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// Copyright (c) 2013 INRIA Sophia-Antipolis (France), // 2014-2015 GeometryFactory (France). // All rights reserved. // // This file is part of CGAL (www.cgal.org). // // $URL: https://github.com/CGAL/cgal/blob/v6.1/Mesh_2/include/CGAL/Mesh_2/Lloyd_move_2.h $ // $Id: include/CGAL/Mesh_2/Lloyd_move_2.h b26b07a1242 $ // SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial // // Author(s) : Jane Tournois, Raul Gallegos, Pierre Alliez // #ifndef CGAL_LLOYD_MOVE_2_H #define CGAL_LLOYD_MOVE_2_H #include #include #include namespace CGAL { namespace Mesh_2 { template > class Lloyd_move_2 { typedef typename CDT::Vertex_handle Vertex_handle; typedef typename CDT::Geom_traits::Point_2 Point_2; typedef typename CDT::Geom_traits::Segment_2 Segment; typedef typename CDT::Geom_traits::Triangle_2 Triangle; typedef typename CDT::Geom_traits::FT FT; typedef typename CDT::Geom_traits::Vector_2 Vector_2; typedef typename CGAL::Constrained_voronoi_diagram_2 CVD; typedef typename CVD::Cvd_cell Cvd_cell; public: typedef SizingField Sizing_field; public: Vector_2 operator()(Vertex_handle v, const CDT& cdt, const Sizing_field& sizing_field = Sizing_field()) const { if(cdt.are_there_incident_constraints(v)) return CGAL::NULL_VECTOR; Point_2 p = v->point(); Vector_2 move = CGAL::NULL_VECTOR; FT sum_masses(0); Cvd_cell cell = CGAL::dual(cdt, v); if(cell.is_infinite() || cell.is_empty()) return CGAL::NULL_VECTOR; //center of mass is at infinity! CGAL_assertion(cell.number_of_vertices() > 2); typename Cvd_cell::segment_iterator sit = cell.segments_begin(); typename CDT::Geom_traits::Compute_area_2 compute_area = cdt.geom_traits().compute_area_2_object(); for( ; sit != cell.segments_end(); ++sit) { Segment s = *sit; Triangle tri(p, s.source(), s.target()); Point_2 tri_centroid = CGAL::centroid(tri); // Compute mass FT density = density_2d(tri_centroid, sizing_field); FT abs_area = CGAL::abs(compute_area(tri[0], tri[1], tri[2])); FT mass = abs_area * density; move = move + mass * Vector_2(p, tri_centroid); sum_masses += mass; } CGAL_assertion(sum_masses != 0.0); return move / sum_masses; } private: FT density_2d(const Point_2& p, const Sizing_field& sizing_field) const { FT s = sizing_field(p); CGAL_assertion( s > 0. ); // 1 / s^(d+2) return ( 1/(s*s*s*s) ); } #ifdef CGAL_MESH_2_OPTIMIZER_VERBOSE public: static std::string name() { return std::string("Lloyd"); } #endif }; } //end namespace Mesh_2 } //end namespace CGAL #endif //CGAL_LLOYD_MOVE_2_H