src/INTERP_KERNEL/InterpolationPlanar.txx

   1 // Copyright (C) 2007-2019  CEA/DEN, EDF R&D
   2 //
   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
   6 // version 2.1 of the License, or (at your option) any later version.
   7 //
   8 // This library is distributed in the hope that it will be useful,
   9 // but WITHOUT ANY WARRANTY; without even the implied warranty of
  10 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  11 // Lesser General Public License for more details.
  12 //
  13 // You should have received a copy of the GNU Lesser General Public
  14 // License along with this library; if not, write to the Free Software
  15 // Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307 USA
  16 //
  17 // See http://www.salome-platform.org/ or email : webmaster.salome@opencascade.com
  18 //
  19 // Author : Anthony Geay (CEA/DEN)
  20
  21 #ifndef __INTERPOLATIONPLANAR_TXX__
  22 #define __INTERPOLATIONPLANAR_TXX__
  23
  24 #include "InterpolationPlanar.hxx"
  25 #include "Interpolation.txx"
  26 #include "InterpolationOptions.hxx"
  27 #include "PlanarIntersector.hxx"
  28 #include "PlanarIntersector.txx"
  29 #include "TriangulationIntersector.hxx"
  30 #include "TriangulationIntersector.txx"
  31 #include "ConvexIntersector.hxx"
  32 #include "ConvexIntersector.txx"
  33 #include "Geometric2DIntersector.hxx"
  34 #include "Geometric2DIntersector.txx"
  35 #include "PointLocator2DIntersector.hxx"
  36 #include "PointLocator2DIntersector.txx"
  37 #include "PlanarIntersectorP0P1PL.hxx"
  38 #include "PlanarIntersectorP0P1PL.txx"
  39 #include "PlanarIntersectorP1P0PL.hxx"
  40 #include "PlanarIntersectorP1P0PL.txx"
  41 #include "PlanarIntersectorP1P1PL.hxx"
  42 #include "PlanarIntersectorP1P1PL.txx"
  43 #include "MappedBarycentric2DIntersectorP1P1.hxx"
  44 #include "MappedBarycentric2DIntersectorP1P1.txx"
  45 #include "VectorUtils.hxx"
  46 #include "BBTree.txx"
  47
  48 #include <limits>
  49 #include <time.h>
  50
  51 namespace INTERP_KERNEL
  52 {
  53   /**
  54    * \defgroup interpolationPlanar InterpolationPlanar
  55    *
  56    * \class InterpolationPlanar
  57    * \brief Class used to compute the coefficients of the interpolation matrix between
  58    * two local meshes in two dimensions. Meshes can contain mixed triangular and quadrangular elements.
  59    */
  60   template<class RealPlanar>
  61   InterpolationPlanar<RealPlanar>::InterpolationPlanar():_dim_caracteristic(1)
  62
  63   {
  64   }
  65
  66   template<class RealPlanar>
  67   InterpolationPlanar<RealPlanar>::InterpolationPlanar(const InterpolationOptions& io):Interpolation< InterpolationPlanar<RealPlanar> >(io),_dim_caracteristic(1)
  68
  69   {
  70   }
  71
  72   /**
  73    *  \brief  Function used to set the options for the intersection calculation
  74    * \details The following options can be modified:
  75    *  -# Intersection_type: the type of algorithm to be used in the computation of the cell-cell intersections.
  76    *   - Values: Triangle, Convex.
  77    *   - Default: Triangle.
  78    *  -# Precision: Level of precision of the computations is precision times the characteristic size of the mesh.
  79    *   - Values: positive real number.
  80    *   - Default: 1.0E-12.
  81    *  -# PrintLevel: Level of verboseness during the computations.
  82    *   - Values: integer between 0 and 3.
  83    *   - Default: 0.
  84    */
  85   template<class RealPlanar>
  86   void InterpolationPlanar<RealPlanar>::setOptions(double precision, int printLevel, IntersectionType intersectionType, int orientation)
  87   {
  88     InterpolationOptions::setPrecision(precision);
  89     InterpolationOptions::setPrintLevel(printLevel);
  90     InterpolationOptions::setIntersectionType(intersectionType);
  91     InterpolationOptions::setOrientation(orientation);
  92   }
  93
  94
  95   /** \brief Main function to interpolate triangular or quadrangular meshes.
  96       \details  The algorithm proceeds in two steps: first a filtering process reduces the number of pairs of elements for which the
  97       * calculation must be carried out by eliminating pairs that do not intersect based on their bounding boxes. Then, the
  98       * volume of intersection is calculated by an object of type IntersectorPlanar for the remaining pairs, and entered into the
  99       * intersection matrix.
 100       *
 101       * The matrix is partially sparse : it is a vector of maps of integer - double pairs.
 102       * The length of the vector is equal to the number of target elements - for each target element there is a map, regardless
 103       * of whether the element intersects any source elements or not. But in the maps there are only entries for those source elements
 104       * which have a non-zero intersection volume with the target element. The vector has indices running from
 105       * 0 to (#target elements - 1), meaning that the map for target element i is stored at index i - 1. In the maps, however,
 106       * the indexing is more natural : the intersection volume of the target element i with source element j is found at matrix[i-1][j].
 107       *
 108
 109       * @param myMeshS  Planar source mesh
 110       * @Param myMeshT  Planar target mesh
 111       * @return            vector containing for each element i of the source mesh, a map giving for each element j
 112       *                    of the target mesh which i intersects, the area of the intersection
 113       *
 114       */
 115   template<class RealPlanar>
 116   template<class MyMeshType, class MatrixType>
 117   typename MyMeshType::MyConnType InterpolationPlanar<RealPlanar>::interpolateMeshes(const MyMeshType& myMeshS, const MyMeshType& myMeshT, MatrixType& result, const std::string& method)
 118   {
 119     static const int SPACEDIM=MyMeshType::MY_SPACEDIM;
 120     typedef typename MyMeshType::MyConnType ConnType;
 121     static const NumberingPolicy numPol=MyMeshType::My_numPol;
 122
 123     long global_start =clock();
 124     std::size_t counter=0;
 125     /***********************************************************/
 126     /* Check both meshes are made of triangles and quadrangles */
 127     /***********************************************************/
 128
 129     ConnType nbMailleS=myMeshS.getNumberOfElements();
 130     ConnType nbMailleT=myMeshT.getNumberOfElements();
 131
 132     /**************************************************/
 133     /* Search the characteristic size of the meshes   */
 134     /**************************************************/
 135
 136     double BoxS[2*SPACEDIM]; myMeshS.getBoundingBox(BoxS);
 137     double BoxT[2*SPACEDIM]; myMeshT.getBoundingBox(BoxT);
 138     double diagonalS,dimCaracteristicS=std::numeric_limits<double>::max();
 139     if(nbMailleS!=0)
 140       {
 141         diagonalS=getDistanceBtw2Pts<SPACEDIM>(BoxS+SPACEDIM,BoxS);
 142         dimCaracteristicS=diagonalS/(double)(nbMailleS);
 143       }
 144     double diagonalT,dimCaracteristicT=std::numeric_limits<double>::max();
 145     if(nbMailleT!=0)
 146       {
 147         diagonalT=getDistanceBtw2Pts<SPACEDIM>(BoxT+SPACEDIM,BoxT);
 148         dimCaracteristicT=diagonalT/(double)(nbMailleT);
 149       }
 150
 151     _dim_caracteristic=std::min(dimCaracteristicS, dimCaracteristicT);
 152     if (InterpolationOptions::getPrintLevel()>=1)
 153       {
 154         std::cout << "  - Characteristic size of the source mesh : " << dimCaracteristicS << std::endl;
 155         std::cout << "  - Characteristic size of the target mesh: " << dimCaracteristicT << std::endl;
 156         std::cout << "InterpolationPlanar::computation of the intersections" << std::endl;
 157       }
 158
 159     PlanarIntersector<MyMeshType,MatrixType>* intersector=0;
 160     std::string meth = InterpolationOptions::filterInterpolationMethod(method);
 161     if(meth=="P0P0")
 162       {
 163         switch (InterpolationOptions::getIntersectionType())
 164           {
 165           case Triangulation:
 166             intersector=new TriangulationIntersector<MyMeshType,MatrixType,PlanarIntersectorP0P0>(myMeshT,myMeshS,_dim_caracteristic,
 167                                                                                                   InterpolationOptions::getPrecision(),
 168                                                                                                   InterpolationOptions::getMaxDistance3DSurfIntersect(),
 169                                                                                                   InterpolationOptions::getMinDotBtwPlane3DSurfIntersect(),
 170                                                                                                   InterpolationOptions::getMedianPlane(),
 171                                                                                                   InterpolationOptions::getOrientation(),
 172                                                                                                   InterpolationOptions::getPrintLevel());
 173             break;
 174           case Convex:
 175             intersector=new ConvexIntersector<MyMeshType,MatrixType,PlanarIntersectorP0P0>(myMeshT,myMeshS,_dim_caracteristic,
 176                                                                                            InterpolationOptions::getPrecision(),
 177                                                                                            InterpolationOptions::getMaxDistance3DSurfIntersect(),
 178                                                                                            InterpolationOptions::getMinDotBtwPlane3DSurfIntersect(),
 179                                                                                            InterpolationOptions::getMedianPlane(),
 180                                                                                            InterpolationOptions::getDoRotate(),
 181                                                                                            InterpolationOptions::getOrientation(),
 182                                                                                            InterpolationOptions::getPrintLevel());
 183             break;
 184           case Geometric2D:
 185             intersector=new Geometric2DIntersector<MyMeshType,MatrixType,PlanarIntersectorP0P0>(myMeshT, myMeshS, _dim_caracteristic,
 186                                                                                                 InterpolationOptions::getMaxDistance3DSurfIntersect(),
 187                                                                                                 InterpolationOptions::getMinDotBtwPlane3DSurfIntersect(),
 188                                                                                                 InterpolationOptions::getMedianPlane(),
 189                                                                                                 InterpolationOptions::getPrecision(),
 190                                                                                                 InterpolationOptions::getOrientation());
 191             break;
 192           case PointLocator:
 193             intersector=new PointLocator2DIntersector<MyMeshType,MatrixType,PlanarIntersectorP0P0>(myMeshT, myMeshS, _dim_caracteristic,
 194                                                                                                    InterpolationOptions::getMaxDistance3DSurfIntersect(),
 195                                                                                                    InterpolationOptions::getMinDotBtwPlane3DSurfIntersect(),
 196                                                                                                    InterpolationOptions::getMedianPlane(),
 197                                                                                                    InterpolationOptions::getPrecision(),
 198                                                                                                    InterpolationOptions::getOrientation());
 199             break;
 200           default:
 201             throw INTERP_KERNEL::Exception("For P0P0 planar interpolation possibities are : Triangulation, Convex, Geometric2D, PointLocator !");
 202           }
 203       }
 204     else if(meth=="P0P1")
 205       {
 206         switch (InterpolationOptions::getIntersectionType())
 207           {
 208           case Triangulation:
 209             intersector=new TriangulationIntersector<MyMeshType,MatrixType,PlanarIntersectorP0P1>(myMeshT,myMeshS,_dim_caracteristic,
 210                                                                                                   InterpolationOptions::getPrecision(),
 211                                                                                                   InterpolationOptions::getMaxDistance3DSurfIntersect(),
 212                                                                                                   InterpolationOptions::getMinDotBtwPlane3DSurfIntersect(),
 213                                                                                                   InterpolationOptions::getMedianPlane(),
 214                                                                                                   InterpolationOptions::getOrientation(),
 215                                                                                                   InterpolationOptions::getPrintLevel());
 216             break;
 217           case Convex:
 218             intersector=new ConvexIntersector<MyMeshType,MatrixType,PlanarIntersectorP0P1>(myMeshT,myMeshS,_dim_caracteristic,
 219                                                                                            InterpolationOptions::getPrecision(),
 220                                                                                            InterpolationOptions::getMaxDistance3DSurfIntersect(),
 221                                                                                            InterpolationOptions::getMinDotBtwPlane3DSurfIntersect(),
 222                                                                                            InterpolationOptions::getMedianPlane(),
 223                                                                                            InterpolationOptions::getDoRotate(),
 224                                                                                            InterpolationOptions::getOrientation(),
 225                                                                                            InterpolationOptions::getPrintLevel());
 226             break;
 227           case Geometric2D:
 228             intersector=new Geometric2DIntersector<MyMeshType,MatrixType,PlanarIntersectorP0P1>(myMeshT, myMeshS, _dim_caracteristic,
 229                                                                                                 InterpolationOptions::getMaxDistance3DSurfIntersect(),
 230                                                                                                 InterpolationOptions::getMinDotBtwPlane3DSurfIntersect(),
 231                                                                                                 InterpolationOptions::getMedianPlane(),
 232                                                                                                 InterpolationOptions::getPrecision(),
 233                                                                                                 InterpolationOptions::getOrientation());
 234             break;
 235           case PointLocator:
 236             intersector=new PlanarIntersectorP0P1PL<MyMeshType,MatrixType>(myMeshT, myMeshS, _dim_caracteristic,
 237                                                                            InterpolationOptions::getMaxDistance3DSurfIntersect(),
 238                                                                            InterpolationOptions::getMinDotBtwPlane3DSurfIntersect(),
 239                                                                            InterpolationOptions::getMedianPlane(),
 240                                                                            InterpolationOptions::getPrecision(),
 241                                                                            InterpolationOptions::getOrientation());
 242             break;
 243           case Barycentric:
 244             intersector=new TriangulationIntersector<MyMeshType,MatrixType,PlanarIntersectorP0P1Bary>(myMeshT,myMeshS,_dim_caracteristic,
 245                                                                                                       InterpolationOptions::getPrecision(),
 246                                                                                                       InterpolationOptions::getMaxDistance3DSurfIntersect(),
 247                                                                                                       InterpolationOptions::getMinDotBtwPlane3DSurfIntersect(),
 248                                                                                                       InterpolationOptions::getMedianPlane(),
 249                                                                                                       InterpolationOptions::getOrientation(),
 250                                                                                                       InterpolationOptions::getPrintLevel());
 251             break;
 252           case BarycentricGeo2D:
 253             intersector=new Geometric2DIntersector<MyMeshType,MatrixType,PlanarIntersectorP0P1Bary>(myMeshT, myMeshS, _dim_caracteristic,
 254                                                                                                     InterpolationOptions::getMaxDistance3DSurfIntersect(),
 255                                                                                                     InterpolationOptions::getMinDotBtwPlane3DSurfIntersect(),
 256                                                                                                     InterpolationOptions::getMedianPlane(),
 257                                                                                                     InterpolationOptions::getPrecision(),
 258                                                                                                     InterpolationOptions::getOrientation());
 259             break;
 260           default:
 261             throw INTERP_KERNEL::Exception("For P0P1 planar interpolation possibities are : Triangulation, Convex, Geometric2D, PointLocator, Barycentric, BarycentricGeo2D !");
 262           }
 263       }
 264     else if(meth=="P1P0")
 265       {
 266         switch (InterpolationOptions::getIntersectionType())
 267           {
 268           case Triangulation:
 269             intersector=new TriangulationIntersector<MyMeshType,MatrixType,PlanarIntersectorP1P0>(myMeshT,myMeshS,_dim_caracteristic,
 270                                                                                                   InterpolationOptions::getPrecision(),
 271                                                                                                   InterpolationOptions::getMaxDistance3DSurfIntersect(),
 272                                                                                                   InterpolationOptions::getMinDotBtwPlane3DSurfIntersect(),
 273                                                                                                   InterpolationOptions::getMedianPlane(),
 274                                                                                                   InterpolationOptions::getOrientation(),
 275                                                                                                   InterpolationOptions::getPrintLevel());
 276             break;
 277           case Convex:
 278             intersector=new ConvexIntersector<MyMeshType,MatrixType,PlanarIntersectorP1P0>(myMeshT,myMeshS,_dim_caracteristic,
 279                                                                                            InterpolationOptions::getPrecision(),
 280                                                                                            InterpolationOptions::getMaxDistance3DSurfIntersect(),
 281                                                                                            InterpolationOptions::getMinDotBtwPlane3DSurfIntersect(),
 282                                                                                            InterpolationOptions::getMedianPlane(),
 283                                                                                            InterpolationOptions::getDoRotate(),
 284                                                                                            InterpolationOptions::getOrientation(),
 285                                                                                            InterpolationOptions::getPrintLevel());
 286             break;
 287           case Geometric2D:
 288             intersector=new Geometric2DIntersector<MyMeshType,MatrixType,PlanarIntersectorP1P0>(myMeshT, myMeshS, _dim_caracteristic,
 289                                                                                                 InterpolationOptions::getMaxDistance3DSurfIntersect(),
 290                                                                                                 InterpolationOptions::getMinDotBtwPlane3DSurfIntersect(),
 291                                                                                                 InterpolationOptions::getMedianPlane(),
 292                                                                                                 InterpolationOptions::getPrecision(),
 293                                                                                                 InterpolationOptions::getOrientation());
 294             break;
 295           case PointLocator:
 296             intersector=new PlanarIntersectorP1P0PL<MyMeshType,MatrixType>(myMeshT, myMeshS, _dim_caracteristic,
 297                                                                            InterpolationOptions::getMaxDistance3DSurfIntersect(),
 298                                                                            InterpolationOptions::getMinDotBtwPlane3DSurfIntersect(),
 299                                                                            InterpolationOptions::getMedianPlane(),
 300                                                                            InterpolationOptions::getPrecision(),
 301                                                                            InterpolationOptions::getOrientation());
 302             break;
 303           case Barycentric:
 304              intersector=new TriangulationIntersector<MyMeshType,MatrixType,PlanarIntersectorP1P0Bary>(myMeshT,myMeshS,_dim_caracteristic,
 305                                                                                                        InterpolationOptions::getPrecision(),
 306                                                                                                        InterpolationOptions::getMaxDistance3DSurfIntersect(),
 307                                                                                                        InterpolationOptions::getMinDotBtwPlane3DSurfIntersect(),
 308                                                                                                        InterpolationOptions::getMedianPlane(),
 309                                                                                                        InterpolationOptions::getOrientation(),
 310                                                                                                        InterpolationOptions::getPrintLevel());
 311              break;
 312           case BarycentricGeo2D:
 313             intersector=new Geometric2DIntersector<MyMeshType,MatrixType,PlanarIntersectorP1P0Bary>(myMeshT, myMeshS, _dim_caracteristic,
 314                                                                                                     InterpolationOptions::getMaxDistance3DSurfIntersect(),
 315                                                                                                     InterpolationOptions::getMinDotBtwPlane3DSurfIntersect(),
 316                                                                                                     InterpolationOptions::getMedianPlane(),
 317                                                                                                     InterpolationOptions::getPrecision(),
 318                                                                                                     InterpolationOptions::getOrientation());
 319             break;
 320           default:
 321             throw INTERP_KERNEL::Exception("For P1P0 planar interpolation possibities are : Triangulation, Convex, Geometric2D, PointLocator, BarycentricGeo2D or Barycentric!");
 322           }
 323       }
 324     else if(meth=="P1P1")
 325       {
 326         switch (InterpolationOptions::getIntersectionType())
 327           {
 328           case Triangulation:
 329             intersector=new TriangulationIntersector<MyMeshType,MatrixType,PlanarIntersectorP1P1>(myMeshT,myMeshS,_dim_caracteristic,
 330                                                                                                   InterpolationOptions::getPrecision(),
 331                                                                                                   InterpolationOptions::getMaxDistance3DSurfIntersect(),
 332                                                                                                   InterpolationOptions::getMinDotBtwPlane3DSurfIntersect(),
 333                                                                                                   InterpolationOptions::getMedianPlane(),
 334                                                                                                   InterpolationOptions::getOrientation(),
 335                                                                                                   InterpolationOptions::getPrintLevel());
 336             break;
 337           case Convex:
 338             intersector=new ConvexIntersector<MyMeshType,MatrixType,PlanarIntersectorP1P1>(myMeshT,myMeshS,_dim_caracteristic,
 339                                                                                            InterpolationOptions::getPrecision(),
 340                                                                                            InterpolationOptions::getMaxDistance3DSurfIntersect(),
 341                                                                                            InterpolationOptions::getMinDotBtwPlane3DSurfIntersect(),
 342                                                                                            InterpolationOptions::getMedianPlane(),
 343                                                                                            InterpolationOptions::getDoRotate(),
 344                                                                                            InterpolationOptions::getOrientation(),
 345                                                                                            InterpolationOptions::getPrintLevel());
 346             break;
 347           case Geometric2D:
 348             intersector=new Geometric2DIntersector<MyMeshType,MatrixType,PlanarIntersectorP1P1>(myMeshT, myMeshS, _dim_caracteristic,
 349                                                                                                 InterpolationOptions::getMaxDistance3DSurfIntersect(),
 350                                                                                                 InterpolationOptions::getMinDotBtwPlane3DSurfIntersect(),
 351                                                                                                 InterpolationOptions::getMedianPlane(),
 352                                                                                                 InterpolationOptions::getPrecision(),
 353                                                                                                 InterpolationOptions::getOrientation());
 354             break;
 355           case PointLocator:
 356             intersector=new PlanarIntersectorP1P1PL<MyMeshType,MatrixType>(myMeshT, myMeshS, _dim_caracteristic,
 357                                                                            InterpolationOptions::getMaxDistance3DSurfIntersect(),
 358                                                                            InterpolationOptions::getMinDotBtwPlane3DSurfIntersect(),
 359                                                                            InterpolationOptions::getMedianPlane(),
 360                                                                            InterpolationOptions::getPrecision(),
 361                                                                            InterpolationOptions::getOrientation());
 362             break;
 363           case MappedBarycentric:
 364             intersector=new MappedBarycentric2DIntersectorP1P1<MyMeshType,MatrixType>(myMeshT, myMeshS, _dim_caracteristic,
 365                                                                                      InterpolationOptions::getMaxDistance3DSurfIntersect(),
 366                                                                                      InterpolationOptions::getMinDotBtwPlane3DSurfIntersect(),
 367                                                                                      InterpolationOptions::getMedianPlane(),
 368                                                                                      InterpolationOptions::getPrecision(),
 369                                                                                      InterpolationOptions::getOrientation());
 370             break;
 371           default:
 372             throw INTERP_KERNEL::Exception("For P1P1 planar interpolation possibities are : Triangulation, Convex, Geometric2D, PointLocator, MappedBarycentric !");
 373           }
 374       }
 375     else
 376       throw INTERP_KERNEL::Exception("Invalid method specified or intersection type ! Must be in : \"P0P0\" \"P0P1\" \"P1P0\" or \"P1P1\"");
 377     /****************************************************************/
 378     /* Create a search tree based on the bounding boxes             */
 379     /* Instantiate the intersector and initialise the result vector */
 380     /****************************************************************/
 381
 382     long start_filtering=clock();
 383
 384     std::vector<double> bbox;
 385     intersector->createBoundingBoxes(myMeshS,bbox); // create the bounding boxes
 386     performAdjustmentOfBB(intersector,bbox);
 387     const double *bboxPtr=0;
 388     if(nbMailleS>0)
 389       bboxPtr=&bbox[0];
 390     BBTree<SPACEDIM,ConnType> my_tree(bboxPtr, 0, 0,nbMailleS);//creating the search structure
 391
 392     long end_filtering=clock();
 393
 394     result.resize(intersector->getNumberOfRowsOfResMatrix());//on initialise.
 395
 396     /****************************************************/
 397     /* Loop on the target cells - core of the algorithm */
 398     /****************************************************/
 399     long start_intersection=clock();
 400     ConnType nbelem_type=myMeshT.getNumberOfElements();
 401     const ConnType *connIndxT=myMeshT.getConnectivityIndexPtr();
 402     for(ConnType iT=0; iT<nbelem_type; iT++)
 403       {
 404         ConnType nb_nodesT=connIndxT[iT+1]-connIndxT[iT];
 405         std::vector<ConnType> intersecting_elems;
 406         double bb[2*SPACEDIM];
 407         intersector->getElemBB(bb,myMeshT,OTT<ConnType,numPol>::indFC(iT),nb_nodesT);
 408         my_tree.getIntersectingElems(bb, intersecting_elems);
 409         intersector->intersectCells(iT,intersecting_elems,result);
 410         counter+=intersecting_elems.size();
 411         intersecting_elems.clear();
 412       }
 413     ConnType ret=intersector->getNumberOfColsOfResMatrix();
 414     delete intersector;
 415
 416     if (InterpolationOptions::getPrintLevel() >=1)
 417       {
 418         long end_intersection=clock();
 419         std::cout << "Filtering time= " << end_filtering-start_filtering << std::endl;
 420         std::cout << "Intersection time= " << end_intersection-start_intersection << std::endl;
 421         long global_end =clock();
 422         std::cout << "Number of computed intersections = " << counter << std::endl;
 423         std::cout << "Global time= " << global_end - global_start << std::endl;
 424       }
 425     return ret;
 426   }
 427 }
 428
 429 #endif