Algorithm.cpp

/***************************************************************************
 *   Copyright (c) 2005 Imetric 3D GmbH                                    *
 *                                                                         *
 *   This file is part of the FreeCAD CAx development system.              *
 *                                                                         *
 *   This library is free software; you can redistribute it and/or         *
 *   modify it under the terms of the GNU Library General Public           *
 *   License as published by the Free Software Foundation; either          *
 *   version 2 of the License, or (at your option) any later version.      *
 *                                                                         *
 *   This library  is distributed in the hope that it will be useful,      *
 *   but WITHOUT ANY WARRANTY; without even the implied warranty of        *
 *   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the         *
 *   GNU Library General Public License for more details.                  *
 *                                                                         *
 *   You should have received a copy of the GNU Library General Public     *
 *   License along with this library; see the file COPYING.LIB. If not,    *
 *   write to the Free Software Foundation, Inc., 59 Temple Place,         *
 *   Suite 330, Boston, MA  02111-1307, USA                                *
 *                                                                         *
 ***************************************************************************/


#include "PreCompiled.h"

#ifndef _PreComp_
# include <algorithm>
#endif

#include "Algorithm.h"
#include "Approximation.h"
#include "Elements.h"
#include "Iterator.h"
#include "Grid.h"
#include "Triangulation.h"

#include <Base/Console.h>
#include <Base/Sequencer.h>

using namespace MeshCore;
using Base::BoundBox3f;
using Base::BoundBox2D;
using Base::Polygon2D;


bool MeshAlgorithm::IsVertexVisible (const Base::Vector3f &rcVertex, const Base::Vector3f &rcView, const MeshFacetGrid &rclGrid ) const
{
  Base::Vector3f cDirection = rcVertex-rcView;
  float fDistance = cDirection.Length();
  Base::Vector3f cIntsct; unsigned long uInd;

  // search for the nearest facet to rcView in direction to rcVertex
  if ( NearestFacetOnRay( rcView, cDirection, /*1.2f*fDistance,*/ rclGrid, cIntsct, uInd) )
  {
    // now check if the facet overlays the point
    float fLen = Base::Distance( rcView, cIntsct );
    if ( fLen < fDistance )
    {
      // is it the same point?
      if ( Base::Distance(rcVertex, cIntsct) > 0.001f )
      {
        // ok facet overlays the vertex
        return false;
      }
    }
  }

  return true; // no facet between the two points
}

bool MeshAlgorithm::NearestFacetOnRay (const Base::Vector3f &rclPt, const Base::Vector3f &rclDir, Base::Vector3f &rclRes,
                                       unsigned long &rulFacet) const
{
    Base::Vector3f clProj, clRes;
    bool bSol = false;
    unsigned long ulInd = 0;

    // langsame Ausfuehrung ohne Grid
    MeshFacetIterator  clFIter(_rclMesh);
    for (clFIter.Init(); clFIter.More(); clFIter.Next()) {
        if (clFIter->Foraminate( rclPt, rclDir, clRes ) == true) {
            if (bSol == false) { // erste Loesung
                bSol   = true;
                clProj = clRes;
                ulInd  = clFIter.Position();
            }
            else {  // liegt Punkt naeher
                if ((clRes - rclPt).Length() < (clProj - rclPt).Length()) {
                    clProj = clRes;
                    ulInd  = clFIter.Position();
                }
            }
        }
    }

    if (bSol) {
        rclRes   = clProj;
        rulFacet = ulInd;
    }

    return bSol;
}

bool MeshAlgorithm::NearestFacetOnRay (const Base::Vector3f &rclPt, const Base::Vector3f &rclDir, const MeshFacetGrid &rclGrid,
                                       Base::Vector3f &rclRes, unsigned long &rulFacet) const
{
    std::vector<unsigned long> aulFacets;
    MeshGridIterator clGridIter(rclGrid);

    if (clGridIter.InitOnRay(rclPt, rclDir, aulFacets) == true) {
        if (RayNearestField(rclPt, rclDir, aulFacets, rclRes, rulFacet) == false) {
            aulFacets.clear();
            while (clGridIter.NextOnRay(aulFacets) == true) {
                if (RayNearestField(rclPt, rclDir, aulFacets, rclRes, rulFacet) == true)
                    return true;
            }
        }
        else
            return true;
    }

    return false;
}

bool MeshAlgorithm::NearestFacetOnRay (const Base::Vector3f &rclPt, const Base::Vector3f &rclDir, float fMaxSearchArea,
                                       const MeshFacetGrid &rclGrid, Base::Vector3f &rclRes, unsigned long &rulFacet) const
{
    std::vector<unsigned long> aulFacets;
    MeshGridIterator  clGridIter(rclGrid);

    if (clGridIter.InitOnRay(rclPt, rclDir, fMaxSearchArea, aulFacets) == true) {
        if (RayNearestField(rclPt, rclDir, aulFacets, rclRes, rulFacet, 1.75f) == false) {
            aulFacets.clear();
            while (clGridIter.NextOnRay(aulFacets) == true) {
                if (RayNearestField(rclPt, rclDir, aulFacets, rclRes, rulFacet, 1.75f) == true)
                    return true;
            }
        }
        else
            return true;
    }

    return false;
}

bool MeshAlgorithm::NearestFacetOnRay (const Base::Vector3f &rclPt, const Base::Vector3f &rclDir, const std::vector<unsigned long> &raulFacets,
                                       Base::Vector3f &rclRes, unsigned long &rulFacet) const
{
    Base::Vector3f  clProj, clRes;
    bool bSol = false;
    unsigned long ulInd = 0;

    for (std::vector<unsigned long>::const_iterator pI = raulFacets.begin(); pI != raulFacets.end(); ++pI) {
        MeshGeomFacet rclSFacet = _rclMesh.GetFacet(*pI);
        if (rclSFacet.Foraminate(rclPt, rclDir, clRes) == true) {
            if (bSol == false) {// erste Loesung
                bSol   = true;
                clProj = clRes;
                ulInd  = *pI;
            }
            else {  // liegt Punkt naeher
                if ((clRes - rclPt).Length() < (clProj - rclPt).Length()) {
                    clProj = clRes;
                    ulInd  = *pI;
                }
            }
        }
    }

    if (bSol) {
        rclRes   = clProj;
        rulFacet = ulInd;
    }

    return bSol;
}

bool MeshAlgorithm::RayNearestField (const Base::Vector3f &rclPt, const Base::Vector3f &rclDir, const std::vector<unsigned long> &raulFacets,
                                     Base::Vector3f &rclRes, unsigned long &rulFacet, float fMaxAngle) const
{
    Base::Vector3f  clProj, clRes;
    bool bSol = false;
    unsigned long ulInd = 0;

    for (std::vector<unsigned long>::const_iterator pF = raulFacets.begin(); pF != raulFacets.end(); ++pF) {
        if (_rclMesh.GetFacet(*pF).Foraminate(rclPt, rclDir, clRes/*, fMaxAngle*/) == true) {
            if (bSol == false) { // erste Loesung
                bSol   = true;
                clProj = clRes;
                ulInd  = *pF;
            }
            else {  // liegt Punkt naeher
                if ((clRes - rclPt).Length() < (clProj - rclPt).Length()) {
                    clProj = clRes;
                    ulInd  = *pF;
                }
            }
        }
    }

    if (bSol) {
        rclRes   = clProj;
        rulFacet = ulInd;
    }

    return bSol;
}

bool MeshAlgorithm::FirstFacetToVertex(const Base::Vector3f &rPt, float fMaxDistance, const MeshFacetGrid &rGrid, unsigned long &uIndex) const
{
    const float fEps = 0.001f;

    bool found = false;
    std::vector<unsigned long> facets;

    // get the facets of the grid the point lies into
    rGrid.GetElements(rPt, facets);

    // Check all facets inside the grid if the point is part of it
    for (std::vector<unsigned long>::iterator it = facets.begin(); it != facets.end(); ++it) {
        MeshGeomFacet cFacet = this->_rclMesh.GetFacet(*it);
        if (cFacet.IsPointOfFace(rPt, fMaxDistance)) {
            found = true;
            uIndex = *it;
            break;
        }
        else {
            // if not then check the distance to the border of the triangle
            Base::Vector3f res = rPt;
            float fDist;
            unsigned short uSide;
            cFacet.ProjectPointToPlane(res);
            cFacet.NearestEdgeToPoint(res, fDist, uSide);
            if (fDist < fEps) {
                found = true;
                uIndex = *it;
                break;
            }
        }
    }

    return found;
}

float MeshAlgorithm::GetAverageEdgeLength() const
{
    float fLen = 0.0f;
    MeshFacetIterator cF(_rclMesh);
    for (cF.Init(); cF.More(); cF.Next()) {
        for (int i=0; i<3; i++)
            fLen += Base::Distance(cF->_aclPoints[i], cF->_aclPoints[(i+1)%3]);
    }

    fLen = fLen / (3.0f * _rclMesh.CountFacets() );
    return fLen;
}

Base::Vector3f MeshAlgorithm::GetGravityPoint() const
{
    Base::Vector3f center;
    MeshPointIterator cP(_rclMesh);
    for (cP.Init(); cP.More(); cP.Next()) {
        center += *cP;
    }

    return center / (float)_rclMesh.CountPoints();
}

void MeshAlgorithm::GetMeshBorders (std::list<std::vector<Base::Vector3f> > &rclBorders) const
{
    std::vector<unsigned long> aulAllFacets(_rclMesh.CountFacets());
    unsigned long k = 0;
    for (std::vector<unsigned long>::iterator pI = aulAllFacets.begin(); pI != aulAllFacets.end(); ++pI)
        *pI = k++;

    GetFacetBorders(aulAllFacets, rclBorders);
}

void MeshAlgorithm::GetMeshBorders (std::list<std::vector<unsigned long> > &rclBorders) const
{
    std::vector<unsigned long> aulAllFacets(_rclMesh.CountFacets());
    unsigned long k = 0;
    for (std::vector<unsigned long>::iterator pI = aulAllFacets.begin(); pI != aulAllFacets.end(); ++pI)
        *pI = k++;

    GetFacetBorders(aulAllFacets, rclBorders, true);
}

void MeshAlgorithm::GetFacetBorders (const std::vector<unsigned long> &raulInd, std::list<std::vector<Base::Vector3f> > &rclBorders) const
{
#if 1
  const MeshPointArray &rclPAry = _rclMesh._aclPointArray;
  std::list<std::vector<unsigned long> > aulBorders;

  GetFacetBorders (raulInd, aulBorders, true);
  for ( std::list<std::vector<unsigned long> >::iterator it = aulBorders.begin(); it != aulBorders.end(); ++it )
  {
    std::vector<Base::Vector3f> boundary;
    boundary.reserve( it->size() );

    for ( std::vector<unsigned long>::iterator jt = it->begin(); jt != it->end(); ++jt )
      boundary.push_back(rclPAry[*jt]);

    rclBorders.push_back( boundary );
  }

#else
  const MeshFacetArray &rclFAry = _rclMesh._aclFacetArray;

  // alle Facets markieren die in der Indizie-Liste vorkommen
  ResetFacetFlag(MeshFacet::VISIT);
  for (std::vector<unsigned long>::const_iterator pIter = raulInd.begin(); pIter != raulInd.end(); pIter++)
    rclFAry[*pIter].SetFlag(MeshFacet::VISIT);

  std::list<std::pair<unsigned long, unsigned long> >  aclEdges;
  // alle Randkanten suchen und ablegen (unsortiert)
  for (std::vector<unsigned long>::const_iterator pIter2 = raulInd.begin(); pIter2 != raulInd.end(); pIter2++)
  {
    const MeshFacet  &rclFacet = rclFAry[*pIter2];
    for (int i = 0; i < 3; i++)
    {
      unsigned long ulNB = rclFacet._aulNeighbours[i];
      if (ulNB != ULONG_MAX)
      {
        if (rclFAry[ulNB].IsFlag(MeshFacet::VISIT) == true)
          continue;
      }

      aclEdges.push_back(rclFacet.GetEdge(i));
    }
  }

  if (aclEdges.size() == 0)
    return; // no borders found (=> solid)

  // Kanten aus der unsortieren Kantenliste suchen
  const MeshPointArray &rclPAry = _rclMesh._aclPointArray;
  unsigned long              ulFirst, ulLast;
  std::list<Base::Vector3f>   clBorder;
  ulFirst = aclEdges.begin()->first;
  ulLast  = aclEdges.begin()->second;

  aclEdges.erase(aclEdges.begin());
  clBorder.push_back(rclPAry[ulFirst]);
  clBorder.push_back(rclPAry[ulLast]);

  while (aclEdges.size() > 0)
  {
    // naechste anliegende Kante suchen
    std::list<std::pair<unsigned long, unsigned long> >::iterator pEI;
    for (pEI = aclEdges.begin(); pEI != aclEdges.end(); pEI++)
    {
      if (pEI->first == ulLast)
      {
        ulLast = pEI->second;
        clBorder.push_back(rclPAry[ulLast]);
        aclEdges.erase(pEI);
        break;
      }
      else if (pEI->second == ulLast)
      {
        ulLast = pEI->first;
        clBorder.push_back(rclPAry[ulLast]);
        aclEdges.erase(pEI);
        break;
      }
      else if (pEI->first == ulFirst)
      {
        ulFirst = pEI->second;
        clBorder.push_front(rclPAry[ulFirst]);
        aclEdges.erase(pEI);
        break;
      }
      else if (pEI->second == ulFirst)
      {
        ulFirst = pEI->first;
        clBorder.push_front(rclPAry[ulFirst]);
        aclEdges.erase(pEI);
        break;
      }
    }
    if ((pEI == aclEdges.end()) || (ulLast == ulFirst))
    {  // keine weitere Kante gefunden bzw. Polylinie geschlossen
      rclBorders.push_back(std::vector<Base::Vector3f>(clBorder.begin(), clBorder.end()));
      clBorder.clear();

      if (aclEdges.size() > 0)
      {  // neue Border anfangen
        ulFirst = aclEdges.begin()->first;
        ulLast  = aclEdges.begin()->second;
        aclEdges.erase(aclEdges.begin());
        clBorder.push_back(rclPAry[ulFirst]);
        clBorder.push_back(rclPAry[ulLast]);
      }
    }
  }
#endif
}

void MeshAlgorithm::GetFacetBorders (const std::vector<unsigned long> &raulInd, 
                                     std::list<std::vector<unsigned long> > &rclBorders,
                                     bool ignoreOrientation) const
{
    const MeshFacetArray &rclFAry = _rclMesh._aclFacetArray;

    // mark all facets that are in the indices list
    ResetFacetFlag(MeshFacet::VISIT);
    for (std::vector<unsigned long>::const_iterator it = raulInd.begin(); it != raulInd.end(); ++it)
        rclFAry[*it].SetFlag(MeshFacet::VISIT);

    // collect all boundary edges (unsorted)
    std::list<std::pair<unsigned long, unsigned long> >  aclEdges;
    for (std::vector<unsigned long>::const_iterator it = raulInd.begin(); it != raulInd.end(); ++it) {
        const MeshFacet  &rclFacet = rclFAry[*it];
        for (int i = 0; i < 3; i++) {
            unsigned long ulNB = rclFacet._aulNeighbours[i];
            if (ulNB != ULONG_MAX) {
                if (rclFAry[ulNB].IsFlag(MeshFacet::VISIT) == true)
                    continue;
            }

            aclEdges.push_back(rclFacet.GetEdge(i));
        }
    }

    if (aclEdges.size() == 0)
        return; // no borders found (=> solid)

    // search for edges in the unsorted list
    unsigned long              ulFirst, ulLast;
    std::list<unsigned long>   clBorder;
    ulFirst = aclEdges.begin()->first;
    ulLast  = aclEdges.begin()->second;

    aclEdges.erase(aclEdges.begin());
    clBorder.push_back(ulFirst);
    clBorder.push_back(ulLast);

    while (aclEdges.size() > 0) {
        // get adjacent edge
        std::list<std::pair<unsigned long, unsigned long> >::iterator pEI;
        for (pEI = aclEdges.begin(); pEI != aclEdges.end(); ++pEI) {
            if (pEI->first == ulLast) {
                ulLast = pEI->second;
                clBorder.push_back(ulLast);
                aclEdges.erase(pEI);
                pEI = aclEdges.begin();
                break;
            }
            else if (pEI->second == ulFirst) {
                ulFirst = pEI->first;
                clBorder.push_front(ulFirst);
                aclEdges.erase(pEI);
                pEI = aclEdges.begin();
                break;
            }
            // Note: Using this might result into boundaries with wrong orientation.
            // But if the mesh has some facets with wrong orientation we might get
            // broken boundary curves.
            else if (pEI->second == ulLast && ignoreOrientation) {
                ulLast = pEI->first;
                clBorder.push_back(ulLast);
                aclEdges.erase(pEI);
                pEI = aclEdges.begin();
                break;
            }
            else if (pEI->first == ulFirst && ignoreOrientation) {
                ulFirst = pEI->second;
                clBorder.push_front(ulFirst);
                aclEdges.erase(pEI);
                pEI = aclEdges.begin();
                break;
            }
        }

        // Note: Calling erase on list iterators doesn't force a re-allocation and
        // thus doesn't invalidate the iterator itself, only the referenced object
        if ((pEI == aclEdges.end()) || aclEdges.empty() || (ulLast == ulFirst)) {
            // no further edge found or closed polyline, respectively
            rclBorders.push_back(std::vector<unsigned long>(clBorder.begin(), clBorder.end()));
            clBorder.clear();

            if (aclEdges.size() > 0) {
                // start new boundary
                ulFirst = aclEdges.begin()->first;
                ulLast  = aclEdges.begin()->second;
                aclEdges.erase(aclEdges.begin());
                clBorder.push_back(ulFirst);
                clBorder.push_back(ulLast);
            }
        }
    }
}

void MeshAlgorithm::GetMeshBorder(unsigned long uFacet, std::list<unsigned long>& rBorder) const
{
    const MeshFacetArray &rFAry = _rclMesh._aclFacetArray;
    std::list<std::pair<unsigned long, unsigned long> >  openEdges;
    if (uFacet >= rFAry.size())
        return;
    // add the open edge to the beginning of the list
    MeshFacetArray::_TConstIterator face = rFAry.begin() + uFacet;
    for (int i = 0; i < 3; i++)
    {
        if (face->_aulNeighbours[i] == ULONG_MAX)
            openEdges.push_back(face->GetEdge(i));
    }

    if (openEdges.empty())
        return; // facet is not a border facet
    
    for (MeshFacetArray::_TConstIterator it = rFAry.begin(); it != rFAry.end(); ++it)
    {
        if (it == face)
            continue;
        for (int i = 0; i < 3; i++)
        {
            if (it->_aulNeighbours[i] == ULONG_MAX)
                openEdges.push_back(it->GetEdge(i));
        }
    }

    // Start with the edge that is associated to uFacet
    unsigned long ulFirst = openEdges.begin()->first;
    unsigned long ulLast  = openEdges.begin()->second;

    openEdges.erase(openEdges.begin());
    rBorder.push_back(ulFirst);
    rBorder.push_back(ulLast);

    while (ulLast != ulFirst)
    {
        // find adjacent edge
        std::list<std::pair<unsigned long, unsigned long> >::iterator pEI;
        for (pEI = openEdges.begin(); pEI != openEdges.end(); ++pEI)
        {
            if (pEI->first == ulLast)
            {
                ulLast = pEI->second;
                rBorder.push_back(ulLast);
                openEdges.erase(pEI);
                pEI = openEdges.begin();
                break;
            }
            else if (pEI->second == ulFirst)
            {
                ulFirst = pEI->first;
                rBorder.push_front(ulFirst);
                openEdges.erase(pEI);
                pEI = openEdges.begin();
                break;
            }
        }

        // cannot close the border
        if (pEI == openEdges.end())
            break;
    }
}

void MeshAlgorithm::SplitBoundaryLoops( std::list<std::vector<unsigned long> >& aBorders )
{
    // Count the number of open edges for each point
    std::map<unsigned long, int> openPointDegree;
    for (MeshFacetArray::_TConstIterator jt = _rclMesh._aclFacetArray.begin();
        jt != _rclMesh._aclFacetArray.end(); ++jt) {
        for (int i=0; i<3; i++) {
            if (jt->_aulNeighbours[i] == ULONG_MAX) {
                openPointDegree[jt->_aulPoints[i]]++;
                openPointDegree[jt->_aulPoints[(i+1)%3]]++;
            }
        }
    }

    // go through all boundaries and split them if needed
    std::list<std::vector<unsigned long> > aSplitBorders;
    for (std::list<std::vector<unsigned long> >::iterator it = aBorders.begin();
        it != aBorders.end(); ++it) {
        bool split=false;
        for (std::vector<unsigned long>::iterator jt = it->begin(); jt != it->end(); ++jt) {
            // two (ore more) boundaries meet in one non-manifold point
            if (openPointDegree[*jt] > 2) {
                split = true;
                break;
            }
        }

        if (!split)
            aSplitBorders.push_back( *it );
        else
            SplitBoundaryLoops( *it, aSplitBorders );
    }

    aBorders = aSplitBorders;
}

void MeshAlgorithm::SplitBoundaryLoops(const std::vector<unsigned long>& rBound,
                                       std::list<std::vector<unsigned long> >& aBorders)
{
    std::map<unsigned long, int> aPtDegree;
    std::vector<unsigned long> cBound;
    for (std::vector<unsigned long>::const_iterator it = rBound.begin(); it != rBound.end(); ++it) {
        int deg = (aPtDegree[*it]++);
        if (deg > 0) {
            for (std::vector<unsigned long>::iterator jt = cBound.begin(); jt != cBound.end(); ++jt) {
                if (*jt == *it) {
                    std::vector<unsigned long> cBoundLoop;
                    cBoundLoop.insert(cBoundLoop.end(), jt, cBound.end());
                    cBoundLoop.push_back(*it);
                    cBound.erase(jt, cBound.end());
                    aBorders.push_back(cBoundLoop);
                    (aPtDegree[*it]--);
                    break;
                }
            }
        }

        cBound.push_back(*it);
    }
}

bool MeshAlgorithm::FillupHole(const std::vector<unsigned long>& boundary, 
                               AbstractPolygonTriangulator& cTria, 
                               MeshFacetArray& rFaces, MeshPointArray& rPoints,
                               int level, const MeshRefPointToFacets* pP2FStructure) const
{
    if (boundary.front() == boundary.back()) {
        // first and last vertex are identical
        if (boundary.size() < 4)
            return false; // something strange
    }
    else if (boundary.size() < 3) {
        return false; // something strange
    }

    // Get a facet as reference coordinate system
    MeshGeomFacet rTriangle;
    MeshFacet rFace;
    unsigned long refPoint0 = *(boundary.begin());
    unsigned long refPoint1 = *(boundary.begin()+1);
    if (pP2FStructure) {
        const std::set<unsigned long>& ring1 = (*pP2FStructure)[refPoint0];
        const std::set<unsigned long>& ring2 = (*pP2FStructure)[refPoint1];
        std::vector<unsigned long> f_int;
        std::set_intersection(ring1.begin(), ring1.end(), ring2.begin(), ring2.end(),
            std::back_insert_iterator<std::vector<unsigned long> >(f_int));
        if (f_int.size() != 1)
            return false; // error, this must be an open edge!

        rFace = _rclMesh._aclFacetArray[f_int.front()];
        rTriangle = _rclMesh.GetFacet(rFace);
    }
    else {
        bool ready = false;
        for (MeshFacetArray::_TConstIterator it = _rclMesh._aclFacetArray.begin(); it != _rclMesh._aclFacetArray.end(); ++it) {
            for (int i=0; i<3; i++) {
                if (((it->_aulPoints[i] == refPoint0) && (it->_aulPoints[(i+1)%3] == refPoint1)) ||
                    ((it->_aulPoints[i] == refPoint1) && (it->_aulPoints[(i+1)%3] == refPoint0))) {
                    rFace = *it;
                    rTriangle = _rclMesh.GetFacet(*it);
                    ready = true;
                    break;
                }
            }

            if (ready)
                break;
        }
    }

    // add points to the polygon
    std::vector<Base::Vector3f> polygon;
    for (std::vector<unsigned long>::const_iterator jt = boundary.begin(); jt != boundary.end(); ++jt) {
        polygon.push_back(_rclMesh._aclPointArray[*jt]);
        rPoints.push_back(_rclMesh._aclPointArray[*jt]);
    }

    // remove the last added point if it is duplicated
    std::vector<unsigned long> bounds = boundary;
    if (boundary.front() == boundary.back()) {
        bounds.pop_back();
        polygon.pop_back();
        rPoints.pop_back();
    }

    // There is no easy way to check whether the boundary is interior (a hole) or exterior before performing the triangulation.
    // Afterwards we can compare the normals of the created triangles with the z-direction of our local coordinate system.
    // If the scalar product is positive it was a hole, otherwise not.
    cTria.SetPolygon(polygon);
    cTria.SetIndices(bounds);

    std::vector<Base::Vector3f> surf_pts = cTria.GetPolygon();
    if (pP2FStructure && level > 0) {
        std::set<unsigned long> index = pP2FStructure->NeighbourPoints(boundary, level);
        for (std::set<unsigned long>::iterator it = index.begin(); it != index.end(); ++it) {
            Base::Vector3f pt(_rclMesh._aclPointArray[*it]);
            surf_pts.push_back(pt);
        }
    }

    if (cTria.TriangulatePolygon()) {
        // if we have enough points then we fit a surface through the points and project
        // the added points onto this surface
        cTria.PostProcessing(surf_pts);
        // get the facets and add the additional points to the array
        rFaces.insert(rFaces.end(), cTria.GetFacets().begin(), cTria.GetFacets().end());
        std::vector<Base::Vector3f> newVertices = cTria.AddedPoints();
        for (std::vector<Base::Vector3f>::iterator pt = newVertices.begin(); pt != newVertices.end(); ++pt) {
            rPoints.push_back((*pt));
        }

        // Unfortunately, some algorithms do not care about the orientation of the polygon so we cannot rely on the normal
        // criterion to decide whether it's a hole or not.
        //
        std::vector<MeshFacet> faces = cTria.GetFacets();
        
        // Special case handling for a hole with three edges: the resulting facet might be coincident with the 
        // reference facet
        if (faces.size()==1){
            MeshFacet first = faces.front();
            if (cTria.NeedsReindexing()) {
                first._aulPoints[0] = boundary[first._aulPoints[0]];
                first._aulPoints[1] = boundary[first._aulPoints[1]];
                first._aulPoints[2] = boundary[first._aulPoints[2]];
            }
            if (first.IsEqual(rFace)) {
                rFaces.clear();
                rPoints.clear();
                cTria.Discard();
                return false;
            }
        }

        // Get the new neighbour to our reference facet
        MeshFacet facet;
        unsigned short ref_side = rFace.Side(refPoint0, refPoint1);
        unsigned short tri_side = USHRT_MAX;
        if (cTria.NeedsReindexing()) {
            // the referenced indices of the polyline
            refPoint0 = 0;
            refPoint1 = 1;
        }
        if (ref_side < USHRT_MAX) {
            for (std::vector<MeshFacet>::iterator it = faces.begin(); it != faces.end(); ++it) {
                tri_side = it->Side(refPoint0, refPoint1);
                if (tri_side < USHRT_MAX) {
                    facet = *it;
                    break;
                }
            }
        }

        // in case the reference facet has not an open edge print a log message 
        if (ref_side == USHRT_MAX || tri_side == USHRT_MAX) {
            Base::Console().Log("MeshAlgorithm::FillupHole: Expected open edge for facet <%d, %d, %d>\n", 
                rFace._aulPoints[0], rFace._aulPoints[1], rFace._aulPoints[2]);
            rFaces.clear();
            rPoints.clear();
            cTria.Discard();
            return false;
        }

#if 1
        MeshGeomFacet triangle;
        triangle = cTria.GetTriangle(rPoints, facet);

        // Now we have two adjacent triangles which we check for overlaps.
        // Therefore we build a separation plane that must separate the two diametrically opposed points.
        Base::Vector3f planeNormal = rTriangle.GetNormal() % (rTriangle._aclPoints[(ref_side+1)%3]-rTriangle._aclPoints[ref_side]);
        Base::Vector3f planeBase = rTriangle._aclPoints[ref_side];
        Base::Vector3f ref_point = rTriangle._aclPoints[(ref_side+2)%3];
        Base::Vector3f tri_point = triangle._aclPoints[(tri_side+2)%3];

        float ref_dist = (ref_point - planeBase) * planeNormal;
        float tri_dist = (tri_point - planeBase) * planeNormal;
        if (ref_dist * tri_dist > 0.0f) {
            rFaces.clear();
            rPoints.clear();
            cTria.Discard();
            return false;
        }

        // we know to have filled a polygon, now check for the orientation
        if ( triangle.GetNormal() * rTriangle.GetNormal() <= 0.0f ) {
            for (MeshFacetArray::_TIterator it = rFaces.begin(); it != rFaces.end(); ++it)
                it->FlipNormal();
        }
#endif

        return true;
    }

    return false;
}

void MeshAlgorithm::SetFacetsProperty(const std::vector<unsigned long> &raulInds, const std::vector<unsigned long> &raulProps) const
{
    if (raulInds.size() != raulProps.size()) return;

    std::vector<unsigned long>::const_iterator iP = raulProps.begin();
    for (std::vector<unsigned long>::const_iterator i = raulInds.begin(); i != raulInds.end(); ++i, ++iP)
        _rclMesh._aclFacetArray[*i].SetProperty(*iP);
}

void MeshAlgorithm::SetFacetsFlag (const std::vector<unsigned long> &raulInds, MeshFacet::TFlagType tF) const
{
    for (std::vector<unsigned long>::const_iterator i = raulInds.begin(); i != raulInds.end(); ++i)
        _rclMesh._aclFacetArray[*i].SetFlag(tF);
}

void MeshAlgorithm::SetPointsFlag (const std::vector<unsigned long> &raulInds, MeshPoint::TFlagType tF) const 
{
    for (std::vector<unsigned long>::const_iterator i = raulInds.begin(); i != raulInds.end(); ++i)
        _rclMesh._aclPointArray[*i].SetFlag(tF);
}

void MeshAlgorithm::GetFacetsFlag (std::vector<unsigned long> &raulInds, MeshFacet::TFlagType tF) const
{
    raulInds.reserve(raulInds.size() + CountFacetFlag(tF));
    MeshFacetArray::_TConstIterator beg = _rclMesh._aclFacetArray.begin();
    MeshFacetArray::_TConstIterator end = _rclMesh._aclFacetArray.end();
    for (MeshFacetArray::_TConstIterator it = beg; it != end; ++it) {
        if (it->IsFlag(tF))
            raulInds.push_back(it-beg);
    }
}

void MeshAlgorithm::GetPointsFlag (std::vector<unsigned long> &raulInds, MeshPoint::TFlagType tF) const
{
    raulInds.reserve(raulInds.size() + CountPointFlag(tF));
    MeshPointArray::_TConstIterator beg = _rclMesh._aclPointArray.begin();
    MeshPointArray::_TConstIterator end = _rclMesh._aclPointArray.end();
    for (MeshPointArray::_TConstIterator it = beg; it != end; ++it) {
        if (it->IsFlag(tF))
            raulInds.push_back(it-beg);
    }
}

void MeshAlgorithm::ResetFacetsFlag (const std::vector<unsigned long> &raulInds, MeshFacet::TFlagType tF) const
{
    for (std::vector<unsigned long>::const_iterator i = raulInds.begin(); i != raulInds.end(); ++i)
        _rclMesh._aclFacetArray[*i].ResetFlag(tF);
}

void MeshAlgorithm::ResetPointsFlag (const std::vector<unsigned long> &raulInds, MeshPoint::TFlagType tF) const
{
    for (std::vector<unsigned long>::const_iterator i = raulInds.begin(); i != raulInds.end(); ++i)
        _rclMesh._aclPointArray[*i].ResetFlag(tF);
}

void MeshAlgorithm::SetFacetFlag (MeshFacet::TFlagType tF) const
{
    _rclMesh._aclFacetArray.SetFlag(tF);
}

void MeshAlgorithm::SetPointFlag (MeshPoint::TFlagType tF) const
{
    _rclMesh._aclPointArray.SetFlag(tF);
}

void MeshAlgorithm::ResetFacetFlag (MeshFacet::TFlagType tF) const
{
    _rclMesh._aclFacetArray.ResetFlag(tF);
}

void MeshAlgorithm::ResetPointFlag (MeshPoint::TFlagType tF) const
{
    _rclMesh._aclPointArray.ResetFlag(tF);
}

unsigned long MeshAlgorithm::CountFacetFlag (MeshFacet::TFlagType tF) const
{
    return std::count_if(_rclMesh._aclFacetArray.begin(), _rclMesh._aclFacetArray.end(),
                    std::bind2nd(MeshIsFlag<MeshFacet>(), tF));
}

unsigned long MeshAlgorithm::CountPointFlag (MeshPoint::TFlagType tF) const
{
    return std::count_if(_rclMesh._aclPointArray.begin(), _rclMesh._aclPointArray.end(),
                    std::bind2nd(MeshIsFlag<MeshPoint>(), tF));
}

void MeshAlgorithm::GetFacetsFromToolMesh( const MeshKernel& rToolMesh, const Base::Vector3f& rcDir, std::vector<unsigned long> &raclCutted ) const
{
    MeshFacetIterator cFIt(_rclMesh);
    MeshFacetIterator cTIt(rToolMesh);

    BoundBox3f cBB = rToolMesh.GetBoundBox();

    Base::SequencerLauncher seq("Check facets...", _rclMesh.CountFacets());

    // check all facets
    Base::Vector3f tmp;
    for (cFIt.Init(); cFIt.More(); cFIt.Next()) {
        // check each point of each facet
        for (int i=0; i<3; i++) {
            // at least the point must be inside the bounding box of the tool mesh
            if (cBB.IsInBox( cFIt->_aclPoints[i])) {
                // should not cause performance problems since the tool mesh is usually rather lightweight
                int ct=0;
                for (cTIt.Init(); cTIt.More(); cTIt.Next()) {
                    if (cTIt->IsPointOfFace( cFIt->_aclPoints[i], MeshPoint::epsilon())) {
                        ct=1;
                        break; // the point lies on the tool mesh
                    }
                    else if (cTIt->Foraminate( cFIt->_aclPoints[i], rcDir, tmp)) {
                        // check if the intersection point lies in direction rcDir of the considered point
                        if ((tmp - cFIt->_aclPoints[i]) * rcDir > 0)
                            ct++;
                    }
                }

                // odd number => point is inside the tool mesh
                if (ct % 2 == 1) {
                    raclCutted.push_back( cFIt.Position() );
                    break;
                }
            }
        }

        seq.next();
    }
}

void MeshAlgorithm::GetFacetsFromToolMesh(const MeshKernel& rToolMesh, const Base::Vector3f& rcDir,
                                          const MeshFacetGrid& rGrid, std::vector<unsigned long> &raclCutted) const
{
    // iterator over grid structure
    MeshGridIterator clGridIter(rGrid);
    BoundBox3f cBB = rToolMesh.GetBoundBox();
    Base::Vector3f tmp;

    MeshFacetIterator cFIt(_rclMesh);
    MeshFacetIterator cTIt(rToolMesh);
    MeshAlgorithm cToolAlg(rToolMesh);

    // To speed up the algorithm we use the grid built up from the associated mesh. For each grid
    // element we check whether it lies completely inside or outside the toolmesh or even intersect
    // with the toolmesh. So we can reduce the number of facets with further tests dramatically.
    // If the grid box is outside the toolmesh all the facets inside can be skipped. If the grid
    // box is inside the toolmesh all facets are stored with no further tests because they must
    // also lie inside the toolmesh. Finally, if the grid box intersect with the toolmesh we must
    // also check for each whether it intersect we the toolmesh as well.
    std::vector<unsigned long> aulInds;
    for (clGridIter.Init(); clGridIter.More(); clGridIter.Next()) {
        int ret = cToolAlg.Surround(clGridIter.GetBoundBox(), rcDir);

        // the box is completely inside the toolmesh
        if (ret == 1) {
            // these facets can be removed without more checks
            clGridIter.GetElements(raclCutted);
        } 
        // the box intersect with toolmesh
        else if (ret == 0) {
            // these facets must be tested for intersectons with the toolmesh
            clGridIter.GetElements(aulInds);
        }
        // the box is outside the toolmesh but this could still mean that the triangles
        // inside the grid intersect with the toolmesh
        else if (ret == -1) {
            // these facets must be tested for intersectons with the toolmesh
            clGridIter.GetElements(aulInds);
        }
    }

    // remove duplicates
    std::sort(aulInds.begin(), aulInds.end());
    aulInds.erase(std::unique(aulInds.begin(), aulInds.end()), aulInds.end());
    std::sort(raclCutted.begin(), raclCutted.end());
    raclCutted.erase(std::unique(raclCutted.begin(), raclCutted.end()), raclCutted.end());

    Base::SequencerLauncher seq("Check facets...", aulInds.size());

    // check all facets
    for (std::vector<unsigned long>::iterator it = aulInds.begin(); it != aulInds.end(); ++it) {
        cFIt.Set(*it);

        // check each point of each facet
        for (int i=0; i<3; i++) {
            // at least the point must be inside the bounding box of the tool mesh
            if (cBB.IsInBox(cFIt->_aclPoints[i])) {
                // should not cause performance problems since the tool mesh is usually rather lightweight
                int ct=0;
                for (cTIt.Init(); cTIt.More(); cTIt.Next()) {
                    if (cTIt->IsPointOfFace(cFIt->_aclPoints[i], MeshPoint::epsilon())) {
                        ct=1;
                        break; // the point lies on the tool mesh
                    }
                    else if (cTIt->Foraminate(cFIt->_aclPoints[i], rcDir, tmp)) {
                        // check if the intersection point lies in direction rcDir of the considered point
                        if ((tmp - cFIt->_aclPoints[i]) * rcDir > 0)
                            ct++;
                    }
                }

                // odd number => point is inside the tool mesh
                if (ct % 2 == 1) {
                    raclCutted.push_back(cFIt.Position());
                    break;
                }
            }
        }

        seq.next();
    }

    // remove duplicates
    std::sort(raclCutted.begin(), raclCutted.end());
    raclCutted.erase(std::unique(raclCutted.begin(), raclCutted.end()), raclCutted.end());
}

int MeshAlgorithm::Surround(const Base::BoundBox3f& rBox, const Base::Vector3f& rcDir)
{
    Base::Vector3f pt1, pt2, tmp;
    const BoundBox3f& cBB = _rclMesh.GetBoundBox();

    // at least both boxes intersect
    if (cBB && rBox) {
        // check for intersections with the actual mesh
        Base::Vector3f cCorner[8] = {
        Base::Vector3f(rBox.MinX,rBox.MinY,rBox.MinZ), Base::Vector3f(rBox.MaxX,rBox.MinY,rBox.MinZ), 
        Base::Vector3f(rBox.MaxX,rBox.MaxY,rBox.MinZ), Base::Vector3f(rBox.MinX,rBox.MaxY,rBox.MinZ),
        Base::Vector3f(rBox.MinX,rBox.MinY,rBox.MaxZ), Base::Vector3f(rBox.MaxX,rBox.MinY,rBox.MaxZ), 
        Base::Vector3f(rBox.MaxX,rBox.MaxY,rBox.MaxZ), Base::Vector3f(rBox.MinX,rBox.MaxY,rBox.MaxZ)};

        MeshFacetIterator cTIt(_rclMesh);

        // triangulation of the box
        int triangles[36] = {
            0,1,2,0,2,3,
            0,1,5,0,5,4,
            0,4,7,0,7,3,
            6,7,4,6,4,5,
            6,2,3,6,3,7,
            6,1,2,6,5,1
        };

        std::vector<MeshGeomFacet> cFacet(12);
        int id=0;
        for (int ii=0; ii<12; ii++) {
            cFacet[ii]._aclPoints[0]=cCorner[triangles[id++]]; 
            cFacet[ii]._aclPoints[1]=cCorner[triangles[id++]]; 
            cFacet[ii]._aclPoints[2]=cCorner[triangles[id++]];
        }

        // check for intersections of the box with the mesh
        for (std::vector<MeshGeomFacet>::iterator it = cFacet.begin(); it != cFacet.end(); ++it) {
            for (cTIt.Init(); cTIt.More(); cTIt.Next()) {
                int ret = cTIt->IntersectWithFacet(*it,pt1, pt2);

                // the box intersects the mesh?
                if (ret != 0)
                    return 0; // => no more investigations required
            }
        }

        // Now we know that the box doesn't intersect with the mesh. This means that either the box
        // is completely inside or outside the mesh. To check this we test one point of the box
        // whether it is inside or outside.
        int ct=0;
        for (cTIt.Init(); cTIt.More(); cTIt.Next()) {
            if (cTIt->IsPointOfFace(cCorner[0], MeshPoint::epsilon())) {
                ct=1;
                break; // the point lies on the tool mesh
            }
            else if (cTIt->Foraminate(cCorner[0], rcDir, tmp)) {
                // check if the intersection point lies in direction rcDir of the considered point
                if ((tmp - cCorner[0]) * rcDir > 0)
                    ct++;
            }
        }

        // odd number => point (i.e. the box) is inside the mesh, even number => point is outside the mesh
        return (ct % 2 == 1) ? 1 : -1;
    }

    // no intersection the box is outside the mesh
    return -1;
}

void MeshAlgorithm::CheckFacets(const MeshFacetGrid& rclGrid, const Base::ViewProjMethod* pclProj, const Base::Polygon2D& rclPoly,
                                bool bInner, std::vector<unsigned long> &raulFacets) const
{
    std::vector<unsigned long>::iterator it;
    MeshFacetIterator clIter(_rclMesh, 0);
    Base::Vector3f clPt2d;
    Base::Vector3f clGravityOfFacet;
    bool bNoPointInside;

    // Falls true, verwende Grid auf Mesh, um Suche zu beschleunigen
    if (bInner)
    {
        BoundBox3f clBBox3d;
        BoundBox2D clViewBBox, clPolyBBox;
        std::vector<unsigned long> aulAllElements;

        //B-Box des Polygons
        clPolyBBox = rclPoly.CalcBoundBox();
        // Iterator fuer die zu durchsuchenden B-Boxen des Grids
        MeshGridIterator clGridIter(rclGrid);
        // alle B-Boxen durchlaufen und die Facets speichern
        for (clGridIter.Init(); clGridIter.More(); clGridIter.Next())
        {
            clBBox3d = clGridIter.GetBoundBox();
            clViewBBox = clBBox3d.ProjectBox(pclProj);
            if (clViewBBox || clPolyBBox)
            {
                // alle Elemente in AllElements sammeln
                clGridIter.GetElements(aulAllElements);
            }
        }
        // doppelte Elemente wieder entfernen
        std::sort(aulAllElements.begin(), aulAllElements.end());
        aulAllElements.erase(std::unique(aulAllElements.begin(), aulAllElements.end()), aulAllElements.end());

        Base::SequencerLauncher seq( "Check facets", aulAllElements.size() );

        for (it = aulAllElements.begin(); it != aulAllElements.end(); ++it)
        {
            bNoPointInside = true;
            clGravityOfFacet.Set(0.0f, 0.0f, 0.0f);
            MeshGeomFacet rclFacet = _rclMesh.GetFacet(*it);
            for (int j=0; j<3; j++)
            {
                clPt2d = pclProj->operator()(rclFacet._aclPoints[j]);
                clGravityOfFacet += clPt2d;
                if (rclPoly.Contains(Base::Vector2D(clPt2d.x, clPt2d.y)) == bInner)
                {
                    raulFacets.push_back(*it);
                    bNoPointInside = false;
                    break;
                }
            }

            // if no facet point is inside the polygon then check also the gravity
            if (bNoPointInside == true)
            {
              clGravityOfFacet *= 1.0f/3.0f;

              if (rclPoly.Contains(Base::Vector2D(clGravityOfFacet.x, clGravityOfFacet.y)) == bInner)
                 raulFacets.push_back(*it);
            }

            seq.next();
        }
    }
    // Dreiecke ausserhalb schneiden, dann alles durchsuchen
    else
    {
      Base::SequencerLauncher seq("Check facets", _rclMesh.CountFacets());
      for (clIter.Init(); clIter.More(); clIter.Next())
      {
          for (int j=0; j<3; j++)
          {
              clPt2d = pclProj->operator()(clIter->_aclPoints[j]);
              if (rclPoly.Contains(Base::Vector2D(clPt2d.x, clPt2d.y)) == bInner)
              {
                  raulFacets.push_back(clIter.Position());
                  break;
              }
          }
          seq.next();
      }
    }
}

void MeshAlgorithm::CheckFacets(const Base::ViewProjMethod* pclProj, const Base::Polygon2D& rclPoly,
                                bool bInner, std::vector<unsigned long> &raulFacets) const
{
    const MeshPointArray& p = _rclMesh.GetPoints();
    const MeshFacetArray& f = _rclMesh.GetFacets();
    Base::Vector3f pt2d;
    unsigned long index=0;
    for (MeshFacetArray::_TConstIterator it = f.begin(); it != f.end(); ++it,++index) {
        for (int i = 0; i < 3; i++) {
            pt2d = (*pclProj)(p[it->_aulPoints[i]]);
            if (rclPoly.Contains(Base::Vector2D(pt2d.x, pt2d.y)) == bInner) {
                raulFacets.push_back(index);
                break;
            }
        }
    }
}

float MeshAlgorithm::Surface (void) const
{
  float              fTotal = 0.0f;
  MeshFacetIterator clFIter(_rclMesh);

  for (clFIter.Init(); clFIter.More(); clFIter.Next())
    fTotal +=  clFIter->Area();
  
  return fTotal;
}

void MeshAlgorithm::SubSampleByDist (float fDist, std::vector<Base::Vector3f> &rclPoints) const
{
    rclPoints.clear();
    MeshFacetIterator clFIter(_rclMesh);
    for (clFIter.Init(); clFIter.More(); clFIter.Next()) {
        size_t k = rclPoints.size();
        clFIter->SubSample(fDist, rclPoints);
        if (rclPoints.size() == k)
            rclPoints.push_back(clFIter->GetGravityPoint()); // min. add middle point
    }
}

void MeshAlgorithm::SubSampleAllPoints (std::vector<Base::Vector3f> &rclPoints) const
{
    rclPoints.clear();

    // Add all Points
    //
    MeshPointIterator clPIter(_rclMesh);
    for (clPIter.Init(); clPIter.More(); clPIter.Next()) {
        rclPoints.push_back(*clPIter);
    }
}

void MeshAlgorithm::SubSampleByCount (unsigned long ulCtPoints, std::vector<Base::Vector3f> &rclPoints) const
{
    float fDist = float(sqrt(Surface() / float(ulCtPoints)));
    SubSampleByDist(fDist, rclPoints);
}

void MeshAlgorithm::SearchFacetsFromPolyline (const std::vector<Base::Vector3f> &rclPolyline, float fRadius,
                                              const MeshFacetGrid& rclGrid, std::vector<unsigned long> &rclResultFacetsIndices) const
{
  rclResultFacetsIndices.clear();
  if ( rclPolyline.size() < 3 )
    return; // no polygon defined

  std::set<unsigned long>  aclFacets;
  for (std::vector<Base::Vector3f>::const_iterator pV = rclPolyline.begin(); pV < (rclPolyline.end() - 1); ++pV)
  {
    const Base::Vector3f &rclP0 = *pV, &rclP1 = *(pV + 1);
   
    // BB eines Polyline-Segments
    BoundBox3f clSegmBB(rclP0.x, rclP0.y, rclP0.z, rclP0.x, rclP0.y, rclP0.z);
    clSegmBB &= rclP1;
    clSegmBB.Enlarge(fRadius);  // BB um Suchradius vergroessern

    std::vector<unsigned long> aclBBFacets;
    unsigned long k = rclGrid.Inside(clSegmBB, aclBBFacets, false);
    for (unsigned long i = 0; i < k; i++)
    {
      if (_rclMesh.GetFacet(aclBBFacets[i]).DistanceToLineSegment(rclP0, rclP1) < fRadius)
        aclFacets.insert(aclBBFacets[i]);
    }
  }

  rclResultFacetsIndices.insert(rclResultFacetsIndices.begin(), aclFacets.begin(), aclFacets.end());
}

void MeshAlgorithm::CutBorderFacets (std::vector<unsigned long> &raclFacetIndices, unsigned short usLevel) const
{
  std::vector<unsigned long> aclToDelete;

  CheckBorderFacets(raclFacetIndices, aclToDelete, usLevel);

  // alle gefunden "Rand"-Facetsindizes" aus dem Array loeschen
  std::vector<unsigned long>  aclResult;
  std::set<unsigned long>     aclTmp(aclToDelete.begin(), aclToDelete.end());

  for (std::vector<unsigned long>::iterator pI = raclFacetIndices.begin(); pI != raclFacetIndices.end(); ++pI)
  {
    if (aclTmp.find(*pI) == aclTmp.end())
      aclResult.push_back(*pI);
  }

  raclFacetIndices = aclResult;
}

unsigned long MeshAlgorithm::CountBorderEdges() const
{
    unsigned long cnt=0;
    const MeshFacetArray &rclFAry = _rclMesh._aclFacetArray;
    MeshFacetArray::_TConstIterator end = rclFAry.end();
    for (MeshFacetArray::_TConstIterator it = rclFAry.begin(); it != end; ++it) {
        for (int i=0; i<3; i++) {
            if (it->_aulNeighbours[i] == ULONG_MAX)
                cnt++;
        }
    }

    return cnt;
}

void MeshAlgorithm::CheckBorderFacets (const std::vector<unsigned long> &raclFacetIndices, std::vector<unsigned long> &raclResultIndices, unsigned short usLevel) const
{
  ResetFacetFlag(MeshFacet::TMP0);
  SetFacetsFlag(raclFacetIndices, MeshFacet::TMP0);

  const MeshFacetArray &rclFAry = _rclMesh._aclFacetArray;

  for (unsigned short usL = 0; usL < usLevel; usL++)
  {
    for (std::vector<unsigned long>::const_iterator pF = raclFacetIndices.begin(); pF != raclFacetIndices.end(); ++pF)
    {
      for (int i = 0; i < 3; i++)
      {
        unsigned long ulNB = rclFAry[*pF]._aulNeighbours[i];
        if (ulNB == ULONG_MAX)
        {
          raclResultIndices.push_back(*pF);
          rclFAry[*pF].ResetFlag(MeshFacet::TMP0);
          continue;
        }
        if (rclFAry[ulNB].IsFlag(MeshFacet::TMP0) == false)
        {
          raclResultIndices.push_back(*pF);
          rclFAry[*pF].ResetFlag(MeshFacet::TMP0);
          continue;
        }
      }
    }
  }
}

void MeshAlgorithm::GetBorderPoints (const std::vector<unsigned long> &raclFacetIndices, std::set<unsigned long> &raclResultPointsIndices) const
{
  ResetFacetFlag(MeshFacet::TMP0);
  SetFacetsFlag(raclFacetIndices, MeshFacet::TMP0);

  const MeshFacetArray &rclFAry = _rclMesh._aclFacetArray;

  for (std::vector<unsigned long>::const_iterator pF = raclFacetIndices.begin(); pF != raclFacetIndices.end(); ++pF)
  {
    for (int i = 0; i < 3; i++)
    {
      const MeshFacet &rclFacet = rclFAry[*pF];
      unsigned long      ulNB     = rclFacet._aulNeighbours[i];
      if (ulNB == ULONG_MAX)
      {
        raclResultPointsIndices.insert(rclFacet._aulPoints[i]);
        raclResultPointsIndices.insert(rclFacet._aulPoints[(i+1)%3]);
        continue;
      }
      if (rclFAry[ulNB].IsFlag(MeshFacet::TMP0) == false)
      {
        raclResultPointsIndices.insert(rclFacet._aulPoints[i]);
        raclResultPointsIndices.insert(rclFacet._aulPoints[(i+1)%3]);
        continue;
      }
    }
  }
}

bool MeshAlgorithm::NearestPointFromPoint (const Base::Vector3f &rclPt, unsigned long &rclResFacetIndex, Base::Vector3f &rclResPoint) const
{
  if (_rclMesh.CountFacets() == 0)
    return false;

  // calc each facet
  float fMinDist = FLOAT_MAX;
  unsigned long ulInd   = ULONG_MAX;
  MeshFacetIterator pF(_rclMesh);
  for (pF.Init(); pF.More(); pF.Next())
  {
    float fDist = pF->DistanceToPoint(rclPt);
    if (fDist < fMinDist)
    {
      fMinDist = fDist;
      ulInd    = pF.Position();
    }
  }

  MeshGeomFacet rclSFacet = _rclMesh.GetFacet(ulInd);
  rclSFacet.DistanceToPoint(rclPt, rclResPoint);
  rclResFacetIndex = ulInd;

  return true;
}

bool MeshAlgorithm::NearestPointFromPoint (const Base::Vector3f &rclPt, const MeshFacetGrid& rclGrid, unsigned long &rclResFacetIndex, Base::Vector3f &rclResPoint) const
{
  unsigned long ulInd = rclGrid.SearchNearestFromPoint(rclPt);

  if (ulInd == ULONG_MAX)
  {
    return false;
  }

  MeshGeomFacet rclSFacet = _rclMesh.GetFacet(ulInd);
  rclSFacet.DistanceToPoint(rclPt, rclResPoint);
  rclResFacetIndex = ulInd;

  return true;
}

bool MeshAlgorithm::NearestPointFromPoint (const Base::Vector3f &rclPt, const MeshFacetGrid& rclGrid, float fMaxSearchArea,
                                           unsigned long &rclResFacetIndex, Base::Vector3f &rclResPoint) const
{
  unsigned long ulInd = rclGrid.SearchNearestFromPoint(rclPt, fMaxSearchArea);

  if (ulInd == ULONG_MAX)
    return false;  // no facets inside BoundingBox

  MeshGeomFacet rclSFacet = _rclMesh.GetFacet(ulInd);
  rclSFacet.DistanceToPoint(rclPt, rclResPoint);
  rclResFacetIndex = ulInd;

  return true;
}

bool MeshAlgorithm::CutWithPlane (const Base::Vector3f &clBase, const Base::Vector3f &clNormal, const MeshFacetGrid &rclGrid,
                                  std::list<std::vector<Base::Vector3f> > &rclResult, float fMinEps, bool bConnectPolygons) const
{
  std::vector<unsigned long>  aulFacets;  

  // Grid durschsuchen
  MeshGridIterator clGridIter(rclGrid);
  for (clGridIter.Init(); clGridIter.More(); clGridIter.Next())
  {  
    // wenn Gridvoxel Ebene schneidet: alle Facets aufnehmen zum Schneiden
    if (clGridIter.GetBoundBox().IsCutPlane(clBase, clNormal) == true)
      clGridIter.GetElements(aulFacets);
  }

  // mehrfach vorhanden Dreiecke entfernen
  std::sort(aulFacets.begin(), aulFacets.end());
  aulFacets.erase(std::unique(aulFacets.begin(), aulFacets.end()), aulFacets.end());  

  // alle Facets mit Ebene schneiden
  std::list<std::pair<Base::Vector3f, Base::Vector3f> > clTempPoly;  // Feld mit Schnittlinien (unsortiert, nicht verkettet)

  for (std::vector<unsigned long>::iterator pF = aulFacets.begin(); pF != aulFacets.end(); ++pF)
  {
    Base::Vector3f  clE1, clE2;
    const MeshGeomFacet clF(_rclMesh.GetFacet(*pF));

    // Facet schneiden und Schnittstrecke ablegen
    if (clF.IntersectWithPlane(clBase, clNormal, clE1, clE2) == true)
      clTempPoly.push_back(std::pair<Base::Vector3f, Base::Vector3f>(clE1, clE2));
  }

  if(bConnectPolygons)
  {
      //std::list<std::pair<Base::Vector3f, Base::Vector3f> > rclTempLines;
      std::list<std::pair<Base::Vector3f, Base::Vector3f> > rclResultLines(clTempPoly.begin(),clTempPoly.end());
      std::list<std::vector<Base::Vector3f> > tempList;
      ConnectLines(clTempPoly, tempList, fMinEps);
      ConnectPolygons(tempList, clTempPoly);

      for(std::list<std::pair<Base::Vector3f, Base::Vector3f> >::iterator iter = clTempPoly.begin(); iter != clTempPoly.end(); ++iter)
      {
        rclResultLines.push_front(*iter);
      }

      return ConnectLines(rclResultLines, rclResult, fMinEps);
  }

  return ConnectLines(clTempPoly, rclResult, fMinEps);
}

bool MeshAlgorithm::ConnectLines (std::list<std::pair<Base::Vector3f, Base::Vector3f> > &rclLines,
                                  std::list<std::vector<Base::Vector3f> > &rclPolylines, float fMinEps) const
{
    typedef std::list<std::pair<Base::Vector3f, Base::Vector3f> >::iterator  TCIter;

    // square search radius
    // const float fMinEps = 1.0e-2f; // := 10 mirometer distance
    fMinEps = fMinEps * fMinEps;

    // remove all lines whose distance is smaller than epsilon
    std::list<TCIter> _clToDelete;
    float fToDelDist = fMinEps / 10.0f;
    for (TCIter pF = rclLines.begin(); pF != rclLines.end(); ++pF) {
    if (Base::DistanceP2(pF->first, pF->second) < fToDelDist)
        _clToDelete.push_back(pF);
    }

    for (std::list<TCIter>::iterator pI = _clToDelete.begin(); pI != _clToDelete.end(); ++pI)
        rclLines.erase(*pI);

    while (!rclLines.empty()) {
        TCIter pF;

        // new polyline
        std::list<Base::Vector3f> clPoly;

        // add first line and delete from the list
        Base::Vector3f clFront = rclLines.begin()->first;  // current start point of the polyline
        Base::Vector3f clEnd   = rclLines.begin()->second; // current end point of the polyline
        clPoly.push_back(clFront);
        clPoly.push_back(clEnd);
        rclLines.erase(rclLines.begin());

        // search for the next line on the begin/end of the polyline and add it
        TCIter pFront, pEnd;
        bool bFoundLine;
        do {
            float  fFrontMin = fMinEps, fEndMin = fMinEps;
            bool   bFrontFirst=false, bEndFirst=false;

            pFront = rclLines.end();
            pEnd   = rclLines.end();
            bFoundLine = false;

            for (pF = rclLines.begin(); pF != rclLines.end(); ++pF) {
                if (Base::DistanceP2(clFront, pF->first) < fFrontMin) {
                    fFrontMin   = Base::DistanceP2(clFront, pF->first);
                    pFront      = pF;
                    bFrontFirst = true;
                }
                else if (Base::DistanceP2(clEnd, pF->first) < fEndMin) {
                    fEndMin     = Base::DistanceP2(clEnd, pF->first);
                    pEnd        = pF;
                    bEndFirst   = true;
                }
                else if (Base::DistanceP2(clFront, pF->second) < fFrontMin) {
                    fFrontMin   = Base::DistanceP2(clFront, pF->second);
                    pFront      = pF;
                    bFrontFirst = false;
                }
                else if (Base::DistanceP2(clEnd, pF->second) < fEndMin) {
                    fEndMin     = Base::DistanceP2(clEnd, pF->second);
                    pEnd        = pF;
                    bEndFirst   = false;
                }
            }

            if (pFront != rclLines.end()) {
                bFoundLine = true;
                if (bFrontFirst) {
                    clPoly.push_front(pFront->second);
                    clFront = pFront->second;
                }
                else {
                    clPoly.push_front(pFront->first);
                    clFront = pFront->first;
                }

                rclLines.erase(pFront);
            }

            if (pEnd != rclLines.end()) {
                bFoundLine = true;
                if (bEndFirst) {
                    clPoly.push_back(pEnd->second);
                    clEnd = pEnd->second;
                }
                else {
                    clPoly.push_back(pEnd->first);
                    clEnd = pEnd->first;
                }

                rclLines.erase(pEnd);
            }
        }
        while (bFoundLine);

        rclPolylines.push_back(std::vector<Base::Vector3f>(clPoly.begin(), clPoly.end()));
    }

    // remove all polylines with too few length
    typedef std::list<std::vector<Base::Vector3f> >::iterator TPIter;
    std::list<TPIter> _clPolyToDelete;
    for (TPIter pJ = rclPolylines.begin(); pJ != rclPolylines.end(); ++pJ) {
        if (pJ->size() == 2) { // only one line segment
            if (Base::DistanceP2(*pJ->begin(), *(pJ->begin() + 1)) <= fMinEps)
                _clPolyToDelete.push_back(pJ);
        }
    }

    for (std::list<TPIter>::iterator pK = _clPolyToDelete.begin(); pK != _clPolyToDelete.end(); ++pK)
        rclPolylines.erase(*pK);

    return true;
}

bool MeshAlgorithm::ConnectPolygons(std::list<std::vector<Base::Vector3f> > &clPolyList,
                                    std::list<std::pair<Base::Vector3f, Base::Vector3f> > &rclLines) const
{

  for(std::list< std::vector<Base::Vector3f> >::iterator OutIter = clPolyList.begin(); OutIter != clPolyList.end(); ++OutIter)
  {
    std::pair<Base::Vector3f,Base::Vector3f> currentSort;
    float fDist = Base::Distance(OutIter->front(),OutIter->back());
    currentSort.first = OutIter->front();
    currentSort.second = OutIter->back();

    for(std::list< std::vector<Base::Vector3f> >::iterator InnerIter = clPolyList.begin(); InnerIter != clPolyList.end(); ++InnerIter)
    {
      if(OutIter == InnerIter) continue;

      if(Base::Distance(OutIter->front(),InnerIter->front()) < fDist)
      {
        currentSort.second = InnerIter->front();
        fDist = Base::Distance(OutIter->front(),InnerIter->front());
      }
      if(Base::Distance(OutIter->front(),InnerIter->back()) < fDist)
      {
        currentSort.second = InnerIter->back();
        fDist = Base::Distance(OutIter->front(),InnerIter->back());
      }
    }

    rclLines.push_front(currentSort);

  }

  return true;
}

void MeshAlgorithm::GetFacetsFromPlane (const MeshFacetGrid &rclGrid, const Base::Vector3f& clNormal, float d, const Base::Vector3f &rclLeft,
                                        const Base::Vector3f &rclRight, std::vector<unsigned long> &rclRes) const
{
    std::vector<unsigned long> aulFacets;

    Base::Vector3f clBase = d * clNormal;

    Base::Vector3f clPtNormal(rclLeft - rclRight);
    clPtNormal.Normalize();

    // search grid 
    MeshGridIterator clGridIter(rclGrid);
    for (clGridIter.Init(); clGridIter.More(); clGridIter.Next()) {
        // add facets from grid if the plane if cut the grid-voxel
        if (clGridIter.GetBoundBox().IsCutPlane(clBase, clNormal) == true)
            clGridIter.GetElements(aulFacets);
    }

    // testing facet against planes
    for (std::vector<unsigned long>::iterator pI = aulFacets.begin(); pI != aulFacets.end(); ++pI) {
        MeshGeomFacet clSFacet = _rclMesh.GetFacet(*pI);
        if (clSFacet.IntersectWithPlane(clBase, clNormal) == true) {
            bool bInner = false;
            for (int i = 0; (i < 3) && (bInner == false); i++) {
                Base::Vector3f clPt = clSFacet._aclPoints[i];
                if ((clPt.DistanceToPlane(rclLeft, clPtNormal) <= 0.0f) && (clPt.DistanceToPlane(rclRight, clPtNormal) >= 0.0f))
                    bInner = true;
            }

            if (bInner == true)
                rclRes.push_back(*pI);
        }
    }
}

void MeshAlgorithm::PointsFromFacetsIndices (const std::vector<unsigned long> &rvecIndices, std::vector<Base::Vector3f> &rvecPoints) const
{
  const MeshFacetArray &rclFAry = _rclMesh._aclFacetArray;
  const MeshPointArray &rclPAry = _rclMesh._aclPointArray;

  std::set<unsigned long> setPoints;

  for (std::vector<unsigned long>::const_iterator itI = rvecIndices.begin(); itI != rvecIndices.end(); ++itI)
  {
    for (int i = 0; i < 3; i++)
      setPoints.insert(rclFAry[*itI]._aulPoints[i]);
  }

  rvecPoints.clear();
  for (std::set<unsigned long>::iterator itP = setPoints.begin(); itP != setPoints.end(); ++itP)
    rvecPoints.push_back(rclPAry[*itP]);
}

bool MeshAlgorithm::Distance (const Base::Vector3f &rclPt, unsigned long ulFacetIdx, float fMaxDistance, float &rfDistance) const
{
  const MeshFacetArray &rclFAry = _rclMesh._aclFacetArray;
  const MeshPointArray &rclPAry = _rclMesh._aclPointArray;
  const unsigned long *pulIdx = rclFAry[ulFacetIdx]._aulPoints;

  BoundBox3f clBB;
  clBB &= rclPAry[*(pulIdx++)];
  clBB &= rclPAry[*(pulIdx++)];
  clBB &= rclPAry[*pulIdx];
  clBB.Enlarge(fMaxDistance);

  if (clBB.IsInBox(rclPt) == false)
    return false;

  rfDistance = _rclMesh.GetFacet(ulFacetIdx).DistanceToPoint(rclPt);

  return rfDistance < fMaxDistance;
}

float MeshAlgorithm::CalculateMinimumGridLength(float fLength, const Base::BoundBox3f& rBBox, unsigned long maxElements) const
{
  // Max. limit of grid elements
  float fMaxGridElements=(float)maxElements;

  // estimate the minimum allowed grid length
  float fMinGridLen = (float)pow((rBBox.LengthX()*rBBox.LengthY()*rBBox.LengthZ()/fMaxGridElements), 0.3333f);
  return std::max<float>(fMinGridLen, fLength);
}

// ----------------------------------------------------

void MeshRefPointToFacets::Rebuild (void)
{
    _map.clear();

    const MeshPointArray& rPoints = _rclMesh.GetPoints();
    const MeshFacetArray& rFacets = _rclMesh.GetFacets();
    _map.resize(rPoints.size());

    MeshFacetArray::_TConstIterator pFBegin = rFacets.begin();
    for (MeshFacetArray::_TConstIterator pFIter = rFacets.begin(); pFIter != rFacets.end(); ++pFIter) {
        _map[pFIter->_aulPoints[0]].insert(pFIter - pFBegin);
        _map[pFIter->_aulPoints[1]].insert(pFIter - pFBegin);
        _map[pFIter->_aulPoints[2]].insert(pFIter - pFBegin);
    }
}

Base::Vector3f MeshRefPointToFacets::GetNormal(unsigned long pos) const
{
    const std::set<unsigned long>& n = _map[pos];
    Base::Vector3f normal;
    MeshGeomFacet f;
    for (std::set<unsigned long>::const_iterator it = n.begin(); it != n.end(); ++it) {
        f = _rclMesh.GetFacet(*it);
        normal += f.Area() * f.GetNormal();
    }

    normal.Normalize();
    return normal;
}

std::set<unsigned long> MeshRefPointToFacets::NeighbourPoints(const std::vector<unsigned long>& pt, int level) const
{
    std::set<unsigned long> cp,nb,lp;
    cp.insert(pt.begin(), pt.end());
    lp.insert(pt.begin(), pt.end());
    MeshFacetArray::_TConstIterator f_it = _rclMesh.GetFacets().begin();
    for (int i=0; i < level; i++) {
        std::set<unsigned long> cur;
        for (std::set<unsigned long>::iterator it = lp.begin(); it != lp.end(); ++it) {
            const std::set<unsigned long>& ft = (*this)[*it];
            for (std::set<unsigned long>::const_iterator jt = ft.begin(); jt != ft.end(); ++jt) {
                for (int j = 0; j < 3; j++) {
                    unsigned long index = f_it[*jt]._aulPoints[j];
                    if (cp.find(index) == cp.end() && nb.find(index) == nb.end()) {
                        nb.insert(index);
                        cur.insert(index);
                    }
                }
            }
        }

        lp = cur;
        if (lp.empty())
            break;
    }
    return nb;
}

void MeshRefPointToFacets::Neighbours (unsigned long ulFacetInd, float fMaxDist, MeshCollector& collect) const
{
    std::set<unsigned long> visited;
    Base::Vector3f  clCenter = _rclMesh.GetFacet(ulFacetInd).GetGravityPoint();

    const MeshFacetArray& rFacets = _rclMesh.GetFacets();
    SearchNeighbours(rFacets, ulFacetInd, clCenter, fMaxDist * fMaxDist, visited, collect);
}

void MeshRefPointToFacets::SearchNeighbours(const MeshFacetArray& rFacets, unsigned long index, const Base::Vector3f &rclCenter,
                                            float fMaxDist2, std::set<unsigned long>& visited, MeshCollector& collect) const
{
    if (visited.find(index) != visited.end())
        return;

    const MeshFacet& face = rFacets[index];
    if (Base::DistanceP2(rclCenter, _rclMesh.GetFacet(face).GetGravityPoint()) > fMaxDist2)
        return;

    visited.insert(index);
    collect.Append(_rclMesh, index);
    for (int i = 0; i < 3; i++) {
        const std::set<unsigned long> &f = (*this)[face._aulPoints[i]];

        for (std::set<unsigned long>::const_iterator j = f.begin(); j != f.end(); ++j) {
            SearchNeighbours(rFacets, *j, rclCenter, fMaxDist2, visited, collect);
        }
    }
}

MeshFacetArray::_TConstIterator
MeshRefPointToFacets::GetFacet (unsigned long index) const
{
    return _rclMesh.GetFacets().begin() + index;
}

const std::set<unsigned long>&
MeshRefPointToFacets::operator[] (unsigned long pos) const
{
    return _map[pos];
}

void MeshRefPointToFacets::AddNeighbour(unsigned long pos, unsigned long facet)
{
    _map[pos].insert(facet);
}

void MeshRefPointToFacets::RemoveNeighbour(unsigned long pos, unsigned long facet)
{
    _map[pos].erase(facet);
}

//----------------------------------------------------------------------------

void MeshRefFacetToFacets::Rebuild (void)
{
    _map.clear();

    const MeshFacetArray& rFacets = _rclMesh.GetFacets();
    _map.resize(rFacets.size());

    MeshRefPointToFacets  vertexFace(_rclMesh);
    MeshFacetArray::_TConstIterator pFBegin = rFacets.begin();
    for (MeshFacetArray::_TConstIterator pFIter = pFBegin; pFIter != rFacets.end(); ++pFIter) {
        for (int i = 0; i < 3; i++) {
            const std::set<unsigned long>& faces = vertexFace[pFIter->_aulPoints[i]];
            for (std::set<unsigned long>::const_iterator it = faces.begin(); it != faces.end(); ++it)
                _map[pFIter - pFBegin].insert(*it);
        }
    }
}

const std::set<unsigned long>&
MeshRefFacetToFacets::operator[] (unsigned long pos) const
{
    return _map[pos];
}

//----------------------------------------------------------------------------

void MeshRefPointToPoints::Rebuild (void)
{
    _map.clear();

    const MeshPointArray& rPoints = _rclMesh.GetPoints();
    _map.resize(rPoints.size());

    const MeshFacetArray& rFacets = _rclMesh.GetFacets();
    for (MeshFacetArray::_TConstIterator pFIter = rFacets.begin(); pFIter != rFacets.end(); ++pFIter) {
        unsigned long ulP0 = pFIter->_aulPoints[0];
        unsigned long ulP1 = pFIter->_aulPoints[1];
        unsigned long ulP2 = pFIter->_aulPoints[2];

        _map[ulP0].insert(ulP1);
        _map[ulP0].insert(ulP2);
        _map[ulP1].insert(ulP0);
        _map[ulP1].insert(ulP2);
        _map[ulP2].insert(ulP0);
        _map[ulP2].insert(ulP1);
    }
}

Base::Vector3f MeshRefPointToPoints::GetNormal(unsigned long pos) const
{
    const MeshPointArray& rPoints = _rclMesh.GetPoints();
    MeshCore::PlaneFit pf;
    pf.AddPoint(rPoints[pos]);
    MeshCore::MeshPoint center = rPoints[pos];
    const std::set<unsigned long>& cv = _map[pos];
    for (std::set<unsigned long>::const_iterator cv_it = cv.begin(); cv_it !=cv.end(); ++cv_it) {
        pf.AddPoint(rPoints[*cv_it]);
        center += rPoints[*cv_it];
    }

    pf.Fit();

    Base::Vector3f normal = pf.GetNormal();
    normal.Normalize();
    return normal;
}

float MeshRefPointToPoints::GetAverageEdgeLength(unsigned long index) const
{
    const MeshPointArray& rPoints = _rclMesh.GetPoints();
    float len=0.0f;
    const std::set<unsigned long>& n = (*this)[index];
    const Base::Vector3f& p = rPoints[index];
    for (std::set<unsigned long>::const_iterator it = n.begin(); it != n.end(); ++it) {
        len += Base::Distance(p, rPoints[*it]);
    }
    return (len/n.size());
}

const std::set<unsigned long>&
MeshRefPointToPoints::operator[] (unsigned long pos) const
{
    return _map[pos];
}

void MeshRefPointToPoints::AddNeighbour(unsigned long pos, unsigned long facet)
{
    _map[pos].insert(facet);
}

void MeshRefPointToPoints::RemoveNeighbour(unsigned long pos, unsigned long facet)
{
    _map[pos].erase(facet);
}

//----------------------------------------------------------------------------

void MeshRefEdgeToFacets::Rebuild (void)
{
    _map.clear();

    const MeshFacetArray& rFacets = _rclMesh.GetFacets();
    unsigned long index = 0;
    for (MeshFacetArray::_TConstIterator it = rFacets.begin(); it != rFacets.end(); ++it, ++index) {
        for (int i=0; i<3; i++) {
            MeshEdge e;
            e.first = it->_aulPoints[i];
            e.second = it->_aulPoints[(i+1)%3];
            std::map<MeshEdge, MeshFacetPair, EdgeOrder>::iterator jt =
                _map.find(e);
            if (jt == _map.end()) {
                _map[e].first = index;
                _map[e].second = ULONG_MAX;
            }
            else {
                _map[e].second = index;
            }
        }
    }
}

const std::pair<unsigned long, unsigned long>&
MeshRefEdgeToFacets::operator[] (const MeshEdge& edge) const
{
    return _map.find(edge)->second;
}

//----------------------------------------------------------------------------

void MeshRefNormalToPoints::Rebuild (void)
{
    _norm.clear();

    const MeshPointArray& rPoints = _rclMesh.GetPoints();
    _norm.resize(rPoints.size());

    const MeshFacetArray& rFacets = _rclMesh.GetFacets();
    for (MeshFacetArray::_TConstIterator pF = rFacets.begin(); pF != rFacets.end(); ++pF) {
        const MeshPoint &p0 = rPoints[pF->_aulPoints[0]];
        const MeshPoint &p1 = rPoints[pF->_aulPoints[1]];
        const MeshPoint &p2 = rPoints[pF->_aulPoints[2]];
        float l2p01 = Base::DistanceP2(p0,p1);
        float l2p12 = Base::DistanceP2(p1,p2);
        float l2p20 = Base::DistanceP2(p2,p0);

        Base::Vector3f facenormal = _rclMesh.GetFacet(*pF).GetNormal();
        _norm[pF->_aulPoints[0]] += facenormal * (1.0f / (l2p01 * l2p20));
        _norm[pF->_aulPoints[1]] += facenormal * (1.0f / (l2p12 * l2p01));
        _norm[pF->_aulPoints[2]] += facenormal * (1.0f / (l2p20 * l2p12));
    }
    for (std::vector<Base::Vector3f>::iterator it = _norm.begin(); it != _norm.end(); ++it)
        it->Normalize();
}

const Base::Vector3f&
MeshRefNormalToPoints::operator[] (unsigned long pos) const
{
    return _norm[pos];
}