+namespace
+{
+ struct Node // node of a triangle
+ {
+ size_t _triaIndex; // triangle index == index of the 1st triangle node in triangulation array
+ size_t _nodeIndex; // node index within triangle [0-2]
+
+ //! return node index within the node array
+ size_t Index() const { return _triaIndex + _nodeIndex; }
+
+ //! return local 3-d index [0-2]
+ static size_t ThirdIndex( size_t i1, size_t i2 )
+ {
+ size_t i3 = ( i2 + 1 ) % 3;
+ if ( i3 == i1 )
+ i3 = ( i2 + 2 ) % 3;
+ return i3;
+ }
+ //! return 3-d node index within the node array
+ static size_t ThirdIndex( const Node& n1, const Node& n2 )
+ {
+ return n1._triaIndex + ThirdIndex( n1._nodeIndex, n2._nodeIndex );
+ }
+ bool operator<(const Node& other) const { return _triaIndex < other._triaIndex; }
+ };
+ typedef boost::container::flat_set< Node > TNodeSet;
+
+}
+
+struct Triangulate::Optimizer
+{
+ std::vector< TNodeSet > _nodeUsage; // inclusions of a node in triangles
+
+ //================================================================================
+ /*!
+ * \brief Optimize triangles by edge swapping
+ * \param [inout] nodes - polygon triangulation, i.e. connectivity of all triangles to optimize
+ * \param [in] points - coordinates of nodes of the input polygon
+ * \param [in] nodeIndices - indices of triangulation nodes within the input polygon
+ */
+ //================================================================================
+
+ void optimize( std::vector< const SMDS_MeshNode*>& nodes,
+ std::vector< PolyVertex > & points,
+ std::vector< size_t > & nodeIndices)
+ {
+ // for each node of the polygon, remember triangles using it
+ _nodeUsage.resize( points.size() );
+ for ( size_t i = 0; i < points.size(); ++i ) // clear old data
+ {
+ _nodeUsage[ i ].clear();
+ }
+ for ( size_t i = 0, iTria = 0; i < nodeIndices.size(); ++iTria )
+ {
+ _nodeUsage[ nodeIndices[ i++ ]].insert({ iTria * 3, 0 });
+ _nodeUsage[ nodeIndices[ i++ ]].insert({ iTria * 3, 1 });
+ _nodeUsage[ nodeIndices[ i++ ]].insert({ iTria * 3, 2 });
+ }
+
+ // optimization
+ for ( size_t iTria = 0; iTria < nodeIndices.size(); iTria += 3 )
+ {
+ double badness1 = computeBadness( nodeIndices[ iTria + 0 ],
+ nodeIndices[ iTria + 1 ],
+ nodeIndices[ iTria + 2 ],
+ points );
+ for ( size_t i = 0; i < 3; ++i ) // loop on triangle edges to find a neighbor triangle
+ {
+ size_t i1 = iTria + i; // node index in nodeIndices
+ size_t i2 = iTria + ( i + 1 ) % 3;
+ size_t ind1 = nodeIndices[ i1 ]; // node index in points
+ size_t ind2 = nodeIndices[ i2 ];
+ TNodeSet & usage1 = _nodeUsage[ ind1 ]; // triangles using a node
+ TNodeSet & usage2 = _nodeUsage[ ind2 ];
+ if ( usage1.size() < 2 ||
+ usage2.size() < 2 )
+ continue;
+
+ // look for another triangle using two nodes
+ TNodeSet::iterator usIt1 = usage1.begin();
+ for ( ; usIt1 != usage1.end(); ++usIt1 )
+ {
+ if ( usIt1->_triaIndex == iTria )
+ continue; // current triangle
+ TNodeSet::iterator usIt2 = usage2.find( *usIt1 );
+ if ( usIt2 == usage2.end() )
+ continue; // no common _triaIndex in two usages
+
+ size_t i3 = iTria + ( i + 2 ) % 3;
+ size_t i4 = Node::ThirdIndex( *usIt1, *usIt2 ); // 4th node of quadrangle
+ size_t ind3 = nodeIndices[ i3 ];
+ size_t ind4 = nodeIndices[ i4 ];
+
+ double badness2 = computeBadness( ind2, ind1, ind4, points );
+ double badness3 = computeBadness( ind1, ind4, ind3, points, /*checkArea=*/true );
+ double badness4 = computeBadness( ind2, ind3, ind4, points, /*checkArea=*/true );
+
+ if ( Max( badness1, badness2 ) < Max( badness3, badness4 ))
+ continue;
+
+ // swap edge by modifying nodeIndices
+
+ nodeIndices[ i2 ] = ind4;
+ _nodeUsage[ ind2 ].erase ({ iTria, i2 - iTria });
+ _nodeUsage[ ind4 ].insert({ iTria, i2 - iTria });
+
+ i1 = usIt1->Index();
+ nodeIndices[ i1 ] = ind3;
+ _nodeUsage[ ind1 ].erase ( *usIt1 );
+ _nodeUsage[ ind3 ].insert( *usIt1 );
+
+ --i; // to re-check a current edge
+ badness1 = badness3;
+ break;
+ }
+ }
+ }
+
+ // update nodes by updated nodeIndices
+ for ( size_t i = 0; i < nodeIndices.size(); ++i )
+ nodes[ i ] = points[ nodeIndices[ i ]]._nxyz.Node();
+
+ return;
+ }
+
+ //================================================================================
+ /*!
+ * \brief Return 1./area. Initially: max cos^2 of triangle angles
+ */
+ //================================================================================
+
+ double computeBadness( size_t i1, size_t i2, size_t i3,
+ std::vector< PolyVertex > & points,
+ bool checkArea = false )
+ {
+ //if ( checkArea )
+ {
+ points[ i2 ]._prev = & points[ i1 ];
+ points[ i2 ]._next = & points[ i3 ];
+ double a = points[ i2 ].TriaArea();
+ if ( a < 0 )
+ return std::numeric_limits<double>::max();
+ return 1. / a;
+
+ if ( points[ i2 ].TriaArea() < 0 )
+ return 2;
+ }
+ const gp_XY & p1 = points[ i1 ]._xy;
+ const gp_XY & p2 = points[ i2 ]._xy;
+ const gp_XY & p3 = points[ i3 ]._xy;
+ gp_XY vec[3] = { p2 - p1,
+ p3 - p2,
+ p1 - p3 };
+ double len[3] = { vec[0].SquareModulus(),
+ vec[1].SquareModulus(),
+ vec[2].SquareModulus() };
+ if ( len[0] < gp::Resolution() ||
+ len[1] < gp::Resolution() ||
+ len[2] < gp::Resolution() )
+ return 2;
+
+ double maxCos2 = 0;
+ for ( int i = 0; i < 3; ++i )
+ {
+ int i2 = ( i+1 ) % 3;
+ double dot = -vec[ i ] * vec[ i2 ];
+ if ( dot > 0 )
+ maxCos2 = Max( maxCos2, dot * dot / len[ i ] / len[ i2 ] );
+ }
+ return maxCos2;
+ }
+};
+