// Copyright (c) 2005 INRIA (France). // All rights reserved. // // This file is part of CGAL (www.cgal.org). // You can redistribute it and/or modify it under the terms of the GNU // General Public License as published by the Free Software Foundation, // either version 3 of the License, or (at your option) any later version. // // Licensees holding a valid commercial license may use this file in // accordance with the commercial license agreement provided with the software. // // This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE // WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. // // $URL$ // $Id$ // // // Author(s) : Laurent Saboret, Pierre Alliez, Bruno Levy #ifndef CGAL_BARYCENTRIC_MAPPING_PARAMETERIZER_3_H #define CGAL_BARYCENTRIC_MAPPING_PARAMETERIZER_3_H #include #include #include /// \file Barycentric_mapping_parameterizer_3.h namespace CGAL { /// \ingroup PkgSurfaceParameterizationMethods /// /// The class Barycentric_mapping_parameterizer_3 implements Tutte Barycentric Mapping algorithm \cgalCite{t-hdg-63}. /// This algorithm is also called Tutte Uniform Weights by other authors. /// /// One-to-one mapping is guaranteed if the surface's border is mapped to a convex polygon. /// /// This class is used by the main /// parameterization algorithm Fixed_border_parameterizer_3::parameterize(). /// - It provides default BorderParameterizer_3 and SparseLinearAlgebraTraits_d template /// parameters that make sense. /// - It implements compute_w_ij() to compute `w_ij = (i,j)` coefficient of matrix A /// for `j` neighbor vertex of `i` based on Tutte Barycentric Mapping method. /// - It implements an optimized version of is_one_to_one_mapping(). /// /// \cgalModels `ParameterizerTraits_3` /// /// /// \tparam ParameterizationMesh_3 3D surface mesh. /// \tparam BorderParameterizer_3 Strategy to parameterize the surface border. /// \tparam SparseLinearAlgebraTraits_d Traits class to solve a sparse linear system. /// Note: the system is *not* symmetric because `Fixed_border_parameterizer_3` /// does not remove (yet) border vertices from the system. /*! \sa `CGAL::Parameterizer_traits_3` \sa `CGAL::Fixed_border_parameterizer_3` \sa `CGAL::Discrete_authalic_parameterizer_3` \sa `CGAL::Discrete_conformal_map_parameterizer_3` \sa `CGAL::LSCM_parameterizer_3` \sa `CGAL::Mean_value_coordinates_parameterizer_3` */ template < class ParameterizationMesh_3, class BorderParameterizer_3 = Circular_border_arc_length_parameterizer_3, class SparseLinearAlgebraTraits_d = Eigen_solver_traits::EigenType, Eigen::IncompleteLUT< double > > > > class Barycentric_mapping_parameterizer_3 : public Fixed_border_parameterizer_3 { // Private types private: // Superclass typedef Fixed_border_parameterizer_3 Base; // Public types public: // We have to repeat the types exported by superclass /// @cond SKIP_IN_MANUAL typedef typename Base::Error_code Error_code; typedef ParameterizationMesh_3 Adaptor; typedef BorderParameterizer_3 Border_param; typedef SparseLinearAlgebraTraits_d Sparse_LA; /// @endcond // Private types private: // Mesh_Adaptor_3 subtypes: typedef typename Adaptor::NT NT; typedef typename Adaptor::Point_2 Point_2; typedef typename Adaptor::Point_3 Point_3; typedef typename Adaptor::Vector_2 Vector_2; typedef typename Adaptor::Vector_3 Vector_3; typedef typename Adaptor::Facet Facet; typedef typename Adaptor::Facet_handle Facet_handle; typedef typename Adaptor::Facet_const_handle Facet_const_handle; typedef typename Adaptor::Facet_iterator Facet_iterator; typedef typename Adaptor::Facet_const_iterator Facet_const_iterator; typedef typename Adaptor::Vertex Vertex; typedef typename Adaptor::Vertex_handle Vertex_handle; typedef typename Adaptor::Vertex_const_handle Vertex_const_handle; typedef typename Adaptor::Vertex_iterator Vertex_iterator; typedef typename Adaptor::Vertex_const_iterator Vertex_const_iterator; typedef typename Adaptor::Border_vertex_iterator Border_vertex_iterator; typedef typename Adaptor::Border_vertex_const_iterator Border_vertex_const_iterator; typedef typename Adaptor::Vertex_around_facet_circulator Vertex_around_facet_circulator; typedef typename Adaptor::Vertex_around_facet_const_circulator Vertex_around_facet_const_circulator; typedef typename Adaptor::Vertex_around_vertex_circulator Vertex_around_vertex_circulator; typedef typename Adaptor::Vertex_around_vertex_const_circulator Vertex_around_vertex_const_circulator; // SparseLinearAlgebraTraits_d subtypes: typedef typename Sparse_LA::Vector Vector; typedef typename Sparse_LA::Matrix Matrix; // Public operations public: /// Constructor Barycentric_mapping_parameterizer_3(Border_param border_param = Border_param(), ///< object that maps the surface's border to 2D space. Sparse_LA sparse_la = Sparse_LA()) ///< Traits object to access a sparse linear system. : Fixed_border_parameterizer_3(border_param, sparse_la) {} // Default copy constructor and operator =() are fine // Protected operations protected: /// Compute w_ij = (i,j) coefficient of matrix A for j neighbor vertex of i. virtual NT compute_w_ij(const Adaptor& /* mesh */, Vertex_const_handle /* main_vertex_v_i */, Vertex_around_vertex_const_circulator /* neighbor_vertex_v_j */ ) { /// Tutte Barycentric Mapping algorithm is the most simple one: /// w_ij = 1 for j neighbor vertex of i. return 1; } /// Check if 3D -> 2D mapping is one-to-one. virtual bool is_one_to_one_mapping (const Adaptor& /* mesh */, const Matrix& /* A */, const Vector& /* Bu */, const Vector& /* Bv */) { /// Theorem: one-to-one mapping is guaranteed if all w_ij coefficients /// are > 0 (for j vertex neighbor of i) and if the surface /// border is mapped onto a 2D convex polygon. /// All w_ij coefficients = 1 (for j vertex neighbor of i), thus mapping /// is guaranteed if the surface border is mapped onto a 2D convex polygon. return Base::get_border_parameterizer().is_border_convex (); } }; } //namespace CGAL #endif //CGAL_BARYCENTRIC_MAPPING_PARAMETERIZER_3_H