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// Copyright (c) 2025 GeometryFactory (France). // All rights reserved. // // This file is part of CGAL (www.cgal.org). // // $URL: https://github.com/CGAL/cgal/blob/v6.1/Poisson_surface_reconstruction_3/include/CGAL/Poisson_mesh_domain_3.h $ // $Id: include/CGAL/Poisson_mesh_domain_3.h b26b07a1242 $ // SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial // // Author(s) : Sven Oesau #ifndef CGAL_POISSON_MESH_DOMAIN_3_H #define CGAL_POISSON_MESH_DOMAIN_3_H #include #include #include namespace CGAL { /*! \ingroup PkgPoissonSurfaceReconstruction3Ref \brief The class `Poisson_mesh_domain_3` derives from `Labeled_mesh_domain_3` for the handling of `Poisson_reconstruction_function`. This class has a constructor taking a labeling function. It has also a static template member function that acts as named constructor:
  • `create_Poisson_mesh_domain()`
    • , to create a domain from a `Poisson_reconstruction_function`
\tparam BGT is a geometric traits class that provides the basic operations to implement intersection tests and intersection computations through a bisection method. This parameter must be instantiated with a model of the concept `BisectionGeometricTraits_3`. \cgalModels{MeshDomain_3} \sa `CGAL::Labeled_mesh_domain_3` \sa `CGAL::make_mesh_3()` */ template class Poisson_mesh_domain_3 #ifndef DOXYGEN_RUNNING : public Labeled_mesh_domain_3 #endif { public: using Base = Labeled_mesh_domain_3; typedef typename Base::Subdomain Subdomain; typedef typename Base::Subdomain_index Subdomain_index; typedef typename Base::Surface_patch_index Surface_patch_index; typedef typename Base::Intersection Intersection; // Type of indexes for cells of the input complex typedef std::optional Surface_patch; // Type of indexes to characterize the lowest dimensional face of the input // complex on which a vertex lie typedef typename CGAL::Mesh_3::internal::Index_generator::Index Index; // Geometric object types #ifdef DOXYGEN_RUNNING /// \name Types imported from the geometric traits class ///@{ /// The point type of the geometric traits class typedef typename Geom_traits::Point_3 Point_3; /// The sphere type of the geometric traits class typedef typename Geom_traits::Sphere_3 Sphere_3; /// The iso-cuboid type of the geometric traits class typedef typename Geom_traits::Iso_cuboid_3 Iso_cuboid_3; /// The bounding box type typedef CGAL::Bbox_3 Bbox_3; /// The number type (a field type) of the geometric traits class typedef typename Geom_traits::FT FT; /// The ray type of the geometric traits class typedef typename Geom_traits::Ray_3 Ray_3; /// The line type of the geometric traits class typedef typename Geom_traits::Line_3 Line_3; /// The segment type of the geometric traits class typedef typename Geom_traits::Segment_3 Segment_3; /// The Poisson function type typedef CGAL::Poisson_reconstruction_function Function; ///@} #else /// The point type of the geometric traits class typedef typename BGT::Point_3 Point_3; /// The sphere type of the geometric traits class typedef typename BGT::Sphere_3 Sphere_3; /// The iso-cuboid type of the geometric traits class typedef typename BGT::Iso_cuboid_3 Iso_cuboid_3; /// The bounding box type typedef CGAL::Bbox_3 Bbox_3; /// The number type (a field type) of the geometric traits class typedef typename BGT::FT FT; /// The ray type of the geometric traits class typedef typename BGT::Ray_3 Ray_3; /// The line type of the geometric traits class typedef typename BGT::Line_3 Line_3; /// The segment type of the geometric traits class typedef typename BGT::Segment_3 Segment_3; /// The Poisson function type typedef CGAL::Poisson_reconstruction_function Function; #endif Function poisson_function; /// \name Creation /// @{ /*! \brief Construction from a function, a bounding object and a relative error bound. * * \tparam Bounding_object either a bounding sphere (of type `Sphere_3`), a bounding box (type `Bbox_3`), * or a bounding `Iso_cuboid_3` * \tparam NamedParameters a sequence of \ref bgl_namedparameters "Named Parameters" * * \param function the Poisson reconstruction function * \param bounding_object the bounding object bounding the meshable space. * \param np an optional sequence of \ref bgl_namedparameters "Named Parameters" among the ones listed below: * * \cgalNamedParamsBegin * \cgalParamNBegin{relative_error_bound} * \cgalParamDescription{the relative error bound used to compute intersection points between the implicit surface and query segments. * The bisection is stopped when the length of the intersected segment is less than the product * of `relative_error_bound` by the diameter of the bounding object.} * \cgalParamDefault{FT(1e-3)} * \cgalParamNEnd * \cgalNamedParamsEnd */ template Poisson_mesh_domain_3(const Function& function, const Bounding_object& bounding_object, const CGAL_NP_CLASS& np = parameters::default_values() #ifndef DOXYGEN_RUNNING , typename std::enable_if>::type* = nullptr #endif // DOXYGEN_RUNNING ) : Base(make_implicit_to_labeling_function_wrapper(function), bounding_object, np), poisson_function(function) {} /*! \brief Construction from a function, a bounding object and a relative error bound. * * \tparam NamedParameters a sequence of \ref bgl_namedparameters "Named Parameters" * * \param function the Poisson reconstruction function * \param np an optional sequence of \ref bgl_namedparameters "Named Parameters" among the ones listed below: * * \cgalNamedParamsBegin * \cgalParamNBegin{relative_error_bound} * \cgalParamDescription{the relative error bound used to compute intersection points between the implicit surface and query segments. * The bisection is stopped when the length of the intersected segment is less than the product * of `relative_error_bound` by the diameter of the bounding object.} * \cgalParamDefault{FT(1e-3)} * \cgalParamNEnd * \cgalNamedParamsEnd */ template Poisson_mesh_domain_3(const Function & function, const CGAL_NP_CLASS& np = parameters::default_values() #ifndef DOXYGEN_RUNNING , typename std::enable_if>::type * = nullptr #endif // DOXYGEN_RUNNING ) : Base(make_implicit_to_labeling_function_wrapper(function), function.bounding_sphere(), np), poisson_function(function) {} ///@} #ifndef DOXYGEN_RUNNING template Poisson_mesh_domain_3(const CGAL_NP_CLASS& np) : Base(np) {} // Overload handling parameters passed with operator= template Poisson_mesh_domain_3(const Function& function, const CGAL_NP_CLASS_1& np1, const CGAL_NP_CLASS_2& np2, const NP& ... nps) : Base(internal_np::combine_named_parameters( CGAL::parameters::function(make_implicit_to_labeling_function_wrapper(function)), np1, np2, nps...)), poisson_function(function) {} #endif /// \name Creation of domains from Poisson implicit functions /// @{ /*! \brief Construction from a Poisson implicit function * * This static method is a named constructor. It constructs a domain * whose bounding surface is described implicitly as the zero level set of a * function. The domain to be discretized is assumed to be the domain where * the function has negative values. * * \tparam NamedParameters a sequence of \ref bgl_namedparameters "Named Parameters" * \tparam Bounding_object either a bounding sphere (of type `Sphere_3`), a bounding box (type `Bbox_3`), * or a bounding `Iso_cuboid_3` which is required to circumscribe * the surface and to have its center inside the domain. * * \param function the Poisson reconstruction function * \param bounding_object object bounding the meshable domain and its center is inside the domain. * \param np an optional sequence of \ref bgl_namedparameters "Named Parameters" among the ones listed below: * * \cgalNamedParamsBegin * \cgalParamNBegin{relative_error_bound} * \cgalParamDescription{ is the relative error * bound, relative to the diameter of the box of the image.} * \cgalParamDefault{FT(1e-3)} * \cgalParamNEnd * \cgalNamedParamsEnd * */ template static Poisson_mesh_domain_3 create_Poisson_mesh_domain(const Function& function, const Bounding_object& bounding_object, const CGAL_NP_CLASS& np = parameters::default_values() #ifndef DOXYGEN_RUNNING ,typename std::enable_if>::type* = nullptr #endif ) { using parameters::get_parameter; using parameters::choose_parameter; FT relative_error_bound_ = choose_parameter(get_parameter(np, internal_np::error_bound), FT(1e-3)); CGAL::Random* p_rng_ = choose_parameter(get_parameter(np, internal_np::rng), nullptr); auto null_subdomain_index_ = choose_parameter(get_parameter(np, internal_np::null_subdomain_index_param), Null_functor()); auto construct_surface_patch_index_ = choose_parameter(get_parameter(np, internal_np::surface_patch_index), Null_functor()); return Poisson_mesh_domain_3(function, bounding_object, CGAL::parameters::relative_error_bound(relative_error_bound_) .function(make_implicit_to_labeling_function_wrapper(function)) .p_rng(p_rng_) .null_subdomain_index(Base::create_null_subdomain_index(null_subdomain_index_)) .construct_surface_patch_index(Base::create_construct_surface_patch_index(construct_surface_patch_index_))); } /// @} #ifndef DOXYGEN_RUNNING template static Poisson_mesh_domain_3 create_Poisson_mesh_domain(const CGAL_NP_CLASS& np) { using parameters::get_parameter; static_assert(!parameters::is_default_parameter::value, "Value for required parameter not found"); static_assert(!parameters::is_default_parameter::value, "Value for required parameter not found"); return create_Poisson_mesh_domain(get_parameter(np, internal_np::function_param), get_parameter(np, internal_np::bounding_object_param), np); } // Overload handling parameters passed with operator= template static Poisson_mesh_domain_3 create_Poisson_mesh_domain(const CGAL_NP_CLASS_1& np1, const CGAL_NP_CLASS_2& np2, const NP& ... nps) { return create_Poisson_mesh_domain(internal_np::combine_named_parameters(np1, np2, nps...)); } #endif /* * Returns a point in the intersection of the primitive `type` * with some boundary surface. * `Type` is either `Segment_3`, `Ray_3` or `Line_3`. */ struct Construct_intersection { Construct_intersection(const Poisson_mesh_domain_3& domain) : domain_(domain) {} Intersection operator()(const Segment_3& s) const { #ifndef CGAL_MESH_3_NO_LONGER_CALLS_DO_INTERSECT_3 CGAL_precondition(r_domain_.do_intersect_surface_object()(s) != std::nullopt); #endif // NOT CGAL_MESH_3_NO_LONGER_CALLS_DO_INTERSECT_3 return this->operator()(s.source(), s.target()); } Intersection operator()(const Ray_3& r) const { return clip_to_segment(r); } Intersection operator()(const Line_3& l) const { return clip_to_segment(l); } private: /* * Returns a point in the intersection of `[a,b]` with the surface * `a` must be the source point, and `b` the out point. It is important * because it drives bisection cuts. * Indeed, the returned point is the first intersection of `[a,b]` * with a subdomain surface. * * The difference from the Labeled_mesh_domain_3::Construct_intersection is that * the underlying Delaunay triangulation in the Poisson function is used for the bisection. */ Intersection operator()(const Point_3& a, const Point_3& b) const { // Functors typename BGT::Compute_squared_distance_3 squared_distance = BGT().compute_squared_distance_3_object(); typename BGT::Construct_midpoint_3 midpoint = BGT().construct_midpoint_3_object(); // Non const points Point_3 p1 = a; Point_3 p2 = b; Point_3 mid = midpoint(p1, p2); FT value_at_p1, value_at_p2; typename Function::Cell_handle c1, c2; bool c1_is_inf, c2_is_inf; std::tie(value_at_p1, c1, c1_is_inf) = domain_.poisson_function.special_func(p1); std::tie(value_at_p2, c2, c2_is_inf) = domain_.poisson_function.special_func(p2); Subdomain_index label_at_p1 = (value_at_p1 < 0) ? 1 : 0; Subdomain_index label_at_p2 = (value_at_p2 < 0) ? 1 : 0; // If both extremities are in the same subdomain, // there is no intersection. // Should only be able to happen during initial point generation. if(label_at_p1 == label_at_p2) return Intersection(); // Else lets find a point (by bisection) // Bisection ends when the point is nearer from surface than the error bound while(true) { if(c1 == c2) { if(c1_is_inf) { std::cout << "Intersection(): c1 == c2 and inf!" << std::endl; return Intersection(); } else { const Surface_patch_index sp_index = domain_.make_surface_index(label_at_p1, label_at_p2); const Index index = domain_.index_from_surface_patch_index(sp_index); return Intersection(Point_3(ORIGIN + ((value_at_p2 * (p1 - ORIGIN)) - (value_at_p1 * (p2 - ORIGIN))) / (value_at_p2 - value_at_p1)), index, 2); } } mid = midpoint(p1, p2); // If the two points are enough close, then we return midpoint if ( squared_distance(p1, p2) < domain_.squared_error_bound_ ) { CGAL_assertion(value_at_p1 * value_at_p2 <= 0); const Surface_patch_index sp_index = domain_.make_surface_index(label_at_p1, label_at_p2); const Index index = domain_.index_from_surface_patch_index(sp_index); return Intersection(mid, index, 2); } // Cannot be const: those values are modified below. FT value_at_mid; typename Function::Cell_handle c_at_mid; bool c_is_inf; std::tie(value_at_mid, c_at_mid, c_is_inf) = domain_.poisson_function.special_func(mid); Subdomain_index label_at_mid = (value_at_mid < 0) ? 1 : 0; // Else we must go on // Here we consider that p1(a) is the source point. Thus, we keep p1 and // change p2 if f(p1)!=f(p2). // That allows us to find the first intersection from a of [a,b] with // a surface. if(label_at_p1 != label_at_mid && !(domain_.null(label_at_p1) && domain_.null(label_at_mid))) { p2 = mid; value_at_p2 = value_at_mid; label_at_p2 = label_at_mid; } else { p1 = mid; value_at_p1 = value_at_mid; label_at_p1 = label_at_mid; } } } // Clips `query` to a segment `s`, and call `operator()(s)` template Intersection clip_to_segment(const Query& query) const { const auto clipped = CGAL::intersection(query, domain_.bbox_); if (clipped) if (const Segment_3* s = std::get_if(&*clipped)) return this->operator()(*s); return Intersection(); } const Poisson_mesh_domain_3& domain_; }; // Returns Construct_intersection object Construct_intersection construct_intersection_object() const { return Construct_intersection(*this); } }; // end class Poisson_mesh_domain_3 } // end namespace CGAL #endif // CGAL_LABELED_MESH_DOMAIN_3_H