21#ifdef DEAL_II_WITH_CGAL
30# include <CGAL/Boolean_set_operations_2.h>
31# include <CGAL/Cartesian.h>
32# include <CGAL/Circular_kernel_intersections.h>
33# include <CGAL/Constrained_Delaunay_triangulation_2.h>
34# include <CGAL/Delaunay_mesh_face_base_2.h>
35# include <CGAL/Delaunay_mesh_size_criteria_2.h>
36# include <CGAL/Delaunay_mesher_2.h>
37# include <CGAL/Delaunay_triangulation_2.h>
38# include <CGAL/Exact_predicates_exact_constructions_kernel_with_sqrt.h>
39# include <CGAL/Kernel_traits.h>
40# include <CGAL/Polygon_2.h>
41# include <CGAL/Polygon_with_holes_2.h>
42# include <CGAL/Projection_traits_xy_3.h>
43# include <CGAL/Segment_3.h>
44# include <CGAL/Simple_cartesian.h>
45# include <CGAL/Tetrahedron_3.h>
46# include <CGAL/Triangle_2.h>
47# include <CGAL/Triangle_3.h>
48# include <CGAL/Triangulation_2.h>
49# include <CGAL/Triangulation_3.h>
50# include <CGAL/Triangulation_face_base_with_id_2.h>
51# include <CGAL/Triangulation_face_base_with_info_2.h>
61 using K = CGAL::Exact_predicates_exact_constructions_kernel_with_sqrt;
62 using K_exact = CGAL::Exact_predicates_exact_constructions_kernel;
92 using Vb = CGAL::Triangulation_vertex_base_2<K>;
93 using Fbb = CGAL::Triangulation_face_base_with_info_2<FaceInfo2, K>;
94 using CFb = CGAL::Constrained_triangulation_face_base_2<K, Fbb>;
95 using Fb = CGAL::Delaunay_mesh_face_base_2<K, CFb>;
96 using Tds = CGAL::Triangulation_data_structure_2<Vb, Fb>;
97 using Itag = CGAL::Exact_predicates_tag;
98 using CDT = CGAL::Constrained_Delaunay_triangulation_2<K, Tds, Itag>;
99 using Criteria = CGAL::Delaunay_mesh_size_criteria_2<CDT>;
111 template <
typename TargetVariant>
112 struct Repackage : boost::static_visitor<TargetVariant>
114 template <
typename T>
116 operator()(
const T &t)
const
118 return TargetVariant(t);
128 template <
typename... Types>
129 std::optional<std::variant<Types...>>
130 convert_boost_to_std(
const boost::optional<boost::variant<Types...>> &x)
139 using std_variant = std::variant<Types...>;
140 return boost::apply_visitor(Repackage<std_variant>(), *x);
157 std::list<CDT::Edge> &border)
159 if (start->info().nesting_level != -1)
163 std::list<Face_handle> queue;
164 queue.push_back(start);
165 while (!queue.empty())
169 if (fh->info().nesting_level == -1)
171 fh->info().nesting_level = index;
172 for (
int i = 0; i < 3; i++)
176 if (n->info().nesting_level == -1)
178 if (ct.is_constrained(e))
193 for (CDT::Face_handle f : cdt.all_face_handles())
195 f->info().nesting_level = -1;
197 std::list<CDT::Edge> border;
199 while (!border.empty())
201 CDT::Edge e = border.front();
204 if (n->info().nesting_level == -1)
206 mark_domains(cdt, n, e.first->info().nesting_level + 1, border);
223 std::vector<CGALPoint2>>>
231 std::array<CGALPoint2, 3> pts0, pts1;
233 std::transform(triangle0.begin(),
236 &CGALWrappers::dealii_point_to_cgal_point<CGALPoint2, 2>);
238 std::transform(triangle1.begin(),
241 &CGALWrappers::dealii_point_to_cgal_point<CGALPoint2, 2>);
245 return convert_boost_to_std(
246 CGAL::intersection(cgal_triangle0, cgal_triangle1));
250 std::optional<std::variant<CGALPoint2, CGALSegment2>>
258 std::array<CGALPoint2, 3> pts0;
259 std::array<CGALPoint2, 2> pts1;
261 std::transform(triangle.begin(),
264 &CGALWrappers::dealii_point_to_cgal_point<CGALPoint2, 2>);
266 std::transform(segment.begin(),
269 &CGALWrappers::dealii_point_to_cgal_point<CGALPoint2, 2>);
273 return convert_boost_to_std(
274 CGAL::intersection(cgal_segment, cgal_triangle));
280 std::vector<Polygon_with_holes_2>
287 std::array<CGALPoint2, 4> pts0, pts1;
289 std::transform(rectangle0.begin(),
292 &CGALWrappers::dealii_point_to_cgal_point<CGALPoint2, 2>);
294 std::transform(rectangle1.begin(),
297 &CGALWrappers::dealii_point_to_cgal_point<CGALPoint2, 2>);
299 const CGALPolygon first_poly{pts0.begin(), pts0.end()};
300 const CGALPolygon second_poly{pts1.begin(), pts1.end()};
302 std::vector<Polygon_with_holes_2> poly_list;
303 CGAL::intersection(first_poly,
305 std::back_inserter(poly_list));
311 std::optional<std::variant<CGALPoint3, CGALSegment3>>
316# if DEAL_II_CGAL_VERSION_GTE(5, 5, 0)
321 std::array<CGALPoint3, 4> pts0;
322 std::array<CGALPoint3, 2> pts1;
324 std::transform(tetrahedron.begin(),
327 &CGALWrappers::dealii_point_to_cgal_point<CGALPoint3, 3>);
329 std::transform(segment.begin(),
332 &CGALWrappers::dealii_point_to_cgal_point<CGALPoint3, 3>);
334 CGALTetra cgal_tetrahedron{pts0[0], pts0[1], pts0[2], pts0[3]};
336 return convert_boost_to_std(
337 CGAL::intersection(cgal_segment, cgal_tetrahedron));
342 "This function requires a version of CGAL greater or equal than 5.5."));
354 std::vector<CGALPoint3>>>
359# if DEAL_II_CGAL_VERSION_GTE(5, 5, 0)
364 std::array<CGALPoint3, 4> pts0;
365 std::array<CGALPoint3, 3> pts1;
367 std::transform(tetrahedron.begin(),
370 &CGALWrappers::dealii_point_to_cgal_point<CGALPoint3, 3>);
372 std::transform(triangle.begin(),
375 &CGALWrappers::dealii_point_to_cgal_point<CGALPoint3, 3>);
377 CGALTetra cgal_tetrahedron{pts0[0], pts0[1], pts0[2], pts0[3]};
379 return convert_boost_to_std(
380 CGAL::intersection(cgal_triangle, cgal_tetrahedron));
386 "This function requires a version of CGAL greater or equal than 5.5."));
394 std::vector<std::array<Point<2>, 3>>
402 const auto intersection_test =
405 if (!intersection_test.empty())
407 const auto &poly = intersection_test[0].outer_boundary();
408 const unsigned int size_poly = poly.size();
414 {{CGALWrappers::cgal_point_to_dealii_point<2>(poly.vertex(0)),
415 CGALWrappers::cgal_point_to_dealii_point<2>(poly.vertex(1)),
416 CGALWrappers::cgal_point_to_dealii_point<2>(
419 else if (size_poly >= 4)
422 std::vector<std::array<Point<2>, 3>> collection;
425 cdt.insert_constraint(poly.vertices_begin(),
433 if (f->info().in_domain() &&
434 CGAL::to_double(cdt.triangle(f).area()) > tol)
436 collection.push_back(
437 {{CGALWrappers::cgal_point_to_dealii_point<2>(
438 cdt.triangle(f).vertex(0)),
439 CGALWrappers::cgal_point_to_dealii_point<2>(
440 cdt.triangle(f).vertex(1)),
441 CGALWrappers::cgal_point_to_dealii_point<2>(
442 cdt.triangle(f).vertex(2))}});
460 std::vector<std::array<Point<2>, 2>>
468 std::array<CGALPoint2, 4> pts;
470 std::transform(quad.begin(),
473 &CGALWrappers::dealii_point_to_cgal_point<CGALPoint2, 2>);
478 CGALWrappers::dealii_point_to_cgal_point<CGALPoint2>(line[0]),
479 CGALWrappers::dealii_point_to_cgal_point<CGALPoint2>(line[1]));
481 cdt.insert_constraint(poly.vertices_begin(), poly.vertices_end(),
true);
482 std::vector<std::array<Point<2>, 2>>
vertices;
486 if (f->info().in_domain() &&
487 CGAL::to_double(cdt.triangle(f).area()) > tol &&
488 CGAL::do_intersect(segm, cdt.triangle(f)))
490 const auto intersection =
491 CGAL::intersection(segm, cdt.triangle(f));
493 boost::get<CGALSegment2>(&*intersection))
496 {{CGALWrappers::cgal_point_to_dealii_point<2>((*s)[0]),
497 CGALWrappers::cgal_point_to_dealii_point<2>((*s)[1])}});
506 std::vector<std::array<Point<3>, 2>>
511# if DEAL_II_CGAL_VERSION_GTE(5, 5, 0)
516 std::array<CGALPoint3_exact, 8> pts;
522 &CGALWrappers::dealii_point_to_cgal_point<CGALPoint3_exact, 3>);
525 CGALWrappers::dealii_point_to_cgal_point<CGALPoint3_exact>(line[0]),
526 CGALWrappers::dealii_point_to_cgal_point<CGALPoint3_exact>(line[1]));
530 std::vector<std::array<Point<3>, 2>>
vertices;
532 cgal_triangulation.insert(pts.begin(), pts.end());
533 for (
const auto &c : cgal_triangulation.finite_cell_handles())
535 const auto &cgal_tetrahedron = cgal_triangulation.tetrahedron(c);
536 if (CGAL::do_intersect(cgal_segment, cgal_tetrahedron))
538 const auto intersection =
539 CGAL::intersection(cgal_segment, cgal_tetrahedron);
541 boost::get<CGALSegment3_exact>(&*intersection))
543 if (s->squared_length() > tol * tol)
546 {{CGALWrappers::cgal_point_to_dealii_point<3>(
548 CGALWrappers::cgal_point_to_dealii_point<3>(
559 "This function requires a version of CGAL greater or equal than 5.5."));
567 std::vector<std::array<Point<3>, 3>>
572# if DEAL_II_CGAL_VERSION_GTE(5, 5, 0)
577 std::array<CGALPoint3_exact, 8> pts_hex;
578 std::array<CGALPoint3_exact, 4> pts_quad;
584 &CGALWrappers::dealii_point_to_cgal_point<CGALPoint3_exact, 3>);
590 &CGALWrappers::dealii_point_to_cgal_point<CGALPoint3_exact, 3>);
593 std::vector<std::array<Point<3>, 3>>
vertices;
595 triangulation_hexa.insert(pts_hex.begin(), pts_hex.end());
599 triangulation_quad.insert(pts_quad.begin(), pts_quad.end());
601 for (
const auto &c : triangulation_hexa.finite_cell_handles())
603 const auto &tet = triangulation_hexa.tetrahedron(c);
605 for (
const auto &f : triangulation_quad.finite_facets())
607 if (CGAL::do_intersect(tet, triangulation_quad.triangle(f)))
609 const auto intersection =
610 CGAL::intersection(triangulation_quad.triangle(f), tet);
613 boost::get<CGALTriangle3_exact>(&*intersection))
615 if (CGAL::to_double(t->squared_area()) > tol * tol)
618 {{cgal_point_to_dealii_point<3>((*t)[0]),
619 cgal_point_to_dealii_point<3>((*t)[1]),
620 cgal_point_to_dealii_point<3>((*t)[2])}});
624 if (
const std::vector<CGALPoint3_exact> *vps =
625 boost::get<std::vector<CGALPoint3_exact>>(
629 tria_inter.insert(vps->begin(), vps->end());
631 for (
auto it = tria_inter.finite_facets_begin();
632 it != tria_inter.finite_facets_end();
635 const auto triangle = tria_inter.triangle(*it);
636 if (CGAL::to_double(triangle.squared_area()) >
639 std::array<Point<3>, 3> verts = {
640 {CGALWrappers::cgal_point_to_dealii_point<3>(
642 CGALWrappers::cgal_point_to_dealii_point<3>(
644 CGALWrappers::cgal_point_to_dealii_point<3>(
660 "This function requires a version of CGAL greater or equal than 5.5."));
668 std::vector<std::array<Point<3>, 4>>
676 std::array<CGALPoint3_exact, 8> pts_hex0;
677 std::array<CGALPoint3_exact, 8> pts_hex1;
683 &CGALWrappers::dealii_point_to_cgal_point<CGALPoint3_exact, 3>);
689 &CGALWrappers::dealii_point_to_cgal_point<CGALPoint3_exact, 3>);
693 std::vector<std::array<Point<3>, 4>>
vertices;
696 tria0.insert(pts_hex0.begin(), pts_hex0.end());
697 tria1.insert(pts_hex1.begin(), pts_hex1.end());
699 for (
const auto &c0 : tria0.finite_cell_handles())
701 const auto &tet0 = tria1.tetrahedron(c0);
702 const auto &tetg0 = CGAL::make_tetrahedron(tet0.vertex(0),
708 for (
const auto &c1 : tria1.finite_cell_handles())
710 const auto &tet1 = tria1.tetrahedron(c1);
711 const auto &tetg1 = CGAL::make_tetrahedron(tet1.vertex(0),
717 namespace PMP = CGAL::Polygon_mesh_processing;
718 const bool test_intersection =
719 PMP::corefine_and_compute_intersection(surf0, surf1, sm);
720 if (PMP::volume(sm) > tol && test_intersection)
724 triangulation_hexa.insert(sm.points().begin(),
726 for (
const auto &c : triangulation_hexa.finite_cell_handles())
728 const auto &tet = triangulation_hexa.tetrahedron(c);
730 {{CGALWrappers::cgal_point_to_dealii_point<3>(
732 CGALWrappers::cgal_point_to_dealii_point<3>(
734 CGALWrappers::cgal_point_to_dealii_point<3>(
736 CGALWrappers::cgal_point_to_dealii_point<3>(
751 template <
int structdim0,
int structdim1,
int spacedim>
752 std::vector<std::array<Point<spacedim>, structdim1 + 1>>
758 const unsigned int n_vertices0 = vertices0.size();
759 const unsigned int n_vertices1 = vertices1.size();
762 n_vertices0 > 0 || n_vertices1 > 0,
764 "The intersection cannot be computed as at least one of the two cells has no vertices."));
766 if constexpr (structdim0 == 2 && structdim1 == 2 && spacedim == 2)
768 if (n_vertices0 == 4 && n_vertices1 == 4)
775 else if constexpr (structdim0 == 2 && structdim1 == 1 && spacedim == 2)
777 if (n_vertices0 == 4 && n_vertices1 == 2)
784 else if constexpr (structdim0 == 3 && structdim1 == 1 && spacedim == 3)
786 if (n_vertices0 == 8 && n_vertices1 == 2)
793 else if constexpr (structdim0 == 3 && structdim1 == 2 && spacedim == 3)
795 if (n_vertices0 == 8 && n_vertices1 == 4)
802 else if constexpr (structdim0 == 3 && structdim1 == 3 && spacedim == 3)
804 if (n_vertices0 == 8 && n_vertices1 == 8)
821 template <
int structdim0,
int structdim1,
int spacedim>
822 std::vector<std::array<Point<spacedim>, structdim1 + 1>>
831 ReferenceCells::get_hypercube<structdim0>().n_vertices(),
834 ReferenceCells::get_hypercube<structdim1>().n_vertices(),
837 const auto &vertices0 =
838 CGALWrappers::get_vertices_in_cgal_order(cell0, mapping0);
839 const auto &vertices1 =
840 CGALWrappers::get_vertices_in_cgal_order(cell1, mapping1);
842 return compute_intersection_of_cells<structdim0, structdim1, spacedim>(
843 vertices0, vertices1, tol);
846# include "intersections.inst"
856template <
int structdim0,
861std::vector<std::array<Point<spacedim>, structdim1 + 1>>
873template <
int structdim0,
int structdim1,
int spacedim>
874std::vector<std::array<Point<spacedim>, structdim1 + 1>>
Abstract base class for mapping classes.
virtual boost::container::small_vector< Point< spacedim >, GeometryInfo< dim >::vertices_per_cell > get_vertices(const typename Triangulation< dim, spacedim >::cell_iterator &cell) const
#define DEAL_II_NAMESPACE_OPEN
#define DEAL_II_NAMESPACE_CLOSE
static ::ExceptionBase & ExcNotImplemented()
#define Assert(cond, exc)
#define AssertDimension(dim1, dim2)
static ::ExceptionBase & ExcNeedsCGAL()
static ::ExceptionBase & ExcMessage(std::string arg1)
#define AssertThrow(cond, exc)
#define DEAL_II_NOT_IMPLEMENTED()
std::vector< std::array< Point< 2 >, 2 > > compute_intersection_quad_line(const ArrayView< const Point< 2 > > &quad, const ArrayView< const Point< 2 > > &line, const double tol)
std::vector< std::array< Point< 3 >, 3 > > compute_intersection_hexa_quad(const ArrayView< const Point< 3 > > &hexa, const ArrayView< const Point< 3 > > &quad, const double tol)
void mark_domains(CDT &ct, Face_handle start, int index, std::list< CDT::Edge > &border)
std::optional< std::variant< CGALPoint3, CGALSegment3 > > compute_intersection_tetra_segment(const ArrayView< const Point< 3 > > &tetrahedron, const ArrayView< const Point< 3 > > &segment)
std::vector< Polygon_with_holes_2 > compute_intersection_rect_rect(const ArrayView< const Point< 2 > > &rectangle0, const ArrayView< const Point< 2 > > &rectangle1)
std::vector< std::array< Point< 3 >, 4 > > compute_intersection_hexa_hexa(const ArrayView< const Point< 3 > > &hexa0, const ArrayView< const Point< 3 > > &hexa1, const double tol)
std::vector< std::array< Point< 3 >, 2 > > compute_intersection_hexa_line(const ArrayView< const Point< 3 > > &hexa, const ArrayView< const Point< 3 > > &line, const double tol)
std::optional< std::variant< CGALPoint3, CGALSegment3, CGALTriangle3, std::vector< CGALPoint3 > > > compute_intersection_tetra_triangle(const ArrayView< const Point< 3 > > &tetrahedron, const ArrayView< const Point< 3 > > &triangle)
std::optional< std::variant< CGALPoint2, CGALSegment2 > > compute_intersection_triangle_segment(const ArrayView< const Point< 2 > > &triangle, const ArrayView< const Point< 2 > > &segment)
std::optional< std::variant< CGALPoint2, CGALSegment2, CGALTriangle2, std::vector< CGALPoint2 > > > compute_intersection_triangle_triangle(const ArrayView< const Point< 2 > > &triangle0, const ArrayView< const Point< 2 > > &triangle1)
std::vector< std::array< Point< 2 >, 3 > > compute_intersection_quad_quad(const ArrayView< const Point< 2 > > &quad0, const ArrayView< const Point< 2 > > &quad1, const double tol)
K::Tetrahedron_3 CGALTetra
CGAL::Surface_mesh< K_exact::Point_3 > Surface_mesh
K::Segment_2 CGALSegment2
CGAL::Exact_predicates_tag Itag
K_exact::Tetrahedron_3 CGALTetra_exact
K_exact::Triangle_3 CGALTriangle3_exact
CDT::Vertex_handle Vertex_handle
K::Triangle_3 CGALTriangle3
K::Segment_3 CGALSegment3
CDT::Face_handle Face_handle
CGAL::Triangulation_3< K_exact > Triangulation3_exact
CGAL::Constrained_Delaunay_triangulation_2< K, Tds, Itag > CDT
std::vector< std::array< Point< spacedim >, structdim1+1 > > compute_intersection_of_cells(const typename Triangulation< structdim0, spacedim >::cell_iterator &cell0, const typename Triangulation< structdim1, spacedim >::cell_iterator &cell1, const Mapping< structdim0, spacedim > &mapping0, const Mapping< structdim1, spacedim > &mapping1, const double tol=1e-9)
CGAL::Delaunay_mesh_size_criteria_2< CDT > Criteria
CGAL::Triangulation_vertex_base_2< K > Vb
CGAL::Polygon_with_holes_2< K > Polygon_with_holes_2
CGAL::Triangulation_data_structure_2< Vb, Fb > Tds
CGAL::Polygon_2< K > CGALPolygon
CGAL::Triangulation_2< K > Triangulation2
CGAL::Exact_predicates_exact_constructions_kernel K_exact
CGAL::Triangulation_3< K > Triangulation3
CGAL::Constrained_triangulation_face_base_2< K, Fbb > CFb
CGAL::Exact_predicates_exact_constructions_kernel_with_sqrt K
K::Triangle_2 CGALTriangle2
CGAL::Delaunay_mesh_face_base_2< K, CFb > Fb
K_exact::Segment_3 CGALSegment3_exact
K_exact::Point_3 CGALPoint3_exact
CGAL::Triangulation_face_base_with_info_2< FaceInfo2, K > Fbb