
			      }
			    if (used2 && !used1)
			      {
				cnt++;
				edgenumber.Set (e1, cnt);
				go_on = 1;
			      }
			  }
		      }
		  }
		while (go_on);
	      }
	  }
	while (found);

	return cnt;
      }
  }




  void BTDefineMarkedTet (const Element & el,
			  INDEX_2_CLOSED_HASHTABLE<int> & edgenumber,
			  MarkedTet & mt)
  {
    int i, j, k;
    for (i = 0; i < 4; i++)
      mt.pnums[i] = el[i];

    mt.marked = 0;
    mt.flagged = 0;

    mt.incorder = 0;
    mt.order = 1;
  
    int val = 0;
    // find marked edge of tet:
    for (i = 0; i < 3; i++)
      for (j = i+1; j < 4; j++)
	{
	  INDEX_2 i2(mt.pnums[i], mt.pnums[j]);
	  i2.Sort();
	  int hval = edgenumber.Get(i2);
	  if (hval > val)
	    {
	      val = hval;
	      mt.tetedge1 = i;
	      mt.tetedge2 = j;    
	    }
	}


    // find marked edges of faces:
    for (k = 0; k < 4; k++)
      {
	val = 0;
	for (i = 0; i < 3; i++)
	  for (j = i+1; j < 4; j++)
	    if (i != k && j != k)
	      {
		INDEX_2 i2(mt.pnums[i], mt.pnums[j]);
		i2.Sort();
		int hval = edgenumber.Get(i2);
		if (hval > val)
		  {
		    val = hval;
                    int hi = 6 - k - i - j;
                    mt.faceedges[k] = char(hi);
		  }
	      }
      }
  }




  void BTDefineMarkedPrism (const Element & el,
			    INDEX_2_CLOSED_HASHTABLE<int> & edgenumber,
			    MarkedPrism & mp)
  {
    int i, j;

    if (el.GetType() == PRISM ||
	el.GetType() == PRISM12)
      {
	for (i = 0; i < 6; i++)
	  mp.pnums[i] = el[i];
      }
    else if (el.GetType() == PYRAMID)
      {
	static int map[6] = 
	  { 1, 2, 5, 4, 3, 5 };
	for (i = 0; i < 6; i++)
	  mp.pnums[i] = el.PNum(map[i]);
      }
    else if (el.GetType() == TET ||
	     el.GetType() == TET10)
      {
	static int map[6] = 
	  { 1, 4, 3, 2, 4, 3 };
	for (i = 0; i < 6; i++)
	  mp.pnums[i] = el.PNum(map[i]);
      
      }
    else
      {
	PrintSysError ("Define marked prism called for non-prism and non-pyramid");
      }
  


    mp.marked = 0;

    mp.incorder = 0;
    mp.order = 1;

    int val = 0;
    for (i = 0; i < 2; i++)
      for (j = i+1; j < 3; j++)
	{
	  INDEX_2 i2(mp.pnums[i], mp.pnums[j]);
	  i2.Sort();
	  int hval = edgenumber.Get(i2);
	  if (hval > val)
	    {
	      val = hval;
	      mp.markededge = 3 - i - j;
	    }
	}
  }



  bool BTDefineMarkedId(const Element2d & el, 
			INDEX_2_CLOSED_HASHTABLE<int> & edgenumber, 
			const Array<int,PointIndex::BASE> & idmap,
			MarkedIdentification & mi)
  {

    bool identified = true;
    mi.np = el.GetNP();
    int min1(0),min2(0);
    for(int j = 0; identified && j < mi.np; j++)
      {
	mi.pnums[j] = el[j];
	mi.pnums[j+mi.np] = idmap[el[j]];

	if(j == 0 || el[j] < min1)
	  min1 = el[j];
	if(j == 0 || mi.pnums[j+mi.np] < min2)
	  min2 = mi.pnums[j+mi.np];

	identified = (mi.pnums[j+mi.np] != 0 && mi.pnums[j+mi.np] != mi.pnums[j]);
      }

    identified = identified && (min1 < min2);

    if(identified)
      {
	mi.marked = 0;
	
	mi.incorder = 0;
	mi.order = 1;

	int val = 0;
	for (int i = 0; i < mi.np; i++)
	  {
	    INDEX_2 i2(mi.pnums[i], mi.pnums[(i+1)%mi.np]);
	    i2.Sort();
	    int hval = edgenumber.Get(i2);
	    if (hval > val)
	      {
		val = hval;
		mi.markededge = i;
	      }
	  }
      }

    return identified;
  }


  void BTDefineMarkedTri (const Element2d & el,
			  INDEX_2_CLOSED_HASHTABLE<int> & edgenumber,
			  MarkedTri & mt)
  {
    int i, j;
    for (i = 0; i < 3; i++)
      {
	mt.pnums[i] = el[i];
	mt.pgeominfo[i] = el.GeomInfoPi (i+1);
      }

    mt.marked = 0;
    mt.surfid = el.GetIndex();

    mt.incorder = 0;
    mt.order = 1;

    int val = 0;
    for (i = 0; i < 2; i++)
      for (j = i+1; j < 3; j++)
	{
	  INDEX_2 i2(mt.pnums[i], mt.pnums[j]);
	  i2.Sort();
	  int hval = edgenumber.Get(i2);
	  if (hval > val)
	    {
	      val = hval;
	      mt.markededge = 3 - i - j;
	    }
	}
  }
  

  
  void PrettyPrint(ostream & ost, const MarkedTri & mt)
  {
    ost << "MarkedTrig: " << endl;
    ost << "  pnums = "; for (int i=0; i<3; i++) ost << mt.pnums[i] << " "; ost << endl; 
    ost << "  marked = " << mt.marked << ", markededge=" << mt.markededge << endl;
    for(int i=0; i<2; i++)
      for(int j=i+1; j<3; j++)
	if(mt.markededge == 3-i-j)
	  ost << "  marked edge pnums = " << mt.pnums[i] << " " << mt.pnums[j] << endl;
  }


  void PrettyPrint(ostream & ost, const MarkedQuad & mq)
  {
    ost << "MarkedQuad: " << endl;
    ost << "  pnums = "; for (int i=0; i<4; i++) ost << mq.pnums[i] << " "; ost << endl; 
    ost << "  marked = " << mq.marked << ", markededge=" << mq.markededge << endl;
  }





  void BTDefineMarkedQuad (const Element2d & el,
			   INDEX_2_CLOSED_HASHTABLE<int> & edgenumber,
			   MarkedQuad & mq)
  {
    int i;
    for (i = 0; i < 4; i++)
      mq.pnums[i] = el[i];
    Swap (mq.pnums[2], mq.pnums[3]);  

    mq.marked = 0;
    mq.markededge = 0;
    mq.surfid = el.GetIndex();
  }




  // mark elements due to local h
  int BTMarkTets (T_MTETS & mtets,
		  T_MPRISMS & mprisms,
		  const Mesh & mesh)
  {
    int marked = 0;

    int np = mesh.GetNP();
    Vector hv(np);
    for (int i = 0; i < np; i++)
      hv(i) = mesh.GetH (mesh.Point(i+1));

    double hfac = 1;
  
    for (int step = 1; step <= 2; step++)
      {
	for (int i = 1; i <= mtets.Size(); i++)
	  {
	    double h = 0;
	  
	    for (int j = 0; j < 3; j++)
	      for (int k = j+1; k < 4; k++)
		{
		  const Point<3> & p1 = mesh.Point (mtets.Get(i).pnums[j]);
		  const Point<3> & p2 = mesh.Point (mtets.Get(i).pnums[k]);
		  double hh = Dist2 (p1, p2);
		  if (hh > h) h = hh;
		}
	    h = sqrt (h);
	  
	    double hshould = 1e10;
	    for (int j = 0; j < 4; j++)
	      {
		double hi = hv (mtets.Get(i).pnums[j]-1);
		if (hi < hshould)
		  hshould = hi;
	      }
	  
	
	    if (step == 1)
	      {
		if (h / hshould > hfac)
		  hfac = h / hshould;
	      }
	    else
	      {
		if (h > hshould * hfac)
		  {
		    mtets.Elem(i).marked = 1;
		    marked = 1;
		  }
		else
		  mtets.Elem(i).marked = 0;
	      }
	  
	  }
	for (int i = 1; i <= mprisms.Size(); i++)
	  {
	    double h = 0;
	  
	    for (int j = 0; j < 2; j++)
	      for (int k = j+1; k < 3; k++)
		{
		  const Point<3> & p1 = mesh.Point (mprisms.Get(i).pnums[j]);
		  const Point<3> & p2 = mesh.Point (mprisms.Get(i).pnums[k]);
		  double hh = Dist2 (p1, p2);
		  if (hh > h) h = hh;
		}
	    h = sqrt (h);
	  
	    double hshould = 1e10;
	    for (int j = 0; j < 6; j++)
	      {
		double hi = hv (mprisms.Get(i).pnums[j]-1);
		if (hi < hshould)
		  hshould = hi;
	      }
	  
	
	    if (step == 1)
	      {
		if (h / hshould > hfac)
		  hfac = h / hshould;
	      }
	    else
	      {
		if (h > hshould * hfac)
		  {
		    mprisms.Elem(i).marked = 1;
		    marked = 1;
		  }
		else
		  mprisms.Elem(i).marked = 0;
	      }
	  
	  }



	if (step == 1)
	  {
	    if (hfac > 2)
	      hfac /= 2;
	    else
	      hfac = 1;
	  }

      }
    return marked;
  }














  void BTBisectTet (const MarkedTet & oldtet, int newp, 
		    MarkedTet & newtet1, MarkedTet & newtet2)
  {
#ifdef DEBUG
    *testout << "bisect tet " << oldtet << endl;
#endif    
    
    int i, j, k;
  
  
    // points vis a vis from tet-edge
    int vis1, vis2;
    vis1 = 0;
    while (vis1 == oldtet.tetedge1 || vis1 == oldtet.tetedge2)
      vis1++;
    vis2 = 6 - vis1 - oldtet.tetedge1 - oldtet.tetedge2;


    


    // is tet of type P ?
    int istypep = 0;
    for (i = 0; i < 4; i++)
      {
	int cnt = 0;
	for (j = 0; j < 4; j++)
	  if (oldtet.faceedges[j] == i)
	    cnt++;
	if (cnt == 3)
	  istypep = 1;
      }


  
    for (i = 0; i < 4; i++)
      {
	newtet1.pnums[i] = oldtet.pnums[i];
	newtet2.pnums[i] = oldtet.pnums[i];
      }
    newtet1.flagged = istypep && !oldtet.flagged;
    newtet2.flagged = istypep && !oldtet.flagged;

    int nm = oldtet.marked - 1;
    if (nm < 0) nm = 0;
    newtet1.marked = nm;
    newtet2.marked = nm;

#ifdef DEBUG
    *testout << "newtet1,before = " << newtet1 << endl;
    *testout << "newtet2,before = " << newtet2 << endl;
#endif

    for (i = 0; i < 4; i++)
      {
	if (i == oldtet.tetedge1)
	  {
	    newtet2.pnums[i] = newp;
	    newtet2.faceedges[i] = oldtet.faceedges[i];  // inherited face
	    newtet2.faceedges[vis1] = i;        // cut faces
	    newtet2.faceedges[vis2] = i;

	    j = 0;
	    while (j == i || j == oldtet.faceedges[i])
	      j++;
	    k = 6 - i - oldtet.faceedges[i] - j;
	    newtet2.tetedge1 = j;                        // tet-edge
	    newtet2.tetedge2 = k;         

	    // new face:
	    if (istypep && oldtet.flagged)
              {
                int hi = 6 - oldtet.tetedge1 - j - k;
                newtet2.faceedges[oldtet.tetedge2] = char(hi);
              }
	    else
	      newtet2.faceedges[oldtet.tetedge2] = oldtet.tetedge1;
            
#ifdef DEBUG
            *testout << "i = " << i << ", j = " << j << " k = " << k 
                     << " oldtet.tetedge1 = " << oldtet.tetedge1 
                     << " oldtet.tetedge2 = " << oldtet.tetedge2
                     << "   6-oldtet.tetedge1-j-k = " <<  6 - oldtet.tetedge1 - j - k 
                     << "   6-oldtet.tetedge1-j-k = " <<  short(6 - oldtet.tetedge1 - j - k)
                     << endl;
            *testout << "vis1 = " << vis1 << ", vis2 = " << vis2 << endl;
            for (int j = 0; j < 4; j++)
              if (newtet2.faceedges[j] > 3)
                {
                  *testout << "ERROR1" << endl;
                }
#endif
	  }

	if (i == oldtet.tetedge2)
	  {
	    newtet1.pnums[i] = newp;
	    newtet1.faceedges[i] = oldtet.faceedges[i];  // inherited face
	    newtet1.faceedges[vis1] = i;
	    newtet1.faceedges[vis2] = i;
	    j = 0;
	    while (j == i || j == oldtet.faceedges[i])
	      j++;
	    k = 6 - i - oldtet.faceedges[i] - j;
	    newtet1.tetedge1 = j;        
	    newtet1.tetedge2 = k;

	    // new face:
	    if (istypep && oldtet.flagged)
              {
                int hi = 6 - oldtet.tetedge2 - j - k;
                newtet1.faceedges[oldtet.tetedge1] = char(hi);
              }
	    else
	      newtet1.faceedges[oldtet.tetedge1] = oldtet.tetedge2;

#ifdef DEBUG
            for (int j = 0; j < 4; j++)
              if (newtet2.faceedges[j] > 3)
                {
                  *testout << "ERROR2" << endl;
                }
#endif
	  }
      }

    newtet1.matindex = oldtet.matindex;
    newtet2.matindex = oldtet.matindex;
    newtet1.incorder = 0;
    newtet1.order = oldtet.order;
    newtet2.incorder = 0;
    newtet2.order = oldtet.order;

    *testout << "newtet1 =  " << newtet1 << endl;
    *testout << "newtet2 =  " << newtet2 << endl;
  }


  

  void BTBisectPrism (const MarkedPrism & oldprism, int newp1, int newp2,
		      MarkedPrism & newprism1, MarkedPrism & newprism2)
  {
    int i;

    for (i = 0; i < 6; i++)
      {
	newprism1.pnums[i] = oldprism.pnums[i];
	newprism2.pnums[i] = oldprism.pnums[i];
      }  
    
    int pe1, pe2;
    pe1 = 0;
    if (pe1 == oldprism.markededge)
      pe1++;
    pe2 = 3 - oldprism.markededge - pe1;

    newprism1.pnums[pe2] = newp1;
    newprism1.pnums[pe2+3] = newp2;
    newprism1.markededge = pe2;
    newprism2.pnums[pe1] = newp1;
    newprism2.pnums[pe1+3] = newp2;
    newprism2.markededge = pe1;

    newprism1.matindex = oldprism.matindex;
    newprism2.matindex = oldprism.matindex;

    int nm = oldprism.marked - 1;
    if (nm < 0) nm = 0;
    newprism1.marked = nm;
    newprism2.marked = nm;

    newprism1.incorder = 0;
    newprism1.order = oldprism.order;
    newprism2.incorder = 0;
    newprism2.order = oldprism.order;
  }


  void BTBisectIdentification (const MarkedIdentification & oldid,
			       Array<int> & newp,
			       MarkedIdentification & newid1,
			       MarkedIdentification & newid2)
  {
    for(int i=0; i<2*oldid.np; i++)
      {
	newid1.pnums[i] = oldid.pnums[i];
	newid2.pnums[i] = oldid.pnums[i];
      }
    newid1.np = newid2.np = oldid.np;

    if(oldid.np == 3)
      {
	newid1.pnums[(oldid.markededge+1)%3] = newp[0];
	newid1.pnums[(oldid.markededge+1)%3+3] = newp[1];
	newid1.markededge = (oldid.markededge+2)%3;

	newid2.pnums[oldid.markededge] = newp[0];
	newid2.pnums[oldid.markededge+3] = newp[1];
	newid2.markededge = (oldid.markededge+1)%3;
      }
    else if(oldid.np == 4)
      {
	newid1.pnums[(oldid.markededge+1)%4] = newp[0];
	newid1.pnums[(oldid.markededge+2)%4] = newp[2];
	newid1.pnums[(oldid.markededge+1)%4+4] = newp[1];
	newid1.pnums[(oldid.markededge+2)%4+4] = newp[3];
	newid1.markededge = (oldid.markededge+3)%4;

	newid2.pnums[oldid.markededge] = newp[0];
	newid2.pnums[(oldid.markededge+3)%4] = newp[2];
	newid2.pnums[oldid.markededge+4] = newp[1];
	newid2.pnums[(oldid.markededge+3)%4+4] = newp[3];
	newid2.markededge = (oldid.markededge+1)%4;
      }

    
    int nm = oldid.marked - 1;
    if (nm < 0) nm = 0;
    newid1.marked = newid2.marked = nm;

    newid1.incorder = newid2.incorder = 0;
    newid1.order = newid2.order = oldid.order;
  }



  void BTBisectTri (const MarkedTri & oldtri, int newp, const PointGeomInfo & newpgi,
		    MarkedTri & newtri1, MarkedTri & newtri2)
  {
    int i;

    for (i = 0; i < 3; i++)
      {
	newtri1.pnums[i] = oldtri.pnums[i];
	newtri1.pgeominfo[i] = oldtri.pgeominfo[i];
	newtri2.pnums[i] = oldtri.pnums[i];
	newtri2.pgeominfo[i] = oldtri.pgeominfo[i];
      }  

    int pe1, pe2;
    pe1 = 0;
    if (pe1 == oldtri.markededge)
      pe1++;
    pe2 = 3 - oldtri.markededge - pe1;

    newtri1.pnums[pe2] = newp;
    newtri1.pgeominfo[pe2] = newpgi;
    newtri1.markededge = pe2;

    newtri2.pnums[pe1] = newp;
    newtri2.pgeominfo[pe1] = newpgi;
    newtri2.markededge = pe1;


    newtri1.surfid = oldtri.surfid;
    newtri2.surfid = oldtri.surfid;

    int nm = oldtri.marked - 1;
    if (nm < 0) nm = 0;
    newtri1.marked = nm;
    newtri2.marked = nm;

    newtri1.incorder = 0;
    newtri1.order = oldtri.order;
    newtri2.incorder = 0;
    newtri2.order = oldtri.order;
    
    
  }


  void BTBisectQuad (const MarkedQuad & oldquad, 
		     int newp1, const PointGeomInfo & npgi1, 
		     int newp2, const PointGeomInfo & npgi2, 
		     MarkedQuad & newquad1, MarkedQuad & newquad2)
  {
    int i;

    for (i = 0; i < 4; i++)
      {
	newquad1.pnums[i] = oldquad.pnums[i];
	newquad1.pgeominfo[i] = oldquad.pgeominfo[i];
	newquad2.pnums[i] = oldquad.pnums[i];
	newquad2.pgeominfo[i] = oldquad.pgeominfo[i];
      }  

/*    if (oldquad.marked==1) // he/sz: 2d quads or 3d prism
    {   
      newquad1.pnums[1] = newp1;
      newquad1.pgeominfo[1] = npgi1;
      newquad1.pnums[3] = newp2;
      newquad1.pgeominfo[3] = npgi2;

      newquad2.pnums[0] = newp1;
      newquad2.pgeominfo[0] = npgi1;
      newquad2.pnums[2] = newp2;
      newquad2.pgeominfo[2] = npgi2;
    }
      
    else if (oldquad.marked==2) // he/sz: 2d quads only
    {
      newquad1.pnums[0] = newp1;
      newquad1.pnums[1] = newp2;
      newquad1.pnums[3] = oldquad.pnums[2];  
      newquad1.pnums[2] = oldquad.pnums[0]; 
      newquad1.pgeominfo[0] = npgi1;
      newquad1.pgeominfo[1] = npgi2;
      newquad1.pgeominfo[3] = oldquad.pgeominfo[2]; 
      newquad1.pgeominfo[2] = oldquad.pgeominfo[0];

      newquad2.pnums[0] = newp2;
      newquad2.pnums[1] = newp1;
      newquad2.pnums[3] = oldquad.pnums[1];  
      newquad2.pnums[2] = oldquad.pnums[3]; 
      newquad2.pgeominfo[0] = npgi2;
      newquad2.pgeominfo[1] = npgi1;
      newquad2.pgeominfo[3] = oldquad.pgeominfo[1]; 
      newquad2.pgeominfo[2] = oldquad.pgeominfo[3];
    }
      
    */
      
    if (oldquad.markededge==0 || oldquad.markededge==2)
    {
      newquad1.pnums[1] = newp1;
      newquad1.pgeominfo[1] = npgi1;
      newquad1.pnums[3] = newp2;
      newquad1.pgeominfo[3] = npgi2;

      newquad2.pnums[0] = newp1;
      newquad2.pgeominfo[0] = npgi1;
      newquad2.pnums[2] = newp2;
      newquad2.pgeominfo[2] = npgi2;
    }
    else // 1 || 3 
    {
      newquad1.pnums[2] = newp1;
      newquad1.pgeominfo[2] = npgi1;
      newquad1.pnums[3] = newp2;
      newquad1.pgeominfo[3] = npgi2;

      newquad2.pnums[0] = newp1;
      newquad2.pgeominfo[0] = npgi1;
      newquad2.pnums[1] = newp2;
      newquad2.pgeominfo[1] = npgi2;
    }
    newquad1.surfid = oldquad.surfid;
    newquad2.surfid = oldquad.surfid;

    int nm = oldquad.marked - 1;
    if (nm < 0) nm = 0;

    newquad1.marked = nm;
    newquad2.marked = nm;
    
    if (nm==1)
    {
      newquad1.markededge=1;
      newquad2.markededge=1;
    }
    else
    {
      newquad1.markededge=0;
      newquad2.markededge=0;
    }
    
  }


  int MarkHangingIdentifications(T_MIDS & mids, 
				 const INDEX_2_CLOSED_HASHTABLE<int> & cutedges)
  {
    int i, j;
    
    int hanging = 0;
    for (i = 1; i <= mids.Size(); i++)
      {
	if (mids.Elem(i).marked)
	  {
	    hanging = 1;
	    continue;
	  }

	const int np = mids.Get(i).np;

	for(j = 0; j < np; j++)
	  {
	    INDEX_2 edge1(mids.Get(i).pnums[j],
			  mids.Get(i).pnums[(j+1) % np]);
	    INDEX_2 edge2(mids.Get(i).pnums[j+np],
			  mids.Get(i).pnums[((j+1) % np) + np]);

	    edge1.Sort();
	    edge2.Sort();
	    if (cutedges.Used (edge1) ||
		cutedges.Used (edge2))
	      {
		mids.Elem(i).marked = 1;
		hanging = 1;
	      }
	  }
      }

    return hanging;
  }


  /*
  void IdentifyCutEdges(Mesh & mesh,
			INDEX_2_CLOSED_HASHTABLE<int> & cutedges)
  {
    int i,j,k;

    Array< Array<int,PointIndex::BASE>* > idmaps;
    for(i=1; i<=mesh.GetIdentifications().GetMaxNr(); i++)
      {
	idmaps.Append(new Array<int,PointIndex::BASE>);
	mesh.GetIdentifications().GetMap(i,*idmaps.Last());
      }


    
    for(SurfaceElementIndex sei = 0; sei < mesh.GetNSE(); sei++)
      {
	const Element2d & el2d = mesh[sei];
	
	for(i = 0; i < el2d.GetNP(); i++)
	  {
	    INDEX_2 e1(el2d[i], el2d[(i+1) % el2d.GetNP()]);
	    e1.Sort();

	    if(!cutedges.Used(e1))
	      continue;

	    
	    for(k = 0; k < idmaps.Size(); k++)
	      {
		INDEX_2 e2((*idmaps[k])[e1.I1()],
			   (*idmaps[k])[e1.I2()]);
		
		if(e2.I1() == 0 || e2.I2() == 0 ||
		   e1.I1() == e2.I1() || e1.I2() == e2.I2())
		  continue;
		
		e2.Sort();

		if(cutedges.Used(e2))
		  continue;

		Point3d np = Center(mesh.Point(e2.I1()),
				    mesh.Point(e2.I2()));
		int newp = mesh.AddPoint(np);
		cutedges.Set(e2,newp);
		(*testout) << "DAAA" << endl;
	      }
	  }
      }

    
    for(i=0; i<idmaps.Size(); i++)
      delete idmaps[i];
    idmaps.DeleteAll();
  }
  */


  int MarkHangingTets (T_MTETS & mtets, 
		       const INDEX_2_CLOSED_HASHTABLE<int> & cutedges)
  {
    int i, j, k;

    int hanging = 0;
    for (i = 1; i <= mtets.Size(); i++)
      {
	MarkedTet & teti = mtets.Elem(i);

	if (teti.marked)
	  {
	    hanging = 1;
	    continue;
	  }

	for (j = 0; j < 3; j++)
	  for (k = j+1; k < 4; k++)
	    {
	      INDEX_2 edge(teti.pnums[j],
			   teti.pnums[k]);
	      edge.Sort();
	      if (cutedges.Used (edge))
		{
		  teti.marked = 1;
		  hanging = 1;
		}
	    }
      }

    return hanging;
  }



  int MarkHangingPrisms (T_MPRISMS & mprisms, 
			 const INDEX_2_CLOSED_HASHTABLE<int> & cutedges)
  {
    int i, j, k;

    int hanging = 0;
    for (i = 1; i <= mprisms.Size(); i++)
      {
	if (mprisms.Elem(i).marked)
	  {
	    hanging = 1;
	    continue;
	  }

	for (j = 0; j < 2; j++)
	  for (k = j+1; k < 3; k++)
	    {
	      INDEX_2 edge1(mprisms.Get(i).pnums[j],
			    mprisms.Get(i).pnums[k]);
	      INDEX_2 edge2(mprisms.Get(i).pnums[j+3],
			    mprisms.Get(i).pnums[k+3]);
	      edge1.Sort();
	      edge2.Sort();
	      if (cutedges.Used (edge1) ||
		  cutedges.Used (edge2))
		{
		  mprisms.Elem(i).marked = 1;
		  hanging = 1;
		}
	    }
      }
    return hanging;
  }



  int MarkHangingTris (T_MTRIS & mtris, 
		       const INDEX_2_CLOSED_HASHTABLE<int> & cutedges)
  {
    int i, j, k;

    int hanging = 0;
    for (i = 1; i <= mtris.Size(); i++)
      {
	if (mtris.Get(i).marked)
	  {
	    hanging = 1;
	    continue;
	  }
	for (j = 0; j < 2; j++)
	  for (k = j+1; k < 3; k++)
	    {
	      INDEX_2 edge(mtris.Get(i).pnums[j],
			   mtris.Get(i).pnums[k]);
	      edge.Sort();
	      if (cutedges.Used (edge))
		{
		  mtris.Elem(i).marked = 1;
		  hanging = 1;
                }
	    }
      }  
      return hanging;
  }



  int MarkHangingQuads (T_MQUADS & mquads, 
			const INDEX_2_CLOSED_HASHTABLE<int> & cutedges)
  {
    int i;

    int hanging = 0;
    for (i = 1; i <= mquads.Size(); i++)
      {
	if (mquads.Elem(i).marked)
	  {
	    hanging = 1;
	    continue;
	  }

	INDEX_2 edge1(mquads.Get(i).pnums[0],
		      mquads.Get(i).pnums[1]);
	INDEX_2 edge2(mquads.Get(i).pnums[2],
		      mquads.Get(i).pnums[3]);
	edge1.Sort();
	edge2.Sort();
	if (cutedges.Used (edge1) ||
	    cutedges.Used (edge2))
	  {
	    mquads.Elem(i).marked = 1;
            mquads.Elem(i).markededge = 0;
	    hanging = 1;
            continue;
	  }
          
        // he/sz: second case: split horizontally
        INDEX_2 edge3(mquads.Get(i).pnums[1],
                      mquads.Get(i).pnums[3]);
        INDEX_2 edge4(mquads.Get(i).pnums[2],
                      mquads.Get(i).pnums[0]);

        edge3.Sort();
        edge4.Sort();
        if (cutedges.Used (edge3) ||
            cutedges.Used (edge4))
        {
          mquads.Elem(i).marked = 1;
          mquads.Elem(i).markededge = 1;
          hanging = 1; 
          continue; 
        }
    
      }
    return hanging;
  }



  void ConnectToNodeRec (int node, int tonode, 
			 const TABLE<int> & conto, Array<int> & connecttonode)
  {
    int i, n2;
    //  (*testout) << "connect " << node << " to " << tonode << endl;
    for (i = 1; i <= conto.EntrySize(node); i++)
      {
	n2 = conto.Get(node, i);
	if (!connecttonode.Get(n2))
	  {
	    connecttonode.Elem(n2) = tonode;
	    ConnectToNodeRec (n2, tonode, conto, connecttonode);
	  }
      }
  }




  T_MTETS mtets;
  T_MPRISMS mprisms;
  T_MIDS mids;
  T_MTRIS mtris;
  T_MQUADS mquads;


  void WriteMarkedElements(ostream & ost)
  {
    ost << "Marked Elements\n";

    ost << mtets.Size() << "\n";
    for(int i=0; i<mtets.Size(); i++)
      ost << mtets[i];

    ost << mprisms.Size() << "\n";
    for(int i=0; i<mprisms.Size(); i++)
      ost << mprisms[i];

    ost << mids.Size() << "\n";
    for(int i=0; i<mids.Size(); i++)
      ost << mids[i];

    ost << mtris.Size() << "\n";
    for(int i=0; i<mtris.Size(); i++)
      ost << mtris[i];

    ost << mquads.Size() << "\n";
    for(int i=0; i<mquads.Size(); i++)
      ost << mquads[i];
    ost << endl;
  }

  bool ReadMarkedElements(istream & ist, const Mesh & mesh)
  {
    string auxstring("");
    if(ist)
      ist >> auxstring;

    if(auxstring != "Marked")
      return false;

    if(ist)
      ist >> auxstring;

    if(auxstring != "Elements")
      return false;

    int size;

    ist >> size;
    mtets.SetSize(size);
    for(int i=0; i<size; i++)
      {
        ist >> mtets[i];
        if(mtets[i].pnums[0] > mesh.GetNV() || 
           mtets[i].pnums[1] > mesh.GetNV() || 
           mtets[i].pnums[2] > mesh.GetNV() || 
           mtets[i].pnums[3] > mesh.GetNV())
          return false;
      }

    ist >> size;
    mprisms.SetSize(size);
    for(int i=0; i<size; i++)
      ist >> mprisms[i];

    ist >> size;
    mids.SetSize(size);
    for(int i=0; i<size; i++)
      ist >> mids[i];

    ist >> size;
    mtris.SetSize(size);
    for(int i=0; i<size; i++)
      ist >> mtris[i];

    ist >> size;
    mquads.SetSize(size);
    for(int i=0; i<size; i++)
      ist >> mquads[i];

    return true;
  }





  void BisectTetsCopyMesh (Mesh & mesh, const class CSGeometry *,
			   BisectionOptions & opt,
			   const Array< Array<int,PointIndex::BASE>* > & idmaps,
			   const string & refinfofile)
  {
    mtets.SetName ("bisection, tets");
    mprisms.SetName ("bisection, prisms");
    mtris.SetName ("bisection, trigs");
    mquads.SetName ("bisection, quads");
    mids.SetName ("bisection, identifications");

    //int np = mesh.GetNP();
    int ne = mesh.GetNE();
    int nse = mesh.GetNSE();
    int i, j, k, l, m;

    /*
      if (mtets.Size() + mprisms.Size() == mesh.GetNE())
      return;
    */

    bool readok = false;

    if(refinfofile != "")
      {
	PrintMessage(3,"Reading marked-element information from \"",refinfofile,"\"");
	ifstream ist(refinfofile.c_str());

	readok = ReadMarkedElements(ist,mesh);

	ist.close();
      }

    if(!readok)
      {
	PrintMessage(3,"resetting marked-element information");
	mtets.SetSize(0);
	mprisms.SetSize(0);
	mids.SetSize(0);
	mtris.SetSize(0);
	mquads.SetSize(0);
	
	
	INDEX_2_HASHTABLE<int> shortedges(100);
	for (i = 1; i <= ne; i++)
	  {
	    const Element & el = mesh.VolumeElement(i);
	    if (el.GetType() == PRISM ||
		el.GetType() == PRISM12)
	      {
		for (j = 1; j <= 3; j++)
		  {
		    INDEX_2 se(el.PNum(j), el.PNum(j+3));
		    se.Sort();
		    shortedges.Set (se, 1);
		  }
	      }
	  }
	
	
	
	// INDEX_2_HASHTABLE<int> edgenumber(np);
	INDEX_2_CLOSED_HASHTABLE<int> edgenumber(9*ne+4*nse);  
	
	BTSortEdges (mesh, idmaps, edgenumber);
	
	
	for (i = 1; i <= ne; i++)
	  {
	    const Element & el = mesh.VolumeElement(i);
	    
	    switch (el.GetType())
	      {
	      case TET:
	      case TET10:
		{
		  // if tet has short edge, it is handled as degenerated prism
		  
		  int foundse = 0;
		  for (j = 1; j <= 3; j++)
		    for (k = j+1; k <= 4; k++)
		      {
			INDEX_2 se(el.PNum(j), el.PNum(k));
			se.Sort();
			if (shortedges.Used (se))
			  {
			    //		      cout << "tet converted to prism" << endl;
			    
			    foundse = 1;
			    int p3 = 1;
			    while (p3 == j || p3 == k)
			      p3++;
			    int p4 = 10 - j - k - p3;
			    
			    // even permutation ?
			    int pi[4];
			    pi[0] = j;
			    pi[1] = k;
			    pi[2] = p3;
			    pi[3] = p4;
			    int cnt = 0;
			    for (l = 1; l <= 4; l++)
			      for (m = 0; m < 3; m++)
				if (pi[m] > pi[m+1])
				  {
				    Swap (pi[m], pi[m+1]);
				    cnt++;
				  }
			    if (cnt % 2)
			      Swap (p3, p4);
			    
			    Element hel = el;
			    hel.PNum(1) = el.PNum(j);
			    hel.PNum(2) = el.PNum(k);
			    hel.PNum(3) = el.PNum(p3);
			    hel.PNum(4) = el.PNum(p4);
			    
			    MarkedPrism mp;
			    BTDefineMarkedPrism (hel, edgenumber, mp);
			    mp.matindex = el.GetIndex();
			    mprisms.Append (mp);
			  }
		      }
		  if (!foundse)
		    {
		      MarkedTet mt;
		      BTDefineMarkedTet (el, edgenumber, mt);
		      mt.matindex = el.GetIndex();
		      mtets.Append (mt);
		    }
		  break;
		}
	      case PYRAMID:
		{
		  // eventually rotate
		  MarkedPrism mp;
		  
		  INDEX_2 se(el.PNum(1), el.PNum(2));
		  se.Sort();
		  if (shortedges.Used (se))
		    {
		      Element hel = el;
		      hel.PNum(1) = el.PNum(2);
		      hel.PNum(2) = el.PNum(3);
		      hel.PNum(3) = el.PNum(4);
		      hel.PNum(4) = el.PNum(1);
		      BTDefineMarkedPrism (hel, edgenumber, mp);
		    }
		  else
		    {
		      BTDefineMarkedPrism (el, edgenumber, mp);
		    }
		  
		  mp.matindex = el.GetIndex();
		  mprisms.Append (mp);
		  break;
		}
	      case PRISM:
	      case PRISM12:
		{
		  MarkedPrism mp;
		  BTDefineMarkedPrism (el, edgenumber, mp);
		  mp.matindex = el.GetIndex();
		  mprisms.Append (mp);
		  break;
		}
              default:
                throw NgException("Bisect, element type not handled in switch, 4");
	      }
	  }
	
	for (i = 1; i <= nse; i++)
	  {
	    const Element2d & el = mesh.SurfaceElement(i);
	    if (el.GetType() == TRIG ||
		el.GetType() == TRIG6)
	      {
		MarkedTri mt;
		BTDefineMarkedTri (el, edgenumber, mt);
		mtris.Append (mt);
	      }
	    else
	      {
		MarkedQuad mq;
		BTDefineMarkedQuad (el, edgenumber, mq);
		mquads.Append (mq);
	      }
	    
	    MarkedIdentification mi;
	    for(j=0; j<idmaps.Size(); j++)
	      if(BTDefineMarkedId(el, edgenumber, *idmaps[j], mi))
		mids.Append(mi);
	  }
      }
	



    mesh.mlparentelement.SetSize(ne);
    for (i = 1; i <= ne; i++)
      mesh.mlparentelement.Elem(i) = 0;
    mesh.mlparentsurfaceelement.SetSize(nse);
    for (i = 1; i <= nse; i++)
      mesh.mlparentsurfaceelement.Elem(i) = 0;
  
    if (printmessage_importance>0)
    {
      ostringstream str1,str2;
      str1 << "copied " << mtets.Size() << " tets, " << mprisms.Size() << " prisms";
      str2 << "       " << mtris.Size() << " trigs, " << mquads.Size() << " quads";

      PrintMessage(4,str1.str());
      PrintMessage(4,str2.str());
    }
  }


  /*
  void UpdateEdgeMarks2(Mesh & mesh,
			const Array< Array<int,PointIndex::BASE>* > & idmaps)
  {
    Array< Array<MarkedTet>*,PointIndex::BASE > mtets_old(mesh.GetNP());
    Array< Array<MarkedPrism>*,PointIndex::BASE > mprisms_old(mesh.GetNP());
    Array< Array<MarkedIdentification>*,PointIndex::BASE > mids_old(mesh.GetNP());
    Array< Array<MarkedTri>*,PointIndex::BASE > mtris_old(mesh.GetNP());
    Array< Array<MarkedQuad>*,PointIndex::BASE > mquads_old(mesh.GetNP());

    for(int i=PointIndex::BASE; i<mesh.GetNP()+PointIndex::BASE; i++)
      mtets_old[i] = new Array<MarkedTet>;
    for(int i=PointIndex::BASE; i<mesh.GetNP()+PointIndex::BASE; i++)
      mprisms_old[i] = new Array<MarkedPrism>;
    for(int i=PointIndex::BASE; i<mesh.GetNP()+PointIndex::BASE; i++)
      mids_old[i] = new Array<MarkedIdentification>;
    for(int i=PointIndex::BASE; i<mesh.GetNP()+PointIndex::BASE; i++)
      mtris_old[i] = new Array<MarkedTri>;
    for(int i=PointIndex::BASE; i<mesh.GetNP()+PointIndex::BASE; i++)
      mquads_old[i] = new Array<MarkedQuad>;

    for(int i=0; i<mtets.Size(); i++)
      mtets_old[mtets[i].pnums[0]]->Append(mtets[i]);
    for(int i=0; i<mprisms.Size(); i++)
      mprisms_old[mprisms[i].pnums[0]]->Append(mprisms[i]);
    for(int i=0; i<mids.Size(); i++)
      mids_old[mids[i].pnums[0]]->Append(mids[i]);
    for(int i=0; i<mtris.Size(); i++)
      {
	(*testout) << "i " << i << endl;
	(*testout) << "mtris[i] " << mtris[i].pnums[0] << " " << mtris[i].pnums[1] << " " << mtris[i].pnums[2] << endl; 
	mtris_old[mtris[i].pnums[0]]->Append(mtris[i]);
      }
    for(int i=0; i<mquads.Size(); i++)
      mquads_old[mquads[i].pnums[0]]->Append(mquads[i]);

   
    
    int np = mesh.GetNP();
    int ne = mesh.GetNE();
    int nse = mesh.GetNSE();
    int i, j, k, l, m;


//       if (mtets.Size() + mprisms.Size() == mesh.GetNE())
//       return;

    

    mtets.SetSize(0);
    mprisms.SetSize(0);
    mids.SetSize(0);
    mtris.SetSize(0);
    mquads.SetSize(0);


    INDEX_2_HASHTABLE<int> shortedges(100);
    for (i = 1; i <= ne; i++)
      {
	const Element & el = mesh.VolumeElement(i);
	if (el.GetType() == PRISM ||
	    el.GetType() == PRISM12)
	  {
	    for (j = 1; j <= 3; j++)
	      {
		INDEX_2 se(el.PNum(j), el.PNum(j+3));
		se.Sort();
		shortedges.Set (se, 1);
	      }
	  }
      }



    // INDEX_2_HASHTABLE<int> edgenumber(np);
    INDEX_2_CLOSED_HASHTABLE<int> edgenumber(9*ne+4*nse);  

    BTSortEdges (mesh, idmaps, edgenumber);


    for (i = 1; i <= ne; i++)
      {
	const Element & el = mesh.VolumeElement(i);
	  
	switch (el.GetType())
	  {
	  case TET:
	  case TET10:
	    {
	      // if tet has short edge, it is handled as degenerated prism

	      int foundse = 0;
	      for (j = 1; j <= 3; j++)
		for (k = j+1; k <= 4; k++)
		  {
		    INDEX_2 se(el.PNum(j), el.PNum(k));
		    se.Sort();
		    if (shortedges.Used (se))
		      {
//		      cout << "tet converted to prism" << endl;

			foundse = 1;
			int p3 = 1;
			while (p3 == j || p3 == k)
			  p3++;
			int p4 = 10 - j - k - p3;

			// even permutation ?
			int pi[4];
			pi[0] = j;
			pi[1] = k;
			pi[2] = p3;
			pi[3] = p4;
			int cnt = 0;
			for (l = 1; l <= 4; l++)
			  for (m = 0; m < 3; m++)
			    if (pi[m] > pi[m+1])
			      {
				Swap (pi[m], pi[m+1]);
				cnt++;
			      }
			if (cnt % 2)
			  Swap (p3, p4);

			Element hel = el;
			hel.PNum(1) = el.PNum(j);
			hel.PNum(2) = el.PNum(k);
			hel.PNum(3) = el.PNum(p3);
			hel.PNum(4) = el.PNum(p4);

			MarkedPrism mp;

			BTDefineMarkedPrism (hel, edgenumber, mp);
			mp.matindex = el.GetIndex();
			mprisms.Append (mp);
		      }
		  }
	      if (!foundse)
		{
		  MarkedTet mt;
		  
		  int oldind = -1;
		  for(l = 0; oldind < 0 && l<mtets_old[el[0]]->Size(); l++)
		    if(el[1] == (*mtets_old[el[0]])[l].pnums[1] &&
		       el[2] == (*mtets_old[el[0]])[l].pnums[2] &&
		       el[3] == (*mtets_old[el[0]])[l].pnums[3])
		      oldind = l;

		  if(oldind >= 0)
		    mtets.Append((*mtets_old[el[0]])[oldind]);
		  else
		    {
		      BTDefineMarkedTet (el, edgenumber, mt);
		      mt.matindex = el.GetIndex();
		      mtets.Append (mt);
		    }
		}
	      break;
	    }
	  case PYRAMID:
	    {
	      // eventually rotate
	      MarkedPrism mp;
	    
	      INDEX_2 se(el.PNum(1), el.PNum(2));
	      se.Sort();
	      if (shortedges.Used (se))
		{
		  Element hel = el;
		  hel.PNum(1) = el.PNum(2);
		  hel.PNum(2) = el.PNum(3);
		  hel.PNum(3) = el.PNum(4);
		  hel.PNum(4) = el.PNum(1);
		  BTDefineMarkedPrism (hel, edgenumber, mp);
		}
	      else
		{
		  BTDefineMarkedPrism (el, edgenumber, mp);
		}

	      mp.matindex = el.GetIndex();
	      mprisms.Append (mp);
	      break;
	    }
	  case PRISM:
	  case PRISM12:
	    {
	      MarkedPrism mp;
	      BTDefineMarkedPrism (el, edgenumber, mp);
	      mp.matindex = el.GetIndex();
	      mprisms.Append (mp);
	      break;
	    }
	  }
      }

    for (i = 1; i <= nse; i++)
      {
	const Element2d & el = mesh.SurfaceElement(i);
	if (el.GetType() == TRIG ||
	    el.GetType() == TRIG6)
	  {
	    MarkedTri mt;
	    BTDefineMarkedTri (el, edgenumber, mt);
	    mtris.Append (mt);
	  }
	else
	  {
	    MarkedQuad mq;
	    BTDefineMarkedQuad (el, edgenumber, mq);
	    mquads.Append (mq);
	  }
	
	MarkedIdentification mi;

	

	for(j=0; j<idmaps.Size(); j++)
	  if(BTDefineMarkedId(el, edgenumber, *idmaps[j], mi))
	    {
	      mids.Append(mi);
		
	      int oldind = -1;
	      for(l = 0; oldind < 0 && l<mids_old[mi.pnums[0]]->Size(); l++)
		{
		  bool equal = true;
		  for(int m = 1; equal && m < mi.np; m++)
		    equal = (mi.pnums[m] == (*mids_old[el[0]])[l].pnums[m]);
		  if(equal)
		    oldind = l;
		}

	      if(oldind >= 0)
		mids.Last() = (*mids_old[mi.pnums[0]])[oldind];
	    }

      }



    for(int i=PointIndex::BASE; i<mesh.GetNP()+PointIndex::BASE; i++)
      delete mtets_old[i];
    for(int i=PointIndex::BASE; i<mesh.GetNP()+PointIndex::BASE; i++)
      delete mprisms_old[i];
    for(int i=PointIndex::BASE; i<mesh.GetNP()+PointIndex::BASE; i++)
      delete mids_old[i];
    for(int i=PointIndex::BASE; i<mesh.GetNP()+PointIndex::BASE; i++)
      delete mtris_old[i];
    for(int i=PointIndex::BASE; i<mesh.GetNP()+PointIndex::BASE; i++)
      delete mquads_old[i];
  }
*/

  
  void UpdateEdgeMarks (Mesh & mesh,
			const Array< Array<int,PointIndex::BASE>* > & idmaps)
  //const Array < Array<Element>* > & elements_before,
  //const Array < Array<int>* > & markedelts_num,
  //		const Array < Array<Element2d>* > & surfelements_before,
  //		const Array < Array<int>* > & markedsurfelts_num)
  {
    T_MTETS mtets_old; mtets_old.Copy(mtets);
    T_MPRISMS mprisms_old; mprisms_old.Copy(mprisms);
    T_MIDS mids_old; mids_old.Copy(mids);
    T_MTRIS mtris_old; mtris_old.Copy(mtris);
    T_MQUADS mquads_old; mquads_old.Copy(mquads);



    
    mtets.SetSize(0);
    mprisms.SetSize(0);
    mids.SetSize(0);
    mtris.SetSize(0);
    mquads.SetSize(0);

    //int nv = mesh.GetNV();


    INDEX_2_CLOSED_HASHTABLE<int> edgenumber(9*mesh.GetNE()+4*mesh.GetNSE());  
    
    int maxnum = BTSortEdges (mesh, idmaps, edgenumber);

    for(int m = 0; m < mtets_old.Size(); m++)
      {
	MarkedTet & mt = mtets_old[m];

	//(*testout) << "old mt " << mt;
	
	INDEX_2 edge (mt.pnums[mt.tetedge1],mt.pnums[mt.tetedge2]);
	edge.Sort();
	if(edgenumber.Used(edge))
	  {
	    int val = edgenumber.Get(edge);
	    //(*testout) << "set voledge " << edge << " from " << val;
	    if(val <= maxnum)
	      {
		val += 2*maxnum;
		edgenumber.Set(edge,val);
	      }
	    else if(val <= 2*maxnum)
	      {
		val += maxnum;
		edgenumber.Set(edge,val);
	      }
	    //(*testout) << " to " << val << endl;
	  }
	
	for(int k=0; k<4; k++)
	  for(int i=0; i<3; i++)
	    for(int j=i+1; i != k && j<4; j++)
	      if(j != k && int(mt.faceedges[k]) == 6-k-i-j)
		{
		  edge[0] = mt.pnums[i];
		  edge[1] = mt.pnums[j];
		  edge.Sort();
		  if(edgenumber.Used(edge))
		    {
		      int val = edgenumber.Get(edge);
		      //(*testout) << "set faceedge " << edge << " from " << val;
		      if(val <= maxnum)
			{
			  val += maxnum;
			  edgenumber.Set(edge,val);
			}
		      //(*testout) << " to " << val << endl;
		    }		      
		}
      }

	
    
    
    for(ElementIndex ei = 0; ei < mesh.GetNE(); ei++)
      {
	const Element & el = mesh[ei];
	
	//int pos = elements_before[el[0]]->Pos(el);
	//int elnum = (pos >= 0) ? (*markedelts_num[el[0]])[pos] : -1;
	 
	switch (el.GetType())
	  {
	  case TET:
	  case TET10:
	    {
	      //if(elnum >= 0)
	      // {
	      //   mtets.Append(mtets_old[elnum]);
	      // } 
	      //else
	      // {
	      MarkedTet mt;
	      BTDefineMarkedTet (el, edgenumber, mt);
	      mt.matindex = el.GetIndex();
	      
	      mtets.Append (mt);
	    
	      //(*testout) << "mtet " << mtets.Last() << endl;
	      break;
	    }
	  case PYRAMID:
	    {
	      cerr << "Refinement :: UpdateEdgeMarks not yet implemented for pyramids"
		   << endl;
	      break;
	    }
	    
	  case PRISM:
	  case PRISM12:
	    {
	      cerr << "Refinement :: UpdateEdgeMarks not yet implemented for prisms"
		   << endl;
	      break;
	    }
          default:
            throw NgException("Bisect, element type not handled in switch, 6");
	  }
	
      }
    

    
     for(SurfaceElementIndex sei = 0; sei < mesh.GetNSE(); sei++)
       {
	 const Element2d & el = mesh[sei];

	 /*
	 for(int k=0; k<3; k++)
	   auxind3[k] = el[k];

	 auxind3.Sort();
	 
	 int pos = oldfaces[auxind3[0]]->Pos(auxind3);
	 if(pos < 0)
	   cout << "UIUIUI" << endl;
	 */	 
	 
	 switch (el.GetType())
	   {
	   case TRIG:
	   case TRIG6:
	     {
	       MarkedTri mt;
	       BTDefineMarkedTri (el, edgenumber, mt);
	       mtris.Append (mt);
	       break;
	     }
	     
	   case QUAD:
	   case QUAD6:
	     {
	       MarkedQuad mt;
	       BTDefineMarkedQuad (el, edgenumber, mt);
	       mquads.Append (mt);
	       break;
	     }
           default:
             throw NgException("Bisect, element type not handled in switch, 5");
	   }

	 
	MarkedIdentification mi;
	for(int j=0; j<idmaps.Size(); j++)
	  if(BTDefineMarkedId(el, edgenumber, *idmaps[j], mi))
	    mids.Append(mi);


	 /*
	 int pos = surfelements_before[el[0]]->Pos(el);
	 int elnum = (pos >= 0) ? (*markedsurfelts_num[el[0]])[pos] : -1;
	 
	 
	 switch (el.GetType())
	   {
	   case TRIG:
	   case TRIG6:
	     {
	       if(elnum >= 0)
		 mtris.Append(mtris_old[elnum]);
	       else
		 {
		   MarkedTri mt;
		   BTDefineMarkedTri (el, edgenumber, mt);
		   mtris.Append (mt);
		   (*testout) << "(new) ";
		 }
	       (*testout) << "mtri " << mtris.Last();
	       break;
	     }
	     
	   case QUAD:
	   case QUAD6:
	     {
	       if(elnum >= 0)
		 mquads.Append(mquads_old[elnum]);
	       else
		 {
		   MarkedQuad mt;
		   BTDefineMarkedQuad (el, edgenumber, mt);
		   mquads.Append (mt);
		 }
	       break;
	     }
	   }
	 */
       }
     
     /*
     for(int i=0; i<oldfaces.Size(); i++)
       {
	 delete oldfaces[i];
	 delete oldmarkededges[i];
       }
     */
     
  }
				      



  void Refinement :: Bisect (Mesh & mesh, 
			     BisectionOptions & opt,
			     Array<double> * quality_loss)
  {
    PrintMessage(1,"Mesh bisection");
    PushStatus("Mesh bisection");

    static int timer = NgProfiler::CreateTimer ("Bisect");
    NgProfiler::RegionTimer reg1 (timer);
    
    

    static int localizetimer = NgProfiler::CreateTimer("localize edgepoints");
    NgProfiler::RegionTimer * loct = new NgProfiler::RegionTimer(localizetimer);   
    LocalizeEdgePoints(mesh);
    delete loct;

    Array< Array<int,PointIndex::BASE>* > idmaps;
    for(int i=1; i<=mesh.GetIdentifications().GetMaxNr(); i++)
      {
	if(mesh.GetIdentifications().GetType(i) == Identifications::PERIODIC)
	  {
	    idmaps.Append(new Array<int,PointIndex::BASE>);
	    mesh.GetIdentifications().GetMap(i,*idmaps.Last(),true);
	  }
      }

    
    string refelementinfofileread = "";
    string refelementinfofilewrite = "";

    if(opt.refinementfilename)
      {
	ifstream inf(opt.refinementfilename);
	string st;
	inf >> st;
	if(st == "refinementinfo")
	  {
	    while(inf)
	      {
		while(inf && st != "markedelementsfile")
		  inf >> st;
		
		if(inf)
		  inf >> st;
		
		if(st == "read" && inf)
		  ReadEnclString(inf,refelementinfofileread,'\"');
		else if(st == "write" && inf)
		  ReadEnclString(inf,refelementinfofilewrite,'\"');
	      }
	  }
	inf.close();
      }
	


    if (mesh.mglevels == 1 || idmaps.Size() > 0)
      BisectTetsCopyMesh(mesh, NULL, opt, idmaps, refelementinfofileread);


    mesh.ComputeNVertices();
  
    int np = mesh.GetNV();
    mesh.SetNP(np);

    // int ne = mesh.GetNE();
    // int nse = mesh.GetNSE();
    int i, j, l;

    // int initnp = np;
    //  int maxsteps = 3;

    mesh.mglevels++;

    /*
      if (opt.refinementfilename || opt.usemarkedelements)
      maxsteps = 3;
    */


    if (opt.refine_p)   
      {
	int ne = mesh.GetNE();
	int nse = mesh.GetNSE();
	int ox,oy,oz; 
	for (ElementIndex ei = 0; ei < ne; ei++)
	  if (mesh[ei].TestRefinementFlag())
	    {
	      mesh[ei].GetOrder(ox,oy,oz);
	      mesh[ei].SetOrder (ox+1,oy+1,oz+1);
	      if (mesh[ei].TestStrongRefinementFlag())
		mesh[ei].SetOrder (ox+2,oy+2,oz+2);
	    }
	for (SurfaceElementIndex sei = 0; sei < nse; sei++)
	  if (mesh[sei].TestRefinementFlag())
	    {
	      mesh[sei].GetOrder(ox,oy);
	      mesh[sei].SetOrder(ox+1,oy+1);
	      if (mesh[sei].TestStrongRefinementFlag())
		mesh[sei].SetOrder(ox+2,oy+2);
	    }

	  #ifndef SABINE //Nachbarelemente mit ordx,ordy,ordz 
      
	  Array<int,PointIndex::BASE> v_order (mesh.GetNP());
	  v_order = 0;

	  for (ElementIndex ei = 0; ei < ne; ei++)
	  for (j = 0; j < mesh[ei].GetNP(); j++)
	  if (mesh[ei].GetOrder() > v_order[mesh[ei][j]])
	  v_order[mesh[ei][j]] = mesh[ei].GetOrder();

	  for (SurfaceElementIndex sei = 0; sei < nse; sei++)
	  for (j = 0; j < mesh[sei].GetNP(); j++)
	  if (mesh[sei].GetOrder() > v_order[mesh[sei][j]])
	  v_order[mesh[sei][j]] = mesh[sei].GetOrder();

	  for (ElementIndex ei = 0; ei < ne; ei++)
	  for (j = 0; j < mesh[ei].GetNP(); j++)
	  if (mesh[ei].GetOrder() < v_order[mesh[ei][j]]-1)
	  mesh[ei].SetOrder(v_order[mesh[ei][j]]-1);

	  for (SurfaceElementIndex sei = 0; sei < nse; sei++)
	  for (j = 0; j < mesh[sei].GetNP(); j++)
	  if (mesh[sei].GetOrder() < v_order[mesh[sei][j]]-1)
	  mesh[sei].SetOrder(v_order[mesh[sei][j]]-1);
	    
	  #endif

	PopStatus();
	return;
      }



    // INDEX_2_HASHTABLE<int> cutedges(10 + 5 * (mtets.Size()+mprisms.Size()+mtris.Size()+mquads.Size()));
    INDEX_2_CLOSED_HASHTABLE<int> cutedges(10 + 9 * (mtets.Size()+mprisms.Size()+mtris.Size()+mquads.Size()));

    bool noprojection = false;

    for (l = 1; l <= 1; l++)
      {
	int marked = 0;
	if (opt.refinementfilename)
	  {
	    ifstream inf(opt.refinementfilename);
	    PrintMessage(3,"load refinementinfo from file ",opt.refinementfilename);

	    string st;
	    inf >> st;
	    if(st == "refinementinfo")
	      // new version
	      {
		for(i=1; i<=mtets.Size(); i++)
		  mtets.Elem(i).marked = 0;
		for(i=1; i<=mprisms.Size(); i++)
		  mprisms.Elem(i).marked = 0;
		for(i=1; i<=mtris.Size(); i++)
		  mtris.Elem(i).marked = 0;
		for(i=1; i<=mquads.Size(); i++)
		  mquads.Elem(i).marked = 0;
		for(i=1; i<=mprisms.Size(); i++)
		  mids.Elem(i).marked = 0;

		inf >> st;
		while(inf)
		  {
		    if(st[0] == '#')
		      {
			inf.ignore(10000,'\n');
			inf >> st;
		      }
		    else if(st == "markedelementsfile")
		      {
			inf >> st;
			ReadEnclString(inf,st,'\"');
			inf >> st;
		      }
		    else if(st == "noprojection")
		      {
			noprojection = true;
			inf >> st;
		      }
		    else if(st == "refine")
		      {
			inf >> st;
			if(st == "elements")
			  {
			    inf >> st;
			    bool isint = true;
				for(string::size_type ii=0; isint && ii<st.size(); ii++)
			      isint = (isdigit(st[ii]) != 0);
			    
			    while(inf && isint)
			      {
				mtets.Elem(atoi(st.c_str())).marked = 3;
				marked = 1;

				inf >> st;
				isint = true;
				for(string::size_type ii=0; isint && ii<st.size(); ii++)
				  isint = (isdigit(st[ii]) != 0);
			      }
			  }
			else if(st == "orthobrick")
			  {
			    double bounds[6];
			    for(i=0; i<6; i++)
			      inf >> bounds[i];
			    
			    int cnt = 0;

			    for(ElementIndex ei = 0; ei < mesh.GetNE(); ei++)
			      {
				const Element & el = mesh[ei];
				
				//
				Point<3> center(0,0,0);
				for(i=0; i<el.GetNP(); i++)
				  {
				    const MeshPoint & point = mesh[el[i]];
				    center(0) += point(0);
				    center(1) += point(1);
				    center(2) += point(2);
				  }
				for(i=0; i<3; i++)
				  center(i) *= 1./double(el.GetNP());
				if(bounds[0] <= center(0) && center(0) <= bounds[3] &&
				   bounds[1] <= center(1) && center(1) <= bounds[4] &&
				   bounds[2] <= center(2) && center(2) <= bounds[5])
				  {
				    mtets[ei].marked = 3;
				    cnt++;
				  }
				
				  
// 				bool contained = false;
// 				for(int i=0; !contained && i<el.GetNP(); i++)
// 				  {
// 				    const MeshPoint & point = mesh[el[i]];
// 				    contained = (bounds[0] <= point.X() && point.X() <= bounds[3] &&
// 						 bounds[1] <= point.Y() && point.Y() <= bounds[4] &&
// 						 bounds[2] <= point.Z() && point.Z() <= bounds[5]);
// 				  }
// 				if(contained)
// 				  {
// 				    mtets[ei].marked = 3;
// 				    cnt++;
// 				  }
			      }


			    ostringstream strstr;
			    strstr.precision(2);
			    strstr << "marked " << float(cnt)/float(mesh.GetNE())*100. 
#ifdef WIN32
				   << "%%"
#else
				   << "%"
#endif
				   <<" of the elements";
			    PrintMessage(4,strstr.str());

			    if(cnt > 0)
			      marked = 1;


			    inf >> st;
			  }
			else
			  {
			    throw NgException("something wrong with refinementinfo file");
			  }
		      }
		  }		
	      }
	    else
	      {
		inf.close();
		inf.open(opt.refinementfilename);

		char ch;
		for (i = 1; i <= mtets.Size(); i++)
		  {
		    inf >> ch;
		    if(!inf)
		      throw NgException("something wrong with refinementinfo file (old format)");
		    mtets.Elem(i).marked = (ch == '1');
		  }
		marked = 1;
	      }
	    inf.close();
	  }

	else if (opt.usemarkedelements)
	  {
	    int cntm = 0;

	    // all in one !
	    if (mprisms.Size())
	      {
		int cnttet = 0;
		int cntprism = 0;
		for (i = 1; i <= mesh.GetNE(); i++)
		  {
		    if (mesh.VolumeElement(i).GetType() == TET ||
			mesh.VolumeElement(i).GetType() == TET10)
		      {
			cnttet++;
			mtets.Elem(cnttet).marked =
			  3 * mesh.VolumeElement(i).TestRefinementFlag();
			if (mtets.Elem(cnttet).marked)
			  cntm++;
		      }
		    else
		      {
			cntprism++;
			mprisms.Elem(cntprism).marked =
			  2 * mesh.VolumeElement(i).TestRefinementFlag();
			if (mprisms.Elem(cntprism).marked)
			  cntm++;
		      }

		  }
	      }
	    else
	      for (i = 1; i <= mtets.Size(); i++)
		{
		  mtets.Elem(i).marked =
		    3 * mesh.VolumeElement(i).TestRefinementFlag();
		  if (mtets.Elem(i).marked)
		    cntm++;
		}

	    // (*testout) << "mtets = " << mtets << endl;

	    /*
	      for (i = 1; i <= mtris.Size(); i++)
	      mtris.Elem(i).marked = 0;
	      for (i = 1; i <= mquads.Size(); i++)
	      mquads.Elem(i).marked = 0;
	    */

	    if (printmessage_importance>0)
	      {
		ostringstream str;
		str << "marked elements: " << cntm;
		PrintMessage(4,str.str());
	      }

	    int cnttrig = 0;
	    int cntquad = 0;
	    for (i = 1; i <= mesh.GetNSE(); i++)
	      {
		if (mesh.SurfaceElement(i).GetType() == TRIG ||
		    mesh.SurfaceElement(i).GetType() == TRIG6)
		  {
		    cnttrig++;
		    mtris.Elem(cnttrig).marked =
		      mesh.SurfaceElement(i).TestRefinementFlag() ? 2 : 0;
		    // mtris.Elem(cnttrig).marked = 0;
		    if (mtris.Elem(cnttrig).marked)
		      cntm++;
		  }
		else
		  {
		    cntquad++;
                    // 2d: marked=2, 3d prisms: marked=1
		    mquads.Elem(cntquad).marked =
                        mesh.SurfaceElement(i).TestRefinementFlag() ? 4-mesh.GetDimension() : 0 ;
		    // mquads.Elem(cntquad).marked = 0;
		    if (mquads.Elem(cntquad).marked)
		      cntm++;
		  }
	      }

              if (printmessage_importance>0)
		{
		  ostringstream str;
		  str << "with surface-elements: " << cntm;
		  PrintMessage(4,str.str());
		}

            // he/sz: das wird oben schon richtig gemacht.
            // hier sind die quads vergessen!
            /*
	    if (mesh.GetDimension() == 2)
	      {
		cntm = 0;
		for (i = 1; i <= mtris.Size(); i++)
		  {
		    mtris.Elem(i).marked =
		      2 * mesh.SurfaceElement(i).TestRefinementFlag();
		    //		  mtris.Elem(i).marked = 2;
		    if (mtris.Elem(i).marked)
		      cntm++;
		  }

		if (!cntm)
		  {
		    for (i = 1; i <= mtris.Size(); i++)
		      {
			mtris.Elem(i).marked = 2;
			cntm++;
		      }
		  }
		cout << "trigs: " << mtris.Size() << " ";
		cout << "marked: " << cntm << endl;
	      }
            */ 
            
	    marked = (cntm > 0);
	  }
	else
	  {
	    marked = BTMarkTets (mtets, mprisms, mesh);
	  }

	if (!marked) break;
        

	//(*testout) << "mtets " << mtets << endl;

	if (opt.refine_p)
	  {
	    PrintMessage(3,"refine p");

	    for (i = 1; i <= mtets.Size(); i++)
	      mtets.Elem(i).incorder = mtets.Elem(i).marked ? 1 : 0;

	    for (i = 1; i <= mtets.Size(); i++)
	      if (mtets.Elem(i).incorder)
		mtets.Elem(i).marked = 0;


	    for (i = 1; i <= mprisms.Size(); i++)
	      mprisms.Elem(i).incorder = mprisms.Elem(i).marked ? 1 : 0;

	    for (i = 1; i <= mprisms.Size(); i++)
	      if (mprisms.Elem(i).incorder)
		mprisms.Elem(i).marked = 0;


	    for (i = 1; i <= mtris.Size(); i++)
	      mtris.Elem(i).incorder = mtris.Elem(i).marked ? 1 : 0;

	    for (i = 1; i <= mtris.Size(); i++)
	      {
		if (mtris.Elem(i).incorder)
		  mtris.Elem(i).marked = 0;
	      }
	  }

	if (opt.refine_hp)
	  {
	    PrintMessage(3,"refine hp");
	    BitArray singv(np);
	    singv.Clear();

	    if (mesh.GetDimension() == 3)
	      {
		for (i = 1; i <= mesh.GetNSeg(); i++)
		  {
		    const Segment & seg = mesh.LineSegment(i);
		    singv.Set (seg[0]);
		    singv.Set (seg[1]);
		  }
		/*
		  for ( i=1; i<= mesh.GetNSE(); i++)
		  {
		  const Element2d & sel = mesh.SurfaceElement(i);
		  for(int j=1; j<=sel.GetNP(); j++)
		  singv.Set(sel.PNum(j));
		  }
		*/
	      }
	    else
	      {
		// vertices with 2 different bnds
		Array<int> bndind(np);
		bndind = 0;
		for (i = 1; i <= mesh.GetNSeg(); i++)
		  {
		    const Segment & seg = mesh.LineSegment(i);
		    for (j = 0; j < 2; j++)
		      {
			int pi = (j == 0) ? seg[0] : seg[1];
			if (bndind.Elem(pi) == 0)
			  bndind.Elem(pi) = seg.edgenr;
			else if (bndind.Elem(pi) != seg.edgenr)
			  singv.Set (pi);
		      }
		  }
	      }



	    for (i = 1; i <= mtets.Size(); i++)
	      mtets.Elem(i).incorder = 1;
	    for (i = 1; i <= mtets.Size(); i++)
	      {
		if (!mtets.Elem(i).marked)
		  mtets.Elem(i).incorder = 0;
		for (j = 0; j < 4; j++)
		  if (singv.Test (mtets.Elem(i).pnums[j]))
		    mtets.Elem(i).incorder = 0;
	      }
	    for (i = 1; i <= mtets.Size(); i++)
	      if (mtets.Elem(i).incorder)
		mtets.Elem(i).marked = 0;


	    for (i = 1; i <= mprisms.Size(); i++)
	      mprisms.Elem(i).incorder = 1;
	    for (i = 1; i <= mprisms.Size(); i++)
	      {
		if (!mprisms.Elem(i).marked)
		  mprisms.Elem(i).incorder = 0;
		for (j = 0; j < 6; j++)
		  if (singv.Test (mprisms.Elem(i).pnums[j]))
		    mprisms.Elem(i).incorder = 0;
	      }
	    for (i = 1; i <= mprisms.Size(); i++)
	      if (mprisms.Elem(i).incorder)
		mprisms.Elem(i).marked = 0;


	    for (i = 1; i <= mtris.Size(); i++)
	      mtris.Elem(i).incorder = 1;
	    for (i = 1; i <= mtris.Size(); i++)
	      {
		if (!mtris.Elem(i).marked)
		  mtris.Elem(i).incorder = 0;
		for (j = 0; j < 3; j++)
		  if (singv.Test (mtris.Elem(i).pnums[j]))
		    mtris.Elem(i).incorder = 0;
	      }
	    for (i = 1; i <= mtris.Size(); i++)
	      {
		if (mtris.Elem(i).incorder)
		  mtris.Elem(i).marked = 0;
	      }
	  }



	int hangingvol, hangingsurf, hangingedge;

	//cout << "write?" << endl;
	//string yn;
	//cin >> yn;

	(*testout) << "refine volume elements" << endl;
	do
	  {
	    // refine volume elements

	    int nel = mtets.Size();
	    for (i = 1; i <= nel; i++)
	      if (mtets.Elem(i).marked)
		{
		  MarkedTet oldtet;
		  MarkedTet newtet1, newtet2;
		  int newp;


		  oldtet = mtets.Get(i);
		  //if(yn == "y")
		  //  (*testout) << "bisected tet " << oldtet;
		  INDEX_2 edge(oldtet.pnums[oldtet.tetedge1],
			       oldtet.pnums[oldtet.tetedge2]);
		  edge.Sort();
		  if (cutedges.Used (edge))
		    {
		      newp = cutedges.Get(edge);
		    }
		  else
		    {
		      Point<3> npt = Center (mesh.Point (edge.I1()),
					   mesh.Point (edge.I2()));
		      newp = mesh.AddPoint (npt);
		      cutedges.Set (edge, newp);
		    }

		  BTBisectTet (oldtet, newp, newtet1, newtet2);

		  mtets.Elem(i) = newtet1;
		  mtets.Append (newtet2);

#ifdef DEBUG
                  *testout << "tet1 has elnr = " << i << ", tet2 has elnr = " << mtets.Size() << endl;
#endif
		  //if(yn == "y")
		  //  (*testout) << "and got " << newtet1 << "and " << newtet2 << endl;

		  mesh.mlparentelement.Append (i);
		}

	    int npr = mprisms.Size();
	    for (i = 1; i <= npr; i++)
	      if (mprisms.Elem(i).marked)
		{
		  MarkedPrism oldprism;
		  MarkedPrism newprism1, newprism2;
		  int newp1, newp2;

		  oldprism = mprisms.Get(i);
		  int pi1 = 0;
		  if (pi1 == oldprism.markededge)
		    pi1++;
		  int pi2 = 3-pi1-oldprism.markededge;

		  INDEX_2 edge1(oldprism.pnums[pi1],
				oldprism.pnums[pi2]);
		  INDEX_2 edge2(oldprism.pnums[pi1+3],
				oldprism.pnums[pi2+3]);
		  edge1.Sort();
		  edge2.Sort();

		  if (cutedges.Used (edge1))
		    newp1 = cutedges.Get(edge1);
		  else
		    {
		      Point<3> npt = Center (mesh.Point (edge1.I1()),
					    mesh.Point (edge1.I2()));
		      newp1 = mesh.AddPoint (npt);
		      cutedges.Set (edge1, newp1);
		    }
		  if (cutedges.Used (edge2))
		    newp2 = cutedges.Get(edge2);
		  else
		    {
		      Point<3> npt = Center (mesh.Point (edge2.I1()),
					    mesh.Point (edge2.I2()));
		      newp2 = mesh.AddPoint (npt);
		      cutedges.Set (edge2, newp2);
		    }
		

		  BTBisectPrism (oldprism, newp1, newp2, newprism1, newprism2);
		  //if(yn == "y")
		  //  (*testout) << "bisected prism " << oldprism << "and got " << newprism1 << "and " << newprism2 << endl;
		  mprisms.Elem(i) = newprism1;
		  mprisms.Append (newprism2);
		}

	    int nid = mids.Size();
	    for (i = 1; i <= nid; i++)
	      if (mids.Elem(i).marked)
		{
		  MarkedIdentification oldid,newid1,newid2;
		  Array<int> newp;

		  oldid = mids.Get(i);
		  
		  Array<INDEX_2> edges;
		  edges.Append(INDEX_2(oldid.pnums[oldid.markededge],
				       oldid.pnums[(oldid.markededge+1)%oldid.np]));
		  edges.Append(INDEX_2(oldid.pnums[oldid.markededge + oldid.np],
				       oldid.pnums[(oldid.markededge+1)%oldid.np + oldid.np]));

		  if(oldid.np == 4)
		    {
		      edges.Append(INDEX_2(oldid.pnums[(oldid.markededge+2)%oldid.np],
					   oldid.pnums[(oldid.markededge+3)%oldid.np]));
		      edges.Append(INDEX_2(oldid.pnums[(oldid.markededge+2)%oldid.np + oldid.np],
					   oldid.pnums[(oldid.markededge+3)%oldid.np + oldid.np]));
		    }
		  for (j = 0; j < edges.Size(); j++)
		    {
		      edges[j].Sort();

		      if(cutedges.Used(edges[j]))
			newp.Append(cutedges.Get(edges[j]));
		      else
			{
			  Point<3> npt = Center (mesh.Point (edges[j].I1()),
						mesh.Point (edges[j].I2()));
			  newp.Append(mesh.AddPoint(npt));
			  cutedges.Set(edges[j],newp[j]);
			}			 
		    }
		  
		  BTBisectIdentification(oldid,newp,newid1,newid2);
		  mids.Elem(i) = newid1;
		  mids.Append(newid2);		  
		}

	    
	    //IdentifyCutEdges(mesh, cutedges);


	    hangingvol = 
	      MarkHangingTets (mtets, cutedges) +
	      MarkHangingPrisms (mprisms, cutedges) +
	      MarkHangingIdentifications (mids, cutedges);


	    int nsel = mtris.Size();

	    for (i = 1; i <= nsel; i++)
	      if (mtris.Elem(i).marked)
		{
		  MarkedTri oldtri;
		  MarkedTri newtri1, newtri2;
		  PointIndex newp;
		
		  oldtri = mtris.Get(i);
		  int oldpi1 = oldtri.pnums[(oldtri.markededge+1)%3];
		  int oldpi2 = oldtri.pnums[(oldtri.markededge+2)%3];
		  INDEX_2 edge(oldpi1, oldpi2);
		  edge.Sort();

		  //		cerr << "edge = " << edge.I1() << "-" << edge.I2() << endl;

		  if (cutedges.Used (edge))
		    {
		      newp = cutedges.Get(edge);
		    }
		  else
		    {
		      Point<3> npt = Center (mesh.Point (edge.I1()),
					    mesh.Point (edge.I2()));
		      newp = mesh.AddPoint (npt);
                      cutedges.Set (edge, newp);
		    }
		  //		newp = cutedges.Get(edge);
		
		  int si = mesh.GetFaceDescriptor (oldtri.surfid).SurfNr();
		  //  geom->GetSurface(si)->Project (mesh.Point(newp));
		  PointGeomInfo npgi;
		
//                   cerr << "project point " << newp << " old: " << mesh.Point(newp);
                  if (mesh[newp].Type() != EDGEPOINT)
                    PointBetween (mesh.Point (oldpi1), mesh.Point (oldpi2),
                                  0.5, si,
                                  oldtri.pgeominfo[(oldtri.markededge+1)%3],
                                  oldtri.pgeominfo[(oldtri.markededge+2)%3],
                                  mesh.Point (newp), npgi);
//                   cerr << " new: " << mesh.Point(newp) << endl;
		
		  BTBisectTri (oldtri, newp, npgi, newtri1, newtri2);
		  //if(yn == "y")
		  //  (*testout) << "bisected tri " << oldtri << "and got " << newtri1 << "and " << newtri2 << endl;
		
		
		  mtris.Elem(i) = newtri1;
		  mtris.Append (newtri2);
		  mesh.mlparentsurfaceelement.Append (i);
		}
	  
	    int nquad = mquads.Size();
	    for (i = 1; i <= nquad; i++)
	      if (mquads.Elem(i).marked)
		{
		  MarkedQuad oldquad;
		  MarkedQuad newquad1, newquad2;
		  int newp1, newp2;
		
		  oldquad = mquads.Get(i);
                  /*
		  INDEX_2 edge1(oldquad.pnums[0],
				oldquad.pnums[1]);
		  INDEX_2 edge2(oldquad.pnums[2],
				oldquad.pnums[3]);
                  */
                  INDEX_2 edge1, edge2;
                  PointGeomInfo pgi11, pgi12, pgi21, pgi22;
                  if (oldquad.markededge==0 || oldquad.markededge==2)
                  {
                    edge1.I1()=oldquad.pnums[0]; pgi11=oldquad.pgeominfo[0];
                    edge1.I2()=oldquad.pnums[1]; pgi12=oldquad.pgeominfo[1];
                    edge2.I1()=oldquad.pnums[2]; pgi21=oldquad.pgeominfo[2];
                    edge2.I2()=oldquad.pnums[3]; pgi22=oldquad.pgeominfo[3];
                  }
                  else // 3 || 1
                  {
                    edge1.I1()=oldquad.pnums[0]; pgi11=oldquad.pgeominfo[0];
                    edge1.I2()=oldquad.pnums[2]; pgi12=oldquad.pgeominfo[2];
                    edge2.I1()=oldquad.pnums[1]; pgi21=oldquad.pgeominfo[1];
                    edge2.I2()=oldquad.pnums[3]; pgi22=oldquad.pgeominfo[3];
                  }
                  
                  edge1.Sort();
		  edge2.Sort();

		  if (cutedges.Used (edge1))
		    {
		      newp1 = cutedges.Get(edge1);
		    }
		  else
		    {
		      Point<3> np1 = Center (mesh.Point (edge1.I1()),
					   mesh.Point (edge1.I2()));
		      newp1 = mesh.AddPoint (np1);
		      cutedges.Set (edge1, newp1);
                    }

		  if (cutedges.Used (edge2))
		    {
		      newp2 = cutedges.Get(edge2);
		    }
		  else
		    {
		      Point<3> np2 = Center (mesh.Point (edge2.I1()),
					   mesh.Point (edge2.I2()));
		      newp2 = mesh.AddPoint (np2);
		      cutedges.Set (edge2, newp2);
                    }

		  PointGeomInfo npgi1, npgi2;
		
		  int si = mesh.GetFaceDescriptor (oldquad.surfid).SurfNr();
		  //		geom->GetSurface(si)->Project (mesh.Point(newp1));
		  //		geom->GetSurface(si)->Project (mesh.Point(newp2));

//                   (*testout)
//                   cerr << "project point 1 " << newp1 << " old: " << mesh.Point(newp1);
                  PointBetween (mesh.Point (edge1.I1()), mesh.Point (edge1.I2()),
				0.5, si,
				pgi11,
				pgi12,
				mesh.Point (newp1), npgi1);
// 		  (*testout)
//                   cerr << " new: " << mesh.Point(newp1) << endl;

		
//                   cerr << "project point 2 " << newp2 << " old: " << mesh.Point(newp2);
                  PointBetween (mesh.Point (edge2.I1()), mesh.Point (edge2.I2()),
				0.5, si,
				pgi21,
				pgi22,
				mesh.Point (newp2), npgi2);
//                   cerr << " new: " << mesh.Point(newp2) << endl;
		

		  BTBisectQuad (oldquad, newp1, npgi1, newp2, npgi2,
				newquad1, newquad2);
                  
		  mquads.Elem(i) = newquad1;
		  mquads.Append (newquad2);
		}
	  

	    hangingsurf = 
	      MarkHangingTris (mtris, cutedges) +
	      MarkHangingQuads (mquads, cutedges);

	    hangingedge = 0;
	  
	    int nseg = mesh.GetNSeg ();
	    for (i = 1; i <= nseg; i++)
	      {
		Segment & seg = mesh.LineSegment (i);
		INDEX_2 edge(seg[0], seg[1]);
		edge.Sort();
		if (cutedges.Used (edge))
		  {
		    hangingedge = 1;
		    Segment nseg1 = seg;
		    Segment nseg2 = seg;
		  
		    int newpi = cutedges.Get(edge);
		  
		    nseg1[1] = newpi;
		    nseg2[0] = newpi;
		  
		    EdgePointGeomInfo newepgi;
		  
 
//                     
//                     cerr << "move edgepoint " << newpi << " from " << mesh.Point(newpi);
		    PointBetween (mesh.Point (seg[0]), mesh.Point (seg[1]),
				  0.5, seg.surfnr1, seg.surfnr2, 
				  seg.epgeominfo[0], seg.epgeominfo[1],
				  mesh.Point (newpi), newepgi);
// 		    cerr << " to " << mesh.Point (newpi) << endl;

		    
		    nseg1.epgeominfo[1] = newepgi;
		    nseg2.epgeominfo[0] = newepgi;
		  
		    mesh.LineSegment (i) = nseg1;
		    mesh.AddSegment (nseg2);
		  }
	      }
	  }
	while (hangingvol || hangingsurf || hangingedge);
        
	/*
        if (printmessage_importance>0)
	  {
	    ostringstream strstr;
	    strstr << mtets.Size() << " tets" << endl
		   << mtris.Size() << " trigs" << endl;
	    if (mprisms.Size())
	      {
		strstr << mprisms.Size() << " prisms" << endl
		       << mquads.Size() << " quads" << endl;
	      }
	    strstr << mesh.GetNP() << " points";
	    PrintMessage(4,strstr.str());
	  }
	*/
	PrintMessage (4, mtets.Size(), " tets");
	PrintMessage (4, mtris.Size(), " trigs");
	if (mprisms.Size())
	  {
	    PrintMessage (4, mprisms.Size(), " prisms");
	    PrintMessage (4, mquads.Size(), " quads");
	  }
	PrintMessage (4, mesh.GetNP(), " points");
      }


    // (*testout) << "mtets = " << mtets << endl;

    if (opt.refine_hp)
      {
	//
	Array<int> v_order (mesh.GetNP());
	v_order = 0;
	if (mesh.GetDimension() == 3)
	  {
	    for (i = 1; i <= mtets.Size(); i++)
	      if (mtets.Elem(i).incorder)
		mtets.Elem(i).order++;
      
	    for (i = 0; i < mtets.Size(); i++)
	      for (j = 0; j < 4; j++)
		if (int(mtets[i].order) > v_order.Elem(mtets[i].pnums[j]))
		  v_order.Elem(mtets[i].pnums[j]) = mtets[i].order;
	    for (i = 0; i < mtets.Size(); i++)
	      for (j = 0; j < 4; j++)
		if (int(mtets[i].order) < v_order.Elem(mtets[i].pnums[j])-1)
		  mtets[i].order = v_order.Elem(mtets[i].pnums[j])-1;
	  }
	else
	  {
	    for (i = 1; i <= mtris.Size(); i++)
	      if (mtris.Elem(i).incorder)
		{
		  mtris.Elem(i).order++;
		}

	    for (i = 0; i < mtris.Size(); i++)
	      for (j = 0; j < 3; j++)
		if (int(mtris[i].order) > v_order.Elem(mtris[i].pnums[j]))
		  v_order.Elem(mtris[i].pnums[j]) = mtris[i].order;
	    for (i = 0; i < mtris.Size(); i++)
	      {
		for (j = 0; j < 3; j++)
		  if (int(mtris[i].order) < v_order.Elem(mtris[i].pnums[j])-1)
		    mtris[i].order = v_order.Elem(mtris[i].pnums[j])-1;
	      }
	  }
      }
  
    mtets.SetAllocSize (mtets.Size());
    mprisms.SetAllocSize (mprisms.Size());
    mids.SetAllocSize (mids.Size());
    mtris.SetAllocSize (mtris.Size());
    mquads.SetAllocSize (mquads.Size());
  
    
    mesh.ClearVolumeElements();
    mesh.VolumeElements().SetAllocSize (mtets.Size()+mprisms.Size());
    for (i = 1; i <= mtets.Size(); i++)
      {
	Element el(TET);
	el.SetIndex (mtets.Get(i).matindex);
	for (j = 1; j <= 4; j++)
	  el.PNum(j) = mtets.Get(i).pnums[j-1];
	el.SetOrder (mtets.Get(i).order);
	mesh.AddVolumeElement (el);
      }
    for (i = 1; i <= mprisms.Size(); i++)
      {
	Element el(PRISM);
	el.SetIndex (mprisms.Get(i).matindex);
	for (j = 1; j <= 6; j++)
	  el.PNum(j) = mprisms.Get(i).pnums[j-1];
	el.SetOrder (mprisms.Get(i).order);

	// degenerated prism ?
	static const int map1[] = { 3, 2, 5, 6, 1 };
	static const int map2[] = { 1, 3, 6, 4, 2 };
	static const int map3[] = { 2, 1, 4, 5, 3 };
      

	const int * map = NULL;
	int deg1 = 0, deg2 = 0, deg3 = 0;
	// int deg = 0;
	if (el.PNum(1) == el.PNum(4)) { map = map1; deg1 = 1; }
	if (el.PNum(2) == el.PNum(5)) { map = map2; deg2 = 1; }
	if (el.PNum(3) == el.PNum(6)) { map = map3; deg3 = 1; }
	  
	switch (deg1+deg2+deg3)
	  {
	  case 1:
	    {
	      for (j = 1; j <= 5; j++)
		el.PNum(j) = mprisms.Get(i).pnums[map[j-1]-1];
	    
	      el.SetType (PYRAMID);
	      break;
	    }
	  case 2:
	    {
	      static const int tetmap1[] = { 1, 2, 3, 4 };
	      static const int tetmap2[] = { 2, 3, 1, 5 };
	      static const int tetmap3[] = { 3, 1, 2, 6 };
	      if (!deg1) map = tetmap1;
	      if (!deg2) map = tetmap2;
	      if (!deg3) map = tetmap3; 
	      for (j = 1; j <= 4; j++)
		el.PNum(j) = mprisms.Get(i).pnums[map[j-1]-1];
	      /*
		if (!deg1) el.PNum(4) = el.PNum(4);
		if (!deg2) el.PNum(4) = el.PNum(5);
		if (!deg3) el.PNum(4) = el.PNum(6);
	      */
	      el.SetType(TET);
	      break;
	    }
	  default:
	    ;
	  }
	mesh.AddVolumeElement (el);
      }
  
    mesh.ClearSurfaceElements();
    for (i = 1; i <= mtris.Size(); i++)
      {
	Element2d el(TRIG);
	el.SetIndex (mtris.Get(i).surfid);
	el.SetOrder (mtris.Get(i).order);
	for (j = 1; j <= 3; j++)
	  {
	    el.PNum(j) = mtris.Get(i).pnums[j-1];
	    el.GeomInfoPi(j) = mtris.Get(i).pgeominfo[j-1];
	  }
	mesh.AddSurfaceElement (el);
      }
    for (i = 1; i <= mquads.Size(); i++)
      {
	Element2d el(QUAD);
	el.SetIndex (mquads.Get(i).surfid);
	for (j = 1; j <= 4; j++)
	  el.PNum(j) = mquads.Get(i).pnums[j-1];
	Swap (el.PNum(3), el.PNum(4));
	mesh.AddSurfaceElement (el);
      }


      
    // write multilevel hierarchy to mesh:
    np = mesh.GetNP();
    mesh.mlbetweennodes.SetSize(np);
    if (mesh.mglevels <= 2)
      {
	PrintMessage(4,"RESETTING mlbetweennodes");
	for (i = 1; i <= np; i++)
	  {
	    mesh.mlbetweennodes.Elem(i).I1() = 0;
	    mesh.mlbetweennodes.Elem(i).I2() = 0;
	  }
      }

    /*
      for (i = 1; i <= cutedges.GetNBags(); i++)
      for (j = 1; j <= cutedges.GetBagSize(i); j++)
      {
      INDEX_2 edge;
      int newpi;
      cutedges.GetData (i, j, edge, newpi);
      mesh.mlbetweennodes.Elem(newpi) = edge;
      }
    */

    BitArray isnewpoint(np);
    isnewpoint.Clear();

    for (i = 1; i <= cutedges.Size(); i++)
      if (cutedges.UsedPos(i))
	{
	  INDEX_2 edge;
	  int newpi;
	  cutedges.GetData (i, edge, newpi);
	  isnewpoint.Set(newpi);
	  mesh.mlbetweennodes.Elem(newpi) = edge;
	}


    /*
      mesh.PrintMemInfo (cout);
      cout << "tets ";
      mtets.PrintMemInfo (cout);
      cout << "prims ";
      mprisms.PrintMemInfo (cout);
      cout << "tris ";
      mtris.PrintMemInfo (cout);
      cout << "quads ";
      mquads.PrintMemInfo (cout);
      cout << "cutedges ";
      cutedges.PrintMemInfo (cout);
    */


    /*

    // find connected nodes (close nodes)
    TABLE<int> conto(np);
    for (i = 1; i <= mprisms.Size(); i++)
    for (j = 1; j <= 6; j++)
    {
    int n1 = mprisms.Get(i).pnums[j-1];
    int n2 = mprisms.Get(i).pnums[(j+2)%6];
    //	    if (n1 != n2)
    {
    int found = 0;
    for (k = 1; k <= conto.EntrySize(n1); k++)
    if (conto.Get(n1, k) == n2)
    {
    found = 1;
    break;
    }
    if (!found)
    conto.Add (n1, n2);
    }
    }
    mesh.connectedtonode.SetSize(np);
    for (i = 1; i <= np; i++)
    mesh.connectedtonode.Elem(i) = 0;
  

    //       (*testout) << "connection table: " << endl;
    //       for (i = 1; i <= np; i++)
    //       {
    //       (*testout) << "node " << i << ": ";
    // 	  for (j = 1; j <= conto.EntrySize(i); j++)
    // 	  (*testout) << conto.Get(i, j) << " ";
    // 	  (*testout) << endl;
    // 	}

  
    for (i = 1; i <= np; i++)
    if (mesh.connectedtonode.Elem(i) == 0)
    {
    mesh.connectedtonode.Elem(i) = i;
    ConnectToNodeRec (i, i, conto, mesh.connectedtonode);
    }
    */  

    //  mesh.BuildConnectedNodes();

    


    mesh.ComputeNVertices();
    mesh.RebuildSurfaceElementLists();
  
    
    // update identification tables
    for (i = 1; i <= mesh.GetIdentifications().GetMaxNr(); i++)
      {
	Array<int,PointIndex::BASE> identmap;

	mesh.GetIdentifications().GetMap (i, identmap);


	/*
	  for (j = 1; j <= cutedges.GetNBags(); j++)
	  for (k = 1; k <= cutedges.GetBagSize(j); k++)
	  {
	  INDEX_2 i2;
	  int newpi;
	  cutedges.GetData (j, k, i2, newpi);
	  INDEX_2 oi2(identmap.Get(i2.I1()),
	  identmap.Get(i2.I2()));
	  oi2.Sort();
	  if (cutedges.Used (oi2))
	  {
	  int onewpi = cutedges.Get(oi2);
	  mesh.GetIdentifications().Add (newpi, onewpi, i);
	  }
	  }
	*/

	for (j = 1; j <= cutedges.Size(); j++)
	  if (cutedges.UsedPos(j))
	    {
	      INDEX_2 i2;
	      int newpi;
	      cutedges.GetData (j, i2, newpi);
	      INDEX_2 oi2(identmap.Get(i2.I1()),
			  identmap.Get(i2.I2()));
	      oi2.Sort();
	      if (cutedges.Used (oi2))
		{
		  int onewpi = cutedges.Get(oi2);
		  mesh.GetIdentifications().Add (newpi, onewpi, i);
		}
	    }
      }


    // Repair works only for tets!
    bool do_repair = mesh.PureTetMesh ();

    do_repair = false;   // JS, March 2009: multigrid crashes

    //if(mesh.mglevels == 3)
    //  noprojection = true;

    //noprojection = true;

    if(noprojection)
      {
	do_repair = false;
	for(int ii=1; ii<=mesh.GetNP(); ii++)
	  {
	    if(isnewpoint.Test(ii) && mesh.mlbetweennodes[ii][0] > 0)
	      {
		mesh.Point(ii) = Center(mesh.Point(mesh.mlbetweennodes[ii][0]),
                                        mesh.Point(mesh.mlbetweennodes[ii][1]));
	      }
	  }
      }


    // Check/Repair

    static bool repaired_once;
    if(mesh.mglevels == 1)
      repaired_once = false;

    //mesh.Save("before.vol");

    static int reptimer = NgProfiler::CreateTimer("check/repair");
	NgProfiler::RegionTimer * regt(NULL);
    regt = new NgProfiler::RegionTimer(reptimer); 

    Array<ElementIndex> bad_elts;
    Array<double> pure_badness;
   
    if(do_repair || quality_loss != NULL)
      {
	pure_badness.SetSize(mesh.GetNP()+2);
	GetPureBadness(mesh,pure_badness,isnewpoint);
      }


    if(do_repair)  // by Markus W
      {
	const double max_worsening = 1;
	
	const bool uselocalworsening = false;
	
	bool repaired = false;
	
	Validate(mesh,bad_elts,pure_badness,max_worsening,uselocalworsening);
	
        if (printmessage_importance>0)
	  {
	    ostringstream strstr;
	    for(int ii=0; ii<bad_elts.Size(); ii++)
	      strstr << "bad element " << bad_elts[ii] << "\n";
	    PrintMessage(1,strstr.str());
	  }
	if(repaired_once || bad_elts.Size() > 0)
	  {
	    clock_t t1(clock());
	    
	    
	    // update id-maps
	    j=0;
	    for(i=1; i<=mesh.GetIdentifications().GetMaxNr(); i++)
	      {
		if(mesh.GetIdentifications().GetType(i) == Identifications::PERIODIC)
		  {
		    mesh.GetIdentifications().GetMap(i,*idmaps[j],true);
		    j++;
		  }
	      }

    
	    // do the repair
	    try
	      {
		RepairBisection(mesh,bad_elts,isnewpoint,*this,
				pure_badness,
				max_worsening,uselocalworsening,
				idmaps);
		repaired = true;
		repaired_once = true;
	      }
	    catch(NgException & ex)
	      {
		PrintMessage(1,string("Problem: ") + ex.What());
	      }


            if (printmessage_importance>0)
            {
	      ostringstream strstr;
              strstr << "Time for Repair: " << double(clock() - t1)/double(CLOCKS_PER_SEC) << endl
		     << "bad elements after repair: " << bad_elts << endl;
	      PrintMessage(1,strstr.str());
            }
	    
	    if(quality_loss != NULL)
	      Validate(mesh,bad_elts,pure_badness,1e100,uselocalworsening,quality_loss);

	    if(idmaps.Size() == 0)
	      UpdateEdgeMarks(mesh,idmaps);
	    
	    /*
	    if(1==1)
	      UpdateEdgeMarks(mesh,idmaps);
	    else
	      mesh.mglevels = 1;
	    */
	    
	    //mesh.ImproveMesh();
	    
	  }
      }
    delete regt;


    
    for(i=0; i<idmaps.Size(); i++)
      delete idmaps[i];
    idmaps.DeleteAll();

    mesh.UpdateTopology();




    if(refelementinfofilewrite != "")
      {
	PrintMessage(3,"writing marked-elements information to \"",refelementinfofilewrite,"\"");
	ofstream ofst(refelementinfofilewrite.c_str());

	WriteMarkedElements(ofst);

	ofst.close();
      }


    mesh.CalcSurfacesOfNode();

    PrintMessage (1, "Bisection done");

    PopStatus();
  }




  BisectionOptions :: BisectionOptions ()
  {
    outfilename = NULL;
    mlfilename = NULL;
    refinementfilename = NULL;
    femcode = NULL;
    maxlevel = 50;
    usemarkedelements = 0;
    refine_hp = 0;
    refine_p = 0;
  }


  Refinement :: Refinement ()
  {
    optimizer2d = NULL;
  }

  Refinement :: ~Refinement ()
  {
    ;
  }


  void Refinement :: PointBetween (const Point<3> & p1, const Point<3> & p2, double secpoint,
				   int surfi, 
				   const PointGeomInfo & gi1, 
				   const PointGeomInfo & gi2,
				   Point<3> & newp, PointGeomInfo & newgi)
  {
    newp = p1+secpoint*(p2-p1);
  }

  void Refinement :: PointBetween (const Point<3> & p1, const Point<3> & p2, double secpoint,
				   int surfi1, int surfi2, 
				   const EdgePointGeomInfo & ap1, 
				   const EdgePointGeomInfo & ap2,
				   Point<3> & newp, EdgePointGeomInfo & newgi)
  {
    newp = p1+secpoint*(p2-p1);
  }


  Vec<3> Refinement :: GetTangent (const Point<3> & p, int surfi1, int surfi2,
                                   const EdgePointGeomInfo & ap1) const
  {
    cerr << "Refinement::GetTangent not overloaded" << endl;
    return Vec<3> (0,0,0);
  }

  Vec<3> Refinement :: GetNormal (const Point<3> & p, int surfi1, 
                                  const PointGeomInfo & gi) const
  {
    cerr << "Refinement::GetNormal not overloaded" << endl;
    return Vec<3> (0,0,0);
  }


  void Refinement :: ProjectToSurface (Point<3> & p, int surfi)
  {
    if (printmessage_importance>0)
      cerr << "Refinement :: ProjectToSurface    ERROR: no geometry set" << endl;
  };

  void Refinement :: ProjectToEdge (Point<3> & p, int surfi1, int surfi2, const EdgePointGeomInfo & egi) const
  {
    cerr << "Refinement::ProjectToEdge not overloaded" << endl;
  }
}