1 // Copyright (C) 2007-2023 CEA/DEN, EDF R&D
3 // This library is free software; you can redistribute it and/or
4 // modify it under the terms of the GNU Lesser General Public
5 // License as published by the Free Software Foundation; either
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11 // Lesser General Public License for more details.
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19 #ifndef __SPLITTERTETRA_TXX__
20 #define __SPLITTERTETRA_TXX__
22 #include "SplitterTetra.hxx"
24 #include "TetraAffineTransform.hxx"
25 #include "TransformedTriangle.hxx"
26 #include "MeshUtils.hxx"
27 #include "VectorUtils.hxx"
28 #include "CellModel.hxx"
30 #include "UnitTetraIntersectionBary.hxx"
31 #include "VolSurfFormulae.hxx"
39 namespace INTERP_KERNEL
41 template<class MyMeshType>
42 const double SplitterTetra<MyMeshType>::SPARSE_TRUNCATION_LIMIT=1.0e-14;
45 * output is expected to be allocated with 24*sizeof(void*) in order to store the 24 tetras.
46 * These tetras have to be deallocated.
48 template<class MyMeshType>
49 void SplitterTetra<MyMeshType>::splitIntoDualCells(SplitterTetra<MyMeshType> **output)
52 const double *tmp2[4]={tmp,tmp+3,tmp+6,tmp+9};
53 typename MyMeshType::MyConnType conn[4]={-1,-1,-1,-1};
56 splitMySelfForDual(tmp,i,conn[0]);
57 output[i]=new SplitterTetra<MyMeshType>(_src_mesh,tmp2,conn);
62 * SplitterTetra class computes for a list of cell ids of a given mesh \a srcMesh (badly named) the intersection with a
63 * single TETRA4 cell given by \a tetraCorners (of length 4) and \a nodesId (of length 4 too). \a nodedIds is given only to establish
64 * if a partial computation of a triangle has already been performed (to increase performance).
66 * The \a srcMesh can contain polyhedron cells.
69 * Constructor creating object from the four corners of the tetrahedron.
71 * @param srcMesh mesh containing the source elements
72 * @param tetraCorners array of four pointers to double[3] arrays containing the coordinates of the
73 * corners of the tetrahedron
75 template<class MyMeshType>
76 SplitterTetra<MyMeshType>::SplitterTetra(const MyMeshType& srcMesh, const double** tetraCorners, const typename MyMeshType::MyConnType *nodesId)
77 : _t(0), _src_mesh(srcMesh)
79 std::copy(nodesId,nodesId+4,_conn);
80 _coords[0]=tetraCorners[0][0]; _coords[1]=tetraCorners[0][1]; _coords[2]=tetraCorners[0][2];
81 _coords[3]=tetraCorners[1][0]; _coords[4]=tetraCorners[1][1]; _coords[5]=tetraCorners[1][2];
82 _coords[6]=tetraCorners[2][0]; _coords[7]=tetraCorners[2][1]; _coords[8]=tetraCorners[2][2];
83 _coords[9]=tetraCorners[3][0]; _coords[10]=tetraCorners[3][1]; _coords[11]=tetraCorners[3][2];
84 // create the affine transform
85 _t=new TetraAffineTransform(_coords);
89 * SplitterTetra class computes for a list of cell ids of a given mesh \a srcMesh (badly named) the intersection with a
90 * single TETRA4 cell given by \a tetraCorners (of length 4) and \a nodesId (of length 4 too). \a nodedIds is given only to establish
91 * if a partial computation of a triangle has already been performed (to increase performance).
93 * The \a srcMesh can contain polyhedron cells.
96 * Constructor creating object from the four corners of the tetrahedron.
98 * \param [in] srcMesh mesh containing the source elements
99 * \param [in] tetraCorners array 4*3 doubles containing corners of input tetrahedron (P0X,P0Y,P0Y,P1X,P1Y,P1Z,P2X,P2Y,P2Z,P3X,P3Y,P3Z).
101 template<class MyMeshType>
102 SplitterTetra<MyMeshType>::SplitterTetra(const MyMeshType& srcMesh, const double tetraCorners[12], const ConnType *conn): _t(0),_src_mesh(srcMesh)
105 { _conn[0]=0; _conn[1]=1; _conn[2]=2; _conn[3]=3; }
107 { _conn[0]=conn[0]; _conn[1]=conn[1]; _conn[2]=conn[2]; _conn[3]=conn[3]; }
108 _coords[0]=tetraCorners[0]; _coords[1]=tetraCorners[1]; _coords[2]=tetraCorners[2]; _coords[3]=tetraCorners[3]; _coords[4]=tetraCorners[4]; _coords[5]=tetraCorners[5];
109 _coords[6]=tetraCorners[6]; _coords[7]=tetraCorners[7]; _coords[8]=tetraCorners[8]; _coords[9]=tetraCorners[9]; _coords[10]=tetraCorners[10]; _coords[11]=tetraCorners[11];
110 // create the affine transform
111 _t=new TetraAffineTransform(_coords);
117 * Deletes _t and the coordinates (double[3] vectors) in _nodes
120 template<class MyMeshType>
121 SplitterTetra<MyMeshType>::~SplitterTetra()
124 for(typename HashMap< ConnType, double* >::iterator iter = _nodes.begin(); iter != _nodes.end() ; ++iter)
125 delete[] iter->second;
129 * \Forget already calculated triangles, which is crucial for calculation of barycenter of intersection
131 template<class MyMeshType>
132 void SplitterTetra<MyMeshType>::clearVolumesCache()
138 * This method destroys the 4 pointers pointed by tetraCorners[0],tetraCorners[1],tetraCorners[2] and tetraCorners[3]
139 * @param i is in 0..23 included.
140 * @param output is expected to be sized of 12 in order to.
142 template<class MyMeshType>
143 void SplitterTetra<MyMeshType>::splitMySelfForDual(double* output, int i, typename MyMeshType::MyConnType& nodeId)
147 nodeId=_conn[offset];
148 tmp[0]=_coords+3*offset; tmp[1]=_coords+((offset+1)%4)*3; tmp[2]=_coords+((offset+2)%4)*3; tmp[3]=_coords+((offset+3)%4)*3;
150 int case1=caseToTreat/2;
151 int case2=caseToTreat%2;
152 const int tab[3][2]={{1,2},{3,2},{1,3}};
153 const int *curTab=tab[case1];
154 double pt0[3]; pt0[0]=(tmp[curTab[case2]][0]+tmp[0][0])/2.; pt0[1]=(tmp[curTab[case2]][1]+tmp[0][1])/2.; pt0[2]=(tmp[curTab[case2]][2]+tmp[0][2])/2.;
155 double pt1[3]; pt1[0]=(tmp[0][0]+tmp[curTab[0]][0]+tmp[curTab[1]][0])/3.; pt1[1]=(tmp[0][1]+tmp[curTab[0]][1]+tmp[curTab[1]][1])/3.; pt1[2]=(tmp[0][2]+tmp[curTab[0]][2]+tmp[curTab[1]][2])/3.;
156 double pt2[3]; pt2[0]=(tmp[0][0]+tmp[1][0]+tmp[2][0]+tmp[3][0])/4.; pt2[1]=(tmp[0][1]+tmp[1][1]+tmp[2][1]+tmp[3][1])/4.; pt2[2]=(tmp[0][2]+tmp[1][2]+tmp[2][2]+tmp[3][2])/4.;
157 std::copy(pt1,pt1+3,output+case2*3);
158 std::copy(pt0,pt0+3,output+(abs(case2-1))*3);
159 std::copy(pt2,pt2+3,output+2*3);
160 std::copy(tmp[0],tmp[0]+3,output+3*3);
164 * Calculates the volume of intersection of an element in the source mesh and the target element.
165 * It first calculates the transformation that takes the target tetrahedron into the unit tetrahedron. After that, the
166 * faces of the source element are triangulated and the calculated transformation is applied
167 * to each triangle. The algorithm of Grandy, implemented in INTERP_KERNEL::TransformedTriangle is used
168 * to calculate the contribution to the volume from each triangle. The volume returned is the sum of these contributions
169 * divided by the determinant of the transformation.
171 * The class will cache the intermediary calculations of transformed nodes of source cells and volumes associated
172 * with triangulated faces to avoid having to recalculate these.
174 * @param element global number of the source element in C mode.
176 template<class MyMeshType>
177 double SplitterTetra<MyMeshType>::intersectSourceCell(typename MyMeshType::MyConnType element,
180 typedef typename MyMeshType::MyConnType ConnType;
181 const NumberingPolicy numPol=MyMeshType::My_numPol;
182 //{ could be done on outside?
183 // check if we have planar tetra element
184 if(_t->determinant() == 0.0)
187 LOG(2, "Planar tetra -- volume 0");
192 NormalizedCellType normCellType=_src_mesh.getTypeOfElement(OTT<ConnType,numPol>::indFC(element));
193 const CellModel& cellModelCell=CellModel::GetCellModel(normCellType);
194 ConnType nbOfNodes4Type=cellModelCell.isDynamic() ? _src_mesh.getNumberOfNodesOfElement(OTT<ConnType,numPol>::indFC(element)) : cellModelCell.getNumberOfNodes();
195 // halfspace filtering
196 bool isOutside[8] = {true, true, true, true, true, true, true, true};
197 bool isTargetOutside = false;
199 // calculate the coordinates of the nodes
200 ConnType *cellNodes=new ConnType[nbOfNodes4Type];
201 for(ConnType i = 0;i<nbOfNodes4Type;++i)
203 // we could store mapping local -> global numbers too, but not sure it is worth it
204 const ConnType globalNodeNum = getGlobalNumberOfNode(i, OTT<ConnType,numPol>::indFC(element), _src_mesh);
205 cellNodes[i]=globalNodeNum;
206 if(_nodes.find(globalNodeNum) == _nodes.end())
208 //for(HashMap< int , double* >::iterator iter3=_nodes.begin();iter3!=_nodes.end();iter3++)
209 // std::cout << (*iter3).first << " ";
210 //std::cout << std::endl << "*** " << globalNodeNum << std::endl;
211 calculateNode(globalNodeNum);
213 CheckIsOutside(_nodes[globalNodeNum], isOutside);
216 // halfspace filtering check
217 // NB : might not be beneficial for caching of triangles
218 for(int i = 0; i < 8; ++i)
222 isTargetOutside = true;
226 double totalVolume = 0.0;
230 /// calculator of intersection barycentre
231 UnitTetraIntersectionBary baryCalculator( _t->determinant() < 0.);
233 // get nb of sons of a cell
234 const ConnType* rawCellConn = _src_mesh.getConnectivityPtr() + OTT<ConnType,numPol>::conn2C( _src_mesh.getConnectivityIndexPtr()[ element ]);
235 const ConnType rawNbCellNodes = _src_mesh.getConnectivityIndexPtr()[ element+1 ] - _src_mesh.getConnectivityIndexPtr()[ element ];
236 unsigned nbOfSons = cellModelCell.getNumberOfSons2(rawCellConn, rawNbCellNodes);
238 for(unsigned ii = 0 ; ii < nbOfSons; ++ii)
240 // get sons connectivity
241 NormalizedCellType faceType;
242 ConnType *faceNodes, nbFaceNodes=-1;
243 if ( cellModelCell.isDynamic() )
245 faceNodes=new ConnType[nbOfNodes4Type];
246 nbFaceNodes = cellModelCell.fillSonCellNodalConnectivity2(ii,rawCellConn,rawNbCellNodes,faceNodes,faceType);
247 for ( ConnType i = 0; i < nbFaceNodes; ++i )
248 faceNodes[i] = OTT<ConnType,numPol>::coo2C(faceNodes[i]);
252 faceType = cellModelCell.getSonType(ii);
253 assert(CellModel::GetCellModel(faceType).getDimension() == 2);
254 nbFaceNodes = cellModelCell.getNumberOfNodesConstituentTheSon(ii);
255 faceNodes = new ConnType[nbFaceNodes];
256 cellModelCell.fillSonCellNodalConnectivity(ii,cellNodes,faceNodes);
258 // intersect a son with the unit tetra
263 // create the face key
264 TriangleFaceKey key = TriangleFaceKey(faceNodes[0], faceNodes[1], faceNodes[2]);
266 // calculate the triangle if needed
267 if(_volumes.find(key) == _volumes.end())
269 TransformedTriangle tri(_nodes[faceNodes[0]], _nodes[faceNodes[1]], _nodes[faceNodes[2]]);
270 calculateVolume(tri, key);
271 totalVolume += _volumes[key];
273 baryCalculator.addSide( tri );
275 // count negative as face has reversed orientation
276 totalVolume -= _volumes[key];
283 // simple triangulation of faces along a diagonal :
294 //? not sure if this always works
296 // calculate the triangles if needed
298 // local nodes 1, 2, 3
299 TriangleFaceKey key1 = TriangleFaceKey(faceNodes[0], faceNodes[1], faceNodes[2]);
300 if(_volumes.find(key1) == _volumes.end())
302 TransformedTriangle tri(_nodes[faceNodes[0]], _nodes[faceNodes[1]], _nodes[faceNodes[2]]);
303 calculateVolume(tri, key1);
304 totalVolume += _volumes[key1];
306 // count negative as face has reversed orientation
307 totalVolume -= _volumes[key1];
310 // local nodes 1, 3, 4
311 TriangleFaceKey key2 = TriangleFaceKey(faceNodes[0], faceNodes[2], faceNodes[3]);
312 if(_volumes.find(key2) == _volumes.end())
314 TransformedTriangle tri(_nodes[faceNodes[0]], _nodes[faceNodes[2]], _nodes[faceNodes[3]]);
315 calculateVolume(tri, key2);
316 totalVolume += _volumes[key2];
320 // count negative as face has reversed orientation
321 totalVolume -= _volumes[key2];
328 ConnType nbTria = nbFaceNodes - 2; // split polygon into nbTria triangles
329 for ( ConnType iTri = 0; iTri < nbTria; ++iTri )
331 TriangleFaceKey key = TriangleFaceKey(faceNodes[0], faceNodes[1+iTri], faceNodes[2+iTri]);
332 if(_volumes.find(key) == _volumes.end())
334 TransformedTriangle tri(_nodes[faceNodes[0]], _nodes[faceNodes[1+iTri]], _nodes[faceNodes[2+iTri]]);
335 calculateVolume(tri, key);
336 totalVolume += _volumes[key];
340 totalVolume -= _volumes[key];
347 std::cout << "+++ Error : Only elements with triangular and quadratilateral faces are supported at the moment." << std::endl;
354 baryCalculator.getBary( baryCentre );
355 _t->reverseApply( baryCentre, baryCentre );
359 // reset if it is very small to keep the matrix sparse
360 // is this a good idea?
361 if(epsilonEqual(totalVolume, 0.0, SPARSE_TRUNCATION_LIMIT))
366 LOG(2, "Volume = " << totalVolume << ", det= " << _t->determinant());
368 // NB : fault in article, Grandy, [8] : it is the determinant of the inverse transformation
369 // that should be used (which is equivalent to dividing by the determinant)
370 return std::fabs(1.0 / _t->determinant() * totalVolume) ;
374 * Calculates the intersection surface of two coplanar triangles.
376 * @param planeNormal normal of the plane for the first triangle
377 * @param planeConstant constant of the equation of the plane for the first triangle
378 * @param p1 coordinates of the first node of the first triangle
379 * @param p2 coordinates of the second node of the first triangle
380 * @param p3 coordinates of the third node of the first triangle
381 * @param p4 coordinates of the first node of the second triangle
382 * @param p5 coordinates of the second node of the second triangle
383 * @param p6 coordinates of the third node of the second triangle
384 * @param dimCaracteristic characteristic size of the meshes containing the triangles
385 * @param precision precision for double float data used for comparison
387 template<class MyMeshType>
388 double SplitterTetra<MyMeshType>::CalculateIntersectionSurfaceOfCoplanarTriangles(const double *const planeNormal,
389 const double planeConstant,
390 const double *const p1, const double *const p2, const double *const p3,
391 const double *const p4, const double *const p5, const double *const p6,
392 const double dimCaracteristic, const double precision)
394 typedef typename MyMeshType::MyConnType ConnType;
395 typedef double Vect2[2];
396 typedef double Triangle2[3][2];
398 const double *const tri0[3] = {p1, p2, p3};
399 const double *const tri1[3] = {p4, p5, p6};
401 // Plane of the first triangle defined by the normal of the triangle and the constant
402 // Project triangles onto coordinate plane most aligned with plane normal
404 double fmax = std::abs(planeNormal[0]);
405 double absMax = std::abs(planeNormal[1]);
411 absMax = std::abs(planeNormal[2]);
417 Triangle2 projTri0, projTri1;
422 // Project onto yz-plane.
423 for (i = 0; i < 3; ++i)
425 projTri0[i][0] = tri0[i][1];
426 projTri0[i][1] = tri0[i][2];
427 projTri1[i][0] = tri1[i][1];
428 projTri1[i][1] = tri1[i][2];
431 else if (maxNormal == 1)
433 // Project onto xz-plane.
434 for (i = 0; i < 3; ++i)
436 projTri0[i][0] = tri0[i][0];
437 projTri0[i][1] = tri0[i][2];
438 projTri1[i][0] = tri1[i][0];
439 projTri1[i][1] = tri1[i][2];
444 // Project onto xy-plane.
445 for (i = 0; i < 3; ++i)
447 projTri0[i][0] = tri0[i][0];
448 projTri0[i][1] = tri0[i][1];
449 projTri1[i][0] = tri1[i][0];
450 projTri1[i][1] = tri1[i][1];
454 // 2D triangle intersection routines require counterclockwise ordering.
458 for (int ii = 0; ii < 2; ++ii)
460 edge0[ii] = projTri0[1][ii] - projTri0[0][ii];
461 edge1[ii] = projTri0[2][ii] - projTri0[0][ii];
463 if ((edge0[0] * edge1[1] - edge0[1] * edge1[0]) < (double) 0.)
465 // Triangle is clockwise, reorder it.
466 for (int ii = 0; ii < 2; ++ii)
468 save[ii] = projTri0[1][ii];
469 projTri0[1][ii] = projTri0[2][ii];
470 projTri0[2][ii] = save[ii];
474 for (int ii = 0; ii < 2; ++ii)
476 edge0[ii] = projTri1[1][ii] - projTri1[0][ii];
477 edge1[ii] = projTri1[2][ii] - projTri1[0][ii];
479 if ((edge0[0] * edge1[1] - edge0[1] * edge1[0]) < (double) 0.)
481 // Triangle is clockwise, reorder it.
482 for (int ii = 0; ii < 2; ++ii)
484 save[ii] = projTri1[1][ii];
485 projTri1[1][ii] = projTri1[2][ii];
486 projTri1[2][ii] = save[ii];
490 std::vector<double> inter2;
491 intersec_de_triangle(projTri0[0], projTri0[1], projTri0[2],
492 projTri1[0], projTri1[1], projTri1[2],
494 dimCaracteristic, precision);
495 ConnType nb_inter=((ConnType)inter2.size())/2;
497 if(nb_inter >3) inter2=reconstruct_polygon(inter2);
500 std::vector<double> inter3;
501 inter3.resize(3 * nb_inter);
502 // Map 2D intersections back to the 3D triangle space.
505 double invNX = ((double) 1.) / planeNormal[0];
506 for (i = 0; i < nb_inter; i++)
508 inter3[3 * i + 1] = inter2[2 * i];
509 inter3[3 * i + 2] = inter2[2 * i + 1];
510 inter3[3 * i] = invNX * (planeConstant - planeNormal[1] * inter3[3 * i + 1] - planeNormal[2] * inter3[3 * i + 2]);
513 else if (maxNormal == 1)
515 double invNY = ((double) 1.) / planeNormal[1];
516 for (i = 0; i < nb_inter; i++)
518 inter3[3 * i] = inter2[2 * i];
519 inter3[3 * i + 2] = inter2[2 * i + 1];
520 inter3[3 * i + 1] = invNY * (planeConstant - planeNormal[0] * inter3[3 * i] - planeNormal[2] * inter3[3 * i + 2]);
525 double invNZ = ((double) 1.) / planeNormal[2];
526 for (i = 0; i < nb_inter; i++)
528 inter3[3 * i] = inter2[2 * i];
529 inter3[3 * i + 1] = inter2[2 * i + 1];
530 inter3[3 * i + 2] = invNZ * (planeConstant - planeNormal[0] * inter3[3 * i] - planeNormal[1] * inter3[3 * i + 1]);
533 surface = polygon_area<3>(inter3);
539 * Determine if a face is coplanar with a triangle.
540 * The first face is characterized by the equation of her plane
542 * @param planeNormal normal of the plane for the first triangle
543 * @param planeConstant constant of the equation of the plane for the first triangle
544 * @param coordsFace coordinates of the triangle face
545 * @param precision precision for double float data used for comparison
547 template<class MyMeshType>
548 bool SplitterTetra<MyMeshType>::IsFacesCoplanar(const double *const planeNormal,
549 const double planeConstant,
550 const double *const *const coordsFace,
551 const double precision)
553 // Compute the signed distances of triangle vertices to the plane. Use an epsilon-thick plane test.
554 // For faces not left
556 for (int i = 0; i < 3; ++i)
558 const double distance = dot(planeNormal, coordsFace[i]) - planeConstant;
559 if (epsilonEqual(distance, precision))
568 * Calculates the surface of intersection of a polygon face in the source mesh and a cell of the target mesh.
569 * It first calculates the transformation that takes the target tetrahedron into the unit tetrahedron. After that, the
570 * faces of the source element are triangulated and the calculated transformation is applied
572 * The algorithm is based on the algorithm of Grandy used in intersectSourceCell to compute
573 * the volume of intersection of two cell elements.
574 * The case with a source face colinear to one of the face of tetrahedrons is taking into account:
575 * the contribution of the face must not be counted two times.
577 * The class will cache the intermediary calculations of transformed nodes of source faces and surfaces associated
578 * with triangulated faces to avoid having to recalculate these.
580 * @param polyType type of the polygon source face
581 * @param polyNodesNbr number of the nodes of the polygon source face
582 * @param polyNodes numbers of the nodes of the polygon source face
583 * @param polyCoords coordinates of the nodes of the polygon source face
584 * @param dimCaracteristic characteristic size of the meshes containing the triangles
585 * @param precision precision for double float data used for comparison
586 * @param listOfTetraFacesTreated list of tetra faces treated
587 * @param listOfTetraFacesColinear list of tetra faces colinear with the polygon source faces
589 template<class MyMeshType>
590 double SplitterTetra<MyMeshType>::intersectSourceFace(const NormalizedCellType polyType,
591 const ConnType polyNodesNbr,
592 const ConnType *const polyNodes,
593 const double *const *const polyCoords,
594 const double dimCaracteristic,
595 const double precision,
596 std::multiset<TriangleFaceKey>& listOfTetraFacesTreated,
597 std::set<TriangleFaceKey>& listOfTetraFacesColinear)
599 double totalSurface = 0.0;
601 // check if we have planar tetra element
602 if(_t->determinant() == 0.0)
605 LOG(2, "Planar tetra -- volume 0");
609 // halfspace filtering
610 bool isOutside[8] = {true, true, true, true, true, true, true, true};
611 bool isStrictlyOutside[8] = {true, true, true, true, true, true, true, true};
612 bool isTargetStrictlyOutside = false;
613 bool isTargetOutside = false;
615 // calculate the coordinates of the nodes
616 for(ConnType i = 0;i<polyNodesNbr;++i)
618 const ConnType globalNodeNum = polyNodes[i];
619 if(_nodes.find(globalNodeNum) == _nodes.end())
621 calculateNode2(globalNodeNum, polyCoords[i]);
624 CheckIsStrictlyOutside(_nodes[globalNodeNum], isStrictlyOutside, precision);
625 CheckIsOutside(_nodes[globalNodeNum], isOutside, precision);
628 // halfspace filtering check
629 // NB : might not be beneficial for caching of triangles
630 for(int i = 0; i < 8; ++i)
632 if(isStrictlyOutside[i])
634 isTargetStrictlyOutside = true;
637 else if (isOutside[i])
639 isTargetOutside = true;
643 if (!isTargetStrictlyOutside)
648 // Faces are parallel
649 const int tetraFacesNodesConn[4][3] = {
654 double planeNormal[3];
655 for (int iTetraFace = 0; iTetraFace < 4; ++iTetraFace)
657 const int * const tetraFaceNodesConn = tetraFacesNodesConn[iTetraFace];
658 TriangleFaceKey key = TriangleFaceKey(_conn[tetraFaceNodesConn[0]],
659 _conn[tetraFaceNodesConn[1]],
660 _conn[tetraFaceNodesConn[2]]);
661 if (listOfTetraFacesTreated.find(key) == listOfTetraFacesTreated.end())
663 const double * const coordsTetraTriNode1 = _coords + tetraFaceNodesConn[0] * MyMeshType::MY_SPACEDIM;
664 const double * const coordsTetraTriNode2 = _coords + tetraFaceNodesConn[1] * MyMeshType::MY_SPACEDIM;
665 const double * const coordsTetraTriNode3 = _coords + tetraFaceNodesConn[2] * MyMeshType::MY_SPACEDIM;
666 calculateNormalForTria(coordsTetraTriNode1, coordsTetraTriNode2, coordsTetraTriNode3, planeNormal);
667 const double normOfTetraTriNormal = norm(planeNormal);
668 if (epsilonEqual(normOfTetraTriNormal, 0.))
670 for (int i = 0; i < 3; ++i)
677 const double invNormOfTetraTriNormal = 1. / normOfTetraTriNormal;
678 for (int i = 0; i < 3; ++i)
680 planeNormal[i] *= invNormOfTetraTriNormal;
683 double planeConstant = dot(planeNormal, coordsTetraTriNode1);
684 if (IsFacesCoplanar(planeNormal, planeConstant, polyCoords, precision))
686 ConnType nbrPolyTri = polyNodesNbr - 2; // split polygon into nbrPolyTri triangles
687 for (ConnType iTri = 0; iTri < nbrPolyTri; ++iTri)
689 double volume = CalculateIntersectionSurfaceOfCoplanarTriangles(planeNormal,
692 polyCoords[1 + iTri],
693 polyCoords[2 + iTri],
699 if (!epsilonEqual(volume, 0.))
701 totalSurface += volume;
702 listOfTetraFacesColinear.insert(key);
707 listOfTetraFacesTreated.insert(key);
712 // intersect a son with the unit tetra
717 // create the face key
718 TriangleFaceKey key = TriangleFaceKey(polyNodes[0], polyNodes[1], polyNodes[2]);
720 // calculate the triangle if needed
721 if (_volumes.find(key) == _volumes.end())
723 TransformedTriangle tri(_nodes[polyNodes[0]], _nodes[polyNodes[1]], _nodes[polyNodes[2]]);
724 calculateSurface(tri, key);
725 totalSurface += _volumes[key];
729 // count negative as face has reversed orientation
730 totalSurface -= _volumes[key];
737 // simple triangulation of faces along a diagonal :
748 //? not sure if this always works
750 // calculate the triangles if needed
752 // local nodes 1, 2, 3
753 TriangleFaceKey key1 = TriangleFaceKey(polyNodes[0], polyNodes[1], polyNodes[2]);
754 if (_volumes.find(key1) == _volumes.end())
756 TransformedTriangle tri(_nodes[polyNodes[0]], _nodes[polyNodes[1]], _nodes[polyNodes[2]]);
757 calculateSurface(tri, key1);
758 totalSurface += _volumes[key1];
762 // count negative as face has reversed orientation
763 totalSurface -= _volumes[key1];
766 // local nodes 1, 3, 4
767 TriangleFaceKey key2 = TriangleFaceKey(polyNodes[0], polyNodes[2], polyNodes[3]);
768 if (_volumes.find(key2) == _volumes.end())
770 TransformedTriangle tri(_nodes[polyNodes[0]], _nodes[polyNodes[2]], _nodes[polyNodes[3]]);
771 calculateSurface(tri, key2);
772 totalSurface += _volumes[key2];
776 // count negative as face has reversed orientation
777 totalSurface -= _volumes[key2];
784 ConnType nbrPolyTri = polyNodesNbr - 2; // split polygon into nbrPolyTri triangles
785 for (ConnType iTri = 0; iTri < nbrPolyTri; ++iTri)
787 TriangleFaceKey key = TriangleFaceKey(polyNodes[0], polyNodes[1 + iTri], polyNodes[2 + iTri]);
788 if (_volumes.find(key) == _volumes.end())
790 TransformedTriangle tri(_nodes[polyNodes[0]], _nodes[polyNodes[1 + iTri]],
791 _nodes[polyNodes[2 + iTri]]);
792 calculateSurface(tri, key);
793 totalSurface += _volumes[key];
797 totalSurface -= _volumes[key];
805 << "+++ Error : Only elements with triangular and quadratilateral faces are supported at the moment."
813 // reset if it is very small to keep the matrix sparse
814 // is this a good idea?
815 if(epsilonEqual(totalSurface, 0.0, SPARSE_TRUNCATION_LIMIT))
820 LOG(2, "Volume = " << totalSurface << ", det= " << _t->determinant());
826 * Calculates the volume of intersection of this tetrahedron with another one.
828 template<class MyMeshType>
829 double SplitterTetra<MyMeshType>::intersectTetra(const double** tetraCorners)
831 //{ could be done on outside?
832 // check if we have planar tetra element
833 if(_t->determinant() == 0.0)
836 LOG(2, "Planar tetra -- volume 0");
840 const unsigned nbOfNodes4Type=4;
841 // halfspace filtering
842 bool isOutside[8] = {true, true, true, true, true, true, true, true};
843 bool isTargetOutside = false;
845 // calculate the transformed coordinates of the nodes
846 double nodes[nbOfNodes4Type][3];
847 for(int i = 0;i<(int)nbOfNodes4Type;++i)
849 _t->apply(nodes[i], tetraCorners[i]);
850 CheckIsOutside(nodes[i], isOutside);
853 // halfspace filtering check
854 // NB : might not be beneficial for caching of triangles
855 for(int i = 0; i < 8; ++i)
859 isTargetOutside = true;
863 double totalVolume = 0.0;
867 const CellModel& cellModelCell=CellModel::GetCellModel(NORM_TETRA4);
868 ConnType cellNodes[4] = { 0, 1, 2, 3 }, faceNodes[3];
870 for(unsigned ii = 0 ; ii < 4 ; ++ii)
872 cellModelCell.fillSonCellNodalConnectivity(ii,cellNodes,faceNodes);
874 TransformedTriangle tri(nodes[faceNodes[0]], nodes[faceNodes[1]], nodes[faceNodes[2]]);
875 double vol = tri.calculateIntersectionVolume();
879 // reset if it is very small to keep the matrix sparse
880 // is this a good idea?
881 if(epsilonEqual(totalVolume, 0.0, SPARSE_TRUNCATION_LIMIT))
886 LOG(2, "Volume = " << totalVolume << ", det= " << _t->determinant());
888 // NB : fault in article, Grandy, [8] : it is the determinant of the inverse transformation
889 // that should be used (which is equivalent to dividing by the determinant)
890 return std::fabs(1.0 / _t->determinant() * totalVolume) ;
893 ////////////////////////////////////////////////////////
895 template<class MyMeshTypeT, class MyMeshTypeS>
896 SplitterTetra2<MyMeshTypeT, MyMeshTypeS>::SplitterTetra2(const MyMeshTypeT& targetMesh, const MyMeshTypeS& srcMesh, SplittingPolicy policy)
897 :_target_mesh(targetMesh),_src_mesh(srcMesh),_splitting_pol(policy)
901 template<class MyMeshTypeT, class MyMeshTypeS>
902 SplitterTetra2<MyMeshTypeT, MyMeshTypeS>::~SplitterTetra2()
907 template<class MyMeshTypeT, class MyMeshTypeS>
908 void SplitterTetra2<MyMeshTypeT, MyMeshTypeS>::releaseArrays()
910 // free potential sub-mesh nodes that have been allocated
911 if(_nodes.size()>=/*8*/_node_ids.size())
913 typename MyMeshTypeT::MyConnType nbOfNodesT = static_cast<typename MyMeshTypeT::MyConnType>(_node_ids.size());
914 std::vector<const double*>::iterator iter = _nodes.begin() + /*8*/nbOfNodesT;
915 while(iter != _nodes.end())
925 * \param [in] targetCell in C mode.
926 * \param [out] tetra is the output result tetra containers.
928 template<class MyMeshTypeT, class MyMeshTypeS>
929 void SplitterTetra2<MyMeshTypeT, MyMeshTypeS>::splitTargetCell2(typename MyMeshTypeT::MyConnType targetCell, typename std::vector< SplitterTetra<MyMeshTypeS>* >& tetra)
931 typedef typename MyMeshTypeT::MyConnType TConnType;
932 const TConnType *refConn(_target_mesh.getConnectivityPtr());
933 const TConnType *cellConn(refConn+_target_mesh.getConnectivityIndexPtr()[targetCell]);
934 INTERP_KERNEL::NormalizedCellType gt(_target_mesh.getTypeOfElement(targetCell));
935 std::vector<TConnType> tetrasNodalConn;
936 std::vector<double> addCoords;
937 const double *coords(_target_mesh.getCoordinatesPtr());
938 SplitIntoTetras(_splitting_pol,gt,cellConn,refConn+_target_mesh.getConnectivityIndexPtr()[targetCell+1],coords,tetrasNodalConn,addCoords);
939 std::size_t nbTetras(tetrasNodalConn.size()/4); tetra.resize(nbTetras);
941 typename MyMeshTypeS::MyConnType tmp2[4];
942 for(std::size_t i=0;i<nbTetras;i++)
946 TConnType cellId(tetrasNodalConn[4*i+j]);
950 tmp[j*3+0]=coords[3*cellId+0];
951 tmp[j*3+1]=coords[3*cellId+1];
952 tmp[j*3+2]=coords[3*cellId+2];
956 tmp[j*3+0]=addCoords[3*(-cellId-1)+0];
957 tmp[j*3+1]=addCoords[3*(-cellId-1)+1];
958 tmp[j*3+2]=addCoords[3*(-cellId-1)+2];
961 tetra[i]=new SplitterTetra<MyMeshTypeS>(_src_mesh,tmp,tmp2);
966 * @param targetCell in C mode.
967 * @param tetra is the output result tetra containers.
969 template<class MyMeshTypeT, class MyMeshTypeS>
970 void SplitterTetra2<MyMeshTypeT, MyMeshTypeS>::splitTargetCell(typename MyMeshTypeT::MyConnType targetCell,
971 typename MyMeshTypeT::MyConnType nbOfNodesT,
972 typename std::vector< SplitterTetra<MyMeshTypeS>* >& tetra)
974 typedef typename MyMeshTypeT::MyConnType ConnType;
975 const NumberingPolicy numPol=MyMeshTypeT::My_numPol;
976 const int numTetra = static_cast<int>(_splitting_pol);
982 const double *nodes[4];
984 for(int node = 0; node < 4 ; ++node)
986 nodes[node]=getCoordsOfNode2(node, OTT<ConnType,numPol>::indFC(targetCell),_target_mesh,conn[node]);
988 std::copy(conn,conn+4,_node_ids.begin());
989 SplitterTetra<MyMeshTypeS>* t = new SplitterTetra<MyMeshTypeS>(_src_mesh, nodes,conn);
993 // Issue 0020634. To pass nbOfNodesT to calculateSubNodes (don't want to add an arg)
994 _node_ids.resize(nbOfNodesT);
996 // pre-calculate nodes
997 calculateSubNodes(_target_mesh, OTT<ConnType,numPol>::indFC(targetCell));
999 tetra.reserve(numTetra);
1000 _nodes.reserve(30); // we never have more than this
1002 switch ( nbOfNodesT )
1006 switch(_splitting_pol)
1010 const int subZone[8] = { 0, 1, 2, 3, 4, 5, 6, 7 };
1011 fiveSplit(subZone,tetra);
1017 const int subZone[8] = { 0, 1, 2, 3, 4, 5, 6, 7 };
1018 sixSplit(subZone,tetra);
1024 calculateGeneral24Tetra(tetra);
1030 calculateGeneral48Tetra(tetra);
1045 splitConvex(targetCell, tetra);
1051 * Splits the hexahedron into five tetrahedra.
1052 * This method adds five SplitterTetra objects to the vector tetra.
1054 * @param subZone the local node numbers corresponding to the hexahedron corners - these are mapped onto {0,..,7}. Providing this allows the
1055 * splitting to be reused on the subzones of the GENERAL_* types of splitting
1057 template<class MyMeshTypeT, class MyMeshTypeS>
1058 void SplitterTetra2<MyMeshTypeT, MyMeshTypeS>::fiveSplit(const int* const subZone, typename std::vector< SplitterTetra<MyMeshTypeS>* >& tetra)
1060 // create tetrahedra
1061 for(int i = 0; i < 5; ++i)
1063 const double* nodes[4];
1064 typename MyMeshTypeS::MyConnType conn[4];
1065 for(int j = 0; j < 4; ++j)
1067 conn[j] = subZone[ SPLIT_NODES_5[4*i+j] ];
1068 nodes[j] = getCoordsOfSubNode(conn[j]);
1070 SplitterTetra<MyMeshTypeS>* t = new SplitterTetra<MyMeshTypeS>(_src_mesh, nodes,conn);
1076 * Splits the hexahedron into six tetrahedra.
1077 * This method adds six SplitterTetra objects to the vector tetra.
1079 * @param subZone the local node numbers corresponding to the hexahedron corners - these are mapped onto {0,..,7}. Providing this allows the
1080 * splitting to be reused on the subzones of the GENERAL_* types of splitting
1082 template<class MyMeshTypeT, class MyMeshTypeS>
1083 void SplitterTetra2<MyMeshTypeT, MyMeshTypeS>::sixSplit(const int* const subZone, typename std::vector< SplitterTetra<MyMeshTypeS>* >& tetra)
1085 for(int i = 0; i < 6; ++i)
1087 const double* nodes[4];
1088 typename MyMeshTypeS::MyConnType conn[4];
1089 for(int j = 0; j < 4; ++j)
1091 conn[j] = subZone[SPLIT_NODES_6[4*i+j]];
1092 nodes[j] = getCoordsOfSubNode(conn[j]);
1094 SplitterTetra<MyMeshTypeS>* t = new SplitterTetra<MyMeshTypeS>(_src_mesh, nodes,conn);
1100 * Splits the hexahedron into 24 tetrahedra.
1101 * The splitting is done by combining the barycenter of the tetrahedron, the barycenter of each face
1102 * and the nodes of each edge of the face. This creates 6 faces * 4 edges / face = 24 tetrahedra.
1103 * The submesh nodes introduced are the barycenters of the faces and the barycenter of the cell.
1106 template<class MyMeshTypeT, class MyMeshTypeS>
1107 void SplitterTetra2<MyMeshTypeT, MyMeshTypeS>::calculateGeneral24Tetra(typename std::vector< SplitterTetra<MyMeshTypeS>* >& tetra)
1109 // The two nodes of the original mesh cell used in each tetrahedron.
1110 // The tetrahedra all have nodes (cellCenter, faceCenter, edgeNode1, edgeNode2)
1111 // For the correspondence of the nodes, see the GENERAL_48_SUB_NODES table in calculateSubNodes
1113 // nodes to use for tetrahedron
1114 const double* nodes[4];
1115 typename MyMeshTypeS::MyConnType conn[4];
1116 // get the cell center
1118 nodes[0] = getCoordsOfSubNode(conn[0]);
1120 for(int faceCenterNode = 8; faceCenterNode < 14; ++faceCenterNode)
1122 // get the face center
1123 conn[1] = faceCenterNode;
1124 nodes[1] = getCoordsOfSubNode(conn[1]);
1125 for(int j = 0; j < 4; ++j)
1127 const int row = 4*(faceCenterNode - 8) + j;
1128 conn[2] = TETRA_EDGES_GENERAL_24[2*row];
1129 conn[3] = TETRA_EDGES_GENERAL_24[2*row + 1];
1130 nodes[2] = getCoordsOfSubNode(conn[2]);
1131 nodes[3] = getCoordsOfSubNode(conn[3]);
1133 SplitterTetra<MyMeshTypeS>* t = new SplitterTetra<MyMeshTypeS>(_src_mesh, nodes, conn);
1141 * Splits the hexahedron into 48 tetrahedra.
1142 * The splitting is done by introducing the midpoints of all the edges
1143 * and the barycenter of the element as submesh nodes. The 8 hexahedral subzones thus defined
1144 * are then split into 6 tetrahedra each, as in Grandy, p. 449. The division of the subzones
1145 * is done by calling sixSplit().
1148 template<class MyMeshTypeT, class MyMeshTypeS>
1149 void SplitterTetra2<MyMeshTypeT, MyMeshTypeS>::calculateGeneral48Tetra(typename std::vector< SplitterTetra<MyMeshTypeS>* >& tetra)
1151 for(int i = 0; i < 8; ++i)
1153 sixSplit(GENERAL_48_SUBZONES+8*i,tetra);
1158 * Splits the NORM_PYRA5 into 2 tetrahedra.
1160 template<class MyMeshTypeT, class MyMeshTypeS>
1161 void SplitterTetra2<MyMeshTypeT, MyMeshTypeS>::splitPyram5(typename std::vector< SplitterTetra<MyMeshTypeS>* >& tetra)
1163 static const int SPLIT_PYPA5[2][4] =
1173 // create tetrahedra
1174 const double* nodes[4];
1175 typename MyMeshTypeS::MyConnType conn[4];
1176 for(int i = 0; i < 2; ++i)
1178 for(int j = 0; j < 4; ++j)
1179 nodes[j] = getCoordsOfSubNode2(SPLIT_PYPA5[i][j],conn[j]);
1180 SplitterTetra<MyMeshTypeS>* t = new SplitterTetra<MyMeshTypeS>(_src_mesh, nodes,conn);
1186 * Splits a convex cell into tetrahedra.
1188 template<class MyMeshTypeT, class MyMeshTypeS>
1189 void SplitterTetra2<MyMeshTypeT, MyMeshTypeS>::splitConvex(typename MyMeshTypeT::MyConnType targetCell,
1190 typename std::vector< SplitterTetra<MyMeshTypeS>* >& tetra)
1192 // Each face of a cell is split into triangles and
1193 // each of triangles and a cell barycenter form a tetrahedron.
1195 typedef typename MyMeshTypeT::MyConnType ConnType;
1196 const NumberingPolicy numPol=MyMeshTypeT::My_numPol;
1198 // get type of cell and nb of cell nodes
1199 NormalizedCellType normCellType=_target_mesh.getTypeOfElement(OTT<ConnType,numPol>::indFC(targetCell));
1200 const CellModel& cellModelCell=CellModel::GetCellModel(normCellType);
1201 ConnType nbOfCellNodes=cellModelCell.isDynamic() ? _target_mesh.getNumberOfNodesOfElement(OTT<ConnType,numPol>::indFC(targetCell)) : cellModelCell.getNumberOfNodes();
1203 // get nb of cell sons (faces)
1204 const ConnType* rawCellConn = _target_mesh.getConnectivityPtr() + OTT<ConnType,numPol>::conn2C( _target_mesh.getConnectivityIndexPtr()[ targetCell ]);
1205 const ConnType rawNbCellNodes = _target_mesh.getConnectivityIndexPtr()[ targetCell+1 ] - _target_mesh.getConnectivityIndexPtr()[ targetCell ];
1206 unsigned nbOfSons = cellModelCell.getNumberOfSons2(rawCellConn, rawNbCellNodes);
1208 // indices of nodes of a son
1209 static std::vector<ConnType> allNodeIndices; // == 0,1,2,...,nbOfCellNodes-1
1210 while ( allNodeIndices.size() < (std::size_t)nbOfCellNodes )
1211 allNodeIndices.push_back( static_cast<ConnType>(allNodeIndices.size()) );
1212 std::vector<ConnType> classicFaceNodes(4);
1213 if(cellModelCell.isQuadratic())
1214 throw INTERP_KERNEL::Exception("SplitterTetra2::splitConvex : quadratic 3D cells are not implemented yet !");
1215 ConnType* faceNodes = cellModelCell.isDynamic() ? &allNodeIndices[0] : &classicFaceNodes[0];
1217 // nodes of tetrahedron
1218 typename MyMeshTypeS::MyConnType conn[4];
1219 const double* nodes[4];
1220 nodes[3] = getCoordsOfSubNode2( nbOfCellNodes,conn[3]); // barycenter
1222 for(unsigned ii = 0 ; ii < nbOfSons; ++ii)
1224 // get indices of son's nodes: it's just next portion of allNodeIndices for polyhedron
1225 // and some of allNodeIndices accodring to cell model for a classsic cell
1226 unsigned nbFaceNodes = cellModelCell.getNumberOfNodesConstituentTheSon2(ii, rawCellConn, rawNbCellNodes);
1227 if ( normCellType != NORM_POLYHED )
1228 cellModelCell.fillSonCellNodalConnectivity(ii,&allNodeIndices[0],faceNodes);
1230 int nbTetra = nbFaceNodes - 2; // split polygon into nbTetra triangles
1232 // create tetrahedra
1233 for(int i = 0; i < nbTetra; ++i)
1235 nodes[0] = getCoordsOfSubNode2( faceNodes[0], conn[0]);
1236 nodes[1] = getCoordsOfSubNode2( faceNodes[1+i],conn[1]);
1237 nodes[2] = getCoordsOfSubNode2( faceNodes[2+i],conn[2]);
1238 SplitterTetra<MyMeshTypeS>* t = new SplitterTetra<MyMeshTypeS>(_src_mesh, nodes,conn);
1242 if ( normCellType == NORM_POLYHED )
1243 faceNodes += nbFaceNodes; // go to the next face
1248 * Precalculates all the nodes.
1249 * Retrieves the mesh nodes and allocates the necessary sub-mesh
1250 * nodes according to the splitting policy used.
1251 * This method is meant to be called once by the constructor.
1253 * @param targetMesh the target mesh
1254 * @param targetCell the global number of the cell that the object represents, in targetMesh mode.
1257 template<class MyMeshTypeT, class MyMeshTypeS>
1258 void SplitterTetra2<MyMeshTypeT, MyMeshTypeS>::calculateSubNodes(const MyMeshTypeT& targetMesh, typename MyMeshTypeT::MyConnType targetCell)
1260 // retrieve real mesh nodes
1262 typename MyMeshTypeT::MyConnType nbOfNodesT = static_cast<typename MyMeshTypeT::MyConnType>(_node_ids.size());// Issue 0020634. _node_ids.resize(8);
1263 for(int node = 0; node < nbOfNodesT ; ++node)
1265 // calculate only normal nodes
1266 _nodes.push_back(getCoordsOfNode2(node, targetCell, targetMesh,_node_ids[node]));
1269 switch ( nbOfNodesT )
1273 // create sub-mesh nodes if needed
1274 switch(_splitting_pol)
1278 for(int i = 0; i < 7; ++i)
1280 double* barycenter = new double[3];
1281 calcBarycenter(4, barycenter, &GENERAL_24_SUB_NODES[4*i]);
1282 _nodes.push_back(barycenter);
1289 for(int i = 0; i < 19; ++i)
1291 double* barycenter = new double[3];
1292 calcBarycenter(2, barycenter, &GENERAL_48_SUB_NODES[2*i]);
1293 _nodes.push_back(barycenter);
1303 case 5: // NORM_PYRA5
1306 default: // convex 3d cell
1308 // add barycenter of a cell
1309 std::vector<int> allIndices(nbOfNodesT);
1310 for ( int i = 0; i < nbOfNodesT; ++i ) allIndices[i] = i;
1311 double* barycenter = new double[3];
1312 calcBarycenter(nbOfNodesT, barycenter, &allIndices[0]);
1313 _nodes.push_back(barycenter);