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// Copyright (c) 2006-2009 INRIA Sophia-Antipolis (France). // Copyright (c) 2011 GeometryFactory Sarl (France) // All rights reserved. // // This file is part of CGAL (www.cgal.org). // // $URL: https://github.com/CGAL/cgal/blob/v6.1/Mesh_3/include/CGAL/Mesh_triangulation_3.h $ // $Id: include/CGAL/Mesh_triangulation_3.h b26b07a1242 $ // SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial // // // Author(s) : Laurent Rineau, Stephane Tayeb #ifndef CGAL_MESH_TRIANGULATION_3_H #define CGAL_MESH_TRIANGULATION_3_H #include #include #include #include #include #include #include #include #include namespace CGAL { namespace details { template struct Mesh_geom_traits_generator { private: typedef Robust_weighted_circumcenter_filtered_traits_3 Geom_traits; public: typedef Geom_traits type; typedef type Type; }; // end struct Mesh_geom_traits_generator } // end namespace details template class Mesh_3_regular_triangulation_3_wrapper : public Regular_triangulation_3 { public: typedef Regular_triangulation_3 Base; typedef typename Base::Geom_traits Geom_traits; typedef typename Geom_traits::FT FT; typedef typename Base::Bare_point Bare_point; typedef typename Base::Weighted_point Weighted_point; typedef typename Base::Triangle Triangle; typedef typename Base::Vertex_handle Vertex_handle; typedef typename Base::Facet Facet; typedef typename Base::Cell_handle Cell_handle; typedef typename Geom_traits::Vector_3 Vector; using Base::geom_traits; using Base::point; using Base::triangle; static std::string io_signature() { return Get_io_signature()(); } // The undocumented, straightforward functions below are required for Mesh_3 // because of Periodic_3_mesh_3: they are functions for which both triangulations // have fundamentally different implementations (usually, Periodic_3_mesh_3 // does not know the offset of a point and must brute-force check for all // possibilities). To enable Periodic_3_mesh_3 to use Mesh_3's files, // each mesh triangulation implements its own version. const Bare_point& get_closest_point(const Bare_point& /*p*/, const Bare_point& q) const { return q; } Triangle get_incident_triangle(const Facet& f, const Vertex_handle) const { return triangle(f); } void set_point(const Vertex_handle v, const Vector& /*move*/, const Weighted_point& new_position) { v->set_point(new_position); } FT compute_power_distance_to_power_sphere(const Cell_handle c, const Vertex_handle v) const { typedef typename Geom_traits::Compute_power_distance_to_power_sphere_3 Critical_radius; Critical_radius critical_radius = geom_traits().compute_power_distance_to_power_sphere_3_object(); return critical_radius(point(c, 0), point(c, 1), point(c, 2), point(c, 3), point(v)); } // \pre c->neighbor(i) is finite FT compute_power_distance_to_power_sphere(const Cell_handle c, const int i) const { Cell_handle nc = c->neighbor(i); CGAL_precondition(!this->is_infinite(nc)); Vertex_handle v = nc->vertex(nc->index(c)); return compute_power_distance_to_power_sphere(c, v); } typename Geom_traits::FT min_squared_distance(const Bare_point& p, const Bare_point& q) const { return geom_traits().compute_squared_distance_3_object()(p, q); } }; /*! \ingroup PkgMesh3MeshClasses The class `Mesh_triangulation_3` is a class template which provides the triangulation type to be used for the 3D triangulation embedding the mesh. \tparam MD must be a model of `MeshDomain_3`. \tparam GT must be a model of `MeshTriangulationTraits_3` or `Default` and defaults to `Kernel_traits::%Kernel`. \tparam ConcurrencyTag enables sequential versus parallel meshing and optimization algorithms. Possible values are `Sequential_tag` (the default), `Parallel_tag`, and `Parallel_if_available_tag`. \tparam VertexBase must be a model of `MeshVertexBase_3` or `Default` and defaults to `Mesh_vertex_base_3`. \tparam CellBase must be a model of `MeshCellBase_3` or `Default` and defaults to `Compact_mesh_cell_base_3`. \warning To improve the robustness of the meshing process, the input traits `GT` is wrapped with the traits class `Robust_weighted_circumcenter_filtered_traits_3`. The class `Robust_weighted_circumcenter_filtered_traits_3` upgrades the functors models of `Kernel::ConstructWeightedCircumcenter_3`, `Kernel::ComputeSquaredRadius_3`, and `Kernel::ComputeSquaredRadiusSmallestOrthogonalSphere_3` that are provided by `GT` to use exact computations when the geometric configuration is close to degenerate (e.g. almost coplanar points).

Users should therefore be aware that the traits class of the triangulation will have type `Robust_weighted_circumcenter_filtered_traits_3`. \sa `make_mesh_3()` \sa `Mesh_complex_3_in_triangulation_3` */ template struct Mesh_triangulation_3 { private: using K = typename Default::Lazy_get >::type; using Geom_traits = typename details::Mesh_geom_traits_generator::type; using Indices_tuple = Mesh_3::internal::Indices_tuple_t; using Vertex_base = typename Default::Get< VertexBase, Mesh_vertex_generator_3 >::type; using Cell_base = typename Default::Get< CellBase, Compact_mesh_cell_generator_3 >::type; using Concurrency_tag = typename Default::Get::type; struct Tds : public Triangulation_data_structure_3 {}; using Triangulation = Mesh_3_regular_triangulation_3_wrapper; public: #ifndef DOXYGEN_RUNNING using type = Triangulation; using Type = type; #else /// \name Types /// @{ /*! The triangulation type to be used for the 3D triangulation embedding the mesh. This type is a wrapper around the type `CGAL::Regular_triangulation_3`, whose vertex and cell base classes are respectively `VertexBase` and `CellBase`. */ typedef unspecified_type type; /// @} #endif // DOXYGEN_RUNNING }; } // end namespace CGAL #include #endif // CGAL_MESH_TRIANGULATION_3_H