2021-03-23 19:44:27 +05:00
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// Copyright (C) 2007-2021 CEA/DEN, EDF R&D, OPEN CASCADE
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2018-02-13 17:16:32 +05:00
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//
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// Copyright (C) 2003-2007 OPEN CASCADE, EADS/CCR, LIP6, CEA/DEN,
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// CEDRAT, EDF R&D, LEG, PRINCIPIA R&D, BUREAU VERITAS
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//
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// This library is free software; you can redistribute it and/or
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// modify it under the terms of the GNU Lesser General Public
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// License as published by the Free Software Foundation; either
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// version 2.1 of the License, or (at your option) any later version.
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//
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// This library is distributed in the hope that it will be useful,
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// but WITHOUT ANY WARRANTY; without even the implied warranty of
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// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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// Lesser General Public License for more details.
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//
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// You should have received a copy of the GNU Lesser General Public
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// License along with this library; if not, write to the Free Software
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// Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
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//
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// See http://www.salome-platform.org/ or email : webmaster.salome@opencascade.com
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//
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// File : SMESH_Triangulate.cxx
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// Created : Thu Jan 18 18:00:13 2018
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// Author : Edward AGAPOV (eap)
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// Extracted from ../DriverSTL/DriverSTL_W_SMDS_Mesh.cxx
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#include "SMESH_MeshAlgos.hxx"
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#include <Standard_ErrorHandler.hxx>
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#include <Standard_Failure.hxx>
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#include <gp_Ax2.hxx>
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2019-01-17 17:53:49 +05:00
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#include <boost/container/flat_set.hpp>
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2018-02-13 17:16:32 +05:00
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using namespace SMESH_MeshAlgos;
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2019-01-17 17:53:49 +05:00
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namespace
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{
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struct Node // node of a triangle
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{
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size_t _triaIndex; // triangle index == index of the 1st triangle node in triangulation array
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size_t _nodeIndex; // node index within triangle [0-2]
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//! return node index within the node array
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size_t Index() const { return _triaIndex + _nodeIndex; }
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//! return local 3-d index [0-2]
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static size_t ThirdIndex( size_t i1, size_t i2 )
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{
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size_t i3 = ( i2 + 1 ) % 3;
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if ( i3 == i1 )
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i3 = ( i2 + 2 ) % 3;
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return i3;
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}
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//! return 3-d node index within the node array
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static size_t ThirdIndex( const Node& n1, const Node& n2 )
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{
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return n1._triaIndex + ThirdIndex( n1._nodeIndex, n2._nodeIndex );
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}
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bool operator<(const Node& other) const { return _triaIndex < other._triaIndex; }
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};
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typedef boost::container::flat_set< Node > TriaNodeSet;
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}
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/*!
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* \brief Vertex of a polygon. Together with 2 neighbor Vertices represents a triangle
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*/
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struct Triangulate::PolyVertex
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{
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SMESH_NodeXYZ _nxyz;
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size_t _index;
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gp_XY _xy;
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PolyVertex* _prev;
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PolyVertex* _next;
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void SetNodeAndNext( const SMDS_MeshNode* n, PolyVertex& v, size_t index );
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void GetTriaNodes( const SMDS_MeshNode** nodes, size_t* nodeIndices) const;
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double TriaArea() const;
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bool IsInsideTria( const PolyVertex* v );
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PolyVertex* Delete();
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// compare PolyVertex'es by node
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bool operator()(const PolyVertex* a, const PolyVertex* b) const
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{
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return ( a->_nxyz.Node() < b->_nxyz.Node() );
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}
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// set of PolyVertex sorted by mesh node
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typedef boost::container::flat_set< PolyVertex*, PolyVertex > PVSet;
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};
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struct Triangulate::Data
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{
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std::vector< PolyVertex > _pv;
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std::vector< size_t > _nodeIndex;
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PolyVertex::PVSet _uniqueNodePV;
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};
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struct Triangulate::Optimizer
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{
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std::vector< TriaNodeSet > _nodeUsage; // inclusions of a node in triangles
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//================================================================================
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/*!
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* \brief Optimize triangles by edge swapping
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* \param [inout] nodes - polygon triangulation, i.e. connectivity of all triangles to optimize
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* \param [in] points - coordinates of nodes of the input polygon
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* \param [in] nodeIndices - indices of triangulation nodes within the input polygon
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*/
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//================================================================================
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void optimize( std::vector< const SMDS_MeshNode*>& nodes,
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std::vector< PolyVertex > & points,
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std::vector< size_t > & nodeIndices)
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{
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// for each node of the polygon, remember triangles using it
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_nodeUsage.resize( points.size() );
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for ( size_t i = 0; i < points.size(); ++i ) // clear old data
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{
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_nodeUsage[ i ].clear();
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}
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for ( size_t i = 0, iTria = 0; i < nodeIndices.size(); ++iTria )
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{
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_nodeUsage[ nodeIndices[ i++ ]].insert({ iTria * 3, 0 });
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_nodeUsage[ nodeIndices[ i++ ]].insert({ iTria * 3, 1 });
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_nodeUsage[ nodeIndices[ i++ ]].insert({ iTria * 3, 2 });
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}
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// optimization
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for ( size_t iTria = 0; iTria < nodeIndices.size(); iTria += 3 )
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{
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double badness1 = computeBadness( nodeIndices[ iTria + 0 ],
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nodeIndices[ iTria + 1 ],
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nodeIndices[ iTria + 2 ],
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points );
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for ( size_t i = 0; i < 3; ++i ) // loop on triangle edges to find a neighbor triangle
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{
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size_t i1 = iTria + i; // node index in nodeIndices
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size_t i2 = iTria + ( i + 1 ) % 3;
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size_t ind1 = nodeIndices[ i1 ]; // node index in points
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size_t ind2 = nodeIndices[ i2 ];
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2019-02-22 23:17:20 +05:00
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TriaNodeSet & usage1 = _nodeUsage[ ind1 ]; // triangles using a node
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TriaNodeSet & usage2 = _nodeUsage[ ind2 ];
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if ( usage1.size() < 2 ||
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usage2.size() < 2 )
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continue;
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// look for another triangle using two nodes
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TriaNodeSet::iterator usIt1 = usage1.begin();
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for ( ; usIt1 != usage1.end(); ++usIt1 )
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{
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if ( usIt1->_triaIndex == iTria )
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continue; // current triangle
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TriaNodeSet::iterator usIt2 = usage2.find( *usIt1 );
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if ( usIt2 == usage2.end() )
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continue; // no common _triaIndex in two usages
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size_t i3 = iTria + ( i + 2 ) % 3;
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size_t i4 = Node::ThirdIndex( *usIt1, *usIt2 ); // 4th node of quadrangle
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size_t ind3 = nodeIndices[ i3 ];
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size_t ind4 = nodeIndices[ i4 ];
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double badness2 = computeBadness( ind2, ind1, ind4, points );
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double badness3 = computeBadness( ind1, ind4, ind3, points, /*checkArea=*/true );
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double badness4 = computeBadness( ind2, ind3, ind4, points, /*checkArea=*/true );
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if ( Max( badness1, badness2 ) < Max( badness3, badness4 ))
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continue;
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// swap edge by modifying nodeIndices
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nodeIndices[ i2 ] = ind4;
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_nodeUsage[ ind4 ].insert({ iTria, i2 - iTria });
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_nodeUsage[ ind2 ].erase ({ iTria, i2 - iTria });
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i1 = usIt1->Index();
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nodeIndices[ i1 ] = ind3;
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_nodeUsage[ ind3 ].insert( *usIt1 );
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_nodeUsage[ ind1 ].erase ( *usIt1 );
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--i; // to re-check a current edge
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badness1 = badness3;
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break;
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}
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}
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}
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// update nodes by updated nodeIndices
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for ( size_t i = 0; i < nodeIndices.size(); ++i )
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nodes[ i ] = points[ nodeIndices[ i ]]._nxyz.Node();
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return;
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}
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//================================================================================
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/*!
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* \brief Return 1./area. Initially: max cos^2 of triangle angles
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*/
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//================================================================================
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double computeBadness( size_t i1, size_t i2, size_t i3,
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std::vector< PolyVertex > & points,
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bool checkArea = false )
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{
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if ( checkArea )
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{
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points[ i2 ]._prev = & points[ i1 ];
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points[ i2 ]._next = & points[ i3 ];
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double a = points[ i2 ].TriaArea();
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2019-02-22 23:17:20 +05:00
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// if ( a < 0 )
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// return std::numeric_limits<double>::max();
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// return 1. / a;
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2019-02-22 23:17:20 +05:00
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if ( a < 0 )
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return 2;
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}
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const gp_XY & p1 = points[ i1 ]._xy;
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const gp_XY & p2 = points[ i2 ]._xy;
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const gp_XY & p3 = points[ i3 ]._xy;
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gp_XY vec[3] = { p2 - p1,
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p3 - p2,
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p1 - p3 };
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double len[3] = { vec[0].SquareModulus(),
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vec[1].SquareModulus(),
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vec[2].SquareModulus() };
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if ( len[0] < gp::Resolution() ||
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len[1] < gp::Resolution() ||
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len[2] < gp::Resolution() )
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return 2;
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double maxCos2 = 0;
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for ( int i = 0; i < 3; ++i )
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{
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int i2 = ( i+1 ) % 3;
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double dot = -vec[ i ] * vec[ i2 ];
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if ( dot > 0 )
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maxCos2 = Max( maxCos2, dot * dot / len[ i ] / len[ i2 ] );
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}
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return maxCos2;
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}
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};
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2018-02-13 17:16:32 +05:00
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//================================================================================
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/*!
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* \brief Initialization
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*/
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//================================================================================
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void Triangulate::PolyVertex::SetNodeAndNext( const SMDS_MeshNode* n,
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PolyVertex& v,
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size_t index )
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{
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_nxyz.Set( n );
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_next = &v;
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v._prev = this;
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_index = index;
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}
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//================================================================================
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/*!
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* \brief Remove self from a polygon
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*/
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//================================================================================
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Triangulate::PolyVertex* Triangulate::PolyVertex::Delete()
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{
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_prev->_next = _next;
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_next->_prev = _prev;
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return _next;
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}
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//================================================================================
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/*!
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* \brief Return nodes of a triangle
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*/
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//================================================================================
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2019-01-17 17:53:49 +05:00
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void Triangulate::PolyVertex::GetTriaNodes( const SMDS_MeshNode** nodes,
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size_t* nodeIndices) const
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{
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nodes[0] = _prev->_nxyz._node;
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nodes[1] = this->_nxyz._node;
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nodes[2] = _next->_nxyz._node;
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nodeIndices[0] = _prev->_index;
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nodeIndices[1] = this->_index;
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nodeIndices[2] = _next->_index;
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2018-02-13 17:16:32 +05:00
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}
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//================================================================================
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/*!
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* \brief Compute triangle area
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*/
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//================================================================================
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inline static double Area( const gp_XY& xy0, const gp_XY& xy1, const gp_XY& xy2 )
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{
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gp_XY vPrev = xy0 - xy1;
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gp_XY vNext = xy2 - xy1;
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return vNext ^ vPrev;
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}
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//================================================================================
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/*!
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* \brief Compute triangle area
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*/
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//================================================================================
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double Triangulate::PolyVertex::TriaArea() const
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{
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return Area( _prev->_xy, this->_xy, _next->_xy );
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}
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//================================================================================
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/*!
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* \brief Check if a vertex is inside a triangle
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*/
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//================================================================================
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bool Triangulate::PolyVertex::IsInsideTria( const PolyVertex* v )
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{
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if ( this ->_nxyz == v->_nxyz ||
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_prev->_nxyz == v->_nxyz ||
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_next->_nxyz == v->_nxyz )
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return false;
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gp_XY p = _prev->_xy - v->_xy;
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gp_XY t = this->_xy - v->_xy;
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gp_XY n = _next->_xy - v->_xy;
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const double tol = -1e-7;
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return (( p ^ t ) >= tol &&
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( t ^ n ) >= tol &&
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( n ^ p ) >= tol );
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// return ( Area( _prev, this, v ) > 0 &&
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// Area( this, _next, v ) > 0 &&
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// Area( _next, _prev, v ) > 0 );
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}
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//================================================================================
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/*!
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* \brief Triangulate a polygon. Assure correct orientation for concave polygons
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*/
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//================================================================================
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bool Triangulate::triangulate( std::vector< const SMDS_MeshNode*>& nodes,
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2019-01-17 17:53:49 +05:00
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const size_t nbNodes)
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2018-02-13 17:16:32 +05:00
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{
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2019-02-22 23:17:20 +05:00
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std::vector< PolyVertex >& _pv = _data->_pv;
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std::vector< size_t >& _nodeIndex = _data->_nodeIndex;
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PolyVertex::PVSet& _uniqueNodePV = _data->_uniqueNodePV;
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2018-02-13 17:16:32 +05:00
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// connect nodes into a ring
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_pv.resize( nbNodes );
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for ( size_t i = 1; i < nbNodes; ++i )
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2019-10-11 21:13:54 +05:00
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_pv[i-1].SetNodeAndNext( nodes[i-1], _pv[i], /*index=*/i-1 );
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2019-01-17 17:53:49 +05:00
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_pv[ nbNodes-1 ].SetNodeAndNext( nodes[ nbNodes-1 ], _pv[0], nbNodes-1 );
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2018-02-13 17:16:32 +05:00
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2019-02-22 23:17:20 +05:00
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// assure correctness of PolyVertex::_index as a node can encounter more than once
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// within a polygon boundary
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if ( _optimizer && nbNodes > 4 )
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{
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_uniqueNodePV.clear();
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for ( size_t i = 0; i < nbNodes; ++i )
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{
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PolyVertex::PVSet::iterator pv = _uniqueNodePV.insert( &_pv[i] ).first;
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_pv[i]._index = (*pv)->_index;
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}
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}
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2018-02-13 17:16:32 +05:00
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// get a polygon normal
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gp_XYZ normal(0,0,0), p0,v01,v02;
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p0 = _pv[0]._nxyz;
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v01 = _pv[1]._nxyz - p0;
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for ( size_t i = 2; i < nbNodes; ++i )
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{
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v02 = _pv[i]._nxyz - p0;
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normal += v01 ^ v02;
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v01 = v02;
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}
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// project nodes to the found plane
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gp_Ax2 axes;
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try {
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axes = gp_Ax2( p0, normal, v01 );
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}
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2020-08-21 10:05:05 +05:00
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catch ( Standard_Failure& ) {
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2018-02-13 17:16:32 +05:00
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return false;
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}
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2019-10-11 21:13:54 +05:00
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double factor = 1.0, modulus = normal.Modulus();
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if ( modulus < 1e-2 )
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factor = 1. / sqrt( modulus );
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2018-02-13 17:16:32 +05:00
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for ( size_t i = 0; i < nbNodes; ++i )
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{
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gp_XYZ p = _pv[i]._nxyz - p0;
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2019-10-11 21:13:54 +05:00
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_pv[i]._xy.SetX( axes.XDirection().XYZ() * p * factor);
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_pv[i]._xy.SetY( axes.YDirection().XYZ() * p * factor );
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2018-02-13 17:16:32 +05:00
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}
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2019-02-22 23:17:20 +05:00
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// compute minimal triangle area
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double sumArea = 0;
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2019-10-11 21:13:54 +05:00
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if ( factor == 1.0 )
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sumArea = modulus;
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else
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for ( size_t i = 0; i < nbNodes; ++i )
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sumArea += _pv[i].TriaArea();
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2019-02-22 23:17:20 +05:00
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const double minArea = 1e-6 * sumArea / ( nbNodes - 2 );
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2018-02-13 17:16:32 +05:00
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// in a loop, find triangles with positive area and having no vertices inside
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int iN = 0, nbTria = nbNodes - 2;
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2019-01-17 17:53:49 +05:00
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nodes.resize( nbTria * 3 );
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_nodeIndex.resize( nbTria * 3 );
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2018-02-13 17:16:32 +05:00
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PolyVertex* v = &_pv[0], *vi;
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int nbVertices = nbNodes, nbBadTria = 0, isGoodTria;
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while ( nbBadTria < nbVertices )
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{
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if (( isGoodTria = v->TriaArea() > minArea ))
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{
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for ( vi = v->_next->_next;
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vi != v->_prev;
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vi = vi->_next )
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{
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if ( v->IsInsideTria( vi ))
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break;
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}
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isGoodTria = ( vi == v->_prev );
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}
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if ( isGoodTria )
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{
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2019-01-17 17:53:49 +05:00
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v->GetTriaNodes( &nodes[ iN ], &_nodeIndex[ iN ] );
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2018-02-13 17:16:32 +05:00
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iN += 3;
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v = v->Delete();
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if ( --nbVertices == 3 )
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{
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// last triangle remains
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2019-01-17 17:53:49 +05:00
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v->GetTriaNodes( &nodes[ iN ], &_nodeIndex[ iN ] );
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if ( _optimizer )
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_optimizer->optimize( nodes, _pv, _nodeIndex );
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2018-02-13 17:16:32 +05:00
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return true;
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}
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nbBadTria = 0;
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}
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else
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{
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v = v->_next;
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++nbBadTria;
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}
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}
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// the polygon is invalid; add triangles with positive area
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nbBadTria = 0;
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while ( nbBadTria < nbVertices )
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{
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isGoodTria = v->TriaArea() > minArea;
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if ( isGoodTria )
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{
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2019-01-17 17:53:49 +05:00
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v->GetTriaNodes( &nodes[ iN ], &_nodeIndex[ iN ] );
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2018-02-13 17:16:32 +05:00
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iN += 3;
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v = v->Delete();
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if ( --nbVertices == 3 )
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{
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// last triangle remains
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2019-01-17 17:53:49 +05:00
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v->GetTriaNodes( &nodes[ iN ], &_nodeIndex[ iN ] );
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2018-02-13 17:16:32 +05:00
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return true;
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}
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nbBadTria = 0;
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}
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else
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{
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v = v->_next;
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++nbBadTria;
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}
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}
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// add all the rest triangles
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while ( nbVertices >= 3 )
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{
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2019-01-17 17:53:49 +05:00
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v->GetTriaNodes( &nodes[ iN ], &_nodeIndex[ iN ] );
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2018-02-13 17:16:32 +05:00
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iN += 3;
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v = v->Delete();
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--nbVertices;
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}
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return true;
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} // triangulate()
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2019-01-17 17:53:49 +05:00
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//================================================================================
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/*!
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* \brief Constructor
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*/
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//================================================================================
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Triangulate::Triangulate( bool optimize ): _optimizer(0)
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{
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2019-02-22 23:17:20 +05:00
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_data = new Data;
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2019-01-17 17:53:49 +05:00
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if ( optimize )
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_optimizer = new Optimizer;
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}
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//================================================================================
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/*!
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* \brief Destructor
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*/
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//================================================================================
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Triangulate::~Triangulate()
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{
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2019-02-22 23:17:20 +05:00
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delete _data;
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2019-01-17 17:53:49 +05:00
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delete _optimizer;
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_optimizer = 0;
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}
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2018-02-13 17:16:32 +05:00
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//================================================================================
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/*!
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* \brief Return nb triangles in a decomposed mesh face
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* \retval int - number of triangles
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*/
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//================================================================================
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int Triangulate::GetNbTriangles( const SMDS_MeshElement* face )
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{
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// WARNING: counting triangles must be coherent with GetTriangles()
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switch ( face->GetEntityType() )
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{
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case SMDSEntity_BiQuad_Triangle:
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case SMDSEntity_BiQuad_Quadrangle:
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return face->NbNodes() - 1;
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// case SMDSEntity_Triangle:
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// case SMDSEntity_Quad_Triangle:
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// case SMDSEntity_Quadrangle:
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// case SMDSEntity_Quad_Quadrangle:
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// case SMDSEntity_Polygon:
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// case SMDSEntity_Quad_Polygon:
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default:
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return face->NbNodes() - 2;
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}
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return 0;
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}
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//================================================================================
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/*!
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* \brief Decompose a mesh face into triangles
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* \retval int - number of triangles
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*/
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//================================================================================
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int Triangulate::GetTriangles( const SMDS_MeshElement* face,
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std::vector< const SMDS_MeshNode*>& nodes)
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{
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if ( face->GetType() != SMDSAbs_Face )
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return 0;
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// WARNING: decomposing into triangles must be coherent with getNbTriangles()
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int nbTria, i = 0, nbNodes = face->NbNodes();
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SMDS_NodeIteratorPtr nIt = face->interlacedNodesIterator();
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nodes.resize( nbNodes * 3 );
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nodes[ i++ ] = nIt->next();
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nodes[ i++ ] = nIt->next();
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const SMDSAbs_EntityType type = face->GetEntityType();
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switch ( type )
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{
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case SMDSEntity_BiQuad_Triangle:
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case SMDSEntity_BiQuad_Quadrangle:
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nbTria = ( type == SMDSEntity_BiQuad_Triangle ) ? 6 : 8;
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nodes[ i++ ] = face->GetNode( nbTria );
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for ( i = 3; i < 3*(nbTria-1); i += 3 )
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{
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nodes[ i+0 ] = nodes[ i-2 ];
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nodes[ i+1 ] = nIt->next();
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nodes[ i+2 ] = nodes[ 2 ];
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}
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nodes[ i+0 ] = nodes[ i-2 ];
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nodes[ i+1 ] = nodes[ 0 ];
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nodes[ i+2 ] = nodes[ 2 ];
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break;
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case SMDSEntity_Triangle:
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nbTria = 1;
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nodes[ i++ ] = nIt->next();
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break;
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default:
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// case SMDSEntity_Quad_Triangle:
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// case SMDSEntity_Quadrangle:
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// case SMDSEntity_Quad_Quadrangle:
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// case SMDSEntity_Polygon:
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// case SMDSEntity_Quad_Polygon:
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nbTria = nbNodes - 2;
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while ( nIt->more() )
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nodes[ i++ ] = nIt->next();
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if ( nbTria > 1 && !triangulate( nodes, nbNodes ))
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{
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nIt = face->interlacedNodesIterator();
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nodes[ 0 ] = nIt->next();
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nodes[ 1 ] = nIt->next();
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nodes[ 2 ] = nIt->next();
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for ( i = 3; i < 3*nbTria; i += 3 )
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{
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nodes[ i+0 ] = nodes[ 0 ];
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nodes[ i+1 ] = nodes[ i-1 ];
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nodes[ i+2 ] = nIt->next();
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}
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}
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}
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return nbTria;
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}
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