netgen/libsrc/meshing/basegeom.cpp

#include <set>

#include <mystdlib.h>
#include "meshing.hpp"
#include <core/register_archive.hpp>

namespace netgen
{
  struct PointTree
  {
      BoxTree<3> tree;

      PointTree( Box<3> bb ) : tree(bb) {}

      void Insert(Point<3> p, PointIndex n)
      {
          tree.Insert(p, p, n);
      }

      PointIndex Find(Point<3> p) const
      {
          ArrayMem<int, 1> points;
          tree.GetIntersecting(p, p, points);
          if(points.Size()==0)
              throw Exception("cannot find mapped point");
          return points[0];
      }

      double GetTolerance() { return tree.GetTolerance(); }
  };

  DLL_HEADER GeometryRegisterArray geometryregister;
  //DLL_HEADER NgArray<GeometryRegister*> geometryregister;

  GeometryRegister :: ~GeometryRegister()
  { ; }

  bool GeometryShape :: IsMappedShape( const GeometryShape & other_, const Transformation<3> & trafo, double tol ) const
  {
      throw Exception("GeometryShape::IsMappedShape not implemented for class " + Demangle(typeid(this).name()));
  }

  bool GeometryVertex :: IsMappedShape( const GeometryShape & other_, const Transformation<3> & trafo, double tol ) const
  {
      const auto other_ptr = dynamic_cast<const GeometryVertex*>(&other_);
      if(!other_ptr)
          return false;

      return Dist(trafo(GetPoint()), other_ptr->GetPoint()) < tol;
  }

  bool GeometryEdge :: IsMappedShape( const GeometryShape & other_, const Transformation<3> & trafo, double tol ) const
  {
      const auto other_ptr = dynamic_cast<const GeometryEdge*>(&other_);
      if(!other_ptr)
          return false;
      auto & e = *other_ptr;

      if(tol < Dist(trafo(GetCenter()), e.GetCenter()))
          return false;

      auto v0 = trafo(GetStartVertex().GetPoint());
      auto v1 = trafo(GetEndVertex().GetPoint());
      auto w0 = e.GetStartVertex().GetPoint();
      auto w1 = e.GetEndVertex().GetPoint();

      // have two closed edges, use midpoints to compare
      if(Dist(v0,v1) < tol && Dist(w0,w1) < tol)
      {
          v1 = trafo(GetPoint(0.5));
          w1 = other_ptr->GetPoint(0.5);
      }

      return( (Dist(v0, w0) < tol && Dist(v1, w1) < tol) ||
              (Dist(v0, w1) < tol && Dist(v1, w0) < tol) );
  }

  bool GeometryFace :: IsMappedShape( const GeometryShape & other_, const Transformation<3> & trafo, double tol ) const
  {
      const auto other_ptr = dynamic_cast<const GeometryFace*>(&other_);
      if(!other_ptr)
          return false;
      auto & f = *other_ptr;

      if(tol < Dist(GetCenter(), f.GetCenter()))
          return false;

      // simple check: check if there is a bijective mapping of mapped edges
      auto & other_edges = f.edges;
      if(edges.Size() != other_edges.Size())
          return false;

      auto nedges = edges.Size();
      Array<bool> is_mapped(nedges);
      is_mapped = false;

      for(auto e : edges)
      {
          int found_mapping = 0;
          for(auto other_e : other_edges)
              if(e->IsMappedShape(*other_e, trafo, tol))
                  found_mapping++;
          if(found_mapping != 1)
              return false;
      }

      return true;
  }

  void GeometryFace :: RestrictHTrig(Mesh& mesh,
                                     const PointGeomInfo& gi0,
                                     const PointGeomInfo& gi1,
                                     const PointGeomInfo& gi2,
                                     const MeshingParameters& mparam,
                                     int depth, double h) const
  {
    auto p0 = GetPoint(gi0);
    auto p1 = GetPoint(gi1);
    auto p2 = GetPoint(gi2);
    auto longest = (p0-p1).Length();
    int cutedge = 2;
    if(auto len = (p0-p2).Length(); len > longest)
      {
        longest = len;
        cutedge = 1;
      }
    if(auto len = (p1-p2).Length(); len > longest)
      {
        longest = len;
        cutedge = 0;
      }
    PointGeomInfo gi_mid;
    gi_mid.u = (gi0.u + gi1.u + gi2.u)/3;
    gi_mid.v = (gi0.v + gi1.v + gi2.v)/3;

    if(depth % 3 == 0)
      {
        double curvature = 0.;
        curvature = max({curvature, GetCurvature(gi_mid),
                         GetCurvature(gi0), GetCurvature(gi1),
                         GetCurvature(gi2)});
        if(curvature < 1e-3)
          return;
        double kappa = curvature * mparam.curvaturesafety;
        h = mparam.maxh * kappa < 1 ? mparam.maxh : 1./kappa;
        if(h < 1e-4 * longest)
          return;
      }

    if(h < longest && depth < 10)
      {
        if(cutedge == 0)
          {
            PointGeomInfo gi_m;
            gi_m.u = 0.5 * (gi1.u + gi2.u);
            gi_m.v = 0.5 * (gi1.v + gi2.v);
            RestrictHTrig(mesh, gi_m, gi2, gi0, mparam, depth+1, h);
            RestrictHTrig(mesh, gi_m, gi0, gi1, mparam, depth+1, h);
          }
        else if(cutedge == 1)
          {
            PointGeomInfo gi_m;
            gi_m.u = 0.5 * (gi0.u + gi2.u);
            gi_m.v = 0.5 * (gi0.v + gi2.v);
            RestrictHTrig(mesh, gi_m, gi1, gi2, mparam, depth+1, h);
            RestrictHTrig(mesh, gi_m, gi0, gi1, mparam, depth+1, h);
          }
        else if(cutedge == 2)
          {
            PointGeomInfo gi_m;
            gi_m.u = 0.5 * (gi0.u + gi1.u);
            gi_m.v = 0.5 * (gi0.v + gi1.v);
            RestrictHTrig(mesh, gi_m, gi1, gi2, mparam, depth+1, h);
            RestrictHTrig(mesh, gi_m, gi2, gi0, mparam, depth+1, h);
          }
      }
    else
      {
        auto pmid = GetPoint(gi_mid);
        for(const auto& p : {p0, p1, p2, pmid})
          mesh.RestrictLocalH(p, h);
      }
  }

  struct Line
  {
    Point<3> p0, p1;
    inline double Length() const { return (p1-p0).Length(); }
    inline double Dist(const Line& other) const
    {
      Vec<3> n = p1-p0;
      Vec<3> q = other.p1-other.p0;
      double nq = n*q;
      Point<3> p = p0 + 0.5*n;
      double lambda = (p-other.p0)*n / (nq + 1e-10);
      if (lambda >= 0 && lambda <= 1)
        return (p-other.p0-lambda*q).Length();
      return 1e99;
    }
  };

  void NetgenGeometry :: ProcessIdentifications()
  {
      for(auto i : Range(vertices))
          vertices[i]->nr = i;
      for(auto i : Range(edges))
          edges[i]->nr = i;
      for(auto i : Range(faces))
          faces[i]->nr = i;
      for(auto i : Range(solids))
          solids[i]->nr = i;

      auto mirror_identifications = [&] ( auto & shapes )
      {
          for(auto i : Range(shapes))
          {
              auto &s = shapes[i];
              s->nr = i;
              for(auto & ident : s->identifications)
                  if(s.get() == ident.from)
                      ident.to->identifications.Append(ident);
          }
      };

      auto tol = 1e-8 * bounding_box.Diam();
      for(auto & f : faces)
        for(auto & ident: f->identifications)
          for(auto e : static_cast<GeometryFace*>(ident.from)->edges)
            for(auto e_other : static_cast<GeometryFace*>(ident.to)->edges)
              if(e->IsMappedShape(*e_other, ident.trafo, tol))
                e->identifications.Append( {e, e_other, ident.trafo, ident.type, ident.name} );

      for(auto & e : edges)
        for(auto & ident: e->identifications)
          {
              auto & from = static_cast<GeometryEdge&>(*ident.from);
              auto & to = static_cast<GeometryEdge&>(*ident.to);

              GeometryVertex * pfrom[] = { &from.GetStartVertex(), &from.GetEndVertex() };
              GeometryVertex * pto[] = { &to.GetStartVertex(), &to.GetEndVertex() };

              // swap points of other edge if necessary
              Point<3> p_from0 = ident.trafo(from.GetStartVertex().GetPoint());
              Point<3> p_from1 = ident.trafo(from.GetEndVertex().GetPoint());
              Point<3> p_to0 = to.GetStartVertex().GetPoint();

              if(Dist(p_from1, p_to0) < Dist(p_from0, p_to0))
                  swap(pto[0], pto[1]);

              for(auto i : Range(2))
                  pfrom[i]->identifications.Append( {pfrom[i], pto[i], ident.trafo, ident.type, ident.name} );
          }

      mirror_identifications(vertices);
      mirror_identifications(edges);
      mirror_identifications(faces);


      auto find_primary = [&] (auto & shapes)
      {
          for(auto &s : shapes)
          {
              s->primary = s.get();
              s->primary_to_me = Transformation<3>{ Vec<3> {0,0,0} }; // init with identity
          }

          bool changed = true;

          while(changed) {
            changed = false;
            for(auto &s : shapes)
            {
              auto current = s->primary;
              for(auto & ident : current->identifications)
              {
                  bool need_inverse = ident.from == s.get();
                  auto other = need_inverse ? ident.to : ident.from;
                  if(other->nr < s->primary->nr)
                  {
                      auto trafo = ident.trafo;
                      if(need_inverse)
                          trafo = trafo.CalcInverse();
                      s->primary = other;
                      s->primary_to_me.Combine(trafo, s->primary_to_me);
                      changed = true;
                  }
                  if(other->primary->nr < s->primary->nr)
                  {
                      auto trafo = ident.trafo;
                      if(need_inverse)
                          trafo = trafo.CalcInverse();
                      s->primary = other->primary;
                      s->primary_to_me.Combine(trafo, other->primary_to_me);
                      changed = true;
                  }
              }
            }
          }
      };

      find_primary(vertices);
      find_primary(edges);
      find_primary(faces);
  }

  void NetgenGeometry :: Analyse(Mesh& mesh,
                                 const MeshingParameters& mparam) const
  {
    static Timer t1("SetLocalMeshsize"); RegionTimer regt(t1);
    mesh.SetGlobalH(mparam.maxh);
    mesh.SetMinimalH(mparam.minh);

    mesh.SetLocalH(bounding_box.PMin(), bounding_box.PMax(),
                   mparam.grading);

    // only set meshsize for edges longer than this
    double mincurvelength = 1e-3 * bounding_box.Diam();

    if(mparam.uselocalh)
      {
        double eps = 1e-10 * bounding_box.Diam();
        const char* savetask = multithread.task;
        multithread.task = "Analyse Edges";

        // restrict meshsize on edges
        for(auto i : Range(edges))
          {
            multithread.percent = 100. * i/edges.Size();
            const auto & edge = edges[i];
            auto length = edge->GetLength();
            // skip very short edges
            if(length < mincurvelength)
              continue;
            static constexpr int npts = 20;
            // restrict mesh size based on edge length
            for(auto i : Range(npts+1))
              mesh.RestrictLocalH(edge->GetPoint(double(i)/npts), length/mparam.segmentsperedge);

            // restrict mesh size based on edge curvature
            double t = 0.;
            auto p_old = edge->GetPoint(t);
            while(t < 1.-eps)
              {
                t += edge->CalcStep(t, 1./mparam.curvaturesafety);
                if(t < 1.)
                  {
                    auto p = edge->GetPoint(t);
                    auto dist = (p-p_old).Length();
                    mesh.RestrictLocalH(p, dist);
                    p_old = p;
                  }
              }
          }

        multithread.task = "Analyse Faces";
        // restrict meshsize on faces
        for(auto i : Range(faces))
          {
            multithread.percent = 100. * i/faces.Size();
            const auto& face = faces[i];
            face->RestrictH(mesh, mparam);
          }

        if(mparam.closeedgefac.has_value())
          {
            multithread.task = "Analyse close edges";
            constexpr int sections = 100;
            Array<Line> lines;
            lines.SetAllocSize(sections*edges.Size());
            BoxTree<3> searchtree(bounding_box.PMin(),
                                  bounding_box.PMax());
            for(const auto& edge : edges)
              {
                if(edge->GetLength() < eps)
                  continue;
                double t = 0.;
                auto p_old = edge->GetPoint(t);
                auto t_old = edge->GetTangent(t);
                t_old.Normalize();
                for(auto i : IntRange(1, sections+1))
                  {
                    t = double(i)/sections;
                    auto p_new = edge->GetPoint(t);
                    auto t_new = edge->GetTangent(t);
                    t_new.Normalize();
                    auto cosalpha = fabs(t_old * t_new);
                    if((i == sections) || (cosalpha < cos(10./180 * M_PI)))
                      {
                        auto index = lines.Append({p_old, p_new});
                        searchtree.Insert(p_old, p_new, index);
                        p_old = p_new;
                        t_old = t_new;
                      }
                  }
              }
            Array<int> linenums;
            for(auto i : Range(lines))
              {
                const auto& line = lines[i];
                if(line.Length() < eps) continue;
                multithread.percent = 100.*i/lines.Size();
                Box<3> box;
                box.Set(line.p0);
                box.Add(line.p1);
                // box.Increase(max2(mesh.GetH(line.p0), mesh.GetH(line.p1)));
                box.Increase(line.Length());
                double mindist = 1e99;
                linenums.SetSize0();
                searchtree.GetIntersecting(box.PMin(), box.PMax(),
                                           linenums);
                for(auto num : linenums)
                  {
                    if(i == num) continue;
                    const auto & other = lines[num];
                    if((line.p0 - other.p0).Length2() < eps ||
                       (line.p0 - other.p1).Length2() < eps ||
                       (line.p1 - other.p0).Length2() < eps ||
                       (line.p1 - other.p1).Length2() < eps)
                      continue;
                    mindist = min2(mindist, line.Dist(other));
                  }
                if(mindist == 1e99) continue;
                mindist /= *mparam.closeedgefac + 1e-10;
                if(mindist < 1e-3 * bounding_box.Diam())
                  {
                    (*testout) << "extremely small local h: " << mindist
                               << " --> setting to " << 1e-3 * bounding_box.Diam() << endl;
                    (*testout) << "somewhere near " << line.p0 << " - " << line.p1 << endl
;
                    mindist = 1e-3 * bounding_box.Diam();
                  }
                mesh.RestrictLocalHLine(line.p0, line.p1, mindist);
              }
          }
        multithread.task = savetask;
      }

    for(const auto& mspnt : mparam.meshsize_points)
      mesh.RestrictLocalH(mspnt.pnt, mspnt.h);

    mesh.LoadLocalMeshSize(mparam.meshsizefilename);
  }

  void DivideEdge(GeometryEdge * edge, const MeshingParameters & mparam, const Mesh & mesh, Array<Point<3>> & points, Array<double> & params)
  {
      static Timer tdivedgesections("Divide edge sections");
      static Timer tdivide("Divide Edges");
      RegionTimer rt(tdivide);
      // -------------------- DivideEdge -----------------
      static constexpr size_t divide_edge_sections = 10000;
      double hvalue[divide_edge_sections+1];
      hvalue[0] = 0;

      Point<3> old_pt = edge->GetPoint(0.);
      // calc local h for edge
      tdivedgesections.Start();
      for(auto i : Range(divide_edge_sections))
      {
          auto pt = edge->GetPoint(double(i+1)/divide_edge_sections);
          hvalue[i+1] = hvalue[i] + 1./mesh.GetH(pt) * (pt-old_pt).Length();
          old_pt = pt;
      }
      int nsubedges = max2(1, int(floor(hvalue[divide_edge_sections]+0.5)));
      tdivedgesections.Stop();
      points.SetSize(nsubedges-1);
      params.SetSize(nsubedges+1);

      int i = 1;
      int i1 = 0;
      do
      {
          if (hvalue[i1]/hvalue[divide_edge_sections]*nsubedges >= i)
          {
              params[i] = (double(i1)/divide_edge_sections);
              points[i-1] = MeshPoint(edge->GetPoint(params[i]));
              i++;
          }
          i1++;
          if (i1 > divide_edge_sections)
          {
              nsubedges = i;
              points.SetSize(nsubedges-1);
              params.SetSize(nsubedges+1);
              cout << "divide edge: local h too small" << endl;
          }

      } while(i < nsubedges);

      params[0] = 0.;
      params[nsubedges] = 1.;

      if(params[nsubedges] <= params[nsubedges-1])
      {
          cout << "CORRECTED" << endl;
          points.SetSize (nsubedges-2);
          params.SetSize (nsubedges);
          params[nsubedges-1] = 1.;
      }
  }

  void NetgenGeometry :: FindEdges(Mesh& mesh,
                                   const MeshingParameters& mparam) const
  {
    static Timer t1("MeshEdges"); RegionTimer regt(t1);
    const char* savetask = multithread.task;
    multithread.task = "Mesh Edges";

    PointTree tree( bounding_box );

    auto & identifications = mesh.GetIdentifications();

    std::map<size_t, PointIndex> vert2meshpt;
    for(auto & vert : vertices)
      {
        auto pi = mesh.AddPoint(vert->GetPoint());
        tree.Insert(mesh[pi], pi);
        vert2meshpt[vert->GetHash()] = pi;
        mesh[pi].Singularity(vert->properties.hpref);

        if(vert->properties.name)
        {
          Element0d el(pi, pi);
          el.name = vert->properties.GetName();
          mesh.SetCD3Name(pi, el.name);
          mesh.pointelements.Append (el);
        }
      }

    for(auto & vert : vertices)
        for(auto & ident : vert->identifications)
            identifications.Add(vert2meshpt[ident.from->GetHash()],
                                vert2meshpt[ident.to->GetHash()],
                                ident.name,
                                ident.type);

    size_t segnr = 0;
    auto nedges = edges.Size();
    Array<Array<PointIndex>> all_pnums(nedges);
    Array<Array<double>> all_params(nedges);

    for (auto edgenr : Range(edges))
    {
        auto edge = edges[edgenr].get();
        PointIndex startp, endp;
        // throws if points are not found
        startp = vert2meshpt.at(edge->GetStartVertex().GetHash());
        endp = vert2meshpt.at(edge->GetEndVertex().GetHash());

        // ignore collapsed edges
        if(startp == endp && edge->GetLength() < 1e-10 * bounding_box.Diam())
            continue;

        // ----------- Add Points to mesh and create segments -----
        auto & pnums = all_pnums[edgenr];
        auto & params = all_params[edgenr];
        Array<Point<3>> edge_points;
        Array<double> edge_params;

        if(edge->primary == edge)
        {
            // check if start and end vertex are identified (if so, we only insert one segement and do z-refinement later)
            bool is_identified_edge = false;
            auto v0 = vertices[edge->GetStartVertex().nr].get();
            auto v1 = vertices[edge->GetEndVertex().nr].get();
            for(auto & ident : v0->identifications)
            {
                auto other = ident.from == v0 ? ident.to : ident.from;
                if(other->nr == v1->nr && ident.type == Identifications::CLOSESURFACES)
                {
                    is_identified_edge = true;
                    break;
                }
            }

            if(is_identified_edge)
            {
                params.SetSize(2);
                params[0] = 0.;
                params[1] = 1.;
            }
            else
            {
                DivideEdge(edge, mparam, mesh, edge_points, params);
            }
        }
        else
        {
            auto nr_primary = edge->primary->nr;
            auto & pnums_primary = all_pnums[nr_primary];
            auto & params_primary = all_params[nr_primary];
            auto trafo = edge->primary_to_me;

            auto np = pnums_primary.Size();
            edge_points.SetSize(np-2);
            edge_params.SetSize(np-2);
            for(auto i : Range(np-2))
            {
                edge_points[i] = trafo(mesh[pnums_primary[i+1]]);
                EdgePointGeomInfo gi;
                edge->ProjectPoint(edge_points[i], &gi);
                edge_params[i] = gi.dist;
            }

            // reverse entries if we have decreasing parameters
            if(edge_params.Size()>2 && edge_params[0] > edge_params.Last())
                for(auto i : Range((np-2)/2))
                {
                    swap(edge_points[i], edge_points[np-3-i]);
                    swap(edge_params[i], edge_params[np-3-i]);
                }

            params.SetSize(edge_params.Size()+2);
            params[0] = 0.;
            params.Last() = 1.;

            for(auto i : Range(edge_params))
                params[i+1] = edge_params[i];
        }

        pnums.SetSize(edge_points.Size() + 2);
        pnums[0] = startp;
        pnums.Last() = endp;


        for(auto i : Range(edge_points))
        {
            auto pi = mesh.AddPoint(edge_points[i]);
            tree.Insert(mesh[pi], pi);
            pnums[i+1] = pi;
        }

        for(auto i : Range(pnums.Size()-1))
        {
            segnr++;
            Segment seg;
            seg[0] = pnums[i];
            seg[1] = pnums[i+1];
            seg.edgenr = edgenr+1;
            seg.si = edgenr+1;
            seg.epgeominfo[0].dist = params[i];
            seg.epgeominfo[1].dist = params[i+1];
            seg.epgeominfo[0].edgenr = edgenr;
            seg.epgeominfo[1].edgenr = edgenr;
            seg.singedge_left = edge->properties.hpref;
            seg.singedge_right = edge->properties.hpref;
            seg.domin = edge->domin+1;
            seg.domout = edge->domout+1;
            mesh.AddSegment(seg);
        }
        mesh.SetCD2Name(edgenr+1, edge->properties.GetName());
    }

    for (auto & edge : edges)
    {
        // identify points on edge
        for(auto & ident : edge->identifications)
          if(ident.from == edge.get())
          {
            auto & pnums = all_pnums[edge->nr];
            // start and end vertex are already identified
            for(auto pi : pnums.Range(1, pnums.Size()-1))
            {
                auto pi_other = tree.Find(ident.trafo(mesh[pi]));
                identifications.Add(pi, pi_other, ident.name, ident.type);
            }
          }
    }
    mesh.CalcSurfacesOfNode();
    multithread.task = savetask;
  }

  bool NetgenGeometry :: MeshFace(Mesh& mesh, const MeshingParameters& mparam,
                     int k, FlatArray<int, PointIndex> glob2loc) const
  {
    multithread.percent = 100. * k/faces.Size();
    const auto& face = *faces[k];
    auto bb = face.GetBoundingBox();
    bb.Increase(bb.Diam()/10);
    Meshing2 meshing(*this, mparam, bb);
    glob2loc = 0;
    int cntp = 0;

    auto segments = face.GetBoundary(mesh);
    for(auto& seg : segments)
      {
        for(auto j : Range(2))
          {
            auto pi = seg[j];
            if(glob2loc[pi] == 0)
              {
                meshing.AddPoint(mesh[pi], pi);
                cntp++;
                glob2loc[pi] = cntp;
              }
          }
      }
    for(auto & seg : segments)
      {
        PointGeomInfo gi0, gi1;
        gi0.trignum = gi1.trignum = k+1;
        gi0.u = seg.epgeominfo[0].u;
        gi0.v = seg.epgeominfo[0].v;
        gi1.u = seg.epgeominfo[1].u;
        gi1.v = seg.epgeominfo[1].v;
        meshing.AddBoundaryElement(glob2loc[seg[0]],
                                   glob2loc[seg[1]],
                                   gi0, gi1);
      }

    // TODO Set max area 2* area of face

    auto noldsurfels = mesh.GetNSE();


    static Timer t("GenerateMesh"); RegionTimer reg(t);
    MESHING2_RESULT res = meshing.GenerateMesh(mesh, mparam, mparam.maxh, k+1);

    for(auto i : Range(noldsurfels, mesh.GetNSE()))
      {
        mesh.SurfaceElements()[i].SetIndex(k+1);
      }
    return res != MESHING2_OK;
  }

  void NetgenGeometry :: MeshSurface(Mesh& mesh,
                                     const MeshingParameters& mparam) const
  {
    static Timer t1("Surface Meshing"); RegionTimer regt(t1);
    const char* savetask = multithread.task;
    multithread.task = "Mesh Surface";

    size_t n_failed_faces = 0;
    Array<int, PointIndex> glob2loc(mesh.GetNP());
    for(auto k : Range(faces))
    {
        auto & face = *faces[k];
        FaceDescriptor fd(k+1, face.domin+1, face.domout+1, k+1);
        mesh.AddFaceDescriptor(fd);
        mesh.SetBCName(k, face.properties.GetName());
        if(face.primary == &face)
        {
            // check if this face connects two identified closesurfaces
            bool is_connecting_closesurfaces = false;
            auto & idents = mesh.GetIdentifications();
            std::set<int> relevant_edges;
            auto segments = face.GetBoundary(mesh);
            for(const auto &s : segments)
                relevant_edges.insert(s.edgenr-1);

            Array<bool, PointIndex> is_point_in_tree(mesh.Points().Size());
            is_point_in_tree = false;
            PointTree tree( bounding_box );
            for(const auto &s : segments)
                for(auto pi : s.PNums())
                    if(!is_point_in_tree[pi])
                    {
                        tree.Insert(mesh[pi], pi);
                        is_point_in_tree[pi] = true;
                    }

            Array<int> mapped_edges(edges.Size());
            constexpr int UNINITIALIZED = -2;
            constexpr int NOT_MAPPED = -1;
            mapped_edges = UNINITIALIZED;

            Transformation<3> trafo;

            for(const auto &s : segments)
            {
                auto edgenr = s.edgenr-1;
                auto & edge = *edges[edgenr];
                ShapeIdentification *edge_mapping;

                // have edgenr first time, search for closesurface identification
                if(mapped_edges[edgenr] == UNINITIALIZED)
                {
                    mapped_edges[edgenr] = NOT_MAPPED;
                    for(auto & edge_ident : edge.identifications)
                    {
                        if(edge_ident.type == Identifications::CLOSESURFACES && 
                                edge_ident.from->nr == edgenr &&
                                relevant_edges.count(edge_ident.to->nr) > 0
                          )
                        {
                            trafo = edge_ident.trafo;
                            mapped_edges[edgenr] = edge_ident.to->nr;
                            is_connecting_closesurfaces = true;
                            break;
                        }
                    }
                }

                // this edge has a closesurface mapping to another -> make connecting quad
                if(mapped_edges[edgenr] != NOT_MAPPED)
                {
                    Element2d sel(4);
                    sel[0] = s[0];
                    sel[1] = s[1];
                    sel[2] = tree.Find(trafo(mesh[s[1]]));
                    sel[3] = tree.Find(trafo(mesh[s[0]]));
                    for(auto i : Range(4))
                        sel.GeomInfo()[i] = face.Project(mesh[sel[i]]);

                    sel.SetIndex(face.nr+1);
                    mesh.AddSurfaceElement(sel);
                }
            }

            if(!is_connecting_closesurfaces)
                if(MeshFace(mesh, mparam, k, glob2loc))
                    n_failed_faces++;
        }
    }

    if(n_failed_faces) 
    {
        cout << "WARNING! NOT ALL FACES HAVE BEEN MESHED" << endl;
        cout << "SURFACE MESHING ERROR OCCURRED IN " << n_failed_faces << " FACES:" << endl;
        return;
    }

    if (mparam.perfstepsend >= MESHCONST_OPTSURFACE)
    {
      mesh.CalcSurfacesOfNode();
      OptimizeSurface(mesh, mparam);
    }

    bool have_identifications = false;
    for(auto & face : faces)
        if(face->primary != face.get())
        {
            have_identifications = true;
            MapSurfaceMesh(mesh, *face);
        }

    // identify points on faces
    if(have_identifications)
    {
        mesh.CalcSurfacesOfNode();
        BitArray is_identified_face(faces.Size());
        is_identified_face = false;
        for(auto & face : faces)
            for(auto & ident : face->identifications)
            {
                is_identified_face.SetBit(ident.from->nr);
                is_identified_face.SetBit(ident.to->nr);
            }

        PointTree tree( bounding_box );
        Array<int, PointIndex> pi_to_face(mesh.GetNP());
        pi_to_face = -1;
        Array<SurfaceElementIndex> si_of_face;
        Array<Array<PointIndex>> pi_of_face(faces.Size());
        for(auto & face : faces)
            if(is_identified_face[face->nr])
            {
                mesh.GetSurfaceElementsOfFace(face->nr+1, si_of_face);
                for(auto si : si_of_face)
                    for(auto pi : mesh[si].PNums())
                    {
                        if(mesh[pi].Type() == SURFACEPOINT && pi_to_face[pi]==-1)
                        {
                            pi_to_face[pi] = face->nr;
                            tree.Insert(mesh[pi], pi);
                            pi_of_face[face->nr].Append(pi);
                        }
                    }
            }

        auto & mesh_ident = mesh.GetIdentifications();
        for(auto & face : faces)
            for(auto & ident : face->identifications)
            {
                if(ident.from == face.get())
                    for(auto pi : pi_of_face[face->nr])
                    {
                        auto pi_other = tree.Find(ident.trafo(mesh[pi]));
                        mesh_ident.Add(pi, pi_other, ident.name, ident.type);
                    }
            }
    }

    mesh.CalcSurfacesOfNode();
    multithread.task = savetask;
  }

  void NetgenGeometry :: MapSurfaceMesh( Mesh & mesh, const GeometryFace & dst ) const
  {
    static Timer timer("MapSurfaceMesh");
    RegionTimer rt(timer);

    const auto & src = dynamic_cast<const GeometryFace&>(*dst.primary);
    auto trafo = dst.primary_to_me;

    PrintMessage(2, "Map face ", src.nr+1, " -> ", dst.nr+1);

    // point map from src to dst
    Array<PointIndex, PointIndex> pmap(mesh.Points().Size());
    pmap = PointIndex::INVALID;

    // first map points on edges (mapped points alread in mesh, use search tree)
    Array<bool, PointIndex> is_point_in_tree(mesh.Points().Size());
    is_point_in_tree = false;
    PointTree tree( bounding_box );

    for (Segment & seg : src.GetBoundary(mesh))
        for(auto i : Range(2))
          {
            auto pi = seg[i];
            if(!is_point_in_tree[pi])
            {
              tree.Insert(trafo(mesh[pi]), pi);
              is_point_in_tree[pi] = true;
            }
          }

    for (Segment & seg : dst.GetBoundary(mesh))
        for(auto i : Range(2))
          {
            auto pi = seg[i];
            if(pmap[pi].IsValid())
              continue;

            pmap[tree.Find(mesh[pi])] = pi;
          }

    xbool do_invert = maybe;

    // now insert mapped surface elements
    for(auto sei : mesh.SurfaceElements().Range())
      {
        auto sel = mesh[sei];
        if(sel.GetIndex() != src.nr+1)
          continue;

        if(do_invert.IsMaybe())
        {
            auto n_src = src.GetNormal(mesh[sel[0]]);
            auto n_dist = dst.GetNormal(mesh[sel[0]]);
            Mat<3> normal_matrix;
            CalcInverse(Trans(trafo.GetMatrix()), normal_matrix);
            do_invert = n_src * (normal_matrix * n_dist) < 0.0;
        }
        auto sel_new = sel;
        sel_new.SetIndex(dst.nr+1);
        for(auto i : Range(sel.PNums()))
          {
            auto pi = sel[i];
            if(!pmap[pi].IsValid())
              {
                pmap[pi] = mesh.AddPoint(trafo(mesh[pi]), 1, SURFACEPOINT);
              }
              sel_new[i] = pmap[pi];
          }
          if(do_invert.IsTrue())
              sel_new.Invert();
          for(auto i : Range(sel.PNums()))
              dst.CalcPointGeomInfo(mesh[sel_new[i]], sel_new.GeomInfo()[i]);
          mesh.AddSurfaceElement(sel_new);
      }
  }

  void NetgenGeometry :: OptimizeSurface(Mesh& mesh, const MeshingParameters& mparam) const
  {
    const auto savetask = multithread.task;
    multithread.task = "Optimizing surface";

    static Timer timer_opt2d("Optimization 2D");
    RegionTimer reg(timer_opt2d);
    auto meshopt = MeshOptimize2d(mesh);
    for(auto i : Range(mparam.optsteps2d))
      {
        PrintMessage(3, "Optimization step ", i);
        int innerstep = 0;
        for(auto optstep : mparam.optimize2d)
          {
            multithread.percent = 100. * (double(innerstep++)/mparam.optimize2d.size() + i)/mparam.optsteps2d;
            switch(optstep)
              {
              case 's':
                meshopt.EdgeSwapping(0);
                break;
              case 'S':
                meshopt.EdgeSwapping(1);
                break;
              case 'm':
                meshopt.ImproveMesh(mparam);
                break;
              case 'c':
                meshopt.CombineImprove();
                break;
              }
          }
      }
    mesh.CalcSurfacesOfNode();
    mesh.Compress();
    multithread.task = savetask;
  }

  void NetgenGeometry :: FinalizeMesh(Mesh& mesh) const
  {
    for (int i = 0; i < mesh.GetNDomains(); i++)
      if (auto name = solids[i]->properties.name)
        mesh.SetMaterial (i+1, *name);
  }
  
  shared_ptr<NetgenGeometry> GeometryRegisterArray :: LoadFromMeshFile (istream & ist) const
  {
    if (!ist.good())
        return nullptr;

    string token;
    ist >> token;
    if(token == "TextOutArchive")
    {
        NetgenGeometry *geo = nullptr;
        size_t string_length;
        ist >> string_length;
        string buffer(string_length+1, '\0');
        ist.read(&buffer[0], string_length);
        auto ss = make_shared<stringstream>(buffer);
        TextInArchive in(ss);
        in & geo;

        return shared_ptr<NetgenGeometry>(geo);
    }
    for (int i = 0; i < Size(); i++)
      {
        NetgenGeometry * hgeom = (*this)[i]->LoadFromMeshFile (ist, token);
        if (hgeom)
          return shared_ptr<NetgenGeometry>(hgeom);
      }
    return nullptr;
  }



  
  int NetgenGeometry :: GenerateMesh (shared_ptr<Mesh> & mesh, MeshingParameters & mp)
  {
    multithread.percent = 0;

    // copy so that we don't change them outside
    MeshingParameters mparam = mp;
    if(restricted_h.Size())
      for(const auto& [pnt, maxh] : restricted_h)
        mparam.meshsize_points.Append({pnt, maxh});

    if(mparam.perfstepsstart <= MESHCONST_ANALYSE)
      {
        if(!mesh)
          mesh = make_shared<Mesh>();
        mesh->geomtype = GetGeomType();
        Analyse(*mesh, mparam);
      }

    if(multithread.terminate || mparam.perfstepsend <= MESHCONST_ANALYSE)
      return 0;

    if(mparam.perfstepsstart <= MESHCONST_MESHEDGES)
      FindEdges(*mesh, mparam);

    if(multithread.terminate || mparam.perfstepsend <= MESHCONST_MESHEDGES)
      return 0;

    if (mparam.perfstepsstart <= MESHCONST_MESHSURFACE)
      {
        MeshSurface(*mesh, mparam);
      }

    if (multithread.terminate || mparam.perfstepsend <= MESHCONST_OPTSURFACE)
      return 0;

    if(dimension == 2)
    {
        FinalizeMesh(*mesh);
        mesh->SetDimension(2);
        return 0;
    }

    if(mparam.perfstepsstart <= MESHCONST_MESHVOLUME)
      {
        multithread.task = "Volume meshing";

        MESHING3_RESULT res = MeshVolume (mparam, *mesh);

        if (res != MESHING3_OK) return 1;
        if (multithread.terminate) return 0;

        RemoveIllegalElements (*mesh);
        if (multithread.terminate) return 0;

        MeshQuality3d (*mesh);
      }

    if (multithread.terminate || mparam.perfstepsend <= MESHCONST_MESHVOLUME)
      return 0;


    if (mparam.perfstepsstart <= MESHCONST_OPTVOLUME)
      {
	multithread.task = "Volume optimization";

	OptimizeVolume (mparam, *mesh);
	if (multithread.terminate) return 0;
      }
    FinalizeMesh(*mesh);
    return 0;
  }

  void NetgenGeometry :: Save (string filename) const
  {
    throw NgException("Cannot save geometry - no geometry available");
  }

  static RegisterClassForArchive<NetgenGeometry> regnggeo;
}