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41 results

terrain_stl.py

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  • GModel.cpp 82.91 KiB
    // Gmsh - Copyright (C) 1997-2011 C. Geuzaine, J.-F. Remacle
    //
    // See the LICENSE.txt file for license information. Please report all
    // bugs and problems to <gmsh@geuz.org>.
    
    #include <stdlib.h>
    #include <sstream>
    #include "GmshConfig.h"
    #include "GmshMessage.h"
    #include "GModel.h"
    #include "GModelFactory.h"
    #include "GFaceCompound.h"
    #include "MPoint.h"
    #include "MLine.h"
    #include "MTriangle.h"
    #include "MQuadrangle.h"
    #include "MTetrahedron.h"
    #include "MHexahedron.h"
    #include "MPrism.h"
    #include "MPyramid.h"
    #include "MElementCut.h"
    #include "MElementOctree.h"
    #include "discreteRegion.h"
    #include "discreteFace.h"
    #include "discreteEdge.h"
    #include "discreteVertex.h"
    #include "gmshSurface.h"
    #include "Geo.h"
    #include "SmoothData.h"
    #include "Context.h"
    #include "OS.h"
    #include "GEdgeLoop.h"
    #include "MVertexPositionSet.h"
    #include "OpenFile.h"
    #include "CreateFile.h"
    
    #if defined(HAVE_MESH)
    #include "Field.h"
    #include "Generator.h"
    #include "meshGFaceOptimize.h"
    #include "meshPartition.h"
    #include "HighOrder.h"
    #endif
    
    std::vector<GModel*> GModel::list;
    int GModel::_current = -1;
    
    GModel::GModel(std::string name)
      : _name(name), _visible(1), _octree(0),
        _geo_internals(0), _occ_internals(0), _acis_internals(0), _fm_internals(0),
        _factory(0), _fields(0), _currentMeshEntity(0), normals(0)
    {
      partitionSize[0] = 0; partitionSize[1] = 0;
    
      list.push_back(this);
      // at the moment we always create (at least an empty) GEO model
      _createGEOInternals();
    
    #if defined(HAVE_OCC)
      setFactory("OpenCASCADE");
    #else
      setFactory("Gmsh");
    #endif
    
    #if defined(HAVE_MESH)
      _fields = new FieldManager();
    #endif
    }
    
    GModel::~GModel()
    {
      std::vector<GModel*>::iterator it = std::find(list.begin(), list.end(), this);
      if(it != list.end()) list.erase(it);
      destroy();
      _deleteGEOInternals();
      _deleteOCCInternals();
    #if defined(HAVE_MESH)
      delete _fields;
    #endif
    }
    
    GModel *GModel::current(int index)
    {
      if(list.empty()){
        Msg::Warning("No current model available: creating one");
        new GModel();
      }
      if(index >= 0) _current = index;
      if(_current < 0 || _current >= (int)list.size()) return list.back();
      return list[_current];
    }
    
    int GModel::setCurrent(GModel *m)
    {
      for (unsigned int i = 0; i < list.size(); i++){
        if (list[i] == m){
          _current = i;
          break;
        }
      }
      return _current;
    }
    
    void GModel::setFactory(std::string name)
    {
      if(_factory) delete _factory;
      if(name == "OpenCASCADE"){
    #if defined(HAVE_OCC)
        _factory = new OCCFactory();
    #else
        Msg::Error("Missing OpenCASCADE support: using Gmsh GEO factory instead");
        _factory = new GeoFactory();
    #endif
      }
      else{
        _factory = new GeoFactory();
      }
    }
    
    GModel *GModel::findByName(std::string name)
    {
      // return last mesh with given name
      for(int i = list.size() - 1; i >= 0; i--)
        if(list[i]->getName() == name) return list[i];
      return 0;
    }
    
    void GModel::destroy()
    {
      _name.clear();
    
      for(riter it = firstRegion(); it != lastRegion(); ++it)
        delete *it;
      regions.clear();
    
      std::vector<GFace*> to_keep;
      for(fiter it = firstFace(); it != lastFace(); ++it){
        // projection faces are persistent
        if((*it)->getNativeType() == GEntity::UnknownModel &&
           (*it)->geomType() == GEntity::ProjectionFace)
          to_keep.push_back(*it);
        else
          delete *it;
      }
      faces.clear();
      faces.insert(to_keep.begin(), to_keep.end());
    
      for(eiter it = firstEdge(); it != lastEdge(); ++it)
        delete *it;
      edges.clear();
    
      for(viter it = firstVertex(); it != lastVertex(); ++it)
        delete *it;
      vertices.clear();
    
      destroyMeshCaches();
    
      MVertex::resetGlobalNumber();
      MElement::resetGlobalNumber();
    
      if(normals) delete normals;
      normals = 0;
    
    #if defined(HAVE_MESH)
      _fields->reset();
    #endif
      gmshSurface::reset();
    }
    
    void GModel::destroyMeshCaches()
    {
      _vertexVectorCache.clear();
      _vertexMapCache.clear();
      _elementVectorCache.clear();
      _elementMapCache.clear();
      _elementIndexCache.clear();
      delete _octree;
      _octree = 0;
    }
    
    void GModel::deleteMesh()
    {
      for(riter it = firstRegion(); it != lastRegion();++it)
        (*it)->deleteMesh();
      for(fiter it = firstFace(); it != lastFace();++it)
        (*it)->deleteMesh();
      for(eiter it = firstEdge(); it != lastEdge();++it)
        (*it)->deleteMesh();
      for(viter it = firstVertex(); it != lastVertex();++it)
        (*it)->deleteMesh();
      destroyMeshCaches();
    }
    
    bool GModel::empty() const
    {
      return vertices.empty() && edges.empty() && faces.empty() && regions.empty();
    }
    
    std::vector<GRegion*> GModel::bindingsGetRegions()
    {
      return std::vector<GRegion*> (regions.begin(), regions.end());
    }
    
    std::vector<GFace*> GModel::bindingsGetFaces()
    {
      return std::vector<GFace*> (faces.begin(), faces.end());
    }
    
    std::vector<GEdge*> GModel::bindingsGetEdges()
    {
      return std::vector<GEdge*> (edges.begin(), edges.end());
    }
    
    std::vector<GVertex*> GModel::bindingsGetVertices()
    {
      return std::vector<GVertex*> (vertices.begin(), vertices.end());
    }
    
    GRegion *GModel::getRegionByTag(int n) const
    {
      GEntity tmp((GModel*)this, n);
      std::set<GRegion*, GEntityLessThan>::const_iterator it = regions.find((GRegion*)&tmp);
      if(it != regions.end())
        return *it;
      else
        return 0;
    }
    
    GFace *GModel::getFaceByTag(int n) const
    {
      GEntity tmp((GModel*)this, n);
      std::set<GFace*, GEntityLessThan>::const_iterator it = faces.find((GFace*)&tmp);
      if(it != faces.end())
        return *it;
      else
        return 0;
    }
    
    GEdge *GModel::getEdgeByTag(int n) const
    {
      GEntity tmp((GModel*)this, n);
      std::set<GEdge*, GEntityLessThan>::const_iterator it = edges.find((GEdge*)&tmp);
      if(it != edges.end())
        return *it;
      else
        return 0;
    }
    
    GVertex *GModel::getVertexByTag(int n) const
    {
      GEntity tmp((GModel*)this, n);
      std::set<GVertex*, GEntityLessThan>::const_iterator it = vertices.find((GVertex*)&tmp);
      if(it != vertices.end())
        return *it;
      else
        return 0;
    }
    
    std::vector<int> GModel::getEdgesByStringTag(const std::string tag) 
    { 
      std::vector<int> nums;
      std::map<int, std::vector<GEntity*> > physicalGroups[4]; 
      getPhysicalGroups(physicalGroups); 
      std::vector<GEntity*> allEdges = physicalGroups[1][this->getPhysicalNumber(1,tag)]; 
      for ( std::vector<GEntity*>::iterator it = allEdges.begin(); it != allEdges.end(); it++){
        GEntity *ge = *it;
        nums.push_back(ge->tag());
      }
    
      return nums;
    }
    
    void GModel::remove(GRegion *r)
    {
      riter it = std::find(firstRegion(), lastRegion(), r);
      if(it != (riter)regions.end()) regions.erase(it);
    }
    
    void GModel::remove(GFace *f)
    {
      fiter it = std::find(firstFace(), lastFace(), f);
      if(it != faces.end()) faces.erase(it);
    }
    
    void GModel::remove(GEdge *e)
    {
      eiter it = std::find(firstEdge(), lastEdge(), e);
      if(it != edges.end()) edges.erase(it);
    }
    
    void GModel::remove(GVertex *v)
    {
      viter it = std::find(firstVertex(), lastVertex(), v);
      if(it != vertices.end()) vertices.erase(it);
    }
    
    void GModel::snapVertices()
    {
      viter vit = firstVertex();
    
      double tol = CTX::instance()->geom.tolerance;
    
      while (vit != lastVertex()){
        std::list<GEdge*> edges = (*vit)->edges();
        for (std::list<GEdge*>::iterator it = edges.begin(); it != edges.end(); ++it){
          Range<double> parb = (*it)->parBounds(0);
          double t;
          if ((*it)->getBeginVertex() == *vit){
            t = parb.low();
          }
          else if ((*it)->getEndVertex() == *vit){
            t = parb.high();
          }
          else{
            Msg::Error("Weird vertex: impossible to snap");
            break;
          }
          GPoint gp = (*it)->point(t);
          double d = sqrt((gp.x() - (*vit)->x()) * (gp.x() - (*vit)->x()) +
                          (gp.y() - (*vit)->y()) * (gp.y() - (*vit)->y()) +
                          (gp.z() - (*vit)->z()) * (gp.z() - (*vit)->z()));
          if (d > tol){
            (*vit)->setPosition(gp);
            Msg::Warning("Geom Vertex %d Corrupted (%12.5E)... Snap performed",
                         (*vit)->tag(), d);
          }
        }
        vit++;
      }
    }
    
    void GModel::getEntities(std::vector<GEntity*> &entities)
    {
      entities.clear();
      entities.insert(entities.end(), vertices.begin(), vertices.end());
      entities.insert(entities.end(), edges.begin(), edges.end());
      entities.insert(entities.end(), faces.begin(), faces.end());
      entities.insert(entities.end(), regions.begin(), regions.end());
    }
    
    int GModel::getMaxElementaryNumber(int dim)
    {
      std::vector<GEntity*> entities;
      getEntities(entities);
      int num = 0;
      for(unsigned int i = 0; i < entities.size(); i++)
        if(dim < 0 || entities[i]->dim() == dim)
          num = std::max(num, std::abs(entities[i]->tag()));
      return num;
    }
    
    bool GModel::noPhysicalGroups()
    {
      std::vector<GEntity*> entities;
      getEntities(entities);
      for(unsigned int i = 0; i < entities.size(); i++)
        if(entities[i]->physicals.size()) return false;
      return true;
    }
    
    void GModel::getPhysicalGroups(std::map<int, std::vector<GEntity*> > groups[4])
    {
      std::vector<GEntity*> entities;
      getEntities(entities);
      for(unsigned int i = 0; i < entities.size(); i++){
        std::map<int, std::vector<GEntity*> > &group(groups[entities[i]->dim()]);
        for(unsigned int j = 0; j < entities[i]->physicals.size(); j++){
          // physicals can be stored with negative signs when the entity
          // should be "reversed"
          int p = std::abs(entities[i]->physicals[j]);
          if(std::find(group[p].begin(), group[p].end(), entities[i]) == group[p].end())
            group[p].push_back(entities[i]);
        }
      }
    }
    
    void GModel::deletePhysicalGroups()
    {
      std::vector<GEntity*> entities;
      getEntities(entities);
      for(unsigned int i = 0; i < entities.size(); i++)
        entities[i]->physicals.clear();
    }
    
    void GModel::deletePhysicalGroup(int dim, int num)
    {
      std::vector<GEntity*> entities;
      getEntities(entities);
      for(unsigned int i = 0; i < entities.size(); i++){
        if(dim == entities[i]->dim()){
          std::vector<int> p;
          for(unsigned int j = 0; j < entities[i]->physicals.size(); j++)
            if(entities[i]->physicals[j] != num)
              p.push_back(entities[i]->physicals[j]);
          entities[i]->physicals = p;
        }
      }
    }
    
    int GModel::getMaxPhysicalNumber(int dim)
    {
      std::vector<GEntity*> entities;
      getEntities(entities);
      int num = 0;
      for(unsigned int i = 0; i < entities.size(); i++)
        if(entities[i]->dim() == dim)
          for(unsigned int j = 0; j < entities[i]->physicals.size(); j++)
            num = std::max(num, std::abs(entities[i]->physicals[j]));
      return num;
    }
    
    int GModel::setPhysicalName(std::string name, int dim, int number)
    {
      // check if the name is already used
      piter it = physicalNames.begin();
      while(it != physicalNames.end()){
        if(name == it->second && dim == it->first.first) return it->first.second;
        ++it;
      }
      // if no number is given, find the next available one
      if(!number) number = getMaxPhysicalNumber(dim) + 1;
      physicalNames[std::pair<int, int>(dim, number)] = name;
      return number;
    }
    
    std::string GModel::getPhysicalName(int dim, int number)
    {
      //Emi debug here
      // printf("getPhysName size %d \n", physicalNames.size());
      // std::map<std::pair<int, int>, std::string>::iterator itt = physicalNames.begin();
      // for (; itt != physicalNames.end(); itt++){
      //   printf("name %s \n", itt->second.c_str());
      //   printf("par (%d,%d) \n", itt->first.first, itt->first.second);
      // }
    
      std::map<std::pair<int, int>, std::string>::iterator it =
        physicalNames.find(std::pair<int, int>(dim, number));
      if(it != physicalNames.end()) return it->second;
      return "";
    }
    
    int GModel::getPhysicalNumber(const int &dim, const std::string &name)
    {
      for(piter physIt = firstPhysicalName(); physIt != lastPhysicalName(); ++physIt)
        if(dim == physIt->first.first && name == physIt->second)
          return physIt->first.second;
      Msg::Warning("No physical group found with the name '%s'", name.c_str());
      return -1;
    }
    
    int GModel::getDim()
    {
      if(getNumRegions() > 0) return 3;
      if(getNumFaces() > 0) return 2;
      if(getNumEdges() > 0) return 1;
      if(getNumVertices() > 0) return 0;
      Msg::Warning("The model is empty, dim = -1");
      return -1;
    }
    
    std::string GModel::getElementaryName(int dim, int number)
    {
      std::map<std::pair<int, int>, std::string>::iterator it =
        elementaryNames.find(std::pair<int, int>(dim, number));
      if(it != elementaryNames.end()) return it->second;
      return "";
    }
    
    void GModel::setSelection(int val)
    {
      std::vector<GEntity*> entities;
      getEntities(entities);
    
      for(unsigned int i = 0; i < entities.size(); i++){
        entities[i]->setSelection(val);
        // reset selection in elements (stored in the visibility flag to
        // save space)
        if(val == 0){
          for(unsigned int j = 0; j < entities[i]->getNumMeshElements(); j++)
            if(entities[i]->getMeshElement(j)->getVisibility() == 2)
              entities[i]->getMeshElement(j)->setVisibility(1);
        }
      }
    }
    
    SBoundingBox3d GModel::bounds(bool aroundVisible)
    {
      std::vector<GEntity*> entities;
      getEntities(entities);
      // using the mesh vertices for now; should use entities[i]->bounds() instead
      SBoundingBox3d bb;
      for(unsigned int i = 0; i < entities.size(); i++)
        if(!aroundVisible || entities[i]->getVisibility()){
          if(entities[i]->dim() == 0)
            bb += static_cast<GVertex*>(entities[i])->xyz();
          else
            for(unsigned int j = 0; j < entities[i]->mesh_vertices.size(); j++)
              bb += entities[i]->mesh_vertices[j]->point();
        }
      return bb;
    }
    
    int GModel::mesh(int dimension)
    {
    #if defined(HAVE_MESH)
      GenerateMesh(this, dimension);
      return true;
    #else
      Msg::Error("Mesh module not compiled");
      return false;
    #endif
    }
    
    int GModel::refineMesh(int linear)
    {
    #if defined(HAVE_MESH)
      RefineMesh(this, linear);
      return true;
    #else
      Msg::Error("Mesh module not compiled");
      return false;
    #endif
    }
    
    int GModel::setOrderN(int order, int linear, int incomplete)
    {
    #if defined(HAVE_MESH)
      SetOrderN(this, order, linear, incomplete);
      return true;
    #else
      Msg::Error("Mesh module not compiled");
      return false;
    #endif
    }
    
    int GModel::getMeshStatus(bool countDiscrete)
    {
      for(riter it = firstRegion(); it != lastRegion(); ++it)
        if((countDiscrete || ((*it)->geomType() != GEntity::DiscreteVolume &&
                              (*it)->meshAttributes.Method != MESH_NONE)) &&
           ((*it)->tetrahedra.size() ||(*it)->hexahedra.size() ||
            (*it)->prisms.size() || (*it)->pyramids.size() ||
            (*it)->polyhedra.size())) return 3;
      for(fiter it = firstFace(); it != lastFace(); ++it)
        if((countDiscrete || ((*it)->geomType() != GEntity::DiscreteSurface &&
                              (*it)->meshAttributes.Method != MESH_NONE)) &&
           ((*it)->triangles.size() || (*it)->quadrangles.size() ||
            (*it)->polygons.size())) return 2;
      for(eiter it = firstEdge(); it != lastEdge(); ++it)
        if((countDiscrete || ((*it)->geomType() != GEntity::DiscreteCurve &&
                              (*it)->meshAttributes.Method != MESH_NONE)) &&
           (*it)->lines.size()) return 1;
      for(viter it = firstVertex(); it != lastVertex(); ++it)
        if((*it)->mesh_vertices.size()) return 0;
      return -1;
    }
    
    int GModel::getNumMeshVertices()
    {
      std::vector<GEntity*> entities;
      getEntities(entities);
      unsigned int n = 0;
      for(unsigned int i = 0; i < entities.size(); i++)
        n += entities[i]->mesh_vertices.size();
      return n;
    }
    
    int GModel::getNumMeshElements()
    {
      std::vector<GEntity*> entities;
      getEntities(entities);
      unsigned int n = 0;
      for(unsigned int i = 0; i < entities.size(); i++)
        n += entities[i]->getNumMeshElements();
      return n;
    }
    
    int GModel::getNumMeshParentElements()
    {
      std::vector<GEntity*> entities;
      getEntities(entities);
      unsigned int n = 0;
      for(unsigned int i = 0; i < entities.size(); i++)
        n += entities[i]->getNumMeshParentElements();
      return n;
    }
    
    int GModel::getNumMeshElements(unsigned c[5])
    {
      c[0] = 0; c[1] = 0; c[2] = 0; c[3] = 0; c[4] = 0;
      for(riter it = firstRegion(); it != lastRegion(); ++it)
        (*it)->getNumMeshElements(c);
      if(c[0] + c[1] + c[2] + c[3] + c[4]) return 3;
      for(fiter it = firstFace(); it != lastFace(); ++it)
        (*it)->getNumMeshElements(c);
      if(c[0] + c[1] + c[2]) return 2;
      for(eiter it = firstEdge(); it != lastEdge(); ++it)
        (*it)->getNumMeshElements(c);
      if(c[0]) return 1;
      return 0;
    }
    
    MElement *GModel::getMeshElementByCoord(SPoint3 &p, int dim)
    {
      if(!_octree){
        Msg::Debug("Rebuilding mesh element octree");
        _octree = new MElementOctree(this);
      }
      return _octree->find(p.x(), p.y(), p.z(), dim);
    }
    
    MVertex *GModel::getMeshVertexByTag(int n)
    {
      if(_vertexVectorCache.empty() && _vertexMapCache.empty()){
        Msg::Debug("Rebuilding mesh vertex cache");
        _vertexVectorCache.clear();
        _vertexMapCache.clear();
        bool dense = (getNumMeshVertices() == MVertex::getGlobalNumber());
        std::vector<GEntity*> entities;
        getEntities(entities);
        if(dense){
          Msg::Debug("Good: we have a dense vertex numbering in the cache");
          // numbering starts at 1
          _vertexVectorCache.resize(MVertex::getGlobalNumber() + 1);
          for(unsigned int i = 0; i < entities.size(); i++)
            for(unsigned int j = 0; j < entities[i]->mesh_vertices.size(); j++)
              _vertexVectorCache[entities[i]->mesh_vertices[j]->getNum()] =
                entities[i]->mesh_vertices[j];
        }
        else{
          for(unsigned int i = 0; i < entities.size(); i++)
            for(unsigned int j = 0; j < entities[i]->mesh_vertices.size(); j++)
              _vertexMapCache[entities[i]->mesh_vertices[j]->getNum()] =
                entities[i]->mesh_vertices[j];
        }
      }
    
      if(n < (int)_vertexVectorCache.size())
        return _vertexVectorCache[n];
      else
        return _vertexMapCache[n];
    }
    
    void GModel::getMeshVerticesForPhysicalGroup(int dim, int num, std::vector<MVertex*> &v)
    {
      v.clear();
      std::map<int, std::vector<GEntity*> > groups[4];
      getPhysicalGroups(groups);
      std::map<int, std::vector<GEntity*> >::const_iterator it = groups[dim].find(num);
      if(it == groups[dim].end()) return;
      const std::vector<GEntity *> &entities = it->second;
      std::set<MVertex*> sv;
      for(unsigned int i = 0; i < entities.size(); i++){
        if(dim == 0){
          GVertex *g = (GVertex*)entities[i];
          sv.insert(g->mesh_vertices[0]);
        }
        else{
          for(unsigned int j = 0; j < entities[i]->getNumMeshElements(); j++){
            MElement *e = entities[i]->getMeshElement(j);
            for(int k = 0; k < e->getNumVertices(); k++)
              sv.insert(e->getVertex(k));
          }
        }
      }
      v.insert(v.begin(), sv.begin(), sv.end());
    }
    
    MElement *GModel::getMeshElementByTag(int n)
    {
      if(_elementVectorCache.empty() && _elementMapCache.empty()){
        Msg::Debug("Rebuilding mesh element cache");
        _elementVectorCache.clear();
        _elementMapCache.clear();
        bool dense = (getNumMeshElements() == MElement::getGlobalNumber());
        std::vector<GEntity*> entities;
        getEntities(entities);
        if(dense){
          Msg::Debug("Good: we have a dense element numbering in the cache");
          // numbering starts at 1
          _elementVectorCache.resize(MElement::getGlobalNumber() + 1);
          for(unsigned int i = 0; i < entities.size(); i++)
            for(unsigned int j = 0; j < entities[i]->getNumMeshElements(); j++){
              MElement *e = entities[i]->getMeshElement(j);
              _elementVectorCache[e->getNum()] = e;
            }
        }
        else{
          for(unsigned int i = 0; i < entities.size(); i++)
            for(unsigned int j = 0; j < entities[i]->getNumMeshElements(); j++){
              MElement *e = entities[i]->getMeshElement(j);
              _elementMapCache[e->getNum()] = e;
            }
        }
      }
    
      if(n < (int)_elementVectorCache.size())
        return _elementVectorCache[n];
      else
        return _elementMapCache[n];
    }
    
    int GModel::getMeshElementIndex(MElement *e)
    {
      if(!e) return 0;
      std::map<int, int>::iterator it = _elementIndexCache.find(e->getNum());
      if(it != _elementIndexCache.end()) return it->second;
      return e->getNum();
    }
    
    void GModel::setMeshElementIndex(MElement *e, int index)
    {
      _elementIndexCache[e->getNum()] = index; 
    }
    
    template <class T>
    static void removeInvisible(std::vector<T*> &elements, bool all)
    {
      std::vector<T*> tmp;
      for(unsigned int i = 0; i < elements.size(); i++){
        if(all || !elements[i]->getVisibility())
          delete elements[i];
        else
          tmp.push_back(elements[i]);
      }
      elements.clear();
      elements = tmp;
    }
    
    void GModel::removeInvisibleElements()
    {
      for(riter it = firstRegion(); it != lastRegion(); ++it){
        bool all = !(*it)->getVisibility();
        removeInvisible((*it)->tetrahedra, all);
        removeInvisible((*it)->hexahedra, all);
        removeInvisible((*it)->prisms, all);
        removeInvisible((*it)->pyramids, all);
        removeInvisible((*it)->polyhedra, all);
        (*it)->deleteVertexArrays();
      }
      for(fiter it = firstFace(); it != lastFace(); ++it){
        bool all = !(*it)->getVisibility();
        removeInvisible((*it)->triangles, all);
        removeInvisible((*it)->quadrangles, all);
        removeInvisible((*it)->polygons, all);
        (*it)->deleteVertexArrays();
      }
      for(eiter it = firstEdge(); it != lastEdge(); ++it){
        bool all = !(*it)->getVisibility();
        removeInvisible((*it)->lines, all);
        (*it)->deleteVertexArrays();
      }
      destroyMeshCaches();
    }
    
    int GModel::indexMeshVertices(bool all, int singlePartition)
    {
      std::vector<GEntity*> entities;
      getEntities(entities);
    
      // tag all mesh vertices with -1 (negative vertices will not be
      // saved)
      for(unsigned int i = 0; i < entities.size(); i++)
        for(unsigned int j = 0; j < entities[i]->mesh_vertices.size(); j++)
          entities[i]->mesh_vertices[j]->setIndex(-1);
    
      // tag all mesh vertices belonging to elements that need to be saved
      // with 0, or with -2 if they need to be taken into account in the
      // numbering but need not to be saved (because we save a single
      // partition and they are not used in that partition)
      for(unsigned int i = 0; i < entities.size(); i++){
        if(all || entities[i]->physicals.size()){
          for(unsigned int j = 0; j < entities[i]->getNumMeshElements(); j++){
            MElement *e = entities[i]->getMeshElement(j);
            for(int k = 0; k < e->getNumVertices(); k++){
              if(!singlePartition || e->getPartition() == singlePartition)
                e->getVertex(k)->setIndex(0);
              else if(e->getVertex(k)->getIndex() == -1)
                e->getVertex(k)->setIndex(-2);
            }
          }
        }
      }
    
      // renumber all the mesh vertices tagged with 0
      int numVertices = 0, index = 0;
      for(unsigned int i = 0; i < entities.size(); i++)
        for(unsigned int j = 0; j < entities[i]->mesh_vertices.size(); j++)
          if(!entities[i]->mesh_vertices[j]->getIndex()){
            index++;
            numVertices++;
            entities[i]->mesh_vertices[j]->setIndex(index);
          }
          else if(entities[i]->mesh_vertices[j]->getIndex() == -2)
            index++;
      
      return numVertices;
    }
    
    void GModel::scaleMesh(double factor)
    {
      std::vector<GEntity*> entities;
      getEntities(entities);
      for(unsigned int i = 0; i < entities.size(); i++)
        for(unsigned int j = 0; j < entities[i]->mesh_vertices.size(); j++){
          MVertex *v = entities[i]->mesh_vertices[j];
          v->x() *= factor;
          v->y() *= factor;
          v->z() *= factor;
        }
    }
    
    void GModel::recomputeMeshPartitions()
    {
      meshPartitions.clear();
      std::vector<GEntity*> entities;
      getEntities(entities);
      for(unsigned int i = 0; i < entities.size(); i++){
        for(unsigned int j = 0; j < entities[i]->getNumMeshElements(); j++){
          int part = entities[i]->getMeshElement(j)->getPartition();
          if(part)  meshPartitions.insert(part);
        }
      }
    }
    
    void GModel::deleteMeshPartitions()
    {
      std::vector<GEntity*> entities;
      getEntities(entities);
      for(unsigned int i = 0; i < entities.size(); i++)
        for(unsigned int j = 0; j < entities[i]->getNumMeshElements(); j++)
          entities[i]->getMeshElement(j)->setPartition(0);
      meshPartitions.clear();
    }
    
    template<class T>
    static void _addElements(std::vector<T*> &dst, const std::vector<MElement*> &src)
    {
      for(unsigned int i = 0; i < src.size(); i++) dst.push_back((T*)src[i]);
    }
    
    void GModel::_storeElementsInEntities(std::map<int, std::vector<MElement*> > &map)
    {
      std::map<int, std::vector<MElement*> >::const_iterator it = map.begin();
      for(; it != map.end(); ++it){
        if(!it->second.size()) continue;
        int type = it->second[0]->getType();
        switch(type){
        case TYPE_PNT:
          {
            GVertex *v = getVertexByTag(it->first);
            if(!v){
              v = new discreteVertex(this, it->first);
              add(v);
            }
            if(!v->points.empty()) { // CAD points already have one by default
              v->points.clear();
              v->mesh_vertices.clear();
            }  
            _addElements(v->points, it->second);
          }
          break;
        case TYPE_LIN:
          {
            GEdge *e = getEdgeByTag(it->first);
            if(!e){
              e = new discreteEdge(this, it->first, 0, 0);
              add(e);
            }
            _addElements(e->lines, it->second);
          }
          break;
        case TYPE_TRI: case TYPE_QUA: case TYPE_POLYG:
          {
            GFace *f = getFaceByTag(it->first);
            if(!f){
              f = new discreteFace(this, it->first);
              add(f);
            }
            if(type == TYPE_TRI) _addElements(f->triangles, it->second);
            else if(type == TYPE_QUA) _addElements(f->quadrangles, it->second);
            else _addElements(f->polygons, it->second);
          }
          break;
        case TYPE_TET: case TYPE_HEX: case TYPE_PYR: case TYPE_PRI: case TYPE_POLYH:
          {
            GRegion *r = getRegionByTag(it->first);
            if(!r){
              r = new discreteRegion(this, it->first);
              add(r);
            }
            if(type == TYPE_TET) _addElements(r->tetrahedra, it->second);
            else if(type == TYPE_HEX) _addElements(r->hexahedra, it->second);
            else if(type == TYPE_PRI) _addElements(r->prisms, it->second);
            else if(type == TYPE_PYR) _addElements(r->pyramids, it->second);
            else _addElements(r->polyhedra, it->second);
          }
          break;
        }
      }
    }
    
    template<class T>
    static void _associateEntityWithElementVertices(GEntity *ge, std::vector<T*> &elements)
    {
      for(unsigned int i = 0; i < elements.size(); i++){
        for(int j = 0; j < elements[i]->getNumVertices(); j++){
          if (!elements[i]->getVertex(j)->onWhat() ||
    	  elements[i]->getVertex(j)->onWhat()->dim() > ge->dim())
    	elements[i]->getVertex(j)->setEntity(ge);
        }
      }
    }
    
    void GModel::_associateEntityWithMeshVertices()
    {
      // loop on regions, then on faces, edges and vertices and store the
      // entity pointer in the the elements' vertices (this way we
      // associate the entity of lowest geometrical degree with each
      // vertex)
      for(riter it = firstRegion(); it != lastRegion(); ++it){
        _associateEntityWithElementVertices(*it, (*it)->tetrahedra);
        _associateEntityWithElementVertices(*it, (*it)->hexahedra);
        _associateEntityWithElementVertices(*it, (*it)->prisms);
        _associateEntityWithElementVertices(*it, (*it)->pyramids);
        _associateEntityWithElementVertices(*it, (*it)->polyhedra);
      }
      for(fiter it = firstFace(); it != lastFace(); ++it){
        _associateEntityWithElementVertices(*it, (*it)->triangles);
        _associateEntityWithElementVertices(*it, (*it)->quadrangles);
        _associateEntityWithElementVertices(*it, (*it)->polygons);
      }
      for(eiter it = firstEdge(); it != lastEdge(); ++it){
        _associateEntityWithElementVertices(*it, (*it)->lines);
      }
      for(viter it = firstVertex(); it != lastVertex(); ++it){
        _associateEntityWithElementVertices(*it, (*it)->points);
      }
    }
    
    void GModel::_storeVerticesInEntities(std::map<int, MVertex*> &vertices)
    {
      std::map<int, MVertex*>::iterator it = vertices.begin();
      for(; it != vertices.end(); ++it){
        MVertex *v = it->second;
        GEntity *ge = v->onWhat();
        if(ge) ge->mesh_vertices.push_back(v);
        else{
          delete v; // we delete all unused vertices
          it->second = 0;
        }
      }
    }
    
    void GModel::_storeVerticesInEntities(std::vector<MVertex*> &vertices)
    {
      for(unsigned int i = 0; i < vertices.size(); i++){
        MVertex *v = vertices[i];
        if(v){ // the vector is allowed to have null entries
          GEntity *ge = v->onWhat();
          if(ge) ge->mesh_vertices.push_back(v);
          else{
            delete v; // we delete all unused vertices
            vertices[i] = 0;
          }
        }
      }
    }
    
    void GModel::checkMeshCoherence(double tolerance)
    {
      int numEle = getNumMeshElements();
      if(!numEle) return;
    
      Msg::StatusBar(2, true, "Checking mesh coherence (%d elements)...", numEle);
    
      SBoundingBox3d bbox = bounds();
      double lc = bbox.empty() ? 1. : norm(SVector3(bbox.max(), bbox.min()));
      double eps = lc * tolerance;
    
      std::vector<GEntity*> entities;
      getEntities(entities);
    
      // check for duplicate mesh vertices
      {
        Msg::Info("Checking for duplicate vertices...");
        std::vector<MVertex*> vertices;
        for(unsigned int i = 0; i < entities.size(); i++)
          vertices.insert(vertices.end(), entities[i]->mesh_vertices.begin(), 
                          entities[i]->mesh_vertices.end());
        MVertexPositionSet pos(vertices);
        for(unsigned int i = 0; i < vertices.size(); i++)
          pos.find(vertices[i]->x(), vertices[i]->y(), vertices[i]->z(), eps);
        int num = 0;
        for(unsigned int i = 0; i < vertices.size(); i++)
          if(!vertices[i]->getIndex()){
            Msg::Info("Duplicate vertex at (%.16g,%.16g,%.16g)",
                      vertices[i]->x(), vertices[i]->y(), vertices[i]->z());
            num++;
          }
        if(num) Msg::Error("%d duplicate vert%s", num, num > 1 ? "ices" : "ex");
      }
    
      // check for duplicate elements
      {
        Msg::Info("Checking for duplicate elements...");
        std::vector<MVertex*> vertices;
        for(unsigned int i = 0; i < entities.size(); i++)
          for(unsigned int j = 0; j < entities[i]->getNumMeshElements(); j++){
            SPoint3 p = entities[i]->getMeshElement(j)->barycenter();
            vertices.push_back(new MVertex(p.x(), p.y(), p.z()));
          }
        MVertexPositionSet pos(vertices);
        for(unsigned int i = 0; i < vertices.size(); i++)
          pos.find(vertices[i]->x(), vertices[i]->y(), vertices[i]->z(), eps);
        int num = 0;
        for(unsigned int i = 0; i < vertices.size(); i++){
          if(!vertices[i]->getIndex()){
            Msg::Info("Duplicate element with barycenter (%.16g,%.16g,%.16g)", 
                      vertices[i]->x(), vertices[i]->y(), vertices[i]->z());
            num++;
          }
          delete vertices[i];
        }
        if(num) Msg::Error("%d duplicate element%s", num, num > 1 ? "s" : "");
      }
    
      Msg::StatusBar(2, true, "Done checking mesh coherence");
    }
    
    int GModel::removeDuplicateMeshVertices(double tolerance)
    {
      Msg::StatusBar(2, true, "Removing duplicate mesh vertices...");
    
      SBoundingBox3d bbox = bounds();
      double lc = bbox.empty() ? 1. : norm(SVector3(bbox.max(), bbox.min()));
      double eps = lc * tolerance;
    
      std::vector<GEntity*> entities;
      getEntities(entities);
    
      std::vector<MVertex*> vertices;
      for(unsigned int i = 0; i < entities.size(); i++)
        for(unsigned int j = 0; j < entities[i]->mesh_vertices.size(); j++){
          MVertex *v = entities[i]->mesh_vertices[j];
          vertices.push_back(new MVertex(v->x(), v->y(), v->z()));
        }
      MVertexPositionSet pos(vertices);
      for(unsigned int i = 0; i < vertices.size(); i++)
        pos.find(vertices[i]->x(), vertices[i]->y(), vertices[i]->z(), eps);
      int num = 0;
      for(unsigned int i = 0; i < vertices.size(); i++)
        if(!vertices[i]->getIndex()) num++;
    
      if(!num){
        for(unsigned int i = 0; i < vertices.size(); i++)
          delete vertices[i];
        Msg::Info("No duplicate vertices found");
        return 0;
      }
    
      std::map<int, std::vector<MElement*> > elements[10];
      for(unsigned int i = 0; i < entities.size(); i++){
        for(unsigned int j = 0; j < entities[i]->getNumMeshElements(); j++){
          MElement *e = entities[i]->getMeshElement(j);
          std::vector<MVertex*> verts;
          for(int k = 0; k < e->getNumVertices(); k++){
            MVertex *v = e->getVertex(k);
            MVertex *v2 = pos.find(v->x(), v->y(), v->z(), eps);
            if(v2) verts.push_back(v2);
          }
          if((int)verts.size() == e->getNumVertices()){
            MElementFactory factory;
            MElement *e2 = factory.create(e->getTypeForMSH(), verts, e->getNum(),
                                          e->getPartition());
            switch(e2->getType()){
            case TYPE_PNT: elements[0][entities[i]->tag()].push_back(e2); break;
            case TYPE_LIN: elements[1][entities[i]->tag()].push_back(e2); break;
            case TYPE_TRI: elements[2][entities[i]->tag()].push_back(e2); break;
            case TYPE_QUA: elements[3][entities[i]->tag()].push_back(e2); break;
            case TYPE_TET: elements[4][entities[i]->tag()].push_back(e2); break;
            case TYPE_HEX: elements[5][entities[i]->tag()].push_back(e2); break;
            case TYPE_PRI: elements[6][entities[i]->tag()].push_back(e2); break;
            case TYPE_PYR: elements[7][entities[i]->tag()].push_back(e2); break;
            case TYPE_POLYG: elements[8][entities[i]->tag()].push_back(e2); break;
            case TYPE_POLYH: elements[9][entities[i]->tag()].push_back(e2); break;
            }
          }
          else
            Msg::Error("Could not recreate element %d", e->getNum());
        }
      }
    
      for(unsigned int i = 0; i < entities.size(); i++)
        entities[i]->deleteMesh();
    
      for(int i = 0; i < (int)(sizeof(elements) / sizeof(elements[0])); i++)
        _storeElementsInEntities(elements[i]);
      _associateEntityWithMeshVertices();
      _storeVerticesInEntities(vertices);
    
      if(num)
        Msg::Info("Removed %d duplicate mesh %s", num, num > 1 ? "vertices" : "vertex");
    
      Msg::StatusBar(2, true, "Done removing duplicate mesh vertices");
      return num;
    }
    
    static void recurConnectMElementsByMFace(const MFace &f,
                                             std::multimap<MFace, MElement*, Less_Face> &e2f,
                                             std::set<MElement*> &group,
                                             std::set<MFace, Less_Face> &touched)
    {
      if (touched.find(f) != touched.end()) return;
      touched.insert(f);
      for (std::multimap<MFace, MElement*, Less_Face>::iterator it = e2f.lower_bound(f);
           it != e2f.upper_bound(f); ++it){
        group.insert(it->second);
        for (int i = 0; i < it->second->getNumFaces(); ++i){
          recurConnectMElementsByMFace(it->second->getFace(i), e2f, group, touched);
        }
      }
    }
    
    static int connectedVolumes(std::vector<MElement*> &elements,
                                std::vector<std::vector<MElement*> > &regs)
    {
      std::multimap<MFace, MElement*, Less_Face> e2f;
      for(unsigned int i = 0; i < elements.size(); ++i){
        for(int j = 0; j < elements[i]->getNumFaces(); j++){
          e2f.insert(std::make_pair(elements[i]->getFace(j), elements[i]));
        }
      }
      while(!e2f.empty()){
        std::set<MElement*> group;
        std::set<MFace, Less_Face> touched;
        recurConnectMElementsByMFace(e2f.begin()->first, e2f, group, touched);
        std::vector<MElement*> temp;
        temp.insert(temp.begin(), group.begin(), group.end());
        regs.push_back(temp);
        for(std::set<MFace, Less_Face>::iterator it = touched.begin();
            it != touched.end(); ++it)
          e2f.erase(*it);
      }
      return regs.size();
    }
    
    static void recurConnectMElementsByMEdge(const MEdge &e,
                                             std::multimap<MEdge, MElement*, Less_Edge> &e2e,
                                             std::set<MElement*> &group,
                                             std::set<MEdge, Less_Edge> &touched)
    {
      if (touched.find(e) != touched.end()) return;
      touched.insert(e);
      for (std::multimap <MEdge, MElement*, Less_Edge>::iterator it = e2e.lower_bound(e);
           it != e2e.upper_bound(e); ++it){
        group.insert(it->second);
        for (int i = 0; i < it->second->getNumEdges(); ++i){
          recurConnectMElementsByMEdge(it->second->getEdge(i), e2e, group, touched);
        }
      }
    }
    
    static int connectedSurfaces(std::vector<MElement*> &elements,
                                 std::vector<std::vector<MElement*> > &faces)
    {
      std::multimap<MEdge, MElement*, Less_Edge> e2e;
      for(unsigned int i = 0; i < elements.size(); ++i){
        for(int j = 0; j < elements[i]->getNumEdges(); j++){
          e2e.insert(std::make_pair(elements[i]->getEdge(j), elements[i]));
        }
      }
      while(!e2e.empty()){
        std::set<MElement*> group;
        std::set<MEdge, Less_Edge> touched;
        recurConnectMElementsByMEdge(e2e.begin()->first, e2e, group, touched);
        std::vector<MElement*> temp;
        temp.insert(temp.begin(), group.begin(), group.end());
        faces.push_back(temp);
        for(std::set<MEdge, Less_Edge>::iterator it = touched.begin();
            it != touched.end(); ++it)
          e2e.erase(*it);
      }
      return faces.size();
    }
    
    static void recurConnectMEdgesByMVertex(MVertex *v,
                                            std::multimap<MVertex*, MEdge> &v2e,
                                            std::set<MEdge, Less_Edge> &group,
                                            std::set<MVertex*> &touched)
    {
      if (touched.find(v) != touched.end()) return;
      touched.insert(v);
      for (std::multimap <MVertex*, MEdge>::iterator it = v2e.lower_bound(v); 
           it != v2e.upper_bound(v) ; ++it){
        group.insert(it->second);
        for (int i = 0; i < it->second.getNumVertices(); ++i){
          recurConnectMEdgesByMVertex(it->second.getVertex(i), v2e, group, touched);
        }
      }
    }
    
    static int connectedSurfaceBoundaries(std::set<MEdge, Less_Edge> &edges, 
                                          std::vector<std::vector<MEdge> > &boundaries)
    {
      std::multimap<MVertex*,MEdge> v2e;
      for(std::set<MEdge, Less_Edge>::iterator it = edges.begin(); it != edges.end(); it++){
        for (int j = 0; j < it->getNumVertices(); j++){
          v2e.insert(std::make_pair(it->getVertex(j), *it));
        }
      }
    
      while (!v2e.empty()){
        std::set<MEdge, Less_Edge> group;
        std::set<MVertex*> touched;
        recurConnectMEdgesByMVertex(v2e.begin()->first, v2e, group, touched);
        std::vector<MEdge> temp;
        temp.insert(temp.begin(), group.begin(), group.end());
        boundaries.push_back(temp);
        for (std::set<MVertex*>::iterator it = touched.begin() ; it != touched.end();++it)
          v2e.erase(*it);
      }
    
      return boundaries.size();
    }
    
    void GModel::makeDiscreteRegionsSimplyConnected()
    {
      Msg::Debug("Making discrete regions simply connected...");
    
      std::vector<discreteRegion*> discRegions;
      for(riter it = firstRegion(); it != lastRegion(); it++)
        if((*it)->geomType() == GEntity::DiscreteVolume)
          discRegions.push_back((discreteRegion*) *it);
    
      std::set<MVertex*> touched;
    
      for(std::vector<discreteRegion*>::iterator itR = discRegions.begin(); 
          itR != discRegions.end(); itR++){
    
        std::vector<MElement*> allElements((*itR)->getNumMeshElements());
        for(unsigned int i = 0; i < (*itR)->getNumMeshElements(); i++)
          allElements[i] = (*itR)->getMeshElement(i);
        
        std::vector<std::vector<MElement*> > conRegions;
        int nbRegions = connectedVolumes(allElements, conRegions);
        remove(*itR);
    
        for(int ire  = 0; ire < nbRegions; ire++){
          int numR = (nbRegions == 1) ? (*itR)->tag() : getMaxElementaryNumber(3) + 1;
          discreteRegion *r = new discreteRegion(this, numR);
          add(r);
          std::vector<MElement*> myElements = conRegions[ire];
          std::set<MVertex*> myVertices;
          for(unsigned int i = 0; i < myElements.size(); i++) {
            MElement *e = myElements[i];
            std::vector<MVertex*> verts;
            e->getVertices(verts);
            for(unsigned int k = 0; k < verts.size(); k++){
              if(verts[k]->onWhat() && verts[k]->onWhat()->dim() == 3){
                if(touched.find(verts[k]) == touched.end()){
                  verts[k]->setEntity(r);
                  myVertices.insert(verts[k]);
                  touched.insert(verts[k]);
                }
              }
            }
            MElementFactory factory;
            MElement *e2 = factory.create(e->getTypeForMSH(), verts, e->getNum(),
                                          e->getPartition());
            switch(e2->getType()){
            case TYPE_TET: r->tetrahedra.push_back((MTetrahedron*)e2); break;
            case TYPE_HEX: r->hexahedra.push_back((MHexahedron*)e2); break;
            case TYPE_PRI: r->prisms.push_back((MPrism*)e2); break;
            case TYPE_PYR: r->pyramids.push_back((MPyramid*)e2); break;
            }
          }
          r->mesh_vertices.insert
            (r->mesh_vertices.begin(), myVertices.begin(), myVertices.end());
        }
      }
    
      Msg::Debug("Done making discrete regions simply connected");
    }
    
    void GModel::makeDiscreteFacesSimplyConnected()
    {
      Msg::Debug("Making discrete faces simply connected...");
    
      std::vector<discreteFace*> discFaces;
      for(fiter it = firstFace(); it != lastFace(); it++)
        if((*it)->geomType() == GEntity::DiscreteSurface)
          discFaces.push_back((discreteFace*) *it);
    
      std::set<MVertex*> touched;
    
      for(std::vector<discreteFace*>::iterator itF = discFaces.begin(); 
          itF != discFaces.end(); itF++){
    
        std::vector<MElement*> allElements((*itF)->getNumMeshElements());
        for(unsigned int i = 0; i < (*itF)->getNumMeshElements(); i++)
          allElements[i] = (*itF)->getMeshElement(i);
        
        std::vector<std::vector<MElement*> > conFaces;
        int nbFaces = connectedSurfaces(allElements, conFaces);
        remove(*itF);
    
        for(int ifa  = 0; ifa < nbFaces; ifa++){
          int numF = (nbFaces == 1) ? (*itF)->tag() : getMaxElementaryNumber(2) + 1;
          discreteFace *f = new discreteFace(this, numF);
          add(f);
          std::vector<MElement*> myElements = conFaces[ifa];
          std::set<MVertex*> myVertices;
          for(unsigned int i = 0; i < myElements.size(); i++) {
            MElement *e = myElements[i];
            std::vector<MVertex*> verts;
            e->getVertices(verts);
            for(unsigned int k = 0; k < verts.size(); k++){
              if(verts[k]->onWhat() && verts[k]->onWhat()->dim() == 2){
                if(touched.find(verts[k]) == touched.end()){
                  verts[k]->setEntity(f);
                  myVertices.insert(verts[k]);
                  touched.insert(verts[k]);
                }
              }
            }
            MElementFactory factory;
            MElement *e2 = factory.create(e->getTypeForMSH(), verts, e->getNum(),
                                          e->getPartition());
            if(e2->getType() == TYPE_TRI) 
              f->triangles.push_back((MTriangle*)e2);
            else
              f->quadrangles.push_back((MQuadrangle*)e2);
          }
          f->mesh_vertices.insert
            (f->mesh_vertices.begin(), myVertices.begin(), myVertices.end());
        }
      }
    
      Msg::Debug("Done making discrete faces simply connected");
    }
    
    void GModel::createTopologyFromMesh(int ignoreHoles)
    {
      Msg::StatusBar(2, true, "Creating topology from mesh...");
      double t1 = Cpu();
    
      removeDuplicateMeshVertices(CTX::instance()->geom.tolerance);
    
      makeDiscreteRegionsSimplyConnected();
      makeDiscreteFacesSimplyConnected();
    
      // create topology for all discrete regions
      std::vector<discreteRegion*> discRegions;
      for(riter it = firstRegion(); it != lastRegion(); it++)
        if((*it)->geomType() == GEntity::DiscreteVolume)
          discRegions.push_back((discreteRegion*) *it);
      createTopologyFromRegions(discRegions);
     
      // create topology for all discrete faces
       std::vector<discreteFace*> discFaces;
       for(fiter it = firstFace(); it != lastFace(); it++)
         if((*it)->geomType() == GEntity::DiscreteSurface)
           discFaces.push_back((discreteFace*) *it);
       createTopologyFromFaces(discFaces, ignoreHoles);
    
      //create old format (necessary for boundary layers)
      exportDiscreteGEOInternals();
     
      double t2 = Cpu();
      Msg::StatusBar(2, true, "Done creating topology from mesh (%g s)", t2 - t1);
    }
    
    void GModel::createTopologyFromRegions(std::vector<discreteRegion*> &discRegions)
    {
      Msg::Debug("Creating topology from regions...");
    
      // find boundary mesh faces of each discrete region and put them in
      // map_faces, which associates each MFace with the tags of the
      // adjacent regions
      std::map<MFace, std::vector<int>, Less_Face > map_faces;
      for (std::vector<discreteRegion*>::iterator it = discRegions.begin(); 
           it != discRegions.end(); it++)
        (*it)->findFaces(map_faces);
    
      // get currently defined discrete faces
      std::vector<discreteFace*> discFaces;
      for(fiter it = firstFace(); it != lastFace(); it++)
        if((*it)->geomType() == GEntity::DiscreteSurface)
          discFaces.push_back((discreteFace*) *it);
    
      // create reverse map storing for each discrete region the list of
      // discrete faces on its boundary
      std::map<int, std::set<int> > region2Faces;
      std::set<MVertex*> touched;
    
      while (!map_faces.empty()){
    
        Msg::Debug("... %d mesh faces left to process", map_faces.size());
        
        // get mesh faces with identical region connections (i.e., a part
        // of region boundaries that can be later defined as a discrete
        // face)
        std::set<MFace, Less_Face> myFaces;
        std::vector<int> tagRegions = map_faces.begin()->second;
        myFaces.insert(map_faces.begin()->first);
        map_faces.erase(map_faces.begin());
        std::map<MFace, std::vector<int>, Less_Face>::iterator itmap = map_faces.begin();
        while (itmap != map_faces.end()){
          std::vector<int> tagRegions2 = itmap->second;
          if (tagRegions2 == tagRegions){
            myFaces.insert(itmap->first);
            map_faces.erase(itmap++);
          }
          else
            itmap++;
        }
        
        // if the mesh already contains discrete faces, check if the
        // candidate discrete face does contain any of those; if not,
        // create a new discreteFace. Then create populate the
        // region2Faces map that associates for each region the (old or
        // new) boundary discrete faces
        for (std::vector<discreteFace*>::iterator itF = discFaces.begin(); 
             itF != discFaces.end(); itF++){
    
          bool candidate = true;
          for (unsigned int i = 0; i < (*itF)->getNumMeshElements(); i++){
            MFace mf = (*itF)->getMeshElement(i)->getFace(0);
            std::set<MFace, Less_Face>::iterator itset = myFaces.find(mf);
            if (itset == myFaces.end()){
              candidate = false;
              break;
            }
          }
    
          if(candidate){
            std::set<int> tagFaces;
            tagFaces.insert((*itF)->tag());
            for (unsigned int i = 0; i < (*itF)->getNumMeshElements(); i++){
              MFace mf = (*itF)->getMeshElement(i)->getFace(0);
              std::set<MFace, Less_Face>::iterator itset = myFaces.find(mf);
              myFaces.erase(itset);
            }
            for(std::vector<int>::iterator itReg = tagRegions.begin(); 
                itReg != tagRegions.end(); itReg++) {
              std::map<int, std::set<int> >::iterator it = region2Faces.find(*itReg);
              if (it == region2Faces.end())
                region2Faces.insert(std::make_pair(*itReg, tagFaces));
              else{
                std::set<int> allFaces = it->second;
                allFaces.insert(tagFaces.begin(), tagFaces.end());
                it->second = allFaces;
              }
            }
          }
        }
    
        // create new discrete face
        if(myFaces.size()){
          int numF = getMaxElementaryNumber(2) + 1;
          discreteFace *f = new discreteFace(this, numF);
          add(f);
          discFaces.push_back(f);
          std::set<MVertex*> myVertices;
          for(std::set<MFace, Less_Face>::iterator it = myFaces.begin(); 
              it != myFaces.end(); it++){
            std::vector<MVertex*> verts(it->getNumVertices());
            for(int i = 0; i < it->getNumVertices(); i++){
              verts[i] = it->getVertex(i);
              if(verts[i]->onWhat() && verts[i]->onWhat()->dim() == 3){
                if(touched.find(verts[i]) != touched.end()){
                  myVertices.insert(verts[i]);
                  verts[i]->setEntity(f);
                  touched.insert(verts[i]);
                }
              }
            }
            if(verts.size() == 4)
              f->quadrangles.push_back(new MQuadrangle(verts));
            else
              f->triangles.push_back(new MTriangle(verts));
          }
          f->mesh_vertices.insert(f->mesh_vertices.begin(), 
                                  myVertices.begin(), myVertices.end());
    
          for (std::vector<int>::iterator itReg = tagRegions.begin(); 
               itReg != tagRegions.end(); itReg++) {
    
            // delete mesh vertices of new edge from adjacent regions
            GRegion *dReg = getRegionByTag(*itReg);
            for (std::set<MVertex*>::iterator itv = myVertices.begin(); 
                 itv != myVertices.end(); itv++) {
              std::vector<MVertex*>::iterator itve =
                std::find(dReg->mesh_vertices.begin(), dReg->mesh_vertices.end(), *itv);
              if (itve != dReg->mesh_vertices.end()) dReg->mesh_vertices.erase(itve);
            }
    
            // fill region2Faces with the new face
            std::map<int, std::set<int> >::iterator r2f = region2Faces.find(*itReg);
            if (r2f == region2Faces.end()){
              std::set<int> tagFaces;
              tagFaces.insert(numF);
              region2Faces.insert(std::make_pair(*itReg, tagFaces));
            }
            else{
              std::set<int> tagFaces = r2f->second;
              tagFaces.insert(numF);
              r2f->second = tagFaces;
            }
    
          }
        }
    
      }
    
      // set boundary faces for each region
      for (std::vector<discreteRegion*>::iterator it = discRegions.begin(); 
           it != discRegions.end(); it++){
        std::map<int, std::set<int> >::iterator itr = region2Faces.find((*it)->tag());
        if (itr != region2Faces.end()){
          std::set<int> bcFaces = itr->second;
          (*it)->setBoundFaces(bcFaces);
        }
      }
    
      Msg::Debug("Done creating topology from regions");
    }
    
    void GModel::createTopologyFromFaces(std::vector<discreteFace*> &discFaces, int ignoreHoles)
    {
      Msg::Debug("Creating topology from faces...");
    
      // find boundary mesh edges of each discrete face and put them in
      // map_edges, which associates each MEdge with the tags of the
      // adjacent faces
      std::map<MEdge, std::vector<int>, Less_Edge > map_edges;
      for (std::vector<discreteFace*>::iterator it = discFaces.begin(); 
           it != discFaces.end(); it++)
        (*it)->findEdges(map_edges);
      
      // return if no boundary edges (torus, sphere, ...)
      if (map_edges.empty()) return;
      
      // get currently defined discrete edges
      std::vector<discreteEdge*> discEdges;
      for(eiter it = firstEdge(); it != lastEdge(); it++){
        if((*it)->geomType() == GEntity::DiscreteCurve)
          discEdges.push_back((discreteEdge*) *it);
      }
      
      // create reverse map storing for each discrete face the list of
      // discrete edges on its boundary
      std::map<int, std::vector<int> > face2Edges;
    
      while (!map_edges.empty()){
    
        Msg::Debug("... %d mesh edges left to process", map_edges.size());
    
        // get mesh edges with identical face connections (i.e., a part of
        // face boundaries that can be later defined as a discrete edge)
        std::set<MEdge, Less_Edge> myEdges;
        std::vector<int> tagFaces = map_edges.begin()->second;
        myEdges.insert(map_edges.begin()->first);
        map_edges.erase(map_edges.begin());
        std::map<MEdge, std::vector<int>, Less_Edge>::iterator itmap = map_edges.begin();
        while (itmap != map_edges.end()){
          std::vector<int> tagFaces2 = itmap->second;
          if (tagFaces2 == tagFaces){
            myEdges.insert(itmap->first);
            map_edges.erase(itmap++);
          }
          else
            itmap++;
        }
    
        // if the mesh already contains discrete edges, check if the
        // candidate discrete edge does contain any of those; if not,
        // create a discreteEdge. Then populate the face2Edges map that
        // associates for each face its boundary discrete edges
        for (std::vector<discreteEdge*>::iterator itE = discEdges.begin(); 
             itE != discEdges.end(); itE++){
    
          bool candidate = true;
          for (unsigned int i = 0; i < (*itE)->getNumMeshElements(); i++){
            MEdge me = (*itE)->getMeshElement(i)->getEdge(0);
            std::set<MEdge, Less_Edge >::iterator itset = myEdges.find(me);
            if (itset == myEdges.end()){
              candidate = false;
              break;
            }
          }
    
          if (candidate){
            std::vector<int> tagEdges;
            tagEdges.push_back((*itE)->tag());
            for (unsigned int i = 0; i < (*itE)->getNumMeshElements(); i++){
              MEdge me = (*itE)->getMeshElement(i)->getEdge(0);
              std::set<MEdge, Less_Edge >::iterator itset = myEdges.find(me);
              myEdges.erase(itset);
            }
            for (std::vector<int>::iterator itFace = tagFaces.begin(); 
                 itFace != tagFaces.end(); itFace++) {
              std::map<int, std::vector<int> >::iterator it = face2Edges.find(*itFace);
              if (it == face2Edges.end())
                face2Edges.insert(std::make_pair(*itFace, tagEdges));
              else{
                std::vector<int> allEdges = it->second;
                allEdges.insert(allEdges.begin(), tagEdges.begin(), tagEdges.end());
                it->second = allEdges;
              }
            }
          }
        }
      
        std::vector<std::vector<MEdge> > boundaries;
        int nbBounds = connectedSurfaceBoundaries(myEdges, boundaries);   
    
        //EMI RBF fix
        if (ignoreHoles && nbBounds > 0){
          int index = 0;
          int boundSize = 0;
          for (int ib = 0; ib < nbBounds; ib++){
    	if (boundaries[ib].size() > boundSize){
    	  boundSize = boundaries[ib].size() ;
    	  index = ib;
    	}
          }
          std::vector<std::vector<MEdge> > new_boundaries;
          new_boundaries.push_back(boundaries[index]);
          boundaries =  new_boundaries;
        }
    
        // create new discrete edges
        for (int ib = 0; ib < boundaries.size(); ib++){
          int numE = getMaxElementaryNumber(1) + 1;
          discreteEdge *e = new discreteEdge(this, numE, 0, 0);
          add(e);
          discEdges.push_back(e);
          std::set<MVertex*> allV;
          for(unsigned int i = 0; i < boundaries[ib].size(); i++) {
            MVertex *v0 = boundaries[ib][i].getVertex(0);
            MVertex *v1 = boundaries[ib][i].getVertex(1);
            e->lines.push_back(new MLine(v0, v1));
    	allV.insert(v0);
    	allV.insert(v1);
            v0->setEntity(e);
            v1->setEntity(e);
          }
          e->mesh_vertices.insert(e->mesh_vertices.begin(), allV.begin(), allV.end());
          for (std::vector<int>::iterator itFace = tagFaces.begin(); 
               itFace != tagFaces.end(); itFace++) {
            // delete mesh vertices of new edge from adjacent faces
            GFace *dFace = getFaceByTag(*itFace);
            for (std::set<MVertex*>::iterator itv = allV.begin(); itv != allV.end(); itv++) {
              std::vector<MVertex*>::iterator itve = 
                std::find(dFace->mesh_vertices.begin(), dFace->mesh_vertices.end(), *itv);
              if (itve != dFace->mesh_vertices.end()) dFace->mesh_vertices.erase(itve);
            }
            // fill face2Edges with the new edge
            std::map<int, std::vector<int> >::iterator f2e = face2Edges.find(*itFace);
            if (f2e == face2Edges.end()){
              std::vector<int> tagEdges;
              tagEdges.push_back(numE);
              face2Edges.insert(std::make_pair(*itFace, tagEdges));
            }
            else{
              std::vector<int> tagEdges = f2e->second;
              tagEdges.push_back(numE);
              f2e->second = tagEdges;
            }
          }
        }
    
      }
    
      // set boundary edges for each face
      for (std::vector<discreteFace*>::iterator it = discFaces.begin();
           it != discFaces.end(); it++){
        std::map<int, std::vector<int> >::iterator ite = face2Edges.find((*it)->tag());
        if (ite != face2Edges.end()){
          std::vector<int> bcEdges = ite->second;
          (*it)->setBoundEdges(bcEdges);
        }
      }
    
      Msg::Debug("Done creating topology from faces");
    
      Msg::Debug("Creating topology for %d edges...", discEdges.size());
    
      // for each discreteEdge, create topology
      std::map<GFace*, std::map<MVertex*, MVertex*, std::less<MVertex*> > > face2Vert;
      std::map<GRegion*, std::map<MVertex*, MVertex*, std::less<MVertex*> > > region2Vert;
      face2Vert.clear();
      region2Vert.clear();
      for (std::vector<discreteEdge*>::iterator it = discEdges.begin();
           it != discEdges.end(); it++){
        (*it)->createTopo();
        (*it)->parametrize(face2Vert, region2Vert);
      }
    
      // fill edgeLoops of Faces or correct sign of l_edges
      // for (std::vector<discreteFace*>::iterator itF = discFaces.begin();
      //       itF != discFaces.end(); itF++){
      //    //EMI, TODO
      //    std::list<GEdgeLoop> edgeLoops = (*itF)->edgeLoops; 
      //    edgeLoops.clear();
      //    GEdgeLoop el((*itF)->edges());
      //    edgeLoops.push_back(el);
      //  }
    
      Msg::Debug("Done creating topology for edges...");
    
    
      // we need to recreate all mesh elements because some mesh vertices
      // might have been changed during the parametrization process
      // (MVertices became MEdgeVertices)
      for (std::map<GFace*, std::map<MVertex*, MVertex*, std::less<MVertex*> > >::iterator
             iFace = face2Vert.begin(); iFace != face2Vert.end(); iFace++){
        std::map<MVertex*, MVertex*, std::less<MVertex*> > old2new = iFace->second;
        GFace *gf = iFace->first;
        std::vector<MTriangle*> newTriangles;
        std::vector<MQuadrangle*> newQuadrangles;
        for (unsigned int i = 0; i < gf->getNumMeshElements(); ++i){
          MElement *e = gf->getMeshElement(i);
          std::vector<MVertex *> v;
          e->getVertices(v);
          for (unsigned int j = 0; j < v.size(); j++){
            std::map<MVertex*, MVertex*, std::less<MVertex*> >::iterator 
              itmap = old2new.find(v[j]);
            if (itmap != old2new.end()) 
              v[j] = itmap->second;
          }
          MElementFactory factory;
          MElement *e2 = factory.create(e->getTypeForMSH(), v, e->getNum(),
                                        e->getPartition());
          switch(e2->getType()){
          case TYPE_TRI: newTriangles.push_back((MTriangle*)e2); break;
          case TYPE_QUA: newQuadrangles.push_back((MQuadrangle*)e2); break;
          }
        }
        gf->deleteVertexArrays();
        for(unsigned int i = 0; i < gf->triangles.size(); i++) delete gf->triangles[i];
        for(unsigned int i = 0; i < gf->quadrangles.size(); i++) delete gf->quadrangles[i];
        gf->triangles = newTriangles;
        gf->quadrangles = newQuadrangles;
      }
      
      for (std::map<GRegion*, std::map<MVertex*, MVertex*, std::less<MVertex*> > >::iterator
             iRegion = region2Vert.begin(); iRegion != region2Vert.end(); iRegion++){
        std::map<MVertex*, MVertex*, std::less<MVertex*> > old2new = iRegion->second;
        GRegion *gr = iRegion->first;
        std::vector<MTetrahedron*> newTetrahedra;
        std::vector<MHexahedron*> newHexahedra;
        std::vector<MPrism*> newPrisms;
        std::vector<MPyramid*> newPyramids;
        for (unsigned int i = 0; i < gr->getNumMeshElements(); ++i){
          MElement *e = gr->getMeshElement(i);
          std::vector<MVertex *> v;
          e->getVertices(v);
          for (unsigned int j = 0; j < v.size(); j++){
            std::map<MVertex*, MVertex*, std::less<MVertex*> >::iterator 
              itmap = old2new.find(v[j]);
            if (itmap != old2new.end()) 
              v[j] = itmap->second;
          }
          MElementFactory factory;
          MElement *e2 = factory.create(e->getTypeForMSH(), v, e->getNum(),
                                        e->getPartition());
          switch(e2->getType()){
          case TYPE_TET: newTetrahedra.push_back((MTetrahedron*)e2); break;
          case TYPE_HEX: newHexahedra.push_back((MHexahedron*)e2); break;
          case TYPE_PRI: newPrisms.push_back((MPrism*)e2); break;
          case TYPE_PYR: newPyramids.push_back((MPyramid*)e2); break;
          }
        }
        gr->deleteVertexArrays();
        for(unsigned int i = 0; i < gr->tetrahedra.size(); i++) delete gr->tetrahedra[i];
        for(unsigned int i = 0; i < gr->hexahedra.size(); i++) delete gr->hexahedra[i];
        for(unsigned int i = 0; i < gr->prisms.size(); i++) delete gr->prisms[i];
        for(unsigned int i = 0; i < gr->pyramids.size(); i++) delete gr->pyramids[i];
        gr->tetrahedra = newTetrahedra;
        gr->hexahedra = newHexahedra;
        gr->prisms = newPrisms;
        gr->pyramids = newPyramids;
      }
    
      Msg::Debug("Done creating topology from edges");
    }
    
    GModel *GModel::buildCutGModel(gLevelset *ls, bool cutElem, bool saveTri)
    {
      
      if (saveTri)
       CTX::instance()->mesh.saveTri = 1;
      else
       CTX::instance()->mesh.saveTri = 0;
    
      std::map<int, std::vector<MElement*> > elements[10];
      std::map<int, std::map<int, std::string> > physicals[4];
      std::map<int, MVertex*> vertexMap;
    
      Msg::Info("Cutting mesh...");
      double t1 = Cpu();
    
      GModel *cutGM = buildCutMesh(this, ls, elements, vertexMap, physicals, cutElem);
    
    
      for(int i = 0; i < (int)(sizeof(elements) / sizeof(elements[0])); i++)
        cutGM->_storeElementsInEntities(elements[i]);
      cutGM->_associateEntityWithMeshVertices();
      cutGM->_storeVerticesInEntities(vertexMap);
    
      for(int i = 0; i < 4; i++){
        cutGM->_storePhysicalTagsInEntities(i, physicals[i]);
        std::map<int, std::map<int, std::string> >::iterator it = physicals[i].begin();
        for(; it != physicals[i].end(); it++){
          std::map<int, std::string>::iterator it2 = it->second.begin();
          for(; it2 != it->second.end(); it2++)
            if(it2->second != "")
              cutGM->setPhysicalName(it2->second, i, it2->first);
        }
      }
    
    
      Msg::Info("Mesh cutting completed (%g s)", Cpu() - t1);
    
      return cutGM;
    }
    
    void GModel::load(std::string fileName)
    {
      GModel *temp = GModel::current();
      GModel::setCurrent(this);
      MergeFile(fileName, true);
      GModel::setCurrent(temp);
    }
    
    void GModel::save(std::string fileName)
    {
      GModel *temp = GModel::current();
      GModel::setCurrent(this);
      int guess = GuessFileFormatFromFileName(fileName);
      CreateOutputFile(fileName, guess);
      GModel::setCurrent(temp);
    }
    
    GFaceCompound* GModel::addCompoundFace(std::vector<GFace*> faces, int typeP, int typeS)
    {
    
      int num =  getMaxElementaryNumber(2) + 1;
    
      std::list<GFace*> comp(faces.begin(), faces.end());
      std::list<GEdge*> U0;
    
      GFaceCompound::typeOfMapping typ = GFaceCompound::HARMONIC;
      if (typeP == 1) typ =  GFaceCompound::CONFORMAL;
      if (typeP == 2) typ =  GFaceCompound::RBF;
    
      GFaceCompound *gfc = new GFaceCompound(this, num, comp, U0, typ, typeS);
    
      add(gfc);
    
      return gfc;
    
    }
    
    GVertex *GModel::addVertex(double x, double y, double z, double lc)
    {
      if(_factory) return _factory->addVertex(this, x, y, z, lc);
      return 0;
    }
    
    GEdge *GModel::addLine(GVertex *v1, GVertex *v2)
    {
      if(_factory) return _factory->addLine(this, v1, v2);
      return 0;
    }
    
    GEdge *GModel::addCircleArcCenter(double x, double y, double z, GVertex *start, 
                                      GVertex *end)
    {
      if(_factory)
        return _factory->addCircleArc(this, GModelFactory::CENTER_START_END,
                                      start, end, SPoint3(x, y, z));
      return 0;
    }
    
    GEdge *GModel::addCircleArc3Points(double x, double y, double z, GVertex *start,
                                       GVertex *end)
    {
      if(_factory) 
        return _factory->addCircleArc(this, GModelFactory::THREE_POINTS, 
                                      start, end, SPoint3(x, y, z));
      return 0;
    }
    
    GEdge *GModel::addBezier(GVertex *start, GVertex *end, 
    			 std::vector<std::vector<double> > points) 
    {
      if(_factory) 
        return _factory->addSpline(this, GModelFactory::BEZIER, start, end, 
                                   points);
      return 0;
    }
    
    GEdge *GModel::addNURBS(GVertex *start, GVertex *end,
    			std::vector<std::vector<double> > points, 
    			std::vector<double> knots,
    			std::vector<double> weights, 
    			std::vector<int> mult)
    { 
      if(_factory)
        return _factory->addNURBS(this, start,end,points,knots,weights, mult);
      return 0;
    }
    
    void GModel::addRuledFaces (std::vector<std::vector<GEdge *> > edges)
    {
      if(_factory)
        _factory->addRuledFaces(this, edges);
    }
    
    GFace* GModel::addFace (std::vector<GEdge *> edges,
                            std::vector< std::vector<double > > points)
    {
      if(_factory)
        return _factory->addFace(this, edges, points);
      return 0;
    }
    
    
    GFace* GModel::addPlanarFace (std::vector<std::vector<GEdge *> > edges){
      if(_factory)
        return _factory->addPlanarFace(this, edges);
      return 0;
    }
    
    GRegion* GModel::addVolume (std::vector<std::vector<GFace *> > faces){
      if(_factory)
        return _factory->addVolume(this, faces);
      return 0;
    }
    
    GEntity *GModel::revolve(GEntity *e, std::vector<double> p1, std::vector<double> p2,
                             double angle)
    {
      if(_factory)
        return _factory->revolve(this, e, p1, p2, angle);
      return 0;
    }
    
    GEntity *GModel::extrude(GEntity *e, std::vector<double> p1, std::vector<double> p2)
    {
      if(_factory) 
        return _factory->extrude(this, e, p1, p2);
      return 0;
    }
    
    GEntity *GModel::addPipe(GEntity *e, std::vector<GEdge *>  edges)
    {
      if(_factory) 
        return _factory->addPipe(this,e,edges);
      return 0;
    }
    
    GEntity *GModel::addSphere(double cx, double cy, double cz, double radius)
    {
      if(_factory) return _factory->addSphere(this, cx, cy, cz, radius);
      return 0;
    }
    
    GEntity *GModel::addCylinder(std::vector<double> p1, std::vector<double> p2, 
                                 double radius)
    {
      if(_factory) return _factory->addCylinder(this, p1, p2, radius);
      return 0;
    }
    
    GEntity *GModel::addTorus(std::vector<double> p1, std::vector<double> p2, 
                              double radius1, double radius2)
    {
      if(_factory) return _factory->addTorus(this, p1, p2, radius1, radius2);
      return 0;
    }
    
    GEntity *GModel::addBlock(std::vector<double> p1, std::vector<double> p2)
    {
      if(_factory) return _factory->addBlock(this, p1, p2);
      return 0;
    }
    
    GEntity *GModel::addCone(std::vector<double> p1, std::vector<double> p2,
                             double radius1, double radius2)
    {
      if(_factory) return _factory->addCone(this, p1, p2,radius1, radius2);
      return 0;
    }
    
    GModel *GModel::computeBooleanUnion(GModel *tool, int createNewModel)
    {
      if(_factory)
        return _factory->computeBooleanUnion(this, tool, createNewModel);
      return 0;
    }
    
    GModel *GModel::computeBooleanIntersection(GModel *tool, int createNewModel)
    {
      if(_factory)
        return _factory->computeBooleanIntersection(this, tool, createNewModel);
      return 0;
    }
    
    GModel *GModel::computeBooleanDifference(GModel *tool, int createNewModel)
    {
      if(_factory)
        return _factory->computeBooleanDifference(this, tool, createNewModel);
      return 0;
    }
    
    static void computeDuplicates(GModel *model, 
                                  std::multimap<GVertex*, GVertex*> &Unique2Duplicates,
                                  std::map<GVertex*, GVertex*> &Duplicates2Unique,
                                  const double &eps)
    {
      // FIXME: currently we use a greedy algorithm in n^2 (using a
      // kd-tree: cf. MVertexPositionSet)
      // FIXME: add option to remove orphaned entities after duplicate check
      std::list<GVertex*> v;
      v.insert(v.begin(), model->firstVertex(), model->lastVertex());
    
      while(!v.empty()){
        GVertex *pv = *v.begin();
        v.erase(v.begin());
        bool found = false;
        for (std::multimap<GVertex*,GVertex*>::iterator it = Unique2Duplicates.begin(); 
             it != Unique2Duplicates.end(); ++it){
          GVertex *unique = it->first;
          const double d = sqrt((unique->x() - pv->x()) * (unique->x() - pv->x()) +
                                (unique->y() - pv->y()) * (unique->y() - pv->y()) +
                                (unique->z() - pv->z()) * (unique->z() - pv->z()));
          if (d <= eps && pv->geomType() == unique->geomType()) {
    	found = true;
    	Unique2Duplicates.insert(std::make_pair(unique, pv));
    	Duplicates2Unique[pv] = unique;
    	break;
          }
        }
        if (!found) {
          Unique2Duplicates.insert(std::make_pair(pv, pv));
          Duplicates2Unique[pv] = pv;
        }
      }  
    }
    
    static void glueVerticesInEdges(GModel *model, 
                                    std::multimap<GVertex*, GVertex*> &Unique2Duplicates,
    				std::map<GVertex*, GVertex*> &Duplicates2Unique)
    {
      Msg::Debug("Gluing Edges");
      for (GModel::eiter it = model->firstEdge(); it != model->lastEdge(); ++it){
        GEdge *e = *it;
        GVertex *v1 = e->getBeginVertex();
        GVertex *v2 = e->getEndVertex();
        GVertex *replacementOfv1 = Duplicates2Unique[v1];
        GVertex *replacementOfv2 = Duplicates2Unique[v2];
        if ((v1 != replacementOfv1) || (v2 != replacementOfv2)){
          Msg::Debug("Model Edge %d is re-build", e->tag());
          e->replaceEndingPoints (replacementOfv1, replacementOfv2);
        }
      }
    }
    
    static void computeDuplicates(GModel *model,
                                  std::multimap<GEdge*, GEdge*> &Unique2Duplicates,
                                  std::map<GEdge*,GEdge*> &Duplicates2Unique,
                                  const double &eps)
    {
      std::list<GEdge*> e;
      e.insert(e.begin(), model->firstEdge(), model->lastEdge());
    
      while(!e.empty()){
        GEdge *pe = *e.begin();
        e.erase(e.begin());
        bool found = false;
        for (std::multimap<GEdge*,GEdge*>::iterator it = Unique2Duplicates.begin(); 
             it != Unique2Duplicates.end(); ++it ){
          GEdge *unique = it->first;
          // first check edges that have same endpoints
          if (((unique->getBeginVertex() == pe->getBeginVertex() && 
                unique->getEndVertex() == pe->getEndVertex()) ||
               (unique->getEndVertex() == pe->getBeginVertex() && 
                unique->getBeginVertex() == pe->getEndVertex())) &&
              unique->geomType() == pe->geomType()){
    	if ((unique->geomType() == GEntity::Line && pe->geomType() == GEntity::Line) ||
                unique->geomType() == GEntity::DiscreteCurve || 
                pe->geomType() == GEntity::DiscreteCurve ||
                unique->geomType() == GEntity::BoundaryLayerCurve || 
                pe->geomType() == GEntity::BoundaryLayerCurve){
    	  found = true;
    	  Unique2Duplicates.insert(std::make_pair(unique,pe));
    	  Duplicates2Unique[pe] = unique;
    	  break;	  
    	} 
            // compute a point
            Range<double> r = pe->parBounds(0);
            GPoint gp = pe->point(0.5 * (r.low() + r.high()));
    	double t;
    	GPoint gp2 = pe->closestPoint(SPoint3(gp.x(),gp.y(),gp.z()),t);
    	const double d = sqrt((gp.x() - gp2.x()) * (gp.x() - gp2.x()) +
    			      (gp.y() - gp2.y()) * (gp.y() - gp2.y()) +
    			      (gp.z() - gp2.z()) * (gp.z() - gp2.z()));
    	if (t >= r.low() && t <= r.high() && d <= eps) {
    	  found = true;
    	  Unique2Duplicates.insert(std::make_pair(unique,pe));
    	  Duplicates2Unique[pe] = unique;
    	  break;
    	}
          }
        }
        if (!found) {
          Unique2Duplicates.insert(std::make_pair(pe,pe));
          Duplicates2Unique[pe] = pe;
        }
      }
    }
    
    static void glueEdgesInFaces(GModel *model, 
                                 std::multimap<GEdge*, GEdge*> &Unique2Duplicates,
    			     std::map<GEdge*, GEdge*> &Duplicates2Unique)
    {
      Msg::Debug("Gluing Model Faces");
      for (GModel::fiter it = model->firstFace(); it != model->lastFace(); ++it){
        GFace *f = *it;
        bool aDifferenceExists = false;
        std::list<GEdge*> old = f->edges(), enew;
        for (std::list<GEdge*>::iterator eit = old.begin(); eit !=old.end(); eit++){
          GEdge *temp = Duplicates2Unique[*eit];
          enew.push_back(temp);
          if (temp != *eit){
    	aDifferenceExists = true;
          }
        }
        if (aDifferenceExists){
          Msg::Debug("Model Face %d is re-build", f->tag());
          f->replaceEdges (enew);
        }
      }
    }
    
    static void computeDuplicates(GModel *model, 
                                  std::multimap<GFace*, GFace*> &Unique2Duplicates,
                                  std::map<GFace*,GFace*> &Duplicates2Unique, 
                                  const double &eps)
    {
      std::list<GFace*> f;
      f.insert(f.begin(),model->firstFace(),model->lastFace());
    
      while(!f.empty()){
        GFace *pf = *f.begin();
        Range<double> r = pf->parBounds(0);
        Range<double> s = pf->parBounds(1);
        f.erase(f.begin());
        std::list<GEdge*> pf_edges = pf->edges();
        pf_edges.sort();
        bool found = false;
        for (std::multimap<GFace*,GFace*>::iterator it = Unique2Duplicates.begin();
             it != Unique2Duplicates.end(); ++it){
          GFace *unique = it->first;      
          std::list<GEdge*> unique_edges = unique->edges();
          if (pf->geomType() == unique->geomType() && 
              unique_edges.size() == pf_edges.size()){
    	unique_edges.sort();
    	std::list<GEdge*>::iterator it_pf = pf_edges.begin();
    	std::list<GEdge*>::iterator it_unique = unique_edges.begin();
    	bool all_similar = true;
    	// first check faces that have same edges
    	for (; it_pf !=  pf_edges.end() ;  ++it_pf,it_unique++){
    	  if (*it_pf != *it_unique) all_similar = false;
    	}
    	if (all_similar){
    	  if (unique->geomType() == GEntity::Plane && pf->geomType() == GEntity::Plane){
    	    found = true;
    	    Unique2Duplicates.insert(std::make_pair(unique,pf));
    	    Duplicates2Unique[pf] = unique;
    	    break;	  
    	  } 
    	  double t[2]={0,0};
              // FIXME: evaluate a point on the surface (use e.g. buildRepresentationCross)
    	  const double d = 1.0; 
    	  if (t[0] >= r.low() && t[0] <= r.high() && 
    	      t[1] >= s.low() && t[1] <= s.high() && d <= eps) {
    	    found = true;
    	    Unique2Duplicates.insert(std::make_pair(unique,pf));
    	    Duplicates2Unique[pf] = unique;
    	    break;
    	  }
    	}
          }
        }
        if (!found) {
          Unique2Duplicates.insert(std::make_pair(pf,pf));
          Duplicates2Unique[pf] = pf;
        }
      }
    }
    
    static void glueFacesInRegions(GModel *model,
                                   std::multimap<GFace*, GFace*> &Unique2Duplicates,
    			       std::map<GFace*, GFace*> &Duplicates2Unique)
    {
      Msg::Debug("Gluing Regions");
      for (GModel::riter it = model->firstRegion(); it != model->lastRegion();++it){
        GRegion *r = *it;
        bool aDifferenceExists = false;
        std::list<GFace*> old = r->faces(), fnew;
        for (std::list<GFace*>::iterator fit = old.begin(); fit != old.end(); fit++){
          std::map<GFace*, GFace*>::iterator itR = Duplicates2Unique.find(*fit);
          if (itR == Duplicates2Unique.end()){
            Msg::Fatal("Error in the gluing process");
          }
          GFace *temp = itR->second;;
          fnew.push_back(temp);
          if (temp != *fit){
    	aDifferenceExists = true;
          }
        }
        if (aDifferenceExists){
          Msg::Debug("Model Region %d is re-build", r->tag());
          r->replaceFaces (fnew);
        }
      }
    }
    
    void GModel::glue(double eps)
    {
      {
        std::multimap<GVertex*,GVertex*> Unique2Duplicates;
        std::map<GVertex*,GVertex*> Duplicates2Unique;
        computeDuplicates(this, Unique2Duplicates, Duplicates2Unique, eps);
        glueVerticesInEdges(this, Unique2Duplicates, Duplicates2Unique);
      }
      {
        std::multimap<GEdge*,GEdge*> Unique2Duplicates;
        std::map<GEdge*,GEdge*> Duplicates2Unique;
        computeDuplicates(this, Unique2Duplicates, Duplicates2Unique, eps);
        glueEdgesInFaces(this, Unique2Duplicates, Duplicates2Unique);
      }    
      {
        std::multimap<GFace*,GFace*> Unique2Duplicates;
        std::map<GFace*,GFace*> Duplicates2Unique;
        computeDuplicates(this, Unique2Duplicates, Duplicates2Unique, eps);
        glueFacesInRegions(this, Unique2Duplicates, Duplicates2Unique);
      }    
    }
    
    GEdge *getNewModelEdge(GFace *gf1, GFace *gf2, 
                           std::map<std::pair<int, int>, GEdge*> &newEdges)
    {
      int t1 = gf1 ? gf1->tag() : -1;
      int t2 = gf2 ? gf2->tag() : -1;
      int i1 = std::min(t1, t2);
      int i2 = std::max(t1, t2);
    
      if(i1 == i2) return 0;
    
      std::map<std::pair<int, int>, GEdge*>::iterator it = 
        newEdges.find(std::make_pair<int, int>(i1, i2));
      if(it == newEdges.end()){
        discreteEdge *ge = new discreteEdge
          (GModel::current(), GModel::current()->getMaxElementaryNumber(1) + 1, 0, 0);
        GModel::current()->add(ge);
        newEdges[std::make_pair<int, int>(i1, i2)] = ge;
        return ge;
      }
      else
        return it->second;  
    }
    
    #if defined(HAVE_MESH)
    
    void recurClassifyEdges(MTri3 *t, std::map<MTriangle*, GFace*> &reverse,
                            std::map<MLine*, GEdge*, compareMLinePtr> &lines,
                            std::set<MLine*> &touched, std::set<MTri3*> &trisTouched,
                            std::map<std::pair<int, int>, GEdge*> &newEdges)
    {
      if(!t->isDeleted()){
        trisTouched.erase(t);
        t->setDeleted(true);
        GFace *gf1 = reverse[t->tri()];
        for(int i = 0; i < 3; i++){
          GFace *gf2 = 0;
          MTri3 *tn = t->getNeigh(i);
          if(tn)
            gf2 = reverse[tn->tri()];
          edgeXface exf(t, i);
          MLine ml(exf.v[0], exf.v[1]);
          std::map<MLine*, GEdge*, compareMLinePtr>::iterator it = lines.find(&ml);
          if(it != lines.end()){
            if(touched.find(it->first) == touched.end()){
              GEdge *ge =  getNewModelEdge(gf1, gf2, newEdges);
              if(ge) ge->lines.push_back(it->first);
              touched.insert(it->first);
            }
          }
          if(tn)
            recurClassifyEdges(tn, reverse, lines, touched, trisTouched,newEdges);
        }
      }
    }
    
    void recurClassify(MTri3 *t, GFace *gf,
                       std::map<MLine*, GEdge*, compareMLinePtr> &lines,
                       std::map<MTriangle*, GFace*> &reverse)
    {
      if(!t->isDeleted()){
        gf->triangles.push_back(t->tri());
        reverse[t->tri()] = gf;
        t->setDeleted(true);
        for(int i = 0; i < 3; i++){
          MTri3 *tn = t->getNeigh(i);
          if(tn){
            edgeXface exf(t, i);
            MLine ml(exf.v[0], exf.v[1]);       
            std::map<MLine*, GEdge*, compareMLinePtr>::iterator it = lines.find(&ml);
            if(it == lines.end())
              recurClassify(tn, gf, lines, reverse);
          }
        }  
      }
    }
    
    #endif
    
    void GModel::detectEdges(double _tresholdAngle)
    {
    #if defined(HAVE_MESH)
      e2t_cont adj;
      std::vector<MTriangle*> elements;
      std::vector<edge_angle> edges_detected, edges_lonly;
      for(GModel::fiter it = GModel::current()->firstFace(); 
          it != GModel::current()->lastFace(); ++it)
        elements.insert(elements.end(), (*it)->triangles.begin(), 
    		    (*it)->triangles.end());  
      buildEdgeToTriangle(elements, adj);
      buildListOfEdgeAngle(adj, edges_detected, edges_lonly);
      GEdge *selected = new discreteEdge
        (this, getMaxElementaryNumber(1) + 1, 0, 0);
      add(selected);
    
      for(unsigned int i = 0; i < edges_detected.size(); i++){
        edge_angle ea = edges_detected[i];
        if(ea.angle <= _tresholdAngle) break;
        selected->lines.push_back(new MLine(ea.v1, ea.v2));
      } 
    	
      for(unsigned int i = 0 ; i < edges_lonly.size(); i++){
        edge_angle ea = edges_lonly[i];
        selected->lines.push_back(new MLine(ea.v1, ea.v2));
      } 
      std::set<GFace*> _temp;
      _temp.insert(faces.begin(),faces.end());
      classifyFaces(_temp);
      remove(selected);
      //  delete selected;
    #endif
    }
    
    void GModel::classifyFaces(std::set<GFace*> &_faces) 
    {
    #if defined(HAVE_MESH)
      std::map<MLine*, GEdge*, compareMLinePtr> lines;
    
      for(GModel::eiter it = GModel::current()->firstEdge(); 
          it != GModel::current()->lastEdge(); ++it){
        for(unsigned int i = 0; i < (*it)->lines.size();i++) 
          lines[(*it)->lines[i]] = *it;
      }
    
      std::map<MTriangle*, GFace*> reverse_old;
      std::list<MTri3*> tris;
      {
        std::set<GFace*>::iterator it = _faces.begin();
        while(it != _faces.end()){
          GFace *gf = *it;
          for(unsigned int i = 0; i < gf->triangles.size(); i++){
            tris.push_back(new MTri3(gf->triangles[i], 0));
    	reverse_old[gf->triangles[i]] = gf;
          }
          gf->triangles.clear();
          gf->mesh_vertices.clear();
          ++it;
        }
      }
      if(tris.empty()) return;
    
      connectTriangles(tris);
    
      std::map<MTriangle*, GFace*> reverse;
      std::multimap<GFace*, GFace*> replacedBy;
      // color all triangles
      std::list<MTri3*> ::iterator it = tris.begin();
      std::list<GFace*> newf;
      while(it != tris.end()){
        if(!(*it)->isDeleted()){
          discreteFace *gf = new discreteFace
            (GModel::current(), GModel::current()->getMaxElementaryNumber(2) + 1);
          recurClassify(*it, gf, lines, reverse);
          GModel::current()->add(gf);
          newf.push_back(gf);
          
          for (unsigned int i = 0; i < gf->triangles.size(); i++){
    	replacedBy.insert(std::make_pair(reverse_old[gf->triangles[i]],gf));
          }
        }
        ++it;
      }
    
      // now we have all faces coloured. If some regions were existing, replace
      // their faces by the new ones
    
      for (riter rit = firstRegion(); rit != lastRegion(); ++rit){
        std::list<GFace *> _xfaces = (*rit)->faces();
        std::set<GFace *> _newFaces;
        for (std::list<GFace *>::iterator itf = _xfaces.begin(); itf != _xfaces.end(); ++itf){
          std::multimap<GFace*, GFace*>::iterator itLow = replacedBy.lower_bound(*itf);
          std::multimap<GFace*, GFace*>::iterator itUp = replacedBy.upper_bound(*itf);
          for (; itLow != itUp; ++itLow)
    	_newFaces.insert(itLow->second);
        }
        std::list<GFace *> _temp;
        _temp.insert(_temp.begin(),_newFaces.begin(),_newFaces.end());
        (*rit)->set(_temp);
      }
    
      // color some lines
      it = tris.begin();
      while(it != tris.end()){
        (*it)->setDeleted(false);
        ++it;
      }
      
      // classify edges that are bound by different GFaces
      std::map<std::pair<int, int>, GEdge*> newEdges;
      std::set<MLine*> touched;
      std::set<MTri3*> trisTouched;
      // bug fix : multiply connected domains
      
      trisTouched.insert(tris.begin(),tris.end());
      while(!trisTouched.empty())
        recurClassifyEdges(*trisTouched.begin(), reverse, lines, touched, trisTouched,newEdges);
    
      std::map<discreteFace*,std::vector<int> > newFaceTopology;
      
      // check if new edges should not be splitted 
      // splitted if composed of several open or closed edges
    
      std::map<MVertex*,GVertex*> modelVertices;
    
      for (std::map<std::pair<int, int>, GEdge*>::iterator ite = newEdges.begin();
           ite != newEdges.end() ; ++ite){
        std::list<MLine*> allSegments;
        for(unsigned int i = 0; i < ite->second->lines.size(); i++)
          allSegments.push_back(ite->second->lines[i]);
    
        while (!allSegments.empty()) {
          std::list<MLine*> segmentsForThisDiscreteEdge;
          MVertex *vB = (*allSegments.begin())->getVertex(0);
          MVertex *vE = (*allSegments.begin())->getVertex(1);
          segmentsForThisDiscreteEdge.push_back(*allSegments.begin());
          allSegments.erase(allSegments.begin());
          while(1){
    	bool found = false;
    	for (std::list<MLine*>::iterator it = allSegments.begin();
                 it != allSegments.end(); ++it){ 
    	  MVertex *v1 = (*it)->getVertex(0);
    	  MVertex *v2 = (*it)->getVertex(1);
    	  if (v1 == vE || v2 == vE){
    	    segmentsForThisDiscreteEdge.push_back(*it);
    	    if (v2 == vE)(*it)->revert();
    	    vE = (v1 == vE) ? v2 : v1;
    	    found = true;
    	    allSegments.erase(it);
    	    break;	  
    	  }
    	  if (v1 == vB || v2 == vB){
    	    segmentsForThisDiscreteEdge.push_front(*it);
    	    if (v1 == vB)(*it)->revert();
    	    vB = (v1 == vB) ? v2 : v1;
    	    found = true;
    	    allSegments.erase(it);
    	    break;	  
    	  }
    	}
    	if (vE == vB)break;
    	if (!found)break;
          }
    
          std::map<MVertex*,GVertex*>::iterator itMV = modelVertices.find(vB);
          if (itMV == modelVertices.end()){
    	GVertex *newGv = new discreteVertex
              (GModel::current(), GModel::current()->getMaxElementaryNumber(0) + 1);
    	newGv->mesh_vertices.push_back(vB);
    	vB->setEntity(newGv);	
    	newGv->points.push_back(new MPoint(vB));
    	GModel::current()->add(newGv);
    	modelVertices[vB] = newGv;
          }
          itMV = modelVertices.find(vE);
          if (itMV == modelVertices.end()){
    	GVertex *newGv = new discreteVertex
              (GModel::current(), GModel::current()->getMaxElementaryNumber(0) + 1);
    	newGv->mesh_vertices.push_back(vE);
    	newGv->points.push_back(new MPoint(vE));
    	vE->setEntity(newGv);	
    	GModel::current()->add(newGv);
    	modelVertices[vE] = newGv;
          }
    
          GEdge *newGe = new discreteEdge
            (GModel::current(), GModel::current()->getMaxElementaryNumber(1) + 1,
             modelVertices[vB], modelVertices[vE]);
          newGe->lines.insert(newGe->lines.end(), segmentsForThisDiscreteEdge.begin(),
                              segmentsForThisDiscreteEdge.end());
    
          for (std::list<MLine*>::iterator itL =  segmentsForThisDiscreteEdge.begin();
    	   itL !=  segmentsForThisDiscreteEdge.end(); ++itL){
    	if((*itL)->getVertex(0)->onWhat()->dim() != 0){
    	  newGe->mesh_vertices.push_back((*itL)->getVertex(0));
    	  (*itL)->getVertex(0)->setEntity(newGe);
    	}
          }
    
          GModel::current()->add(newGe);
          discreteFace *gf1 = dynamic_cast<discreteFace*>
            (GModel::current()->getFaceByTag(ite->first.first));
          discreteFace *gf2 = dynamic_cast<discreteFace*> 
            (GModel::current()->getFaceByTag(ite->first.second));
          if (gf1)newFaceTopology[gf1].push_back(newGe->tag());
          if (gf2)newFaceTopology[gf2].push_back(newGe->tag());
        }
      }
    
      std::map<discreteFace*,std::vector<int> >::iterator itFT =  newFaceTopology.begin();
      for (;itFT != newFaceTopology.end();++itFT){
        itFT->first->setBoundEdges(itFT->second);
      }
    
      for (std::map<std::pair<int, int>, GEdge*>::iterator it = newEdges.begin();
           it != newEdges.end(); ++it){
        GEdge *ge = it->second;
        GModel::current()->remove(ge);
        //    delete ge;
      }
      
      it = tris.begin();
      while(it != tris.end()){
        delete *it;
        ++it;
      }
    
      // delete empty mesh faces and reclasssify
      std::set<GFace*, GEntityLessThan> fac = faces;
      for (fiter fit = fac.begin() ; fit !=fac.end() ; ++fit){
        std::set<MVertex *> _verts;
        (*fit)->mesh_vertices.clear();
        for (unsigned int i = 0; i < (*fit)->triangles.size(); i++){
          for (int j = 0; j < 3; j++){
    	if ((*fit)->triangles[i]->getVertex(j)->onWhat()->dim() > 1){
    	  (*fit)->triangles[i]->getVertex(j)->setEntity(*fit);
    	  _verts.insert((*fit)->triangles[i]->getVertex(j));
    	}
          }      
        }
        if ((*fit)->triangles.size())
          (*fit)->mesh_vertices.insert((*fit)->mesh_vertices.begin(),
                                       _verts.begin(), _verts.end());
        else
          remove(*fit);
      }
    #endif
    }
    
    void GModel::createPartitionBoundaries(int createGhostCells)
    {
    #if (defined(HAVE_CHACO) || defined(HAVE_METIS)) && defined(HAVE_MESH)
      CreatePartitionBoundaries(this, createGhostCells);
    #endif
    }