netgen/libsrc/meshing/improve3.cpp

#include <mystdlib.h>
#include <algorithm>

#include <core/taskmanager.hpp>
#include <core/logging.hpp>

#include "meshing.hpp"

#ifdef SOLIDGEOM
#include <csg.hpp>
#endif
#include <opti.hpp>

namespace netgen
{

static constexpr int IMPROVEMENT_CONFORMING_EDGE = -1e6;

static inline bool NotTooBad(double bad1, double bad2)
{
  return (bad2 <= bad1) ||
         (bad2 <= 100 * bad1 && bad2 <= 1e18) ||
         (bad2 <= 1e8);
}

// Calc badness of new element where pi1 and pi2 are replaced by pnew
double CalcBadReplacePoints (const Mesh::T_POINTS & points, const MeshingParameters & mp, const Element & elem, double h, PointIndex &pi1, PointIndex &pi2, MeshPoint &pnew)
  {
    if (elem.GetType() != TET) return 0;

    MeshPoint* p[] = {&points[elem[0]], &points[elem[1]], &points[elem[2]], &points[elem[3]]};

    for (auto i : Range(4))
        if(elem[i]==pi1 || elem[i]==pi2) p[i] = &pnew;

    return CalcTetBadness (*p[0], *p[1], *p[2], *p[3], h, mp);
  }

static ArrayMem<Element, 3> SplitElement (Element old, PointIndex pi0, PointIndex pi1, PointIndex pinew)
{
  ArrayMem<Element, 3> new_elements;
  // split element by cutting edge pi0,pi1 at pinew
  auto np = old.GetNP();
  old.Touch();
  if(np == 4)
  {
    // Split tet into two tets
    Element newel0 = old;
    Element newel1 = old;
    for (int i : Range(4))
    {
      if(newel0[i] == pi0) newel0[i] = pinew;
      if(newel1[i] == pi1) newel1[i] = pinew;
    }
    new_elements.Append(newel0);
    new_elements.Append(newel1);
  }
  else if (np == 5)
  {
    // split pyramid into pyramid and two tets
    Element new_pyramid = old;
    new_pyramid[4] = pinew;
    new_elements.Append(new_pyramid);

    auto pibase = (pi0==old[4]) ? pi1 : pi0;
    auto pitop = (pi0==old[4]) ? pi0 : pi1;

    Element new_tet0 = old;
    Element new_tet1 = old;
    new_tet0.SetType(TET);
    new_tet1.SetType(TET);

    size_t pibase_index=0;
    for(auto i : Range(4))
      if(old[i]==pibase)
        pibase_index = i;

    new_tet0[0] = old[(pibase_index+1)%4];
    new_tet0[1] = old[(pibase_index+2)%4];
    new_tet0[2] = pinew;
    new_tet0[3] = pitop;
    new_elements.Append(new_tet0);

    new_tet1[0] = old[(pibase_index+2)%4];
    new_tet1[1] = old[(pibase_index+3)%4];
    new_tet1[2] = pinew;
    new_tet1[3] = pitop;
    new_elements.Append(new_tet1);
  }

  return new_elements;
}

static double SplitElementBadness (const Mesh::T_POINTS & points, const MeshingParameters & mp, Element old, PointIndex pi0, PointIndex pi1, MeshPoint & pnew)
{
  double badness = 0;
  auto np = old.GetNP();
  PointIndex dummy{-1};
  if(np == 4)
  {
    // Split tet into two tets
    badness += CalcBadReplacePoints ( points, mp, old, 0, pi0, dummy, pnew );
    badness += CalcBadReplacePoints ( points, mp, old, 0, pi1, dummy, pnew );
  }
  else if (np == 5)
  {
    // split pyramid into pyramid and two tets
    auto pibase = (pi0==old[4]) ? pi1 : pi0;
    auto pitop = (pi0==old[4]) ? pi0 : pi1;

    badness += CalcBadReplacePoints ( points, mp, old, 0, pitop, dummy, pnew );

    Element tet = old;
    tet.SetType(TET);

    size_t pibase_index=0;
    for(auto i : Range(4))
      if(old[i]==pibase)
        pibase_index = i;

    MeshPoint p[4];
    p[0] = points[old[(pibase_index+1)%4]];
    p[1] = points[old[(pibase_index+2)%4]];
    p[2] = pnew;
    p[3] = points[pitop];
    badness += CalcTetBadness (p[0], p[1], p[2], p[3], 0, mp);

    p[0] = points[old[(pibase_index+2)%4]];
    p[1] = points[old[(pibase_index+3)%4]];
    p[2] = pnew;
    p[3] = points[pitop];
    badness += CalcTetBadness (p[0], p[1], p[2], p[3], 0, mp);
  }

  return badness;
}


tuple<double, double> MeshOptimize3d :: UpdateBadness()
{
  static Timer tbad("UpdateBadness");
  RegionTimer reg(tbad);

  double totalbad = 0.0;
  double maxbad = 0.0;
  ParallelForRange(Range(mesh.GetNE()), [&] (auto myrange) {
    double totalbad_local = 0.0;
    double maxbad_local = 0.0;
    for (ElementIndex ei : myrange)
    {
      auto & el = mesh[ei];
      if(mp.only3D_domain_nr && mp.only3D_domain_nr != el.GetIndex()) continue;
      if(!el.BadnessValid())
        el.SetBadness(CalcBad(mesh.Points(), el, 0));
      totalbad_local += el.GetBadness();
      maxbad_local = max(maxbad_local, static_cast<double>(el.GetBadness()));
    }
    AtomicAdd(totalbad, totalbad_local);
    AtomicMax(maxbad, maxbad_local);
  });
  return {totalbad, maxbad};
}

bool MeshOptimize3d :: HasBadElement(FlatArray<ElementIndex> els)
{
  for(auto ei : els)
    if(mesh[ei].GetBadness()>min_badness)
      return true;
  return false;
}

bool MeshOptimize3d :: HasIllegalElement(FlatArray<ElementIndex> els)
{
  for(auto ei : els)
    if(!mesh.LegalTet(mesh[ei]))
      return true;
  return false;
}


/*
  Combine two points to one.
  Set new point into the center, if both are
  inner points.
  Connect inner point to boundary point, if one
  point is inner point.
*/
double MeshOptimize3d :: CombineImproveEdge (
                            Table<ElementIndex, PointIndex> & elements_of_point,
                            PointIndex pi0, PointIndex pi1,
                            FlatArray<bool, PointIndex> is_point_removed,
                            bool check_only)
{
  if (pi1 < pi0) Swap (pi0, pi1);
  if(is_point_removed[pi0] || is_point_removed[pi1]) return false;

  MeshPoint p0 = mesh[pi0];
  MeshPoint p1 = mesh[pi1];

  if (p1.Type() != INNERPOINT)
      return false;

  ArrayMem<ElementIndex, 50> has_one_point;
  ArrayMem<ElementIndex, 50> has_both_points;

  for (auto ei : elements_of_point[pi0] )
  {
      Element & elem = mesh[ei];
      if (elem.IsDeleted()) return false;
      if(elem.GetType() != TET) return false; // TODO: implement case where pi0 or pi1 is top of a pyramid

      if (elem[0] == pi1 || elem[1] == pi1 || elem[2] == pi1 || elem[3] == pi1)
      {
          if(!has_both_points.Contains(ei))
            has_both_points.Append (ei);
      }
      else
      {
          if(!has_one_point.Contains(ei))
              has_one_point.Append (ei);
      }
  }

  for (auto ei : elements_of_point[pi1] )
  {
      Element & elem = mesh[ei];
      if (elem.IsDeleted()) return false;

      if (elem[0] == pi0 || elem[1] == pi0 || elem[2] == pi0 || elem[3] == pi0)
      {
          ;
      }
      else
      {
          if(!has_one_point.Contains(ei))
            has_one_point.Append (ei);
      }
  }

  double badness_old = 0.0;
  for (auto ei : has_one_point)
      badness_old += mesh[ei].GetBadness();
  for (auto ei : has_both_points)
      badness_old += mesh[ei].GetBadness();

  MeshPoint pnew = p0;
  if (p0.Type() == INNERPOINT)
      pnew = Center (p0, p1);

  ArrayMem<double, 50> one_point_badness(has_one_point.Size());

  double badness_new = 0;
  for (auto i : Range(has_one_point))
  {
      const Element & elem = mesh[has_one_point[i]];
      double badness = CalcBadReplacePoints (mesh.Points(), mp, elem, 0, pi0, pi1, pnew);
      badness_new += badness;
      one_point_badness[i] = badness;
  }

  // Check if changed tets are topologically legal
  if (p0.Type() != INNERPOINT)
  {
      for (auto ei : has_one_point)
      {
          Element elem = mesh[ei];
          // int l;
          for (int l = 0; l < 4; l++)
              if (elem[l] == pi1)
              {
                  elem[l] = pi0;
                  break;
              }

          elem.Touch();
          if (!mesh.LegalTet(elem))
              badness_new += 1e4;
      }
  }

  double d_badness = badness_new / has_one_point.Size() - badness_old / (has_one_point.Size()+has_both_points.Size());

  // Do the actual combine operation
  if (d_badness < 0.0 && !check_only)
  {
      is_point_removed[pi1] = true;
      mesh[pi0] = pnew;

      for (auto ei : elements_of_point[pi1])
      {
          Element & elem = mesh[ei];
          if (elem.IsDeleted()) continue;

          for (int l = 0; l < elem.GetNP(); l++)
              if (elem[l] == pi1)
                  elem[l] = pi0;

          elem.Touch();
          if (!mesh.LegalTet (elem))
              (*testout) << "illegal tet " << ei << endl;
      }

      for (auto i : Range(has_one_point))
          mesh[has_one_point[i]].SetBadness(one_point_badness[i]);

      for (auto ei : has_both_points)
      {
          mesh[ei].Touch();
          mesh[ei].Delete();
      }
  }

  return d_badness;
}

void MeshOptimize3d :: CombineImprove ()
{
  static Timer t("MeshOptimize3d::CombineImprove"); RegionTimer reg(t);
  static Timer topt("Optimize");
  static Timer tsearch("Search");
  static Timer tbuild_elements_table("Build elements table");

  mesh.BuildBoundaryEdges(false);
  
  int np = mesh.GetNP();
  int ne = mesh.GetNE();
  int ntasks = 4*ngcore::TaskManager::GetNumThreads();

  Array<bool, PointIndex> is_point_removed (np);
  is_point_removed = false;

  PrintMessage (3, "CombineImprove");
  (*testout)  << "Start CombineImprove" << "\n";

  //  mesh.CalcSurfacesOfNode ();
  const char * savetask = multithread.task;
  multithread.task = "Optimize Volume: Combine Improve";


  UpdateBadness();

  if (goal == OPT_QUALITY && testout->good())
    {
      double totalbad = mesh.CalcTotalBad (mp);
      (*testout) << "Total badness = " << totalbad << endl;
    }

  auto elementsonnode = mesh.CreatePoint2ElementTable(nullopt, mp.only3D_domain_nr);

  Array<std::tuple<PointIndex,PointIndex>> edges;
  BuildEdgeList(mesh, elementsonnode, edges);

  // Find edges with improvement
  Array<std::tuple<double, int>> combine_candidate_edges(edges.Size());
  std::atomic<int> improvement_counter(0);

  tsearch.Start();
  ParallelForRange(Range(edges), [&] (auto myrange)
  {
    for(auto i : myrange)
    {
      auto [p0,p1] = edges[i];
      double d_badness = CombineImproveEdge (elementsonnode, p0, p1, is_point_removed, true);
      if(d_badness<0.0)
      {
        int index = improvement_counter++;
        combine_candidate_edges[index] = make_tuple(d_badness, i);
      }
    }
  }, ntasks);
  tsearch.Stop();

  auto edges_with_improvement = combine_candidate_edges.Part(0, improvement_counter.load());

  QuickSort(edges_with_improvement);
  PrintMessage(5, edges.Size(), " edges");
  PrintMessage(5, edges_with_improvement.Size(), " edges with improvement");

  // Apply actual optimizations
  topt.Start();
  int cnt = 0;
  for(auto [d_badness, ei] : edges_with_improvement)
  {
      auto [p0,p1] = edges[ei];
      if (CombineImproveEdge (elementsonnode, p0, p1, is_point_removed, false) < 0.0)
        cnt++;
  }
  topt.Stop();

  mesh.Compress();
  mesh.MarkIllegalElements();

  PrintMessage (5, cnt, " elements combined");
  (*testout) << "CombineImprove done" << "\n";

  if (goal == OPT_QUALITY && testout->good())
    {
      double totalbad = mesh.CalcTotalBad (mp);
      (*testout) << "Total badness = " << totalbad << endl;

      int cntill = 0;
      for (ElementIndex ei = 0; ei < ne; ei++)
	if(!(mesh.GetDimension()==3 && mp.only3D_domain_nr && mp.only3D_domain_nr != mesh.VolumeElement(ei).GetIndex()))
	  if (!mesh.LegalTet (mesh[ei]))
	    cntill++;

      PrintMessage (5, cntill, " illegal tets");
    }
  multithread.task = savetask;
} 



double MeshOptimize3d :: SplitImproveEdge (Table<ElementIndex,PointIndex> & elementsonnode, NgArray<INDEX_3> &locfaces, double badmax, PointIndex pi1, PointIndex pi2, PointIndex ptmp, bool check_only)
{
  double d_badness = 0.0;
  // int cnt = 0;

  ArrayMem<ElementIndex, 20> hasbothpoints;

  if (mesh.BoundaryEdge (pi1, pi2)) return 0.0;

  for (ElementIndex ei : elementsonnode[pi1])
    {
      Element & el = mesh[ei];

      if(el.IsDeleted()) return 0.0;
      if (mesh[ei].GetType() != TET) return 0.0;

      bool has1 = el.PNums().Contains(pi1);
      bool has2 = el.PNums().Contains(pi2);

      if (has1 && has2)
          if (!hasbothpoints.Contains (ei))
              hasbothpoints.Append (ei);
    }

  if(mp.only3D_domain_nr)
      for(auto ei : hasbothpoints)
          if(mp.only3D_domain_nr != mesh[ei].GetIndex())
              return 0.0;

  if ((goal == OPT_LEGAL) && !HasIllegalElement(hasbothpoints))
    return 0.0;

  double bad1 = 0.0;
  double bad1_max = 0.0;
  for (ElementIndex ei : hasbothpoints)
    {
      double bad = mesh[ei].GetBadness();
      bad1 += bad;
      bad1_max = max(bad1_max, bad);
    }

  if(bad1_max < 100.0)
      return 0.0;

  bool puretet = 1;
  for (ElementIndex ei : hasbothpoints)
      if (mesh[ei].GetType() != TET)
          puretet = 0;
  if (!puretet) return 0.0;

  Point3d p1 = mesh[pi1];
  Point3d p2 = mesh[pi2];

  locfaces.SetSize(0);
  for (ElementIndex ei : hasbothpoints)
    {
      const Element & el = mesh[ei];

      for (int l = 0; l < 4; l++)
          if (el[l] == pi1 || el[l] == pi2)
            {
              INDEX_3 i3;
              Element2d face(TRIG);
              el.GetFace (l+1, face);
              for (int kk = 1; kk <= 3; kk++)
                  i3.I(kk) = face.PNum(kk);
              locfaces.Append (i3);
            }
    }

  PointFunction1 pf (mesh.Points(), locfaces, mp, -1);
  OptiParameters par;
  par.maxit_linsearch = 50;
  par.maxit_bfgs = 20;

  Point3d pnew = Center (p1, p2);
  Vector px(3);
  px(0) = pnew.X();
  px(1) = pnew.Y();
  px(2) = pnew.Z();

  if (bad1_max > 0.1 * badmax)
    {
      int pok = pf.Func (px) < 1e10;
      if (!pok)
          pok = FindInnerPoint (mesh.Points(), locfaces, pnew);

      if(pok)
        {
          px(0) = pnew.X();
          px(1) = pnew.Y();
          px(2) = pnew.Z();
          BFGS (px, pf, par);
          pnew.X() = px(0);
          pnew.Y() = px(1);
          pnew.Z() = px(2);
        }
    }

  double bad2 = pf.Func (px);

  mesh[ptmp] = Point<3>(pnew);

  for (int k = 0; k < hasbothpoints.Size(); k++)
    {
      Element & oldel = mesh[hasbothpoints[k]];
      Element newel1 = oldel;
      Element newel2 = oldel;

      newel1.Touch();
      newel2.Touch();

      for (int l = 0; l < 4; l++)
        {
          if (newel1[l] == pi2) newel1[l] = ptmp;
          if (newel2[l] == pi1) newel2[l] = ptmp;
        }

      if (!mesh.LegalTet (oldel)) bad1 += 1e6;
      if (!mesh.LegalTet (newel1)) bad2 += 1e6;
      if (!mesh.LegalTet (newel2)) bad2 += 1e6;
    }

  d_badness = bad2-bad1;
  if(check_only)
      return d_badness;

  if (d_badness<0.0)
    {
      // cnt++;

      PointIndex pinew = mesh.AddPoint (pnew);

      for (ElementIndex ei : hasbothpoints)
        {
          Element & oldel = mesh[ei];
          Element newel1 = oldel;
          Element newel2 = oldel;

          oldel.Touch();
          oldel.Delete();

          newel1.Touch();
          newel2.Touch();

          for (int l = 0; l < 4; l++)
            {
              if (newel1[l] == pi2) newel1[l] = pinew;
              if (newel2[l] == pi1) newel2[l] = pinew;
            }

          mesh.AddVolumeElement (newel1);
          mesh.AddVolumeElement (newel2);
        }
    }
  return d_badness;
}

void MeshOptimize3d :: SplitImprove ()
{
  static Timer t("MeshOptimize3d::SplitImprove"); RegionTimer reg(t);
  static Timer topt("Optimize");
  static Timer tsearch("Search");

  // int np = mesh.GetNP();
  int ne = mesh.GetNE();
  double bad = 0.0;
  double badmax = 0.0;

  auto elementsonnode = mesh.CreatePoint2ElementTable(nullopt, mp.only3D_domain_nr);

  const char * savetask = multithread.task;
  multithread.task = "Optimize Volume: Split Improve";

  PrintMessage (3, "SplitImprove");
  (*testout)  << "start SplitImprove" << "\n";
  mesh.BuildBoundaryEdges(false);

  UpdateBadness();

  if (goal == OPT_QUALITY && testout->good())
    {
      bad = mesh.CalcTotalBad (mp);
      (*testout) << "Total badness = " << bad << endl;
    }

  Array<std::tuple<PointIndex,PointIndex>> edges;
  BuildEdgeList(mesh, elementsonnode, edges);

  // Find edges with improvement
  Array<std::tuple<double, int>> candidate_edges(edges.Size());
  std::atomic<int> improvement_counter(0);
  auto ptmp = mesh.AddPoint( {0,0,0} );

  tsearch.Start();
  ParallelForRange(Range(edges), [&] (auto myrange)
  {
    NgArray<INDEX_3> locfaces;

    for(auto i : myrange)
    {
      auto [p0,p1] = edges[i];
      double d_badness = SplitImproveEdge (elementsonnode, locfaces, badmax, p0, p1, ptmp, true);
      if(d_badness<0.0)
      {
        int index = improvement_counter++;
        candidate_edges[index] = make_tuple(d_badness, i);
      }
    }
  }, ngcore::TasksPerThread(4));
  tsearch.Stop();

  auto edges_with_improvement = candidate_edges.Part(0, improvement_counter.load());

  QuickSort(edges_with_improvement);
  PrintMessage(5, edges.Size(), " edges");
  PrintMessage(5, edges_with_improvement.Size(), " edges with improvement");

  // Apply actual optimizations
  topt.Start();
  int cnt = 0;
  NgArray<INDEX_3> locfaces;
  for(auto [d_badness, ei] : edges_with_improvement)
  {
      auto [p0,p1] = edges[ei];
      if (SplitImproveEdge (elementsonnode, locfaces, badmax, p0, p1, ptmp, false) < 0.0)
        cnt++;
  }
  topt.Stop();
  mesh.Compress();
  PrintMessage (5, cnt, " splits performed");
  (*testout) << "Splitt - Improve done" << "\n";

  if (goal == OPT_QUALITY)
    {
      if(testout->good())
      {
        bad = mesh.CalcTotalBad (mp);
        (*testout) << "Total badness = " << bad << endl;
      }

      [[maybe_unused]] int cntill = 0;
      ne = mesh.GetNE();
      for (ElementIndex ei = 0; ei < ne; ei++)
        if (!mesh.LegalTet (mesh[ei]))
          cntill++;
      //      cout << cntill << " illegal tets" << endl;
    }

  multithread.task = savetask;
}


double MeshOptimize3d :: SwapImproveEdge (
        const NgBitArray * working_elements,
        Table<ElementIndex, PointIndex> & elementsonnode,
        INDEX_3_HASHTABLE<int> & faces,
        PointIndex pi1, PointIndex pi2, bool check_only)
{
  PointIndex pi3(PointIndex::INVALID), pi4(PointIndex::INVALID),
             pi5(PointIndex::INVALID), pi6(PointIndex::INVALID);

  double bad1, bad2, bad3;

  Element el21(TET), el22(TET), el31(TET), el32(TET), el33(TET);
  Element el1(TET), el2(TET), el3(TET), el4(TET);
  Element el1b(TET), el2b(TET), el3b(TET), el4b(TET);
  ArrayMem<ElementIndex, 20> hasbothpoints;

  double d_badness = 0.0;
  if (pi2 < pi1) Swap (pi1, pi2);

  if (mesh.BoundaryEdge (pi1, pi2)) return 0.0;


  hasbothpoints.SetSize (0);
  for (ElementIndex elnr : elementsonnode[pi1])
    {
      bool has1 = 0, has2 = 0;
      const Element & elem = mesh[elnr];

      if (elem.IsDeleted()) return 0.0;

      for (int l = 0; l < elem.GetNP(); l++)
        {
          if (elem[l] == pi1) has1 = 1;
          if (elem[l] == pi2) has2 = 1;
        }

      if (has1 && has2)
        { // only once
          if (hasbothpoints.Contains (elnr))
              has1 = false;

          if (has1)
            {
              hasbothpoints.Append (elnr);
            }
        }
    }

  for (ElementIndex ei : hasbothpoints)
    {
      if (mesh[ei].GetType () != TET)
          return 0.0;

      if (mp.only3D_domain_nr && mp.only3D_domain_nr != mesh.VolumeElement(ei).GetIndex())
          return 0.0;


      if ((mesh.ElementType(ei)) == FIXEDELEMENT)
          return 0.0;

      if(working_elements &&
              ei < working_elements->Size() &&
              !working_elements->Test(ei))
          return 0.0;

      if (mesh[ei].IsDeleted())
          return 0.0;
    }

  if ((goal == OPT_LEGAL) && !HasIllegalElement(hasbothpoints))
    return 0.0;

  int nsuround = hasbothpoints.Size();
  int mattyp = mesh[hasbothpoints[0]].GetIndex();

  if ( nsuround == 3 )
    {
      Element & elem = mesh[hasbothpoints[0]];
      for (int l = 0; l < 4; l++)
          if (elem[l] != pi1 && elem[l] != pi2)
            {
              pi4 = pi3;
              pi3 = elem[l];
            }

      el31[0] = pi1;
      el31[1] = pi2;
      el31[2] = pi3;
      el31[3] = pi4;
      el31.SetIndex (mattyp);

      if (WrongOrientation (mesh.Points(), el31))
        {
          Swap (pi3, pi4);
          el31[2] = pi3;
          el31[3] = pi4;
        }

      pi5.Invalidate();
      for (int k = 0; k < 3; k++)   // JS, 201212
        {
          const Element & elemk = mesh[hasbothpoints[k]];
          bool has1 = false;
          for (int l = 0; l < 4; l++)
              if (elemk[l] == pi4)
                  has1 = true;
          if (has1)
            {
              for (int l = 0; l < 4; l++)
                  if (elemk[l] != pi1 && elemk[l] != pi2 && elemk[l] != pi4)
                      pi5 = elemk[l];
            }
        }

      if (!pi5.IsValid())
          throw NgException("Illegal state observed in SwapImprove");


      el32[0] = pi1;
      el32[1] = pi2;
      el32[2] = pi4;
      el32[3] = pi5;
      el32.SetIndex (mattyp);

      el33[0] = pi1;
      el33[1] = pi2;
      el33[2] = pi5;
      el33[3] = pi3;
      el33.SetIndex (mattyp);

      bad1 = CalcBad (mesh.Points(), el31, 0) +
          CalcBad (mesh.Points(), el32, 0) +
          CalcBad (mesh.Points(), el33, 0);

      el31.Touch();
      el32.Touch();
      el33.Touch();

      if (!mesh.LegalTet(el31) ||
              !mesh.LegalTet(el32) ||
              !mesh.LegalTet(el33))
          bad1 += 1e4;

      el21[0] = pi3;
      el21[1] = pi4;
      el21[2] = pi5;
      el21[3] = pi2;
      el21.SetIndex (mattyp);

      el22[0] = pi5;
      el22[1] = pi4;
      el22[2] = pi3;
      el22[3] = pi1;
      el22.SetIndex (mattyp);

      bad2 = CalcBad (mesh.Points(), el21, 0) +
          CalcBad (mesh.Points(), el22, 0);

      el21.Touch();
      el22.Touch();

      if (!mesh.LegalTet(el21) ||
              !mesh.LegalTet(el22))
          bad2 += 1e4;


      if ((goal == OPT_CONFORM) && NotTooBad(bad1, bad2))
        {
          INDEX_3 face(pi3, pi4, pi5);
          face.Sort();
          if (faces.Used(face))
            {
              // (*testout) << "3->2 swap, could improve conformity, bad1 = " << bad1
              //				 << ", bad2 = " << bad2 << endl;
                bad2 = bad1 + IMPROVEMENT_CONFORMING_EDGE;
            }
        }

      if (bad2 < bad1)
        {
          //		  (*mycout) << "3->2 " << flush;
          //		  (*testout) << "3->2 conversion" << endl;
          d_badness = bad2-bad1;
          if(check_only)
              return d_badness;


          /*
             (*testout) << "3->2 swap, old els = " << endl
             << mesh[hasbothpoints[0]] << endl
             << mesh[hasbothpoints[1]] << endl
             << mesh[hasbothpoints[2]] << endl
             << "new els = " << endl
             << el21 << endl
             << el22 << endl;
             */

          mesh[hasbothpoints[0]].Delete();
          mesh[hasbothpoints[1]].Delete();
          mesh[hasbothpoints[2]].Delete();

          el21.Touch();
          el22.Touch();
          mesh.AddVolumeElement(el21);
          mesh.AddVolumeElement(el22);
        }
    }

  if (nsuround == 4)
    {
      const Element & elem1 = mesh[hasbothpoints[0]];
      for (int l = 0; l < 4; l++)
          if (elem1[l] != pi1 && elem1[l] != pi2)
            {
              pi4 = pi3;
              pi3 = elem1[l];
            }

      el1[0] = pi1; el1[1] = pi2;
      el1[2] = pi3; el1[3] = pi4;
      el1.SetIndex (mattyp);

      if (WrongOrientation (mesh.Points(), el1))
        {
          Swap (pi3, pi4);
          el1[2] = pi3;
          el1[3] = pi4;
        }

      pi5.Invalidate();
      for (int k = 0; k < 4; k++)
        {
          const Element & elem = mesh[hasbothpoints[k]];
          bool has1 = elem.PNums().Contains(pi4);
          if (has1)
            {
              for (int l = 0; l < 4; l++)
                  if (elem[l] != pi1 && elem[l] != pi2 && elem[l] != pi4)
                      pi5 = elem[l];
            }
        }

      pi6.Invalidate();
      for (int k = 0; k < 4; k++)
        {
          const Element & elem = mesh[hasbothpoints[k]];
          bool has1 = elem.PNums().Contains(pi3);
          if (has1)
            {
              for (int l = 0; l < 4; l++)
                  if (elem[l] != pi1 && elem[l] != pi2 && elem[l] != pi3)
                      pi6 = elem[l];
            }
        }

      el1[0] = pi1; el1[1] = pi2;
      el1[2] = pi3; el1[3] = pi4;
      el1.SetIndex (mattyp);

      el2[0] = pi1; el2[1] = pi2;
      el2[2] = pi4; el2[3] = pi5;
      el2.SetIndex (mattyp);

      el3[0] = pi1; el3[1] = pi2;
      el3[2] = pi5; el3[3] = pi6;
      el3.SetIndex (mattyp);

      el4[0] = pi1; el4[1] = pi2;
      el4[2] = pi6; el4[3] = pi3;
      el4.SetIndex (mattyp);

      bad1 = CalcBad (mesh.Points(), el1, 0) +
          CalcBad (mesh.Points(), el2, 0) +
          CalcBad (mesh.Points(), el3, 0) +
          CalcBad (mesh.Points(), el4, 0);


      el1.Touch();
      el2.Touch();
      el3.Touch();
      el4.Touch();


      if (goal != OPT_CONFORM)
        {
          if (!mesh.LegalTet(el1) ||
                  !mesh.LegalTet(el2) ||
                  !mesh.LegalTet(el3) ||
                  !mesh.LegalTet(el4))
              bad1 += 1e4;
        }

      el1[0] = pi3; el1[1] = pi5;
      el1[2] = pi2; el1[3] = pi4;
      el1.SetIndex (mattyp);

      el2[0] = pi3; el2[1] = pi5;
      el2[2] = pi4; el2[3] = pi1;
      el2.SetIndex (mattyp);

      el3[0] = pi3; el3[1] = pi5;
      el3[2] = pi1; el3[3] = pi6;
      el3.SetIndex (mattyp);

      el4[0] = pi3; el4[1] = pi5;
      el4[2] = pi6; el4[3] = pi2;  	
      el4.SetIndex (mattyp);

      bad2 = CalcBad (mesh.Points(), el1, 0) +
          CalcBad (mesh.Points(), el2, 0) +
          CalcBad (mesh.Points(), el3, 0) +
          CalcBad (mesh.Points(), el4, 0);

      el1.Touch();
      el2.Touch();
      el3.Touch();
      el4.Touch();

      if (goal != OPT_CONFORM)
        {
          if (!mesh.LegalTet(el1) ||
                  !mesh.LegalTet(el2) ||
                  !mesh.LegalTet(el3) ||
                  !mesh.LegalTet(el4))
              bad2 += 1e4;
        }


      el1b[0] = pi4; el1b[1] = pi6;
      el1b[2] = pi3; el1b[3] = pi2;
      el1b.SetIndex (mattyp);

      el2b[0] = pi4; el2b[1] = pi6;
      el2b[2] = pi2; el2b[3] = pi5;
      el2b.SetIndex (mattyp);

      el3b[0] = pi4; el3b[1] = pi6;
      el3b[2] = pi5; el3b[3] = pi1;
      el3b.SetIndex (mattyp);

      el4b[0] = pi4; el4b[1] = pi6;
      el4b[2] = pi1; el4b[3] = pi3;
      el4b.SetIndex (mattyp);

      bad3 = CalcBad (mesh.Points(), el1b, 0) +
          CalcBad (mesh.Points(), el2b, 0) +
          CalcBad (mesh.Points(), el3b, 0) +
          CalcBad (mesh.Points(), el4b, 0);

      el1b.Touch();
      el2b.Touch();
      el3b.Touch();
      el4b.Touch();

      if (goal != OPT_CONFORM)
        {
          if (!mesh.LegalTet(el1b) ||
                  !mesh.LegalTet(el2b) ||
                  !mesh.LegalTet(el3b) ||
                  !mesh.LegalTet(el4b))
              bad3 += 1e4;
        }

      bool swap2, swap3;

      if (goal == OPT_CONFORM)
        {
          swap2 = mesh.BoundaryEdge (pi3, pi5) && NotTooBad(bad1, bad2);
          swap3 = mesh.BoundaryEdge (pi4, pi6) && NotTooBad(bad1, bad3);

          if(swap2 || swap3)
            d_badness = IMPROVEMENT_CONFORMING_EDGE;
        }

      if (goal != OPT_CONFORM || (!swap2 && !swap3))
        {
          swap2 = (bad2 < bad1) && (bad2 < bad3);
          swap3 = !swap2 && (bad3 < bad1);
          d_badness = swap2 ? bad2-bad1 : bad3-bad1;
        }

      if(check_only)
          return d_badness;

      if (swap2)
        {
          for (auto i : IntRange(4))
              mesh[hasbothpoints[i]].Delete();

          el1.Touch();
          el2.Touch();
          el3.Touch();
          el4.Touch();
          mesh.AddVolumeElement (el1);
          mesh.AddVolumeElement (el2);
          mesh.AddVolumeElement (el3);
          mesh.AddVolumeElement (el4);
        }
      else if (swap3)
        {
          for (auto i : IntRange(4))
              mesh[hasbothpoints[i]].Delete();

          el1b.Touch();
          el2b.Touch();
          el3b.Touch();
          el4b.Touch();
          mesh.AddVolumeElement (el1b);
          mesh.AddVolumeElement (el2b);
          mesh.AddVolumeElement (el3b);
          mesh.AddVolumeElement (el4b);
        }
    }

  // if (goal == OPT_QUALITY)
  if (nsuround >= 5)
    {
      Element hel(TET);

      NgArrayMem<PointIndex, 50> suroundpts(nsuround);
      NgArrayMem<bool, 50> tetused(nsuround);

      Element & elem = mesh[hasbothpoints[0]];

      for (int l = 0; l < 4; l++)
          if (elem[l] != pi1 && elem[l] != pi2)
            {
              pi4 = pi3;
              pi3 = elem[l];
            }

      hel[0] = pi1;
      hel[1] = pi2;
      hel[2] = pi3;
      hel[3] = pi4;
      hel.SetIndex (mattyp);

      if (WrongOrientation (mesh.Points(), hel))
        {
          Swap (pi3, pi4);
          hel[2] = pi3;
          hel[3] = pi4;
        }


      // suroundpts.SetSize (nsuround);
      suroundpts = PointIndex::INVALID;
      suroundpts[0] = pi3;
      suroundpts[1] = pi4;

      tetused = false;
      tetused[0] = true;

      for (int l = 2; l < nsuround; l++)
        {
          PointIndex oldpi = suroundpts[l-1];
          PointIndex newpi;
          newpi.Invalidate();

          for (int k = 0; k < nsuround && !newpi.IsValid(); k++)
              if (!tetused[k])
                {
                  const Element & nel = mesh[hasbothpoints[k]];
                  for (int k2 = 0; k2 < 4 && !newpi.IsValid(); k2++)
                      if (nel[k2] == oldpi)
                        {
                          newpi =
                              nel[0] + nel[1] + nel[2] + nel[3]
                              - pi1 - pi2 - oldpi;

                          tetused[k] = true;
                          suroundpts[l] = newpi;
                        }
                }
        }


      bad1 = 0;
      for (int k = 0; k < nsuround; k++)
        {
          hel[0] = pi1;
          hel[1] = pi2;
          hel[2] = suroundpts[k];
          hel[3] = suroundpts[(k+1) % nsuround];
          hel.SetIndex (mattyp);

          bad1 += CalcBad (mesh.Points(), hel, 0);
        }

      //  (*testout) << "nsuround = " << nsuround << " bad1 = " << bad1 << endl;


      int bestl = -1;
      int confface = -1;
      int confedge = -1;
      double badopt = bad1;

      for (int l = 0; l < nsuround; l++)
        {
          bad2 = 0;

          for (int k = l+1; k <= nsuround + l - 2; k++)
            {
              hel[0] = suroundpts[l];
              hel[1] = suroundpts[k % nsuround];
              hel[2] = suroundpts[(k+1) % nsuround];
              hel[3] = pi2;

              bad2 += CalcBad (mesh.Points(), hel, 0);
              hel.Touch();
              if (!mesh.LegalTet(hel)) bad2 += 1e4;

              hel[2] = suroundpts[k % nsuround];
              hel[1] = suroundpts[(k+1) % nsuround];
              hel[3] = pi1;

              bad2 += CalcBad (mesh.Points(), hel, 0);

              hel.Touch();
              if (!mesh.LegalTet(hel)) bad2 += 1e4;
            }
          // (*testout) << "bad2," << l << " = " << bad2 << endl;

          if ( bad2 < badopt )
            {
              bestl = l;
              badopt = bad2;
            }


          if (goal == OPT_CONFORM)
            {
              bool nottoobad = NotTooBad(bad1, bad2);

              for (int k = l+1; k <= nsuround + l - 2; k++)
                {
                  INDEX_3 hi3(suroundpts[l],
                          suroundpts[k % nsuround],
                          suroundpts[(k+1) % nsuround]);
                  hi3.Sort();
                  if (faces.Used(hi3))
                    {
                      // (*testout) << "could improve face conformity, bad1 = " << bad1
                      // << ", bad 2 = " << bad2 << ", nottoobad = " << nottoobad << endl;
                      if (nottoobad)
                          confface = l;
                    }
                }

              for (int k = l+2; k <= nsuround+l-2; k++)
                {
                  if (mesh.BoundaryEdge (suroundpts[l],
                              suroundpts[k % nsuround]))
                    {
                      /*
                       *testout << "could improve edge conformity, bad1 = " << bad1
                       << ", bad 2 = " << bad2 << ", nottoobad = " << nottoobad << endl;
                       */
                      if (nottoobad)
                          confedge = l;
                    }
                }
            }
        }

      if (confedge != -1)
          bestl = confedge;
      if (confface != -1)
          bestl = confface;

      if(confface != -1 || confedge != -1)
          badopt = bad1 + IMPROVEMENT_CONFORMING_EDGE;

      if (bestl != -1)
        {
          // (*mycout) << nsuround << "->" << 2 * (nsuround-2) << " " << flush;
          d_badness = badopt-bad1;
          if(check_only)
              return d_badness;

          for (int k = bestl+1; k <= nsuround + bestl - 2; k++)
            {
              // int k1;

              hel[0] = suroundpts[bestl];
              hel[1] = suroundpts[k % nsuround];
              hel[2] = suroundpts[(k+1) % nsuround];
              hel[3] = pi2;
              hel.Touch();

              /*
                 (*testout) << nsuround << "-swap, new el,top = "
                 << hel << endl;
                 */
              mesh.AddVolumeElement (hel);

              hel[2] = suroundpts[k % nsuround];
              hel[1] = suroundpts[(k+1) % nsuround];
              hel[3] = pi1;

              /*
                 (*testout) << nsuround << "-swap, new el,bot = "
                 << hel << endl;
                 */

              mesh.AddVolumeElement (hel);
            }

          for (int k = 0; k < nsuround; k++)
            {
              Element & rel = mesh[hasbothpoints[k]];
              /*
                 (*testout) << nsuround << "-swap, old el = "
                 << rel << endl;
                 */
              rel.Delete();
              for (int k1 = 0; k1 < 4; k1++)
                  rel[k1].Invalidate();
            }
        }
    }
  return d_badness;
}

void MeshOptimize3d :: SwapImprove (const NgBitArray * working_elements)
{
  static Timer t("MeshOptimize3d::SwapImprove"); RegionTimer reg(t);
  static Timer tloop("MeshOptimize3d::SwapImprove loop");

  int cnt = 0;

  // int np = mesh.GetNP();
  // int ne = mesh.GetNE();

  mesh.BuildBoundaryEdges(false);
  BitArray free_points(mesh.GetNP()+PointIndex::BASE);
  free_points.Clear();

  ParallelForRange(mesh.VolumeElements().Range(), [&] (auto myrange)
      {
        for (ElementIndex eli : myrange)
          {
            const auto & el = mesh[eli];
            if(el.Flags().fixed)
              continue;

            if(mp.only3D_domain_nr && mp.only3D_domain_nr != el.GetIndex())
              continue;

            for (auto pi : el.PNums())
              if(!free_points[pi])
                  free_points.SetBitAtomic(pi);
          }
      });

  auto elementsonnode = mesh.CreatePoint2ElementTable(free_points, mp.only3D_domain_nr );

  NgArray<ElementIndex> hasbothpoints;

  PrintMessage (3, "SwapImprove ");
  (*testout) << "\n" << "Start SwapImprove" << endl;

  const char * savetask = multithread.task;
  multithread.task = "Optimize Volume: Swap Improve";

  INDEX_3_HASHTABLE<int> faces(mesh.GetNOpenElements()/3 + 2);
  if (goal == OPT_CONFORM)
    {
      for (int i = 1; i <= mesh.GetNOpenElements(); i++)
	{
	  const Element2d & hel = mesh.OpenElement(i);
	  INDEX_3 face(hel[0], hel[1], hel[2]);
	  face.Sort();
	  faces.Set (face, i);
	}
    }

  // Calculate total badness
  if (goal == OPT_QUALITY && testout->good())
    {
      double bad1 = mesh.CalcTotalBad (mp);
      (*testout) << "Total badness = " << bad1 << endl;
    }

  Array<std::tuple<PointIndex,PointIndex>> edges;
  BuildEdgeList(mesh, elementsonnode, edges);

  Array<std::tuple<double, int>> candidate_edges(edges.Size());
  std::atomic<int> improvement_counter(0);

  tloop.Start();

  auto num_elements_before = mesh.VolumeElements().Range().Next();

  ParallelForRange(Range(edges), [&] (auto myrange)
  {
    for(auto i : myrange)
    {
      if (multithread.terminate)
        break;

      auto [pi0, pi1] = edges[i];
      double d_badness = SwapImproveEdge (working_elements, elementsonnode, faces, pi0, pi1, true);
      if(d_badness<0.0)
      {
        int index = improvement_counter++;
        candidate_edges[index] = make_tuple(d_badness, i);
      }
    }
  }, TasksPerThread (4));

  auto edges_with_improvement = candidate_edges.Part(0, improvement_counter.load());
  QuickSort(edges_with_improvement);

  for(auto [d_badness, ei] : edges_with_improvement)
  {
      auto [pi0,pi1] = edges[ei];
      if(SwapImproveEdge (working_elements, elementsonnode, faces, pi0, pi1, false) < 0.0)
          cnt++;
  }

  tloop.Stop();

  PrintMessage (5, cnt, " swaps performed");

  if(goal == OPT_CONFORM)
  {
      // Remove open elements that were closed by new tets
      auto & open_els = mesh.OpenElements();

      for (auto & el : mesh.VolumeElements().Range( num_elements_before, mesh.VolumeElements().Range().Next() ))
      {
          for (auto i : Range(1,5))
          {
              Element2d sel;
              el.GetFace(i, sel);
              INDEX_3 face(sel[0], sel[1], sel[2]);
              face.Sort();
              if(faces.Used(face))
                  open_els[faces.Get(face)-1].Delete();
          }
      }

      for(int i=open_els.Size()-1; i>=0; i--)
          if(open_els[i].IsDeleted())
              open_els.Delete(i);

      mesh.DeleteBoundaryEdges();
  }
  mesh.Compress ();

  multithread.task = savetask;
}
  





void MeshOptimize3d :: SwapImproveSurface (
					   const NgBitArray * working_elements,
					   const NgArray< NgArray<int,PointIndex::BASE>* > * idmaps)
{
  NgArray< NgArray<int,PointIndex::BASE>* > locidmaps;
  const NgArray< NgArray<int,PointIndex::BASE>* > * used_idmaps;

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


  PointIndex pi1, pi2; // , pi3, pi4, pi5, pi6;
  PointIndex pi1other, pi2other;
  int cnt = 0;

  //double bad1, bad2, bad3, sbad;
  double bad1, sbad;
  double h;

  int np = mesh.GetNP();
  int ne = mesh.GetNE();
  int nse = mesh.GetNSE();

  int mattype, othermattype;

  
  // contains at least all elements at node
  TABLE<ElementIndex,PointIndex::BASE> elementsonnode(np);
  TABLE<SurfaceElementIndex,PointIndex::BASE> surfaceelementsonnode(np);
  TABLE<int,PointIndex::BASE> surfaceindicesonnode(np);

  NgArray<ElementIndex> hasbothpoints;
  NgArray<ElementIndex> hasbothpointsother;

  PrintMessage (3, "SwapImproveSurface ");
  (*testout) << "\n" << "Start SwapImproveSurface" << endl;

  const char * savetask = multithread.task;
  multithread.task = "Swap Improve Surface";
    
      
  
  // find elements on node
  for (ElementIndex ei = 0; ei < ne; ei++)
    for (int j = 0; j < mesh[ei].GetNP(); j++)
      elementsonnode.Add (mesh[ei][j], ei);

  for (SurfaceElementIndex sei = 0; sei < nse; sei++)
    for(int j=0; j<mesh[sei].GetNP(); j++)
      {
	surfaceelementsonnode.Add(mesh[sei][j], sei);
	if(!surfaceindicesonnode[mesh[sei][j]].Contains(mesh[sei].GetIndex()))
	  surfaceindicesonnode.Add(mesh[sei][j],mesh[sei].GetIndex());
      }

  bool periodic;
  int idnum(-1);

  // INDEX_2_HASHTABLE<int> edgeused(2 * ne + 5);
  INDEX_2_CLOSED_HASHTABLE<int> edgeused(12 * ne + 5);

  for (ElementIndex ei = 0; ei < ne; ei++)
    {
      if (multithread.terminate)
	break;
      
      multithread.percent = 100.0 * (ei+1) / ne;

      if (mesh.ElementType(ei) == FIXEDELEMENT)
	continue;
      
      if(working_elements && 
	 ei < working_elements->Size() &&
	 !working_elements->Test(ei))
	continue;

      if (mesh[ei].IsDeleted())
	continue;

      if (goal == OPT_LEGAL && mesh.LegalTet (mesh[ei]))
	continue;

      const Element & elemi = mesh[ei];
      //Element elemi = mesh[ei];
      if (elemi.IsDeleted()) continue;


      mattype = elemi.GetIndex();

      bool swapped = false;

      for (int j = 0; !swapped && j < 6; j++)
	{
	  // loop over edges

	  
	  static const int tetedges[6][2] =
	    { { 0, 1 }, { 0, 2 }, { 0, 3 },
	      { 1, 2 }, { 1, 3 }, { 2, 3 } };

	  pi1 = elemi[tetedges[j][0]];
	  pi2 = elemi[tetedges[j][1]];

	  
	  if (pi2 < pi1)
	    Swap (pi1, pi2);
	    	  
	  
	  bool found = false;
	  for(int k=0; !found && k<used_idmaps->Size(); k++)
	    {
	      if(pi2 < (*used_idmaps)[k]->Size() + PointIndex::BASE)
		{
		  pi1other = (*(*used_idmaps)[k])[pi1];
		  pi2other = (*(*used_idmaps)[k])[pi2];
		  found = (pi1other != 0 && pi2other != 0 && pi1other != pi1 && pi2other != pi2);
		  if(found)
		    idnum = k;
		}
	    }
	  if(found)
	    periodic = true;
	  else
	    {
	      periodic = false;
	      pi1other = pi1; pi2other = pi2;
	    }


	 	  
	  if (!mesh.BoundaryEdge (pi1, pi2) ||
	      mesh.IsSegment(pi1, pi2)) continue;

	  othermattype = -1;

	  
	  INDEX_2 i2 (pi1, pi2);
	  i2.Sort();
	  if (edgeused.Used(i2)) continue;
	  edgeused.Set (i2, 1);
	  if(periodic)
	    {
	      i2.I1() = pi1other;
	      i2.I2() = pi2other;
	      i2.Sort();
	      edgeused.Set(i2,1);
	    }
	  
	  
	  hasbothpoints.SetSize (0);
	  hasbothpointsother.SetSize (0);
	  for (int k = 0; k < elementsonnode[pi1].Size(); k++)
	    {
	      bool has1 = false, has2 = false;
	      ElementIndex elnr = elementsonnode[pi1][k];
	      const Element & elem = mesh[elnr];
	      
	      if (elem.IsDeleted()) continue;
	      
	      for (int l = 0; l < elem.GetNP(); l++)
		{
		  if (elem[l] == pi1) has1 = true;
		  if (elem[l] == pi2) has2 = true;
		}

	      if (has1 && has2) 
		{ 
		  if(othermattype == -1 && elem.GetIndex() != mattype)
		    othermattype = elem.GetIndex();

		  if(elem.GetIndex() == mattype)
		    {
		      // only once
		      for (int l = 0; l < hasbothpoints.Size(); l++)
			if (hasbothpoints[l] == elnr)
			  has1 = 0;
		      
		      if (has1)
			hasbothpoints.Append (elnr);
		    }
		  else if(elem.GetIndex() == othermattype)
		    {
		      // only once
		      for (int l = 0; l < hasbothpointsother.Size(); l++)
			if (hasbothpointsother[l] == elnr)
			  has1 = 0;
		      
		      if (has1)
			hasbothpointsother.Append (elnr);
		    }
		  else
		    {
		      cout << "problem with domain indices" << endl;
		      (*testout) << "problem: mattype = " << mattype << ", othermattype = " << othermattype 
				 << " elem " << elem << " mt " << elem.GetIndex() << endl
				 << " pi1 " << pi1 << " pi2 " << pi2 << endl;
		      (*testout) << "hasbothpoints:" << endl;
		      for(int ii=0; ii < hasbothpoints.Size(); ii++)
			(*testout) << mesh[hasbothpoints[ii]] << endl;
		      (*testout) << "hasbothpointsother:" << endl;
		      for(int ii=0; ii < hasbothpointsother.Size(); ii++)
			(*testout) << mesh[hasbothpointsother[ii]] << endl;
		    }
		}
	    }

	  if(hasbothpointsother.Size() > 0 && periodic)
	    throw NgException("SwapImproveSurface: Assumption about interface/periodicity wrong!");

	  if(periodic)
	    {
	      for (int k = 0; k < elementsonnode[pi1other].Size(); k++)
		{
		  bool has1 = false, has2 = false;
		  ElementIndex elnr = elementsonnode[pi1other][k];
		  const Element & elem = mesh[elnr];
	      
		  if (elem.IsDeleted()) continue;
	      
		  for (int l = 0; l < elem.GetNP(); l++)
		    {
		      if (elem[l] == pi1other) has1 = true;
		      if (elem[l] == pi2other) has2 = true;
		    }
		  
		  if (has1 && has2) 
		    { 
		      if(othermattype == -1)
			othermattype = elem.GetIndex();

		      // only once
		      for (int l = 0; l < hasbothpointsother.Size(); l++)
			if (hasbothpointsother[l] == elnr)
			  has1 = 0;
		      
		      if (has1)
			hasbothpointsother.Append (elnr);
		    }
		}
	    }


	  //for(k=0; k<hasbothpoints.Size(); k++)
	  //  (*testout) << "hasbothpoints["<<k<<"]: " << mesh[hasbothpoints[k]] << endl;

	  
	  SurfaceElementIndex sel1=-1,sel2=-1;
	  SurfaceElementIndex sel1other=-1,sel2other=-1;
	  for(int k = 0; k < surfaceelementsonnode[pi1].Size(); k++)
	    {
	      bool has1 = false, has2 = false;
	      SurfaceElementIndex elnr = surfaceelementsonnode[pi1][k];
	      const Element2d & elem = mesh[elnr];

	      if (elem.IsDeleted()) continue;

	      for (int l = 0; l < elem.GetNP(); l++)
		{
		  if (elem[l] == pi1) has1 = true;
		  if (elem[l] == pi2) has2 = true;
		}

	      if(has1 && has2 && elnr != sel2)
		{
		  sel1 = sel2;
		  sel2 = elnr;
		}
	    }

	  if(periodic)
	    {
	      for(int k = 0; k < surfaceelementsonnode[pi1other].Size(); k++)
		{
		  bool has1 = false, has2 = false;
		  SurfaceElementIndex elnr = surfaceelementsonnode[pi1other][k];
		  const Element2d & elem = mesh[elnr];

		  if (elem.IsDeleted()) continue;

		  for (int l = 0; l < elem.GetNP(); l++)
		    {
		      if (elem[l] == pi1other) has1 = true;
		      if (elem[l] == pi2other) has2 = true;
		    }

		  if(has1 && has2 && elnr != sel2other)
		    {
		      sel1other = sel2other;
		      sel2other = elnr;
		    }
		}
	    }
	  else
	    {
	      sel1other = sel1; sel2other = sel2;
	    }

	  //(*testout) << "sel1 " << sel1 << " sel2 " << sel2 << " el " << mesh[sel1] << " resp. " << mesh[sel2] << endl;

	  PointIndex sp1(0), sp2(0);
	  PointIndex sp1other, sp2other;
	  for(int l=0; l<mesh[sel1].GetNP(); l++)
	    if(mesh[sel1][l] != pi1 && mesh[sel1][l] != pi2)
	      sp1 = mesh[sel1][l];
	  for(int l=0; l<mesh[sel2].GetNP(); l++)
	    if(mesh[sel2][l] != pi1 && mesh[sel2][l] != pi2)
	      sp2 = mesh[sel2][l];

	  if(periodic)
	    {
	      sp1other = (*(*used_idmaps)[idnum])[sp1];
	      sp2other = (*(*used_idmaps)[idnum])[sp2];

	      bool change = false;
	      for(int l=0; !change && l<mesh[sel1other].GetNP(); l++)
		change = (sp2other == mesh[sel1other][l]);
	      
	      if(change)
		{
		  SurfaceElementIndex aux = sel1other;
		  sel1other = sel2other;
		  sel2other = aux;
		}

	    }
	  else
	    {
	      sp1other = sp1; sp2other = sp2;
	    }
	  
	  Vec<3> v1 = mesh[sp1]-mesh[pi1],
	    v2 = mesh[sp2]-mesh[pi1],
	    v3 = mesh[sp1]-mesh[pi2],
	    v4 = mesh[sp2]-mesh[pi2];
	  double vol = 0.5*(Cross(v1,v2).Length() + Cross(v3,v4).Length());
	  h = sqrt(vol);
	  h = 0;

	  sbad = CalcTriangleBadness (mesh[pi1],mesh[pi2],mesh[sp1],0,0) + 
	    CalcTriangleBadness (mesh[pi2],mesh[pi1],mesh[sp2],0,0);
	  


	  bool puretet = true;
	  for (int k = 0; puretet && k < hasbothpoints.Size(); k++)
	    if (mesh[hasbothpoints[k]].GetType () != TET)
	      puretet = false;
	  for (int k = 0; puretet && k < hasbothpointsother.Size(); k++)
	    if (mesh[hasbothpointsother[k]].GetType () != TET)
	      puretet = false;
	  if (!puretet)
	    continue;

	  int nsuround = hasbothpoints.Size();
	  int nsuroundother = hasbothpointsother.Size();

	  NgArray < int > outerpoints(nsuround+1);
	  outerpoints[0] = sp1;

	  for(int i=0; i<nsuround; i++)
	    {
	      bool done = false;
	      for(int jj=i; !done && jj<hasbothpoints.Size(); jj++)
		{
		  for(int k=0; !done && k<4; k++)
		    if(mesh[hasbothpoints[jj]][k] == outerpoints[i])
		      {
			done = true;
			for(int l=0; l<4; l++)
			  if(mesh[hasbothpoints[jj]][l] != pi1 &&
			     mesh[hasbothpoints[jj]][l] != pi2 &&
			     mesh[hasbothpoints[jj]][l] != outerpoints[i])
			    outerpoints[i+1] = mesh[hasbothpoints[jj]][l];
		      }
		  if(done)
		    {
		      ElementIndex aux = hasbothpoints[i];
		      hasbothpoints[i] = hasbothpoints[jj];
		      hasbothpoints[jj] = aux;
		    }
		}
	    }
	  if(outerpoints[nsuround] != sp2)
	    {
	      cerr << "OJE OJE OJE" << endl;
	      (*testout) << "OJE OJE OJE" << endl;
	      (*testout) << "hasbothpoints: " << endl;
	      for(int ii=0; ii < hasbothpoints.Size(); ii++)
		{
		  (*testout) << mesh[hasbothpoints[ii]] << endl;
		  for(int jj=0; jj<mesh[hasbothpoints[ii]].GetNP(); jj++)
		    if(mesh.mlbetweennodes[mesh[hasbothpoints[ii]][jj]][0] > 0)
		      (*testout) << mesh[hasbothpoints[ii]][jj] << " between "
				 << mesh.mlbetweennodes[mesh[hasbothpoints[ii]][jj]][0] << " and "
				 << mesh.mlbetweennodes[mesh[hasbothpoints[ii]][jj]][1] << endl;
		}
	      (*testout) << "outerpoints: " << outerpoints << endl;
	      (*testout) << "sel1 " << mesh[sel1] << endl
			 << "sel2 " << mesh[sel2] << endl;
	      for(int ii=0; ii<3; ii++)
		{
		  if(mesh.mlbetweennodes[mesh[sel1][ii]][0] > 0)
		    (*testout) << mesh[sel1][ii] << " between "
			       << mesh.mlbetweennodes[mesh[sel1][ii]][0] << " and "
			       << mesh.mlbetweennodes[mesh[sel1][ii]][1] << endl;
		  if(mesh.mlbetweennodes[mesh[sel2][ii]][0] > 0)
		    (*testout) << mesh[sel2][ii] << " between "
			       << mesh.mlbetweennodes[mesh[sel2][ii]][0] << " and "
			       << mesh.mlbetweennodes[mesh[sel2][ii]][1] << endl;
		}
	    }

	  
	  NgArray < int > outerpointsother;

	  if(nsuroundother > 0)
	    {
	      outerpointsother.SetSize(nsuroundother+1);
	      outerpointsother[0] = sp2other;
	    }

	  for(int i=0; i<nsuroundother; i++)
	    {
	      bool done = false;
	      for(int jj=i; !done && jj<hasbothpointsother.Size(); jj++)
		{
		  for(int k=0; !done && k<4; k++)
		    if(mesh[hasbothpointsother[jj]][k] == outerpointsother[i])
		      {
			done = true;
			for(int l=0; l<4; l++)
			  if(mesh[hasbothpointsother[jj]][l] != pi1other &&
			     mesh[hasbothpointsother[jj]][l] != pi2other &&
			     mesh[hasbothpointsother[jj]][l] != outerpointsother[i])
			    outerpointsother[i+1] = mesh[hasbothpointsother[jj]][l];
		      }
		  if(done)
		    {
		      ElementIndex aux = hasbothpointsother[i];
		      hasbothpointsother[i] = hasbothpointsother[jj];
		      hasbothpointsother[jj] = aux;
		    }
		}
	    }
	  if(nsuroundother > 0 && outerpointsother[nsuroundother] != sp1other)
	    {
	      cerr << "OJE OJE OJE (other)" << endl;
	      (*testout) << "OJE OJE OJE (other)" << endl;
	      (*testout) << "pi1 " << pi1 << " pi2 " << pi2 << " sp1 " << sp1 << " sp2 " << sp2 << endl;
	      (*testout) << "hasbothpoints: " << endl;
	      for(int ii=0; ii < hasbothpoints.Size(); ii++)
		{
		  (*testout) << mesh[hasbothpoints[ii]] << endl;
		  for(int jj=0; jj<mesh[hasbothpoints[ii]].GetNP(); jj++)
		    if(mesh.mlbetweennodes[mesh[hasbothpoints[ii]][jj]][0] > 0)
		      (*testout) << mesh[hasbothpoints[ii]][jj] << " between "
				 << mesh.mlbetweennodes[mesh[hasbothpoints[ii]][jj]][0] << " and "
				 << mesh.mlbetweennodes[mesh[hasbothpoints[ii]][jj]][1] << endl;
		}
	      (*testout) << "outerpoints: " << outerpoints << endl;
	      (*testout) << "sel1 " << mesh[sel1] << endl
			 << "sel2 " << mesh[sel2] << endl;
	      for(int ii=0; ii<3; ii++)
		{
		  if(mesh.mlbetweennodes[mesh[sel1][ii]][0] > 0)
		    (*testout) << mesh[sel1][ii] << " between "
			       << mesh.mlbetweennodes[mesh[sel1][ii]][0] << " and "
			       << mesh.mlbetweennodes[mesh[sel1][ii]][1] << endl;
		  if(mesh.mlbetweennodes[mesh[sel2][ii]][0] > 0)
		    (*testout) << mesh[sel2][ii] << " between "
			       << mesh.mlbetweennodes[mesh[sel2][ii]][0] << " and "
			       << mesh.mlbetweennodes[mesh[sel2][ii]][1] << endl;
		}
		  
	      (*testout) << "pi1other " << pi1other << " pi2other " << pi2other << " sp1other " << sp1other << " sp2other " << sp2other << endl;
	      (*testout) << "hasbothpointsother: " << endl;
	      for(int ii=0; ii < hasbothpointsother.Size(); ii++)
		{
		  (*testout) << mesh[hasbothpointsother[ii]] << endl;
		  for(int jj=0; jj<mesh[hasbothpointsother[ii]].GetNP(); jj++)
		    if(mesh.mlbetweennodes[mesh[hasbothpointsother[ii]][jj]][0] > 0)
		      (*testout) << mesh[hasbothpointsother[ii]][jj] << " between "
				 << mesh.mlbetweennodes[mesh[hasbothpointsother[ii]][jj]][0] << " and "
				 << mesh.mlbetweennodes[mesh[hasbothpointsother[ii]][jj]][1] << endl;
		}
	      (*testout) << "outerpoints: " << outerpointsother << endl;
	      (*testout) << "sel1other " << mesh[sel1other] << endl
			 << "sel2other " << mesh[sel2other] << endl;
	      for(int ii=0; ii<3; ii++)
		{
		  if(mesh.mlbetweennodes[mesh[sel1other][ii]][0] > 0)
		    (*testout) << mesh[sel1other][ii] << " between "
			       << mesh.mlbetweennodes[mesh[sel1other][ii]][0] << " and "
			       << mesh.mlbetweennodes[mesh[sel1other][ii]][1] << endl;
		  if(mesh.mlbetweennodes[mesh[sel2other][ii]][0] > 0)
		    (*testout) << mesh[sel2other][ii] << " between "
			       << mesh.mlbetweennodes[mesh[sel2other][ii]][0] << " and "
			       << mesh.mlbetweennodes[mesh[sel2other][ii]][1] << endl;
		}
	    }

	  bad1=0;
	  for(int i=0; i<hasbothpoints.Size(); i++)
	    bad1 += CalcBad(mesh.Points(), mesh[hasbothpoints[i]],h);
	  for(int i=0; i<hasbothpointsother.Size(); i++)
	    bad1 += CalcBad(mesh.Points(), mesh[hasbothpointsother[i]],h);
	  bad1 /= double(hasbothpoints.Size() + hasbothpointsother.Size());

	  
	  int startpoints,startpointsother;


	  if(outerpoints.Size() == 3)
	    startpoints = 1;
	  else if(outerpoints.Size() == 4)
	    startpoints = 2;
	  else
	    startpoints = outerpoints.Size();
	  
	  if(outerpointsother.Size() == 3)
	    startpointsother = 1;
	  else if(outerpointsother.Size() == 4)
	    startpointsother = 2;
	  else
	    startpointsother = outerpointsother.Size();
	  

	  NgArray < NgArray < Element* > * > newelts(startpoints);
	  NgArray < NgArray < Element* > * > neweltsother(startpointsother);

	  double minbad = 1e50, minbadother = 1e50, currbad;
	  int minpos = -1, minposother = -1;

	  //(*testout) << "pi1 " << pi1 << " pi2 " << pi2 << " outerpoints " << outerpoints << endl;

	  for(int i=0; i<startpoints; i++)
	    {
	      newelts[i] = new NgArray <Element*>(2*(nsuround-1));
	      
	      for(int jj=0; jj<nsuround-1; jj++)
		{
		  (*newelts[i])[2*jj] = new Element(TET);
		  (*newelts[i])[2*jj+1] = new Element(TET);
		  Element & newel1 = *((*newelts[i])[2*jj]);
		  Element & newel2 = *((*newelts[i])[2*jj+1]);

		  newel1[0] = pi1;
		  newel1[1] = outerpoints[i];
		  newel1[2] = outerpoints[(i+jj+1)%outerpoints.Size()];
		  newel1[3] = outerpoints[(i+jj+2)%outerpoints.Size()];

		  newel2[0] = pi2;
		  newel2[1] = outerpoints[i];
		  newel2[2] = outerpoints[(i+jj+2)%outerpoints.Size()];
		  newel2[3] = outerpoints[(i+jj+1)%outerpoints.Size()];
		  

		  //(*testout) << "j " << j << " newel1 " << newel1[0] << " "<< newel1[1] << " "<< newel1[2] << " "<< newel1[3] << endl
		  //     << " newel2 " << newel2[0] << " "<< newel2[1] << " "<< newel2[2] << " "<< newel2[3] << endl;
		  
		  newel1.SetIndex(mattype);
		  newel2.SetIndex(mattype);

		}

	      bool wrongorientation = true;
	      for(int jj = 0; wrongorientation && jj<newelts[i]->Size(); jj++)
		wrongorientation = wrongorientation && WrongOrientation(mesh.Points(), *(*newelts[i])[jj]);
	      
	      currbad = 0;

	      for(int jj=0; jj<newelts[i]->Size(); jj++)
		{
		  if(wrongorientation)
		    Swap((*(*newelts[i])[jj])[2],(*(*newelts[i])[jj])[3]);


		  // not two new faces on same surface
		  NgArray<int> face_index;
		  for(int k = 0; k<surfaceindicesonnode[(*(*newelts[i])[jj])[0]].Size(); k++)
		    face_index.Append(surfaceindicesonnode[(*(*newelts[i])[jj])[0]][k]);

		  for(int k=1; k<4; k++)
		    {
		      for(int l=0; l<face_index.Size(); l++)
			{
			  if(face_index[l] != -1 && 
			     !(surfaceindicesonnode[(*(*newelts[i])[jj])[k]].Contains(face_index[l])))
			    face_index[l] = -1;
			}

		    }
		      
		  for(int k=0; k<face_index.Size(); k++)
		    if(face_index[k] != -1)
		      currbad += 1e12;


		  currbad += CalcBad(mesh.Points(),*(*newelts[i])[jj],h);


		}  

	      //currbad /= double(newelts[i]->Size());
		    


	      if(currbad < minbad)
		{
		  minbad = currbad;
		  minpos = i;
		}

	    }

	  if(startpointsother == 0)
	    minbadother = 0;

	  for(int i=0; i<startpointsother; i++)
	    {
	      neweltsother[i] = new NgArray <Element*>(2*(nsuroundother));
	      
	      for(int jj=0; jj<nsuroundother; jj++)
		{
		  (*neweltsother[i])[2*jj] = new Element(TET);
		  (*neweltsother[i])[2*jj+1] = new Element(TET);
		  Element & newel1 = *((*neweltsother[i])[2*jj]);
		  Element & newel2 = *((*neweltsother[i])[2*jj+1]);

		  newel1[0] = pi1other;
		  newel1[1] = outerpointsother[i];
		  newel1[2] = outerpointsother[(i+jj+1)%outerpointsother.Size()];
		  newel1[3] = outerpointsother[(i+jj+2)%outerpointsother.Size()];

		  newel2[0] = pi2other;
		  newel2[1] = outerpointsother[i];
		  newel2[2] = outerpointsother[(i+jj+2)%outerpointsother.Size()];
		  newel2[3] = outerpointsother[(i+jj+1)%outerpointsother.Size()];
		  

		  //(*testout) << "j " << j << " newel1 " << newel1[0] << " "<< newel1[1] << " "<< newel1[2] << " "<< newel1[3] << endl
		  //	     << " newel2 " << newel2[0] << " "<< newel2[1] << " "<< newel2[2] << " "<< newel2[3] << endl;
		  
		  newel1.SetIndex(othermattype);
		  newel2.SetIndex(othermattype);

		}

	      bool wrongorientation = true;
	      for(int jj = 0; wrongorientation && jj<neweltsother[i]->Size(); jj++)
		wrongorientation = wrongorientation && WrongOrientation(mesh.Points(), *(*neweltsother[i])[jj]);
	      
	      currbad = 0;

	      for(int jj=0; jj<neweltsother[i]->Size(); jj++)
		{
		  if(wrongorientation)
		    Swap((*(*neweltsother[i])[jj])[2],(*(*neweltsother[i])[jj])[3]);

		  currbad += CalcBad(mesh.Points(),*(*neweltsother[i])[jj],h);
		}  

	      //currbad /= double(neweltsother[i]->Size());
		    


	      if(currbad < minbadother)
		{
		  minbadother = currbad;
		  minposother = i;
		}

	    }

	  //(*testout) << "minbad " << minbad << " bad1 " << bad1 << endl;

	  
	  double sbadnew = CalcTriangleBadness (mesh[pi1],mesh[sp2],mesh[sp1],0,0) + 
	    CalcTriangleBadness (mesh[pi2],mesh[sp1],mesh[sp2],0,0);
	  

	  int denom = newelts[minpos]->Size();
	  if(minposother >= 0)
	    denom += neweltsother[minposother]->Size();
	  

	  if((minbad+minbadother)/double(denom) < bad1 && 
	     sbadnew < sbad)
	    {
	      cnt++;

	      swapped = true;


	      int start1 = -1;
	      for(int l=0; l<3; l++)
		if(mesh[sel1][l] == pi1)
		  start1 = l;
	      if(mesh[sel1][(start1+1)%3] == pi2)
		{
		  mesh[sel1][0] = pi1;
		  mesh[sel1][1] = sp2;
		  mesh[sel1][2] = sp1;
		  mesh[sel2][0] = pi2;
		  mesh[sel2][1] = sp1;
		  mesh[sel2][2] = sp2;
		}
	      else
		{
		  mesh[sel1][0] = pi2;
		  mesh[sel1][1] = sp2;
		  mesh[sel1][2] = sp1;
		  mesh[sel2][0] = pi1;
		  mesh[sel2][1] = sp1;
		  mesh[sel2][2] = sp2;
		}
	      //(*testout) << "changed surface element " << sel1 << " to " << mesh[sel1] << ", " << sel2 << " to " << mesh[sel2] << endl;

	      for(int l=0; l<3; l++)
		{
		  surfaceelementsonnode.Add(mesh[sel1][l],sel1);
		  surfaceelementsonnode.Add(mesh[sel2][l],sel2);
		}
	      


	      if(periodic)
		{
		  start1 = -1;
		  for(int l=0; l<3; l++)
		    if(mesh[sel1other][l] == pi1other)
		      start1 = l;
		  


		  //(*testout) << "changed surface elements " << mesh[sel1other] << " and " << mesh[sel2other] << endl;
		  if(mesh[sel1other][(start1+1)%3] == pi2other)
		    {
		      mesh[sel1other][0] = pi1other;
		      mesh[sel1other][1] = sp2other;
		      mesh[sel1other][2] = sp1other;
		      mesh[sel2other][0] = pi2other;
		      mesh[sel2other][1] = sp1other;
		      mesh[sel2other][2] = sp2other;
		      //(*testout) << "       with rule 1" << endl;
		    }
		  else
		    {
		      mesh[sel1other][0] = pi2other;
		      mesh[sel1other][1] = sp2other;
		      mesh[sel1other][2] = sp1other;
		      mesh[sel2other][0] = pi1other;
		      mesh[sel2other][1] = sp1other;
		      mesh[sel2other][2] = sp2other;
		      //(*testout) << "       with rule 2" << endl;
		    }
		  //(*testout) << "         to " << mesh[sel1other] << " and " << mesh[sel2other] << endl;
		  
		  //(*testout) << "  and surface element " << sel1other << " to " << mesh[sel1other] << ", " << sel2other << " to " << mesh[sel2other] << endl;

		  for(int l=0; l<3; l++)
		    {
		      surfaceelementsonnode.Add(mesh[sel1other][l],sel1other);
		      surfaceelementsonnode.Add(mesh[sel2other][l],sel2other);
		    }
		}




	      for(int i=0; i<hasbothpoints.Size(); i++)
		{
		  mesh[hasbothpoints[i]] = *(*newelts[minpos])[i];

		  for(int l=0; l<4; l++)
		    elementsonnode.Add((*(*newelts[minpos])[i])[l],hasbothpoints[i]);
		}

	      for(int i=hasbothpoints.Size(); i<(*newelts[minpos]).Size(); i++)
		{
		  ElementIndex ni = mesh.AddVolumeElement(*(*newelts[minpos])[i]);
		  
		  for(int l=0; l<4; l++)
		    elementsonnode.Add((*(*newelts[minpos])[i])[l],ni);
		}

	      if(hasbothpointsother.Size() > 0)
		{
		  for(int i=0; i<hasbothpointsother.Size(); i++)
		    {
		      mesh[hasbothpointsother[i]] = *(*neweltsother[minposother])[i];
		      for(int l=0; l<4; l++)
			elementsonnode.Add((*(*neweltsother[minposother])[i])[l],hasbothpointsother[i]);
		    }
		  
		  for(int i=hasbothpointsother.Size(); i<(*neweltsother[minposother]).Size(); i++)
		    {
		      ElementIndex ni = mesh.AddVolumeElement(*(*neweltsother[minposother])[i]);
		      for(int l=0; l<4; l++)
			elementsonnode.Add((*(*neweltsother[minposother])[i])[l],ni);
		    }
		}

	      

	    }

	  for(int i=0; i<newelts.Size(); i++)
	    {
	      for(int jj=0; jj<newelts[i]->Size(); jj++)
		delete (*newelts[i])[jj];
	      delete newelts[i];
	    }

	  for(int i=0; i<neweltsother.Size(); i++)
	    {
	      for(int jj=0; jj<neweltsother[i]->Size(); jj++)
		delete (*neweltsother[i])[jj];
	      delete neweltsother[i];
	    }
	
	}
    }

  PrintMessage (5, cnt, " swaps performed");


  for(int i=0; i<locidmaps.Size(); i++)
    delete locidmaps[i];


  mesh.Compress ();

  multithread.task = savetask;
}
  







/*
  2 -> 3 conversion
*/

double MeshOptimize3d :: SwapImprove2 ( ElementIndex eli1, int face,
  Table<ElementIndex, PointIndex> & elementsonnode,
  TABLE<SurfaceElementIndex, PointIndex::BASE> & belementsonnode, bool check_only )
{
  PointIndex pi1, pi2, pi3, pi4, pi5;
  Element el21(TET), el22(TET), el31(TET), el32(TET), el33(TET);
  int j = face;
  double bad1, bad2;
  double d_badness = 0.0;

  Element & elem = mesh[eli1];
  if (elem.IsDeleted()) return 0.0;

  int mattyp = elem.GetIndex();

  switch (j)
  {
    case 0:
      pi1 = elem.PNum(1); pi2 = elem.PNum(2);
      pi3 = elem.PNum(3); pi4 = elem.PNum(4);
      break;
    case 1:
      pi1 = elem.PNum(1); pi2 = elem.PNum(4);
      pi3 = elem.PNum(2); pi4 = elem.PNum(3);
      break;
    case 2:
      pi1 = elem.PNum(1); pi2 = elem.PNum(3);
      pi3 = elem.PNum(4); pi4 = elem.PNum(2);
      break;
    case 3:
      pi1 = elem.PNum(2); pi2 = elem.PNum(4);
      pi3 = elem.PNum(3); pi4 = elem.PNum(1);
      break;
  }


  bool bface = 0;
  for (int k = 0; k < belementsonnode[pi1].Size(); k++)
  {
      const Element2d & bel =
        mesh[belementsonnode[pi1][k]];

      bool bface1 = 1;
      for (int l = 0; l < 3; l++)
          if (bel[l] != pi1 && bel[l] != pi2 && bel[l] != pi3)
          {
              bface1 = 0;
              break;
          }

      if (bface1)
      {
          bface = 1;
          break;
      }
  }

  if (bface) return 0.0;


  FlatArray<ElementIndex> row = elementsonnode[pi1];
  for(auto ei : row)
      if (mesh[ei].IsDeleted()) return 0.0;

  for(auto ei : elementsonnode[pi2])
      if (mesh[ei].IsDeleted()) return 0.0;

  for(auto ei : elementsonnode[pi3])
      if (mesh[ei].IsDeleted()) return 0.0;

  for(auto ei : elementsonnode[pi4])
      if (mesh[ei].IsDeleted()) return 0.0;

  for (int k = 0; k < row.Size(); k++)
  {
      ElementIndex eli2 = row[k];

      if ( eli1 != eli2 )
      {
          Element & elem2 = mesh[eli2];
          if (elem2.GetType() != TET)
              continue;

          int comnodes=0;
          for (int l = 1; l <= 4; l++)
              if (elem2.PNum(l) == pi1 || elem2.PNum(l) == pi2 ||
                  elem2.PNum(l) == pi3)
              {
                  comnodes++;
              }
              else
              {
                  pi5 = elem2.PNum(l);
              }

          if (comnodes == 3)
          {
              bad1 = CalcBad (mesh.Points(), elem, 0) +
                CalcBad (mesh.Points(), elem2, 0);

              if (!mesh.LegalTet(elem) ||
                  !mesh.LegalTet(elem2))
                  bad1 += 1e4;


              el31.PNum(1) = pi1;
              el31.PNum(2) = pi2;
              el31.PNum(3) = pi5;
              el31.PNum(4) = pi4;
              el31.SetIndex (mattyp);

              el32.PNum(1) = pi2;
              el32.PNum(2) = pi3;
              el32.PNum(3) = pi5;
              el32.PNum(4) = pi4;
              el32.SetIndex (mattyp);

              el33.PNum(1) = pi3;
              el33.PNum(2) = pi1;
              el33.PNum(3) = pi5;
              el33.PNum(4) = pi4;
              el33.SetIndex (mattyp);

              bad2 = CalcBad (mesh.Points(), el31, 0) +
                CalcBad (mesh.Points(), el32, 0) +
                CalcBad (mesh.Points(), el33, 0);


              el31.Touch();
              el32.Touch();
              el33.Touch();

              if (!mesh.LegalTet(el31) ||
                  !mesh.LegalTet(el32) ||
                  !mesh.LegalTet(el33))
                  bad2 += 1e4;


              d_badness = bad2 - bad1;

              if ( ((bad2 < 1e6) || (bad2 < 10 * bad1)) &&
                  mesh.BoundaryEdge (pi4, pi5))
                  d_badness = -1e4;

              if(check_only)
                  return d_badness;

              if (d_badness<0.0)
              {
                  el31.Touch();
                  el32.Touch();
                  el33.Touch();

                  mesh[eli1].Delete();
                  mesh[eli2].Delete();
                  mesh.AddVolumeElement (el31);
                  mesh.AddVolumeElement (el32);
                  mesh.AddVolumeElement (el33);
              }
              return d_badness;
          }
      }
  }
  return d_badness;
}

/*
  2 -> 3 conversion
*/

void MeshOptimize3d :: SwapImprove2 ()
{
  static Timer t("MeshOptimize3d::SwapImprove2"); RegionTimer reg(t);

  if (goal == OPT_CONFORM) return;

  mesh.BuildBoundaryEdges(false);

  int cnt = 0;
  // double bad1, bad2;

  int np = mesh.GetNP();
  int ne = mesh.GetNE();
  int nse = mesh.GetNSE();

  // contains at least all elements at node
  TABLE<SurfaceElementIndex, PointIndex::BASE> belementsonnode(np);

  PrintMessage (3, "SwapImprove2 ");
  (*testout) << "\n" << "Start SwapImprove2" << "\n";

  if(testout->good())
  {
    double bad1 = mesh.CalcTotalBad (mp);
    (*testout) << "Total badness = " << bad1 << endl;
  }

  // find elements on node

  auto elementsonnode = mesh.CreatePoint2ElementTable(nullopt, mp.only3D_domain_nr);
  // todo: respect mp.only3D_domain_nr
  
  for (SurfaceElementIndex sei = 0; sei < nse; sei++)
    for (int j = 0; j < 3; j++)
      belementsonnode.Add (mesh[sei][j], sei);

  int num_threads = ngcore::TaskManager::GetNumThreads();

  Array<std::tuple<double, ElementIndex, int>> faces_with_improvement;
  Array<Array<std::tuple<double, ElementIndex, int>>> faces_with_improvement_threadlocal(num_threads);

  ParallelForRange( Range(ne), [&]( auto myrange )
      {
        int tid = ngcore::TaskManager::GetThreadId();
        auto & my_faces_with_improvement = faces_with_improvement_threadlocal[tid];
        for (ElementIndex eli1 : myrange)
          {
            if (multithread.terminate)
              break;

            if (mesh.ElementType (eli1) == FIXEDELEMENT)
              continue;

            if (mesh[eli1].GetType() != TET)
              continue;

            if (goal == OPT_LEGAL && mesh.LegalTet (mesh[eli1]))
              continue;

            if(mesh.GetDimension()==3 && mp.only3D_domain_nr && mp.only3D_domain_nr != mesh.VolumeElement(eli1).GetIndex())
              continue;

            for (int j = 0; j < 4; j++)
              {
                double d_badness = SwapImprove2( eli1, j, elementsonnode, belementsonnode, true);
                if(d_badness<0.0)
                    my_faces_with_improvement.Append( std::make_tuple(d_badness, eli1, j) );
              }
          }
      });

  for (auto & a : faces_with_improvement_threadlocal)
    faces_with_improvement.Append(a);

  QuickSort(faces_with_improvement);

  for (auto [dummy, eli,j] : faces_with_improvement)
    {
      if(mesh[eli].IsDeleted())
          continue;
      if(SwapImprove2( eli, j, elementsonnode, belementsonnode, false) < 0.0)
          cnt++;
    }

  PrintMessage (5, cnt, " swaps performed");

  mesh.Compress();
  if(testout->good())
  {
    double bad1 = mesh.CalcTotalBad (mp);
    (*testout) << "Total badness = " << bad1 << endl;
    (*testout) << "swapimprove2 done" << "\n";
  }
}

double MeshOptimize3d :: SplitImprove2Element (
                            ElementIndex ei,
                            const Table<ElementIndex, PointIndex> & elements_of_point,
                            bool check_only)
{
  auto & el = mesh[ei];
  if(el.GetType() != TET)
    return false;

  // Optimize only bad elements
  if(el.GetBadness() < 100)
    return false;

  // search for very flat tets, with two disjoint edges nearly crossing, like a rectangle with diagonals
  static constexpr int tetedges[6][2] =
  { { 0, 1 }, { 0, 2 }, { 0, 3 },
    { 1, 2 }, { 1, 3 }, { 2, 3 } };

  int minedge = -1;
  double mindist = 1e99;
  double minlam0, minlam1;

  for (int i : Range(3))
  {
    auto pi0 = el[tetedges[i][0]];
    auto pi1 = el[tetedges[i][1]];
    auto pi2 = el[tetedges[5-i][0]];
    auto pi3 = el[tetedges[5-i][1]];

    double lam0, lam1;
    double dist = MinDistLL2(mesh[pi0], mesh[pi1], mesh[pi2], mesh[pi3], lam0, lam1 );
    if(dist<mindist)
    {
      mindist = dist;
      minedge = i;
      minlam0 = lam0;
      minlam1 = lam1;
    }
  }

  if(minedge==-1)
    return false;

  auto pi0 = el[tetedges[minedge][0]];
  auto pi1 = el[tetedges[minedge][1]];
  auto pi2 = el[tetedges[5-minedge][0]];
  auto pi3 = el[tetedges[5-minedge][1]];

  // we cannot split edges on the boundary
  if(mesh.BoundaryEdge (pi0,pi1) || mesh.BoundaryEdge(pi2, pi3))
    return false;

  ArrayMem<ElementIndex, 50> has_both_points0;
  ArrayMem<ElementIndex, 50> has_both_points1;

  Point3d p[4] = { mesh[el[0]], mesh[el[1]], mesh[el[2]], mesh[el[3]] };
  auto center = Center(p[0]+minlam0*(p[1]-p[0]), p[2]+minlam1*(p[3]-p[2]));
  MeshPoint pnew;

  pnew(0) = center.X();
  pnew(1) = center.Y();
  pnew(2) = center.Z();

  // find all tets with edge (pi0,pi1) or (pi2,pi3)
  for (auto ei0 : elements_of_point[pi0] )
  {
    Element & elem = mesh[ei0];
    if (elem.IsDeleted()) return false;
    if (ei0 == ei) continue;

    if (elem[0] == pi1 || elem[1] == pi1 || elem[2] == pi1 || elem[3] == pi1 || (elem.GetNP()==5 && elem[4]==pi1) )
      if(!has_both_points0.Contains(ei0))
        has_both_points0.Append (ei0);
  }

  for (auto ei1 : elements_of_point[pi2] )
  {
    Element & elem = mesh[ei1];
    if (elem.IsDeleted()) return false;
    if (ei1 == ei) continue;

    if (elem[0] == pi3 || elem[1] == pi3 || elem[2] == pi3 || elem[3] == pi3 || (elem.GetNP()==5 && elem[4]==pi3))
      if(!has_both_points1.Contains(ei1))
        has_both_points1.Append (ei1);
  }

  double badness_before = mesh[ei].GetBadness();
  double badness_after = 0.0;

  for (auto ei0 : has_both_points0)
  {
    if(mesh[ei0].GetType()!=TET)
      return false;
    badness_before += mesh[ei0].GetBadness();
    badness_after += SplitElementBadness (mesh.Points(), mp, mesh[ei0], pi0, pi1, pnew);
  }
  for (auto ei1 : has_both_points1)
  {
    if(mesh[ei1].GetType()!=TET)
      return false;
    badness_before += mesh[ei1].GetBadness();
    badness_after += SplitElementBadness (mesh.Points(), mp, mesh[ei1], pi2, pi3, pnew);
  }

  if(check_only)
    return badness_after-badness_before;

  if(badness_after<badness_before)
  {
    PointIndex pinew = mesh.AddPoint (center);
    el.Touch();
    el.Delete();

    for (auto ei1 : has_both_points0)
    {
      auto new_els = SplitElement(mesh[ei1], pi0, pi1, pinew);
      for(const auto & el : new_els)
        mesh.AddVolumeElement(el);
      mesh[ei1].Delete();
    }
    for (auto ei1 : has_both_points1)
    {
      auto new_els = SplitElement(mesh[ei1], pi2, pi3, pinew);
      for(const auto & el : new_els)
        mesh.AddVolumeElement(el);
      mesh[ei1].Delete();
    }
  }
  return badness_after-badness_before;
}

// Split two opposite edges of very flat tet and let all 4 new segments have one common vertex
// Imagine a square with 2 diagonals -> new point where diagonals cross, remove the flat tet
void MeshOptimize3d :: SplitImprove2 ()
{
  static Timer t("MeshOptimize3d::SplitImprove2"); RegionTimer reg(t);
  static Timer tsearch("Search");
  static Timer topt("Optimize");

  int ne = mesh.GetNE();
  auto elements_of_point = mesh.CreatePoint2ElementTable(nullopt, mp.only3D_domain_nr);
  int ntasks = 4*ngcore::TaskManager::GetNumThreads();

  const char * savetask = multithread.task;
  multithread.task = "Optimize Volume: Split Improve 2";

  UpdateBadness();
  mesh.BuildBoundaryEdges(false);

  Array<std::tuple<double, ElementIndex>> split_candidates(ne);
  std::atomic<int> improvement_counter(0);

  tsearch.Start();
  ParallelForRange(Range(ne), [&] (auto myrange)
  {
    for(ElementIndex ei : myrange)
    {
      if(mp.only3D_domain_nr && mp.only3D_domain_nr != mesh[ei].GetIndex())
        continue;
      double d_badness = SplitImprove2Element(ei, elements_of_point, true);
      if(d_badness<0.0)
      {
        int index = improvement_counter++;
        split_candidates[index] = make_tuple(d_badness, ei);
      }
    }
  }, ntasks);
  tsearch.Stop();

  auto elements_with_improvement = split_candidates.Part(0, improvement_counter.load());
  QuickSort(elements_with_improvement);

  size_t cnt = 0;
  topt.Start();
  for(auto [d_badness, ei] : elements_with_improvement)
  {
    if( SplitImprove2Element(ei, elements_of_point, false) < 0.0)
      cnt++;
  }
  topt.Stop();

  PrintMessage (5, cnt, " elements split");
  (*testout) << "SplitImprove2 done" << "\n";

  if(cnt>0)
    mesh.Compress();
  multithread.task = savetask;
}


/*
  void Mesh :: SwapImprove2 (OPTIMIZEGOAL goal)
  {
  int i, j;
  int eli1, eli2;
  int mattyp;

  Element el31(4), el32(4), el33(4);
  double bad1, bad2;


  INDEX_3_HASHTABLE<INDEX_2> elsonface (GetNE());

  (*mycout) << "SwapImprove2 " << endl;
  (*testout) << "\n" << "Start SwapImprove2" << "\n";

  // Calculate total badness

  if (goal == OPT_QUALITY)
  {
  double bad1 = CalcTotalBad (points, volelements);
  (*testout) << "Total badness = " << bad1 << endl;
  }

  // find elements on node


  Element2d face;
  for (i = 1; i <= GetNE(); i++)
  if ( (i > eltyps.Size()) || (eltyps.Get(i) != FIXEDELEMENT) )
  {
  const Element & el = VolumeElement(i);
  if (!el.PNum(1)) continue;

  for (j = 1; j <= 4; j++)
  {
  el.GetFace (j, face);
  INDEX_3 i3 (face.PNum(1), face.PNum(2), face.PNum(3));
  i3.Sort();


  int bnr, posnr;
  if (!elsonface.PositionCreate (i3, bnr, posnr))
  {
  INDEX_2 i2;
  elsonface.GetData (bnr, posnr, i3, i2);
  i2.I2() = i;
  elsonface.SetData (bnr, posnr, i3, i2);
  }
  else
  {
  INDEX_2 i2 (i, 0);
  elsonface.SetData (bnr, posnr, i3, i2);
  }

  //  	    if (elsonface.Used (i3))
  //  	      {
  //  		INDEX_2 i2 = elsonface.Get(i3);
  //  		i2.I2() = i;
  //  		elsonface.Set (i3, i2);
  //  	      }
  //  	    else
  //  	      {
  //  		INDEX_2 i2 (i, 0);
  //  		elsonface.Set (i3, i2);
  //  	      }

  }
  }

  NgBitArray original(GetNE());
  original.Set();

  for (i = 1; i <= GetNSE(); i++)
  {
  const Element2d & sface = SurfaceElement(i);
  INDEX_3 i3 (sface.PNum(1), sface.PNum(2), sface.PNum(3));
  i3.Sort();
  INDEX_2 i2(0,0);
  elsonface.Set (i3, i2);
  }


  for (i = 1; i <= elsonface.GetNBags(); i++)
  for (j = 1; j <= elsonface.GetBagSize(i); j++)
  {
  INDEX_3 i3;
  INDEX_2 i2;
  elsonface.GetData (i, j, i3, i2);


  int eli1 = i2.I1();
  int eli2 = i2.I2();

  if (eli1 && eli2 && original.Test(eli1) && original.Test(eli2) )
  {
  Element & elem = volelements.Elem(eli1);
  Element & elem2 = volelements.Elem(eli2);

  int pi1 = i3.I1();
  int pi2 = i3.I2();
  int pi3 = i3.I3();

  int pi4 = elem.PNum(1) + elem.PNum(2) + elem.PNum(3) + elem.PNum(4) - pi1 - pi2 - pi3;
  int pi5 = elem2.PNum(1) + elem2.PNum(2) + elem2.PNum(3) + elem2.PNum(4) - pi1 - pi2 - pi3;






  el31.PNum(1) = pi1;
  el31.PNum(2) = pi2;
  el31.PNum(3) = pi3;
  el31.PNum(4) = pi4;
  el31.SetIndex (mattyp);
	    
  if (WrongOrientation (points, el31))
  swap (pi1, pi2);


  bad1 = CalcBad (points, elem, 0) + 
  CalcBad (points, elem2, 0); 
	    
  //	    if (!LegalTet(elem) || !LegalTet(elem2))
  //	      bad1 += 1e4;

	    
  el31.PNum(1) = pi1;
  el31.PNum(2) = pi2;
  el31.PNum(3) = pi5;
  el31.PNum(4) = pi4;
  el31.SetIndex (mattyp);
	    
  el32.PNum(1) = pi2;
  el32.PNum(2) = pi3;
  el32.PNum(3) = pi5;
  el32.PNum(4) = pi4;
  el32.SetIndex (mattyp);
		      
  el33.PNum(1) = pi3;
  el33.PNum(2) = pi1;
  el33.PNum(3) = pi5;
  el33.PNum(4) = pi4;
  el33.SetIndex (mattyp);
	    
  bad2 = CalcBad (points, el31, 0) + 
  CalcBad (points, el32, 0) +
  CalcBad (points, el33, 0); 
	    
  //	    if (!LegalTet(el31) || !LegalTet(el32) ||
  //		!LegalTet(el33))
  //	      bad2 += 1e4;
	    
	    
  int swap = (bad2 < bad1);

  INDEX_2 hi2b(pi4, pi5);
  hi2b.Sort();
	    
  if ( ((bad2 < 1e6) || (bad2 < 10 * bad1)) &&
  boundaryedges->Used (hi2b) )
  swap = 1;
	    
  if (swap)
  {
  (*mycout) << "2->3 " << flush;
		
  volelements.Elem(eli1) = el31;
  volelements.Elem(eli2) = el32;
  volelements.Append (el33);
		
  original.Clear (eli1);
  original.Clear (eli2);
  }
  }
  }
  
  (*mycout) << endl;

  if (goal == OPT_QUALITY)
  {
  bad1 = CalcTotalBad (points, volelements);
  (*testout) << "Total badness = " << bad1 << endl;
  }

  //  FindOpenElements ();

  (*testout) << "swapimprove2 done" << "\n";
  }

*/
}