1 // Copyright (C) 2007-2016 CEA/DEN, EDF R&D, OPEN CASCADE
3 // Copyright (C) 2003-2007 OPEN CASCADE, EADS/CCR, LIP6, CEA/DEN,
4 // CEDRAT, EDF R&D, LEG, PRINCIPIA R&D, BUREAU VERITAS
6 // This library is free software; you can redistribute it and/or
7 // modify it under the terms of the GNU Lesser General Public
8 // License as published by the Free Software Foundation; either
9 // version 2.1 of the License, or (at your option) any later version.
11 // This library is distributed in the hope that it will be useful,
12 // but WITHOUT ANY WARRANTY; without even the implied warranty of
13 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
14 // Lesser General Public License for more details.
16 // You should have received a copy of the GNU Lesser General Public
17 // License along with this library; if not, write to the Free Software
18 // Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
20 // See http://www.salome-platform.org/ or email : webmaster.salome@opencascade.com
22 // File : SMESH_MeshAlgos.hxx
23 // Created : Tue Apr 30 18:00:36 2013
24 // Author : Edward AGAPOV (eap)
26 // This file holds some low level algorithms extracted from SMESH_MeshEditor
27 // to make them accessible from Controls package
29 #include "SMESH_MeshAlgos.hxx"
31 #include "SMDS_FaceOfNodes.hxx"
32 #include "SMDS_LinearEdge.hxx"
33 #include "SMDS_Mesh.hxx"
34 #include "SMDS_PolygonalFaceOfNodes.hxx"
35 #include "SMDS_VolumeTool.hxx"
36 #include "SMESH_OctreeNode.hxx"
38 #include <GC_MakeSegment.hxx>
39 #include <GeomAPI_ExtremaCurveCurve.hxx>
40 #include <Geom_Line.hxx>
41 #include <IntAna_IntConicQuad.hxx>
42 #include <IntAna_Quadric.hxx>
51 //=======================================================================
53 * \brief Implementation of search for the node closest to point
55 //=======================================================================
57 struct SMESH_NodeSearcherImpl: public SMESH_NodeSearcher
59 //---------------------------------------------------------------------
63 SMESH_NodeSearcherImpl( const SMDS_Mesh* theMesh = 0,
64 SMDS_ElemIteratorPtr theElemIt = SMDS_ElemIteratorPtr() )
66 myMesh = ( SMDS_Mesh* ) theMesh;
68 TIDSortedNodeSet nodes;
70 SMDS_NodeIteratorPtr nIt = theMesh->nodesIterator(/*idInceasingOrder=*/true);
72 nodes.insert( nodes.end(), nIt->next() );
76 while ( theElemIt->more() )
78 const SMDS_MeshElement* e = theElemIt->next();
79 nodes.insert( e->begin_nodes(), e->end_nodes() );
82 myOctreeNode = new SMESH_OctreeNode(nodes) ;
84 // get max size of a leaf box
85 SMESH_OctreeNode* tree = myOctreeNode;
86 while ( !tree->isLeaf() )
88 SMESH_OctreeNodeIteratorPtr cIt = tree->GetChildrenIterator();
92 myHalfLeafSize = tree->maxSize() / 2.;
95 //---------------------------------------------------------------------
97 * \brief Move node and update myOctreeNode accordingly
99 void MoveNode( const SMDS_MeshNode* node, const gp_Pnt& toPnt )
101 myOctreeNode->UpdateByMoveNode( node, toPnt );
102 myMesh->MoveNode( node, toPnt.X(), toPnt.Y(), toPnt.Z() );
105 //---------------------------------------------------------------------
109 const SMDS_MeshNode* FindClosestTo( const gp_Pnt& thePnt )
111 map<double, const SMDS_MeshNode*> dist2Nodes;
112 myOctreeNode->NodesAround( thePnt.Coord(), dist2Nodes, myHalfLeafSize );
113 if ( !dist2Nodes.empty() )
114 return dist2Nodes.begin()->second;
115 list<const SMDS_MeshNode*> nodes;
116 //myOctreeNode->NodesAround( &tgtNode, &nodes, myHalfLeafSize );
118 double minSqDist = DBL_MAX;
119 if ( nodes.empty() ) // get all nodes of OctreeNode's closest to thePnt
121 // sort leafs by their distance from thePnt
122 typedef map< double, SMESH_OctreeNode* > TDistTreeMap;
123 TDistTreeMap treeMap;
124 list< SMESH_OctreeNode* > treeList;
125 list< SMESH_OctreeNode* >::iterator trIt;
126 treeList.push_back( myOctreeNode );
128 gp_XYZ pointNode( thePnt.X(), thePnt.Y(), thePnt.Z() );
129 bool pointInside = myOctreeNode->isInside( pointNode, myHalfLeafSize );
130 for ( trIt = treeList.begin(); trIt != treeList.end(); ++trIt)
132 SMESH_OctreeNode* tree = *trIt;
133 if ( !tree->isLeaf() ) // put children to the queue
135 if ( pointInside && !tree->isInside( pointNode, myHalfLeafSize )) continue;
136 SMESH_OctreeNodeIteratorPtr cIt = tree->GetChildrenIterator();
137 while ( cIt->more() )
138 treeList.push_back( cIt->next() );
140 else if ( tree->NbNodes() ) // put a tree to the treeMap
142 const Bnd_B3d& box = *tree->getBox();
143 double sqDist = thePnt.SquareDistance( 0.5 * ( box.CornerMin() + box.CornerMax() ));
144 pair<TDistTreeMap::iterator,bool> it_in = treeMap.insert( make_pair( sqDist, tree ));
145 if ( !it_in.second ) // not unique distance to box center
146 treeMap.insert( it_in.first, make_pair( sqDist + 1e-13*treeMap.size(), tree ));
149 // find distance after which there is no sense to check tree's
150 double sqLimit = DBL_MAX;
151 TDistTreeMap::iterator sqDist_tree = treeMap.begin();
152 if ( treeMap.size() > 5 ) {
153 SMESH_OctreeNode* closestTree = sqDist_tree->second;
154 const Bnd_B3d& box = *closestTree->getBox();
155 double limit = sqrt( sqDist_tree->first ) + sqrt ( box.SquareExtent() );
156 sqLimit = limit * limit;
158 // get all nodes from trees
159 for ( ; sqDist_tree != treeMap.end(); ++sqDist_tree) {
160 if ( sqDist_tree->first > sqLimit )
162 SMESH_OctreeNode* tree = sqDist_tree->second;
163 tree->NodesAround( tree->GetNodeIterator()->next(), &nodes );
166 // find closest among nodes
168 const SMDS_MeshNode* closestNode = 0;
169 list<const SMDS_MeshNode*>::iterator nIt = nodes.begin();
170 for ( ; nIt != nodes.end(); ++nIt ) {
171 double sqDist = thePnt.SquareDistance( SMESH_TNodeXYZ( *nIt ) );
172 if ( minSqDist > sqDist ) {
180 //---------------------------------------------------------------------
182 * \brief Finds nodes located within a tolerance near a point
184 int FindNearPoint(const gp_Pnt& point,
185 const double tolerance,
186 std::vector< const SMDS_MeshNode* >& foundNodes)
188 myOctreeNode->NodesAround( point.Coord(), foundNodes, tolerance );
189 return foundNodes.size();
192 //---------------------------------------------------------------------
196 ~SMESH_NodeSearcherImpl() { delete myOctreeNode; }
198 //---------------------------------------------------------------------
200 * \brief Return the node tree
202 const SMESH_OctreeNode* getTree() const { return myOctreeNode; }
205 SMESH_OctreeNode* myOctreeNode;
207 double myHalfLeafSize; // max size of a leaf box
210 // ========================================================================
211 namespace // Utils used in SMESH_ElementSearcherImpl::FindElementsByPoint()
213 const int MaxNbElemsInLeaf = 10; // maximal number of elements in a leaf of tree
214 const int MaxLevel = 7; // maximal tree height -> nb terminal boxes: 8^7 = 2097152
215 const double NodeRadius = 1e-9; // to enlarge bnd box of element
217 //=======================================================================
219 * \brief Octal tree of bounding boxes of elements
221 //=======================================================================
223 class ElementBndBoxTree : public SMESH_Octree
227 ElementBndBoxTree(const SMDS_Mesh& mesh,
228 SMDSAbs_ElementType elemType,
229 SMDS_ElemIteratorPtr theElemIt = SMDS_ElemIteratorPtr(),
230 double tolerance = NodeRadius );
231 void getElementsNearPoint( const gp_Pnt& point, TIDSortedElemSet& foundElems );
232 void getElementsNearLine ( const gp_Ax1& line, TIDSortedElemSet& foundElems);
233 void getElementsInSphere ( const gp_XYZ& center,
234 const double radius, TIDSortedElemSet& foundElems);
235 size_t getSize() { return std::max( _size, _elements.size() ); }
236 virtual ~ElementBndBoxTree();
239 ElementBndBoxTree():_size(0) {}
240 SMESH_Octree* newChild() const { return new ElementBndBoxTree; }
241 void buildChildrenData();
242 Bnd_B3d* buildRootBox();
244 //!< Bounding box of element
245 struct ElementBox : public Bnd_B3d
247 const SMDS_MeshElement* _element;
248 int _refCount; // an ElementBox can be included in several tree branches
249 ElementBox(const SMDS_MeshElement* elem, double tolerance);
251 vector< ElementBox* > _elements;
255 //================================================================================
257 * \brief ElementBndBoxTree creation
259 //================================================================================
261 ElementBndBoxTree::ElementBndBoxTree(const SMDS_Mesh& mesh, SMDSAbs_ElementType elemType, SMDS_ElemIteratorPtr theElemIt, double tolerance)
262 :SMESH_Octree( new SMESH_TreeLimit( MaxLevel, /*minSize=*/0. ))
264 int nbElems = mesh.GetMeshInfo().NbElements( elemType );
265 _elements.reserve( nbElems );
267 SMDS_ElemIteratorPtr elemIt = theElemIt ? theElemIt : mesh.elementsIterator( elemType );
268 while ( elemIt->more() )
269 _elements.push_back( new ElementBox( elemIt->next(),tolerance ));
274 //================================================================================
278 //================================================================================
280 ElementBndBoxTree::~ElementBndBoxTree()
282 for ( size_t i = 0; i < _elements.size(); ++i )
283 if ( --_elements[i]->_refCount <= 0 )
287 //================================================================================
289 * \brief Return the maximal box
291 //================================================================================
293 Bnd_B3d* ElementBndBoxTree::buildRootBox()
295 Bnd_B3d* box = new Bnd_B3d;
296 for ( size_t i = 0; i < _elements.size(); ++i )
297 box->Add( *_elements[i] );
301 //================================================================================
303 * \brief Redistrubute element boxes among children
305 //================================================================================
307 void ElementBndBoxTree::buildChildrenData()
309 for ( size_t i = 0; i < _elements.size(); ++i )
311 for (int j = 0; j < 8; j++)
313 if ( !_elements[i]->IsOut( *myChildren[j]->getBox() ))
315 _elements[i]->_refCount++;
316 ((ElementBndBoxTree*)myChildren[j])->_elements.push_back( _elements[i]);
319 _elements[i]->_refCount--;
321 _size = _elements.size();
322 SMESHUtils::FreeVector( _elements ); // = _elements.clear() + free memory
324 for (int j = 0; j < 8; j++)
326 ElementBndBoxTree* child = static_cast<ElementBndBoxTree*>( myChildren[j]);
327 if ((int) child->_elements.size() <= MaxNbElemsInLeaf )
328 child->myIsLeaf = true;
330 if ( child->_elements.capacity() - child->_elements.size() > 1000 )
331 SMESHUtils::CompactVector( child->_elements );
335 //================================================================================
337 * \brief Return elements which can include the point
339 //================================================================================
341 void ElementBndBoxTree::getElementsNearPoint( const gp_Pnt& point,
342 TIDSortedElemSet& foundElems)
344 if ( getBox()->IsOut( point.XYZ() ))
349 for ( size_t i = 0; i < _elements.size(); ++i )
350 if ( !_elements[i]->IsOut( point.XYZ() ))
351 foundElems.insert( _elements[i]->_element );
355 for (int i = 0; i < 8; i++)
356 ((ElementBndBoxTree*) myChildren[i])->getElementsNearPoint( point, foundElems );
360 //================================================================================
362 * \brief Return elements which can be intersected by the line
364 //================================================================================
366 void ElementBndBoxTree::getElementsNearLine( const gp_Ax1& line,
367 TIDSortedElemSet& foundElems)
369 if ( getBox()->IsOut( line ))
374 for ( size_t i = 0; i < _elements.size(); ++i )
375 if ( !_elements[i]->IsOut( line ))
376 foundElems.insert( _elements[i]->_element );
380 for (int i = 0; i < 8; i++)
381 ((ElementBndBoxTree*) myChildren[i])->getElementsNearLine( line, foundElems );
385 //================================================================================
387 * \brief Return elements from leaves intersecting the sphere
389 //================================================================================
391 void ElementBndBoxTree::getElementsInSphere ( const gp_XYZ& center,
393 TIDSortedElemSet& foundElems)
395 if ( getBox()->IsOut( center, radius ))
400 for ( size_t i = 0; i < _elements.size(); ++i )
401 if ( !_elements[i]->IsOut( center, radius ))
402 foundElems.insert( _elements[i]->_element );
406 for (int i = 0; i < 8; i++)
407 ((ElementBndBoxTree*) myChildren[i])->getElementsInSphere( center, radius, foundElems );
411 //================================================================================
413 * \brief Construct the element box
415 //================================================================================
417 ElementBndBoxTree::ElementBox::ElementBox(const SMDS_MeshElement* elem, double tolerance)
421 SMDS_ElemIteratorPtr nIt = elem->nodesIterator();
422 while ( nIt->more() )
423 Add( SMESH_TNodeXYZ( nIt->next() ));
424 Enlarge( tolerance );
429 //=======================================================================
431 * \brief Implementation of search for the elements by point and
432 * of classification of point in 2D mesh
434 //=======================================================================
436 SMESH_ElementSearcher::~SMESH_ElementSearcher()
440 struct SMESH_ElementSearcherImpl: public SMESH_ElementSearcher
443 SMDS_ElemIteratorPtr _meshPartIt;
444 ElementBndBoxTree* _ebbTree [SMDSAbs_NbElementTypes];
445 int _ebbTreeHeight[SMDSAbs_NbElementTypes];
446 SMESH_NodeSearcherImpl* _nodeSearcher;
447 SMDSAbs_ElementType _elementType;
449 bool _outerFacesFound;
450 set<const SMDS_MeshElement*> _outerFaces; // empty means "no internal faces at all"
452 SMESH_ElementSearcherImpl( SMDS_Mesh& mesh,
454 SMDS_ElemIteratorPtr elemIt=SMDS_ElemIteratorPtr())
455 : _mesh(&mesh),_meshPartIt(elemIt),_nodeSearcher(0),_tolerance(tol),_outerFacesFound(false)
457 for ( int i = 0; i < SMDSAbs_NbElementTypes; ++i )
460 _ebbTreeHeight[i] = -1;
463 virtual ~SMESH_ElementSearcherImpl()
465 for ( int i = 0; i < SMDSAbs_NbElementTypes; ++i )
467 delete _ebbTree[i]; _ebbTree[i] = NULL;
469 if ( _nodeSearcher ) delete _nodeSearcher; _nodeSearcher = 0;
471 virtual int FindElementsByPoint(const gp_Pnt& point,
472 SMDSAbs_ElementType type,
473 vector< const SMDS_MeshElement* >& foundElements);
474 virtual TopAbs_State GetPointState(const gp_Pnt& point);
475 virtual const SMDS_MeshElement* FindClosestTo( const gp_Pnt& point,
476 SMDSAbs_ElementType type );
478 void GetElementsNearLine( const gp_Ax1& line,
479 SMDSAbs_ElementType type,
480 vector< const SMDS_MeshElement* >& foundElems);
481 void GetElementsInSphere( const gp_XYZ& center,
483 SMDSAbs_ElementType type,
484 vector< const SMDS_MeshElement* >& foundElems);
485 double getTolerance();
486 bool getIntersParamOnLine(const gp_Lin& line, const SMDS_MeshElement* face,
487 const double tolerance, double & param);
488 void findOuterBoundary(const SMDS_MeshElement* anyOuterFace);
489 bool isOuterBoundary(const SMDS_MeshElement* face) const
491 return _outerFaces.empty() || _outerFaces.count(face);
495 if ( _ebbTreeHeight[ _elementType ] < 0 )
496 _ebbTreeHeight[ _elementType ] = _ebbTree[ _elementType ]->getHeight();
497 return _ebbTreeHeight[ _elementType ];
500 struct TInters //!< data of intersection of the line and the mesh face (used in GetPointState())
502 const SMDS_MeshElement* _face;
504 bool _coincides; //!< the line lays in face plane
505 TInters(const SMDS_MeshElement* face, const gp_Vec& faceNorm, bool coinc=false)
506 : _face(face), _faceNorm( faceNorm ), _coincides( coinc ) {}
508 struct TFaceLink //!< link and faces sharing it (used in findOuterBoundary())
511 TIDSortedElemSet _faces;
512 TFaceLink( const SMDS_MeshNode* n1, const SMDS_MeshNode* n2, const SMDS_MeshElement* face)
513 : _link( n1, n2 ), _faces( &face, &face + 1) {}
517 ostream& operator<< (ostream& out, const SMESH_ElementSearcherImpl::TInters& i)
519 return out << "TInters(face=" << ( i._face ? i._face->GetID() : 0)
520 << ", _coincides="<<i._coincides << ")";
523 //=======================================================================
525 * \brief define tolerance for search
527 //=======================================================================
529 double SMESH_ElementSearcherImpl::getTolerance()
531 if ( _tolerance < 0 )
533 const SMDS_MeshInfo& meshInfo = _mesh->GetMeshInfo();
536 if ( _nodeSearcher && meshInfo.NbNodes() > 1 )
538 double boxSize = _nodeSearcher->getTree()->maxSize();
539 _tolerance = 1e-8 * boxSize/* / meshInfo.NbNodes()*/;
541 else if ( _ebbTree[_elementType] && meshInfo.NbElements() > 0 )
543 double boxSize = _ebbTree[_elementType]->maxSize();
544 _tolerance = 1e-8 * boxSize/* / meshInfo.NbElements()*/;
546 if ( _tolerance == 0 )
548 // define tolerance by size of a most complex element
549 int complexType = SMDSAbs_Volume;
550 while ( complexType > SMDSAbs_All &&
551 meshInfo.NbElements( SMDSAbs_ElementType( complexType )) < 1 )
553 if ( complexType == SMDSAbs_All ) return 0; // empty mesh
555 if ( complexType == int( SMDSAbs_Node ))
557 SMDS_NodeIteratorPtr nodeIt = _mesh->nodesIterator();
559 if ( meshInfo.NbNodes() > 2 )
560 elemSize = SMESH_TNodeXYZ( nodeIt->next() ).Distance( nodeIt->next() );
564 SMDS_ElemIteratorPtr elemIt = _mesh->elementsIterator( SMDSAbs_ElementType( complexType ));
565 const SMDS_MeshElement* elem = elemIt->next();
566 SMDS_ElemIteratorPtr nodeIt = elem->nodesIterator();
567 SMESH_TNodeXYZ n1( nodeIt->next() );
569 while ( nodeIt->more() )
571 double dist = n1.Distance( static_cast<const SMDS_MeshNode*>( nodeIt->next() ));
572 elemSize = max( dist, elemSize );
575 _tolerance = 1e-4 * elemSize;
581 //================================================================================
583 * \brief Find intersection of the line and an edge of face and return parameter on line
585 //================================================================================
587 bool SMESH_ElementSearcherImpl::getIntersParamOnLine(const gp_Lin& line,
588 const SMDS_MeshElement* face,
595 GeomAPI_ExtremaCurveCurve anExtCC;
596 Handle(Geom_Curve) lineCurve = new Geom_Line( line );
598 int nbNodes = face->IsQuadratic() ? face->NbNodes()/2 : face->NbNodes();
599 for ( int i = 0; i < nbNodes && nbInts < 2; ++i )
601 GC_MakeSegment edge( SMESH_TNodeXYZ( face->GetNode( i )),
602 SMESH_TNodeXYZ( face->GetNode( (i+1)%nbNodes) ));
603 anExtCC.Init( lineCurve, edge.Value() );
604 if ( anExtCC.NbExtrema() > 0 && anExtCC.LowerDistance() <= tol)
606 Quantity_Parameter pl, pe;
607 anExtCC.LowerDistanceParameters( pl, pe );
613 if ( nbInts > 0 ) param /= nbInts;
616 //================================================================================
618 * \brief Find all faces belonging to the outer boundary of mesh
620 //================================================================================
622 void SMESH_ElementSearcherImpl::findOuterBoundary(const SMDS_MeshElement* outerFace)
624 if ( _outerFacesFound ) return;
626 // Collect all outer faces by passing from one outer face to another via their links
627 // and BTW find out if there are internal faces at all.
629 // checked links and links where outer boundary meets internal one
630 set< SMESH_TLink > visitedLinks, seamLinks;
632 // links to treat with already visited faces sharing them
633 list < TFaceLink > startLinks;
635 // load startLinks with the first outerFace
636 startLinks.push_back( TFaceLink( outerFace->GetNode(0), outerFace->GetNode(1), outerFace));
637 _outerFaces.insert( outerFace );
639 TIDSortedElemSet emptySet;
640 while ( !startLinks.empty() )
642 const SMESH_TLink& link = startLinks.front()._link;
643 TIDSortedElemSet& faces = startLinks.front()._faces;
645 outerFace = *faces.begin();
646 // find other faces sharing the link
647 const SMDS_MeshElement* f;
648 while (( f = SMESH_MeshAlgos::FindFaceInSet(link.node1(), link.node2(), emptySet, faces )))
651 // select another outer face among the found
652 const SMDS_MeshElement* outerFace2 = 0;
653 if ( faces.size() == 2 )
655 outerFace2 = (outerFace == *faces.begin() ? *faces.rbegin() : *faces.begin());
657 else if ( faces.size() > 2 )
659 seamLinks.insert( link );
661 // link direction within the outerFace
662 gp_Vec n1n2( SMESH_TNodeXYZ( link.node1()),
663 SMESH_TNodeXYZ( link.node2()));
664 int i1 = outerFace->GetNodeIndex( link.node1() );
665 int i2 = outerFace->GetNodeIndex( link.node2() );
666 bool rev = ( abs(i2-i1) == 1 ? i1 > i2 : i2 > i1 );
667 if ( rev ) n1n2.Reverse();
669 gp_XYZ ofNorm, fNorm;
670 if ( SMESH_MeshAlgos::FaceNormal( outerFace, ofNorm, /*normalized=*/false ))
672 // direction from the link inside outerFace
673 gp_Vec dirInOF = gp_Vec( ofNorm ) ^ n1n2;
674 // sort all other faces by angle with the dirInOF
675 map< double, const SMDS_MeshElement* > angle2Face;
676 set< const SMDS_MeshElement*, TIDCompare >::const_iterator face = faces.begin();
677 for ( ; face != faces.end(); ++face )
679 if ( *face == outerFace ) continue;
680 if ( !SMESH_MeshAlgos::FaceNormal( *face, fNorm, /*normalized=*/false ))
682 gp_Vec dirInF = gp_Vec( fNorm ) ^ n1n2;
683 double angle = dirInOF.AngleWithRef( dirInF, n1n2 );
684 if ( angle < 0 ) angle += 2. * M_PI;
685 angle2Face.insert( make_pair( angle, *face ));
687 if ( !angle2Face.empty() )
688 outerFace2 = angle2Face.begin()->second;
691 // store the found outer face and add its links to continue seaching from
694 _outerFaces.insert( outerFace2 );
695 int nbNodes = outerFace2->NbCornerNodes();
696 for ( int i = 0; i < nbNodes; ++i )
698 SMESH_TLink link2( outerFace2->GetNode(i), outerFace2->GetNode((i+1)%nbNodes));
699 if ( visitedLinks.insert( link2 ).second )
700 startLinks.push_back( TFaceLink( link2.node1(), link2.node2(), outerFace2 ));
703 startLinks.pop_front();
705 _outerFacesFound = true;
707 if ( !seamLinks.empty() )
709 // There are internal boundaries touching the outher one,
710 // find all faces of internal boundaries in order to find
711 // faces of boundaries of holes, if any.
720 //=======================================================================
722 * \brief Find elements of given type where the given point is IN or ON.
723 * Returns nb of found elements and elements them-selves.
725 * 'ALL' type means elements of any type excluding nodes, balls and 0D elements
727 //=======================================================================
729 int SMESH_ElementSearcherImpl::
730 FindElementsByPoint(const gp_Pnt& point,
731 SMDSAbs_ElementType type,
732 vector< const SMDS_MeshElement* >& foundElements)
734 foundElements.clear();
737 double tolerance = getTolerance();
739 // =================================================================================
740 if ( type == SMDSAbs_Node || type == SMDSAbs_0DElement || type == SMDSAbs_Ball)
742 if ( !_nodeSearcher )
745 _nodeSearcher = new SMESH_NodeSearcherImpl( 0, _meshPartIt );
747 _nodeSearcher = new SMESH_NodeSearcherImpl( _mesh );
749 std::vector< const SMDS_MeshNode* > foundNodes;
750 _nodeSearcher->FindNearPoint( point, tolerance, foundNodes );
752 if ( type == SMDSAbs_Node )
754 foundElements.assign( foundNodes.begin(), foundNodes.end() );
758 for ( size_t i = 0; i < foundNodes.size(); ++i )
760 SMDS_ElemIteratorPtr elemIt = foundNodes[i]->GetInverseElementIterator( type );
761 while ( elemIt->more() )
762 foundElements.push_back( elemIt->next() );
766 // =================================================================================
767 else // elements more complex than 0D
769 if ( !_ebbTree[type] )
771 _ebbTree[_elementType] = new ElementBndBoxTree( *_mesh, type, _meshPartIt, tolerance );
773 TIDSortedElemSet suspectElems;
774 _ebbTree[ type ]->getElementsNearPoint( point, suspectElems );
775 TIDSortedElemSet::iterator elem = suspectElems.begin();
776 for ( ; elem != suspectElems.end(); ++elem )
777 if ( !SMESH_MeshAlgos::IsOut( *elem, point, tolerance ))
778 foundElements.push_back( *elem );
780 return foundElements.size();
783 //=======================================================================
785 * \brief Find an element of given type most close to the given point
787 * WARNING: Only face search is implemeneted so far
789 //=======================================================================
791 const SMDS_MeshElement*
792 SMESH_ElementSearcherImpl::FindClosestTo( const gp_Pnt& point,
793 SMDSAbs_ElementType type )
795 const SMDS_MeshElement* closestElem = 0;
798 if ( type == SMDSAbs_Face || type == SMDSAbs_Volume )
800 ElementBndBoxTree*& ebbTree = _ebbTree[ type ];
802 ebbTree = new ElementBndBoxTree( *_mesh, type, _meshPartIt );
804 TIDSortedElemSet suspectElems;
805 ebbTree->getElementsNearPoint( point, suspectElems );
807 if ( suspectElems.empty() && ebbTree->maxSize() > 0 )
809 gp_Pnt boxCenter = 0.5 * ( ebbTree->getBox()->CornerMin() +
810 ebbTree->getBox()->CornerMax() );
812 if ( ebbTree->getBox()->IsOut( point.XYZ() ))
813 radius = point.Distance( boxCenter ) - 0.5 * ebbTree->maxSize();
815 radius = ebbTree->maxSize() / pow( 2., getTreeHeight()) / 2;
816 while ( suspectElems.empty() )
818 ebbTree->getElementsInSphere( point.XYZ(), radius, suspectElems );
822 double minDist = std::numeric_limits<double>::max();
823 multimap< double, const SMDS_MeshElement* > dist2face;
824 TIDSortedElemSet::iterator elem = suspectElems.begin();
825 for ( ; elem != suspectElems.end(); ++elem )
827 double dist = SMESH_MeshAlgos::GetDistance( *elem, point );
828 if ( dist < minDist + 1e-10)
831 dist2face.insert( dist2face.begin(), make_pair( dist, *elem ));
834 if ( !dist2face.empty() )
836 multimap< double, const SMDS_MeshElement* >::iterator d2f = dist2face.begin();
837 closestElem = d2f->second;
838 // if there are several elements at the same distance, select one
839 // with GC closest to the point
840 typedef SMDS_StdIterator< SMESH_TNodeXYZ, SMDS_ElemIteratorPtr > TXyzIterator;
841 double minDistToGC = 0;
842 for ( ++d2f; d2f != dist2face.end() && fabs( d2f->first - minDist ) < 1e-10; ++d2f )
844 if ( minDistToGC == 0 )
847 gc = accumulate( TXyzIterator(closestElem->nodesIterator()),
848 TXyzIterator(), gc ) / closestElem->NbNodes();
849 minDistToGC = point.SquareDistance( gc );
852 gc = accumulate( TXyzIterator( d2f->second->nodesIterator()),
853 TXyzIterator(), gc ) / d2f->second->NbNodes();
854 double d = point.SquareDistance( gc );
855 if ( d < minDistToGC )
858 closestElem = d2f->second;
861 // cout << "FindClosestTo( " <<point.X()<<", "<<point.Y()<<", "<<point.Z()<<" ) FACE "
862 // <<closestElem->GetID() << " DIST " << minDist << endl;
867 // NOT IMPLEMENTED SO FAR
873 //================================================================================
875 * \brief Classify the given point in the closed 2D mesh
877 //================================================================================
879 TopAbs_State SMESH_ElementSearcherImpl::GetPointState(const gp_Pnt& point)
881 double tolerance = getTolerance();
883 _elementType = SMDSAbs_Face;
885 ElementBndBoxTree*& ebbTree = _ebbTree[ SMDSAbs_Face ];
887 ebbTree = new ElementBndBoxTree( *_mesh, _elementType, _meshPartIt );
889 // Algo: analyse transition of a line starting at the point through mesh boundary;
890 // try three lines parallel to axis of the coordinate system and perform rough
891 // analysis. If solution is not clear perform thorough analysis.
893 const int nbAxes = 3;
894 gp_Dir axisDir[ nbAxes ] = { gp::DX(), gp::DY(), gp::DZ() };
895 map< double, TInters > paramOnLine2TInters[ nbAxes ];
896 list< TInters > tangentInters[ nbAxes ]; // of faces whose plane includes the line
897 multimap< int, int > nbInt2Axis; // to find the simplest case
898 for ( int axis = 0; axis < nbAxes; ++axis )
900 gp_Ax1 lineAxis( point, axisDir[axis]);
901 gp_Lin line ( lineAxis );
903 TIDSortedElemSet suspectFaces; // faces possibly intersecting the line
904 ebbTree->getElementsNearLine( lineAxis, suspectFaces );
906 // Intersect faces with the line
908 map< double, TInters > & u2inters = paramOnLine2TInters[ axis ];
909 TIDSortedElemSet::iterator face = suspectFaces.begin();
910 for ( ; face != suspectFaces.end(); ++face )
914 if ( !SMESH_MeshAlgos::FaceNormal( *face, fNorm, /*normalized=*/false)) continue;
915 gp_Pln facePlane( SMESH_TNodeXYZ( (*face)->GetNode(0)), fNorm );
917 // perform intersection
918 IntAna_IntConicQuad intersection( line, IntAna_Quadric( facePlane ));
919 if ( !intersection.IsDone() )
921 if ( intersection.IsInQuadric() )
923 tangentInters[ axis ].push_back( TInters( *face, fNorm, true ));
925 else if ( ! intersection.IsParallel() && intersection.NbPoints() > 0 )
927 double tol = 1e-4 * Sqrt( fNorm.Modulus() );
928 gp_Pnt intersectionPoint = intersection.Point(1);
929 if ( !SMESH_MeshAlgos::IsOut( *face, intersectionPoint, tol ))
930 u2inters.insert(make_pair( intersection.ParamOnConic(1), TInters( *face, fNorm )));
933 // Analyse intersections roughly
935 int nbInter = u2inters.size();
939 double f = u2inters.begin()->first, l = u2inters.rbegin()->first;
940 if ( nbInter == 1 ) // not closed mesh
941 return fabs( f ) < tolerance ? TopAbs_ON : TopAbs_UNKNOWN;
943 if ( fabs( f ) < tolerance || fabs( l ) < tolerance )
946 if ( (f<0) == (l<0) )
949 int nbIntBeforePoint = std::distance( u2inters.begin(), u2inters.lower_bound(0));
950 int nbIntAfterPoint = nbInter - nbIntBeforePoint;
951 if ( nbIntBeforePoint == 1 || nbIntAfterPoint == 1 )
954 nbInt2Axis.insert( make_pair( min( nbIntBeforePoint, nbIntAfterPoint ), axis ));
956 if ( _outerFacesFound ) break; // pass to thorough analysis
958 } // three attempts - loop on CS axes
960 // Analyse intersections thoroughly.
961 // We make two loops maximum, on the first one we only exclude touching intersections,
962 // on the second, if situation is still unclear, we gather and use information on
963 // position of faces (internal or outer). If faces position is already gathered,
964 // we make the second loop right away.
966 for ( int hasPositionInfo = _outerFacesFound; hasPositionInfo < 2; ++hasPositionInfo )
968 multimap< int, int >::const_iterator nb_axis = nbInt2Axis.begin();
969 for ( ; nb_axis != nbInt2Axis.end(); ++nb_axis )
971 int axis = nb_axis->second;
972 map< double, TInters > & u2inters = paramOnLine2TInters[ axis ];
974 gp_Ax1 lineAxis( point, axisDir[axis]);
975 gp_Lin line ( lineAxis );
977 // add tangent intersections to u2inters
979 list< TInters >::const_iterator tgtInt = tangentInters[ axis ].begin();
980 for ( ; tgtInt != tangentInters[ axis ].end(); ++tgtInt )
981 if ( getIntersParamOnLine( line, tgtInt->_face, tolerance, param ))
982 u2inters.insert(make_pair( param, *tgtInt ));
983 tangentInters[ axis ].clear();
985 // Count intersections before and after the point excluding touching ones.
986 // If hasPositionInfo we count intersections of outer boundary only
988 int nbIntBeforePoint = 0, nbIntAfterPoint = 0;
989 double f = numeric_limits<double>::max(), l = -numeric_limits<double>::max();
990 map< double, TInters >::iterator u_int1 = u2inters.begin(), u_int2 = u_int1;
991 bool ok = ! u_int1->second._coincides;
992 while ( ok && u_int1 != u2inters.end() )
994 double u = u_int1->first;
995 bool touchingInt = false;
996 if ( ++u_int2 != u2inters.end() )
998 // skip intersections at the same point (if the line passes through edge or node)
1000 while ( u_int2 != u2inters.end() && fabs( u_int2->first - u ) < tolerance )
1006 // skip tangent intersections
1008 if ( u_int2 != u2inters.end() )
1010 const SMDS_MeshElement* prevFace = u_int1->second._face;
1011 while ( ok && u_int2->second._coincides )
1013 if ( SMESH_MeshAlgos::GetCommonNodes(prevFace , u_int2->second._face).empty() )
1019 ok = ( u_int2 != u2inters.end() );
1025 // skip intersections at the same point after tangent intersections
1028 double u2 = u_int2->first;
1030 while ( u_int2 != u2inters.end() && fabs( u_int2->first - u2 ) < tolerance )
1036 // decide if we skipped a touching intersection
1037 if ( nbSamePnt + nbTgt > 0 )
1039 double minDot = numeric_limits<double>::max(), maxDot = -numeric_limits<double>::max();
1040 map< double, TInters >::iterator u_int = u_int1;
1041 for ( ; u_int != u_int2; ++u_int )
1043 if ( u_int->second._coincides ) continue;
1044 double dot = u_int->second._faceNorm * line.Direction();
1045 if ( dot > maxDot ) maxDot = dot;
1046 if ( dot < minDot ) minDot = dot;
1048 touchingInt = ( minDot*maxDot < 0 );
1053 if ( !hasPositionInfo || isOuterBoundary( u_int1->second._face ))
1064 u_int1 = u_int2; // to next intersection
1066 } // loop on intersections with one line
1070 if ( fabs( f ) < tolerance || fabs( l ) < tolerance )
1073 if ( nbIntBeforePoint == 0 || nbIntAfterPoint == 0)
1076 if ( nbIntBeforePoint + nbIntAfterPoint == 1 ) // not closed mesh
1077 return fabs( f ) < tolerance ? TopAbs_ON : TopAbs_UNKNOWN;
1079 if ( nbIntBeforePoint == 1 || nbIntAfterPoint == 1 )
1082 if ( (f<0) == (l<0) )
1085 if ( hasPositionInfo )
1086 return nbIntBeforePoint % 2 ? TopAbs_IN : TopAbs_OUT;
1088 } // loop on intersections of the tree lines - thorough analysis
1090 if ( !hasPositionInfo )
1092 // gather info on faces position - is face in the outer boundary or not
1093 map< double, TInters > & u2inters = paramOnLine2TInters[ 0 ];
1094 findOuterBoundary( u2inters.begin()->second._face );
1097 } // two attempts - with and w/o faces position info in the mesh
1099 return TopAbs_UNKNOWN;
1102 //=======================================================================
1104 * \brief Return elements possibly intersecting the line
1106 //=======================================================================
1108 void SMESH_ElementSearcherImpl::GetElementsNearLine( const gp_Ax1& line,
1109 SMDSAbs_ElementType type,
1110 vector< const SMDS_MeshElement* >& foundElems)
1112 _elementType = type;
1113 ElementBndBoxTree*& ebbTree = _ebbTree[ type ];
1115 ebbTree = new ElementBndBoxTree( *_mesh, _elementType, _meshPartIt );
1117 TIDSortedElemSet suspectFaces; // elements possibly intersecting the line
1118 ebbTree->getElementsNearLine( line, suspectFaces );
1119 foundElems.assign( suspectFaces.begin(), suspectFaces.end());
1122 //=======================================================================
1124 * Return elements whose bounding box intersects a sphere
1126 //=======================================================================
1128 void SMESH_ElementSearcherImpl::GetElementsInSphere( const gp_XYZ& center,
1129 const double radius,
1130 SMDSAbs_ElementType type,
1131 vector< const SMDS_MeshElement* >& foundElems)
1133 _elementType = type;
1134 ElementBndBoxTree*& ebbTree = _ebbTree[ type ];
1136 ebbTree = new ElementBndBoxTree( *_mesh, _elementType, _meshPartIt );
1138 TIDSortedElemSet suspectFaces; // elements possibly intersecting the line
1139 ebbTree->getElementsInSphere( center, radius, suspectFaces );
1140 foundElems.assign( suspectFaces.begin(), suspectFaces.end() );
1143 //=======================================================================
1145 * \brief Return true if the point is IN or ON of the element
1147 //=======================================================================
1149 bool SMESH_MeshAlgos::IsOut( const SMDS_MeshElement* element, const gp_Pnt& point, double tol )
1151 if ( element->GetType() == SMDSAbs_Volume)
1153 return SMDS_VolumeTool( element ).IsOut( point.X(), point.Y(), point.Z(), tol );
1156 // get ordered nodes
1158 vector< SMESH_TNodeXYZ > xyz; xyz.reserve( element->NbNodes()+1 );
1160 SMDS_ElemIteratorPtr nodeIt = element->interlacedNodesElemIterator();
1161 for ( int i = 0; nodeIt->more(); ++i )
1162 xyz.push_back( SMESH_TNodeXYZ( nodeIt->next() ));
1164 int i, nbNodes = (int) xyz.size(); // central node of biquadratic is missing
1166 if ( element->GetType() == SMDSAbs_Face ) // --------------------------------------------------
1168 // compute face normal
1169 gp_Vec faceNorm(0,0,0);
1170 xyz.push_back( xyz.front() );
1171 for ( i = 0; i < nbNodes; ++i )
1173 gp_Vec edge1( xyz[i+1], xyz[i]);
1174 gp_Vec edge2( xyz[i+1], xyz[(i+2)%nbNodes] );
1175 faceNorm += edge1 ^ edge2;
1177 double fNormSize = faceNorm.Magnitude();
1178 if ( fNormSize <= tol )
1180 // degenerated face: point is out if it is out of all face edges
1181 for ( i = 0; i < nbNodes; ++i )
1183 SMDS_LinearEdge edge( xyz[i]._node, xyz[i+1]._node );
1184 if ( !IsOut( &edge, point, tol ))
1189 faceNorm /= fNormSize;
1191 // check if the point lays on face plane
1192 gp_Vec n2p( xyz[0], point );
1193 double dot = n2p * faceNorm;
1194 if ( Abs( dot ) > tol ) // not on face plane
1197 if ( nbNodes > 3 ) // maybe the face is not planar
1199 double elemThick = 0;
1200 for ( i = 1; i < nbNodes; ++i )
1202 gp_Vec n2n( xyz[0], xyz[i] );
1203 elemThick = Max( elemThick, Abs( n2n * faceNorm ));
1205 isOut = Abs( dot ) > elemThick + tol;
1211 // check if point is out of face boundary:
1212 // define it by closest transition of a ray point->infinity through face boundary
1213 // on the face plane.
1214 // First, find normal of a plane perpendicular to face plane, to be used as a cutting tool
1215 // to find intersections of the ray with the boundary.
1217 gp_Vec plnNorm = ray ^ faceNorm;
1218 double n2pSize = plnNorm.Magnitude();
1219 if ( n2pSize <= tol ) return false; // point coincides with the first node
1220 if ( n2pSize * n2pSize > fNormSize * 100 ) return true; // point is very far
1222 // for each node of the face, compute its signed distance to the cutting plane
1223 vector<double> dist( nbNodes + 1);
1224 for ( i = 0; i < nbNodes; ++i )
1226 gp_Vec n2p( xyz[i], point );
1227 dist[i] = n2p * plnNorm;
1229 dist.back() = dist.front();
1230 // find the closest intersection
1232 double rClosest = 0, distClosest = 1e100;
1234 for ( i = 0; i < nbNodes; ++i )
1237 if ( fabs( dist[i] ) < tol )
1239 else if ( fabs( dist[i+1]) < tol )
1241 else if ( dist[i] * dist[i+1] < 0 )
1242 r = dist[i] / ( dist[i] - dist[i+1] );
1244 continue; // no intersection
1245 gp_Pnt pInt = xyz[i] * (1.-r) + xyz[i+1] * r;
1246 gp_Vec p2int( point, pInt);
1247 double intDist = p2int.SquareMagnitude();
1248 if ( intDist < distClosest )
1253 distClosest = intDist;
1257 return true; // no intesections - out
1259 // analyse transition
1260 gp_Vec edge( xyz[iClosest], xyz[iClosest+1] );
1261 gp_Vec edgeNorm = -( edge ^ faceNorm ); // normal to intersected edge pointing out of face
1262 gp_Vec p2int ( point, pClosest );
1263 bool out = (edgeNorm * p2int) < -tol;
1264 if ( rClosest > 0. && rClosest < 1. ) // not node intersection
1267 // the ray passes through a face node; analyze transition through an adjacent edge
1268 gp_Pnt p1 = xyz[ (rClosest == 0.) ? ((iClosest+nbNodes-1) % nbNodes) : (iClosest+1) ];
1269 gp_Pnt p2 = xyz[ (rClosest == 0.) ? iClosest : ((iClosest+2) % nbNodes) ];
1270 gp_Vec edgeAdjacent( p1, p2 );
1271 gp_Vec edgeNorm2 = -( edgeAdjacent ^ faceNorm );
1272 bool out2 = (edgeNorm2 * p2int) < -tol;
1274 bool covexCorner = ( edgeNorm * edgeAdjacent * (rClosest==1. ? 1. : -1.)) < 0;
1275 return covexCorner ? (out || out2) : (out && out2);
1278 if ( element->GetType() == SMDSAbs_Edge ) // --------------------------------------------------
1280 // point is out of edge if it is NOT ON any straight part of edge
1281 // (we consider quadratic edge as being composed of two straight parts)
1282 for ( i = 1; i < nbNodes; ++i )
1284 gp_Vec edge( xyz[i-1], xyz[i] );
1285 gp_Vec n1p ( xyz[i-1], point );
1286 double u = ( edge * n1p ) / edge.SquareMagnitude(); // param [0,1] on the edge
1288 if ( n1p.SquareMagnitude() < tol * tol )
1293 if ( point.SquareDistance( xyz[i] ) < tol * tol )
1297 gp_XYZ proj = ( 1. - u ) * xyz[i-1] + u * xyz[i]; // projection of the point on the edge
1298 double dist2 = point.SquareDistance( proj );
1299 if ( dist2 > tol * tol )
1301 return false; // point is ON this part
1306 // Node or 0D element -------------------------------------------------------------------------
1308 gp_Vec n2p ( xyz[0], point );
1309 return n2p.SquareMagnitude() > tol * tol;
1314 //=======================================================================
1317 // Position of a point relative to a segment
1321 // VERTEX 1 o----ON-----> VERTEX 2
1325 enum PositionName { POS_LEFT = 1, POS_VERTEX = 2, POS_RIGHT = 4, //POS_ON = 8,
1326 POS_ALL = POS_LEFT | POS_RIGHT | POS_VERTEX };
1330 int _index; // index of vertex or segment
1332 PointPos( PositionName n, int i=-1 ): _name(n), _index(i) {}
1333 bool operator < (const PointPos& other ) const
1335 if ( _name == other._name )
1336 return ( _index < 0 || other._index < 0 ) ? false : _index < other._index;
1337 return _name < other._name;
1341 //================================================================================
1343 * \brief Return of a point relative to a segment
1344 * \param point2D - the point to analyze position of
1345 * \param xyVec - end points of segments
1346 * \param index0 - 0-based index of the first point of segment
1347 * \param posToFindOut - flags of positions to detect
1348 * \retval PointPos - point position
1350 //================================================================================
1352 PointPos getPointPosition( const gp_XY& point2D,
1353 const gp_XY* segEnds,
1354 const int index0 = 0,
1355 const int posToFindOut = POS_ALL)
1357 const gp_XY& p1 = segEnds[ index0 ];
1358 const gp_XY& p2 = segEnds[ index0+1 ];
1359 const gp_XY grad = p2 - p1;
1361 if ( posToFindOut & POS_VERTEX )
1363 // check if the point2D is at "vertex 1" zone
1364 gp_XY pp1[2] = { p1, gp_XY( p1.X() - grad.Y(),
1365 p1.Y() + grad.X() ) };
1366 if ( getPointPosition( point2D, pp1, 0, POS_LEFT|POS_RIGHT )._name == POS_LEFT )
1367 return PointPos( POS_VERTEX, index0 );
1369 // check if the point2D is at "vertex 2" zone
1370 gp_XY pp2[2] = { p2, gp_XY( p2.X() - grad.Y(),
1371 p2.Y() + grad.X() ) };
1372 if ( getPointPosition( point2D, pp2, 0, POS_LEFT|POS_RIGHT )._name == POS_RIGHT )
1373 return PointPos( POS_VERTEX, index0 + 1);
1375 double edgeEquation =
1376 ( point2D.X() - p1.X() ) * grad.Y() - ( point2D.Y() - p1.Y() ) * grad.X();
1377 return PointPos( edgeEquation < 0 ? POS_LEFT : POS_RIGHT, index0 );
1381 //=======================================================================
1383 * \brief Return minimal distance from a point to an element
1385 * Currently we ignore non-planarity and 2nd order of face
1387 //=======================================================================
1389 double SMESH_MeshAlgos::GetDistance( const SMDS_MeshElement* elem,
1390 const gp_Pnt& point )
1392 switch ( elem->GetType() )
1394 case SMDSAbs_Volume:
1395 return GetDistance( dynamic_cast<const SMDS_MeshVolume*>( elem ), point);
1397 return GetDistance( dynamic_cast<const SMDS_MeshFace*>( elem ), point);
1399 return GetDistance( dynamic_cast<const SMDS_MeshEdge*>( elem ), point);
1401 return point.Distance( SMESH_TNodeXYZ( elem ));
1407 //=======================================================================
1409 * \brief Return minimal distance from a point to a face
1411 * Currently we ignore non-planarity and 2nd order of face
1413 //=======================================================================
1415 double SMESH_MeshAlgos::GetDistance( const SMDS_MeshFace* face,
1416 const gp_Pnt& point )
1418 double badDistance = -1;
1419 if ( !face ) return badDistance;
1421 // coordinates of nodes (medium nodes, if any, ignored)
1422 typedef SMDS_StdIterator< SMESH_TNodeXYZ, SMDS_ElemIteratorPtr > TXyzIterator;
1423 vector<gp_XYZ> xyz( TXyzIterator( face->nodesIterator()), TXyzIterator() );
1424 xyz.resize( face->NbCornerNodes()+1 );
1426 // transformation to get xyz[0] lies on the origin, xyz[1] lies on the Z axis,
1427 // and xyz[2] lies in the XZ plane. This is to pass to 2D space on XZ plane.
1429 gp_Vec OZ ( xyz[0], xyz[1] );
1430 gp_Vec OX ( xyz[0], xyz[2] );
1431 if ( OZ.Magnitude() < std::numeric_limits<double>::min() )
1433 if ( xyz.size() < 4 ) return badDistance;
1434 OZ = gp_Vec ( xyz[0], xyz[2] );
1435 OX = gp_Vec ( xyz[0], xyz[3] );
1439 tgtCS = gp_Ax3( xyz[0], OZ, OX );
1441 catch ( Standard_Failure ) {
1444 trsf.SetTransformation( tgtCS );
1446 // move all the nodes to 2D
1447 vector<gp_XY> xy( xyz.size() );
1448 for ( size_t i = 0;i < xyz.size()-1; ++i )
1450 gp_XYZ p3d = xyz[i];
1451 trsf.Transforms( p3d );
1452 xy[i].SetCoord( p3d.X(), p3d.Z() );
1454 xyz.back() = xyz.front();
1455 xy.back() = xy.front();
1457 // // move the point in 2D
1458 gp_XYZ tmpPnt = point.XYZ();
1459 trsf.Transforms( tmpPnt );
1460 gp_XY point2D( tmpPnt.X(), tmpPnt.Z() );
1462 // loop on segments of the face to analyze point position ralative to the face
1463 set< PointPos > pntPosSet;
1464 for ( size_t i = 1; i < xy.size(); ++i )
1466 PointPos pos = getPointPosition( point2D, &xy[0], i-1 );
1467 pntPosSet.insert( pos );
1471 PointPos pos = *pntPosSet.begin();
1472 // cout << "Face " << face->GetID() << " DIST: ";
1473 switch ( pos._name )
1476 // point is most close to a segment
1477 gp_Vec p0p1( point, xyz[ pos._index ] );
1478 gp_Vec p1p2( xyz[ pos._index ], xyz[ pos._index+1 ]); // segment vector
1480 double projDist = p0p1 * p1p2; // distance projected to the segment
1481 gp_Vec projVec = p1p2 * projDist;
1482 gp_Vec distVec = p0p1 - projVec;
1483 // cout << distVec.Magnitude() << ", SEG " << face->GetNode(pos._index)->GetID()
1484 // << " - " << face->GetNodeWrap(pos._index+1)->GetID() << endl;
1485 return distVec.Magnitude();
1488 // point is inside the face
1489 double distToFacePlane = tmpPnt.Y();
1490 // cout << distToFacePlane << ", INSIDE " << endl;
1491 return Abs( distToFacePlane );
1494 // point is most close to a node
1495 gp_Vec distVec( point, xyz[ pos._index ]);
1496 // cout << distVec.Magnitude() << " VERTEX " << face->GetNode(pos._index)->GetID() << endl;
1497 return distVec.Magnitude();
1504 //=======================================================================
1506 * \brief Return minimal distance from a point to an edge
1508 //=======================================================================
1510 double SMESH_MeshAlgos::GetDistance( const SMDS_MeshEdge* seg, const gp_Pnt& point )
1512 double dist = Precision::Infinite();
1513 if ( !seg ) return dist;
1515 int i = 0, nbNodes = seg->NbNodes();
1517 vector< SMESH_TNodeXYZ > xyz( nbNodes );
1518 SMDS_ElemIteratorPtr nodeIt = seg->interlacedNodesElemIterator();
1519 while ( nodeIt->more() )
1520 xyz[ i++ ].Set( nodeIt->next() );
1522 for ( i = 1; i < nbNodes; ++i )
1524 gp_Vec edge( xyz[i-1], xyz[i] );
1525 gp_Vec n1p ( xyz[i-1], point );
1526 double u = ( edge * n1p ) / edge.SquareMagnitude(); // param [0,1] on the edge
1528 dist = Min( dist, n1p.SquareMagnitude() );
1530 else if ( u >= 1. ) {
1531 dist = Min( dist, point.SquareDistance( xyz[i] ));
1534 gp_XYZ proj = ( 1. - u ) * xyz[i-1] + u * xyz[i]; // projection of the point on the edge
1535 dist = Min( dist, point.SquareDistance( proj ));
1538 return Sqrt( dist );
1541 //=======================================================================
1543 * \brief Return minimal distance from a point to a volume
1545 * Currently we ignore non-planarity and 2nd order
1547 //=======================================================================
1549 double SMESH_MeshAlgos::GetDistance( const SMDS_MeshVolume* volume, const gp_Pnt& point )
1551 SMDS_VolumeTool vTool( volume );
1552 vTool.SetExternalNormal();
1553 const int iQ = volume->IsQuadratic() ? 2 : 1;
1556 double minDist = 1e100, dist;
1557 for ( int iF = 0; iF < vTool.NbFaces(); ++iF )
1559 // skip a facet with normal not "looking at" the point
1560 if ( !vTool.GetFaceNormal( iF, n[0], n[1], n[2] ) ||
1561 !vTool.GetFaceBaryCenter( iF, bc[0], bc[1], bc[2] ))
1563 gp_XYZ bcp = point.XYZ() - gp_XYZ( bc[0], bc[1], bc[2] );
1564 if ( gp_XYZ( n[0], n[1], n[2] ) * bcp < 1e-6 )
1567 // find distance to a facet
1568 const SMDS_MeshNode** nodes = vTool.GetFaceNodes( iF );
1569 switch ( vTool.NbFaceNodes( iF ) / iQ ) {
1572 SMDS_FaceOfNodes tmpFace( nodes[0], nodes[ 1*iQ ], nodes[ 2*iQ ] );
1573 dist = GetDistance( &tmpFace, point );
1578 SMDS_FaceOfNodes tmpFace( nodes[0], nodes[ 1*iQ ], nodes[ 2*iQ ], nodes[ 3*iQ ]);
1579 dist = GetDistance( &tmpFace, point );
1583 vector<const SMDS_MeshNode *> nvec( nodes, nodes + vTool.NbFaceNodes( iF ));
1584 SMDS_PolygonalFaceOfNodes tmpFace( nvec );
1585 dist = GetDistance( &tmpFace, point );
1587 minDist = Min( minDist, dist );
1592 //================================================================================
1594 * \brief Returns barycentric coordinates of a point within a triangle.
1595 * A not returned bc2 = 1. - bc0 - bc1.
1596 * The point lies within the triangle if ( bc0 >= 0 && bc1 >= 0 && bc0+bc1 <= 1 )
1598 //================================================================================
1600 void SMESH_MeshAlgos::GetBarycentricCoords( const gp_XY& p,
1607 const double // matrix 2x2
1608 T11 = t0.X()-t2.X(), T12 = t1.X()-t2.X(),
1609 T21 = t0.Y()-t2.Y(), T22 = t1.Y()-t2.Y();
1610 const double Tdet = T11*T22 - T12*T21; // matrix determinant
1611 if ( Abs( Tdet ) < std::numeric_limits<double>::min() )
1617 const double t11 = T22, t12 = -T12, t21 = -T21, t22 = T11;
1619 const double r11 = p.X()-t2.X(), r12 = p.Y()-t2.Y();
1620 // barycentric coordinates: mutiply matrix by vector
1621 bc0 = (t11 * r11 + t12 * r12)/Tdet;
1622 bc1 = (t21 * r11 + t22 * r12)/Tdet;
1625 //=======================================================================
1626 //function : FindFaceInSet
1627 //purpose : Return a face having linked nodes n1 and n2 and which is
1628 // - not in avoidSet,
1629 // - in elemSet provided that !elemSet.empty()
1630 // i1 and i2 optionally returns indices of n1 and n2
1631 //=======================================================================
1633 const SMDS_MeshElement*
1634 SMESH_MeshAlgos::FindFaceInSet(const SMDS_MeshNode* n1,
1635 const SMDS_MeshNode* n2,
1636 const TIDSortedElemSet& elemSet,
1637 const TIDSortedElemSet& avoidSet,
1643 const SMDS_MeshElement* face = 0;
1645 SMDS_ElemIteratorPtr invElemIt = n1->GetInverseElementIterator(SMDSAbs_Face);
1646 while ( invElemIt->more() && !face ) // loop on inverse faces of n1
1648 const SMDS_MeshElement* elem = invElemIt->next();
1649 if (avoidSet.count( elem ))
1651 if ( !elemSet.empty() && !elemSet.count( elem ))
1654 i1 = elem->GetNodeIndex( n1 );
1655 // find a n2 linked to n1
1656 int nbN = elem->IsQuadratic() ? elem->NbNodes()/2 : elem->NbNodes();
1657 for ( int di = -1; di < 2 && !face; di += 2 )
1659 i2 = (i1+di+nbN) % nbN;
1660 if ( elem->GetNode( i2 ) == n2 )
1663 if ( !face && elem->IsQuadratic())
1665 // analysis for quadratic elements using all nodes
1666 SMDS_ElemIteratorPtr anIter = elem->interlacedNodesElemIterator();
1667 const SMDS_MeshNode* prevN = static_cast<const SMDS_MeshNode*>( anIter->next() );
1668 for ( i1 = -1, i2 = 0; anIter->more() && !face; i1++, i2++ )
1670 const SMDS_MeshNode* n = static_cast<const SMDS_MeshNode*>( anIter->next() );
1671 if ( n1 == prevN && n2 == n )
1675 else if ( n2 == prevN && n1 == n )
1677 face = elem; swap( i1, i2 );
1683 if ( n1ind ) *n1ind = i1;
1684 if ( n2ind ) *n2ind = i2;
1688 //================================================================================
1690 * \brief Calculate normal of a mesh face
1692 //================================================================================
1694 bool SMESH_MeshAlgos::FaceNormal(const SMDS_MeshElement* F, gp_XYZ& normal, bool normalized)
1696 if ( !F || F->GetType() != SMDSAbs_Face )
1699 normal.SetCoord(0,0,0);
1700 int nbNodes = F->NbCornerNodes();
1701 for ( int i = 0; i < nbNodes-2; ++i )
1704 for ( int n = 0; n < 3; ++n )
1706 const SMDS_MeshNode* node = F->GetNode( i + n );
1707 p[n].SetCoord( node->X(), node->Y(), node->Z() );
1709 normal += ( p[2] - p[1] ) ^ ( p[0] - p[1] );
1711 double size2 = normal.SquareModulus();
1712 bool ok = ( size2 > numeric_limits<double>::min() * numeric_limits<double>::min());
1713 if ( normalized && ok )
1714 normal /= sqrt( size2 );
1719 //=======================================================================
1720 //function : GetCommonNodes
1721 //purpose : Return nodes common to two elements
1722 //=======================================================================
1724 vector< const SMDS_MeshNode*> SMESH_MeshAlgos::GetCommonNodes(const SMDS_MeshElement* e1,
1725 const SMDS_MeshElement* e2)
1727 vector< const SMDS_MeshNode*> common;
1728 for ( int i = 0 ; i < e1->NbNodes(); ++i )
1729 if ( e2->GetNodeIndex( e1->GetNode( i )) >= 0 )
1730 common.push_back( e1->GetNode( i ));
1734 //=======================================================================
1736 * \brief Return SMESH_NodeSearcher
1738 //=======================================================================
1740 SMESH_NodeSearcher* SMESH_MeshAlgos::GetNodeSearcher(SMDS_Mesh& mesh)
1742 return new SMESH_NodeSearcherImpl( &mesh );
1745 //=======================================================================
1747 * \brief Return SMESH_NodeSearcher
1749 //=======================================================================
1751 SMESH_NodeSearcher* SMESH_MeshAlgos::GetNodeSearcher(SMDS_ElemIteratorPtr elemIt)
1753 return new SMESH_NodeSearcherImpl( 0, elemIt );
1756 //=======================================================================
1758 * \brief Return SMESH_ElementSearcher
1760 //=======================================================================
1762 SMESH_ElementSearcher* SMESH_MeshAlgos::GetElementSearcher(SMDS_Mesh& mesh,
1765 return new SMESH_ElementSearcherImpl( mesh, tolerance );
1768 //=======================================================================
1770 * \brief Return SMESH_ElementSearcher acting on a sub-set of elements
1772 //=======================================================================
1774 SMESH_ElementSearcher* SMESH_MeshAlgos::GetElementSearcher(SMDS_Mesh& mesh,
1775 SMDS_ElemIteratorPtr elemIt,
1778 return new SMESH_ElementSearcherImpl( mesh, tolerance, elemIt );