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// Copyright (c) 2009 INRIA Sophia-Antipolis (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/lloyd_optimize_mesh_3.h $ // $Id: include/CGAL/lloyd_optimize_mesh_3.h b26b07a1242 $ // SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial // // // Author(s) : Stephane Tayeb // //****************************************************************************** // File Description : lloyd_optimize_mesh_3 function definition. //****************************************************************************** #ifndef CGAL_LLOYD_OPTIMIZE_MESH_3_H #define CGAL_LLOYD_OPTIMIZE_MESH_3_H #include #include #include #include #include #include #include #include namespace CGAL { /*! * \ingroup PkgMesh3Functions * * The function `lloyd_optimize_mesh_3()` is a mesh optimization process * based on the minimization of a global energy function. * * In `lloyd_optimize_mesh_3()`, the minimized global energy may be interpreted * as the \f$ L^1\f$-norm of the error achieved * when the function \f$ x^2\f$ is interpolated on the mesh domain * using a piecewise linear function which is linear * in each cell of the Voronoi diagram of the mesh vertices. * * The optimizer `lloyd_optimize_mesh_3()` works in iterative steps. * At each iteration, mesh vertices are moved into * positions that bring to zero the energy gradient * and the Delaunay triangulation is updated. * Vertices on the mesh boundaries are handled * in a special way so as to preserve an accurate * representation of the domain boundaries. * * \tparam C3T3 a model of the concept `MeshComplex_3InTriangulation_3`. * \tparam MD a model of the concept `MeshDomain_3`. * \tparam NamedParameters a sequence of \ref bgl_namedparameters "Named Parameters" * * @param c3t3 the initial mesh that will be modified by the algorithm to represent the final optimized mesh. * @param domain the domain used to create the `c3t3` parameter * @param np an optional sequence of \ref bgl_namedparameters "Named Parameters" among the ones listed below: * * \cgalNamedParamsBegin * \cgalParamNBegin{time_limit} * \cgalParamDescription{to set up, in seconds, a CPU time limit after which the optimization process is stopped. * This time is measured using `CGAL::Real_timer`. 0 means that there is no time limit.} * \cgalParamType{`double`} * \cgalParamPrecondition{`time_limit >= 0`} * \cgalParamDefault{0} * \cgalParamNEnd * \cgalParamNBegin{max_iteration_number} * \cgalParamDescription{limit on the number of performed iterations. 0 means that there is * no limit on the number of performed iterations.} * \cgalParamPrecondition{`max_iteration_number >=0`} * \cgalParamType{`int`} * \cgalParamDefault{0} * \cgalParamNEnd * \cgalParamNBegin{freeze_bound} * \cgalParamDescription{designed to reduce running time of each optimization iteration. * Any vertex that has a displacement less than a given fraction of the length * of its shortest incident edge, is frozen (i.e.\ is not relocated). * The parameter `freeze_bound` gives the threshold ratio. * If it is set to 0, freezing of vertices is disabled.} * \cgalParamPrecondition{`0<= freeze_bound <=1`} * \cgalParamType{`double`} * \cgalParamDefault{0.01} * \cgalParamNEnd * \cgalParamNBegin{convergence} * \cgalParamDescription{threshold ratio of stopping criterion based on convergence: the optimization process is stopped * when at the last iteration the displacement of any vertex is less than * a given fraction of the length of the shortest edge incident to that vertex.} * \cgalParamPrecondition{`0 <=convergence <= 1`} * \cgalParamType{`double`} * \cgalParamDefault{0.02} * \cgalParamNEnd * \cgalParamNBegin{do_freeze} * \cgalParamDescription{completes the `freeze_bound` parameter. If it is set to `true` (default value), * frozen vertices will not move anymore in next iterations. Otherwise, at each iteration, any vertex that * moves, unfreezes all its incident vertices.} * \cgalParamType{`bool`} * \cgalParamDefault{true} * \cgalParamNEnd * \cgalNamedParamsEnd * * \return a value of type `CGAL::Mesh_optimization_return_code` which is: *
    *
  • `CGAL::TIME_LIMIT_REACHED` when the time limit is reached. *
  • `CGAL::MAX_ITERATION_NUMBER_REACHED` when `lloyd_optimize_mesh_3()` stops because it has performed `max_iteration_number` iterations. *
  • `CGAL::CONVERGENCE_REACHED` when `lloyd_optimize_mesh_3()` stops because the convergence criterion * is achieved. *
  • `CGAL::ALL_VERTICES_FROZEN` when all vertices have been frozen, when the * `do_freeze` parameter is set to true. *
  • `CGAL::CANT_IMPROVE_ANYMORE` when `lloyd_optimize_mesh_3()` stops because * most vertices have been frozen, and no better convergence can be reached. *
* * \cgalHeading{Example} * * * \code{.cpp} * // Lloyd-smoothing until convergence reaches 0.01, freezing vertices which * // move less than 0.001*shortest_incident_edge_length * lloyd_optimize_mesh_3(c3t3, * domain, * parameters::convergence(0.01). * parameters::freeze_bound(0.001). * parameters::do_freeze(true)); * * \endcode * * \sa `CGAL::Mesh_optimization_return_code` * \sa `CGAL::make_mesh_3()` * \sa `CGAL::refine_mesh_3()` * \sa `CGAL::exude_mesh_3()` * \sa `CGAL::perturb_mesh_3()` * \sa `CGAL::odt_optimize_mesh_3()` * * \note This function requires the \ref thirdpartyEigen library. */ template Mesh_optimization_return_code lloyd_optimize_mesh_3(C3T3& c3t3, const MeshDomain& domain,const CGAL_NP_CLASS& np = parameters::default_values()) { using parameters::choose_parameter; using parameters::get_parameter; std::size_t max_iterations = choose_parameter(get_parameter(np, internal_np::number_of_iterations), 0); const double convergence_ratio = choose_parameter(get_parameter(np, internal_np::convergence_ratio), parameters::default_values_for_mesh_3::lloyd_convergence_ratio); const double freeze_bound = choose_parameter(get_parameter(np, internal_np::vertex_freeze_bound), parameters::default_values_for_mesh_3::lloyd_freeze_ratio); const double time_limit = choose_parameter(get_parameter(np, internal_np::maximum_running_time), parameters::default_values_for_mesh_3::time_limit); bool do_freeze = choose_parameter(get_parameter(np,internal_np::freeze),true); return lloyd_optimize_mesh_3_impl(c3t3, domain, time_limit, max_iterations, convergence_ratio, freeze_bound, do_freeze); } #ifndef DOXYGEN_RUNNING // Overload handling parameters passed with operator= template Mesh_optimization_return_code lloyd_optimize_mesh_3(C3T3& c3t3, const MeshDomain& domain, const CGAL_NP_CLASS_1& np1, const CGAL_NP_CLASS_2& np2, const NP& ... nps) { return lloyd_optimize_mesh_3(c3t3,domain, internal_np::combine_named_parameters(np1, np2, nps...)); } template Mesh_optimization_return_code lloyd_optimize_mesh_3_impl(C3T3& c3t3, const MeshDomain& domain, const double time_limit, std::size_t max_iteration_number, const double convergence, const double freeze_bound , const bool do_freeze) { CGAL_precondition( !Mesh_3::internal::has_non_protecting_weights(c3t3.triangulation(), domain)); typedef typename C3T3::Triangulation Tr; typedef Mesh_3::Mesh_sizing_field Sizing; typedef typename Mesh_3::Lloyd_move Move; typedef typename Mesh_3::Mesh_global_optimizer Lloyd_optimizer; // Create optimizer Lloyd_optimizer opt (c3t3, domain, freeze_bound, do_freeze, convergence); // Set max time opt.set_time_limit(time_limit); // 1000 iteration max to avoid infinite loops if ( 0 == max_iteration_number ) max_iteration_number = 1000; // Launch optimization return opt(static_cast(max_iteration_number)); } #endif //DOXYGEN_RUNNING } // end namespace CGAL #endif // CGAL_LLOYD_OPTIMIZE_MESH_3_H