829 lines
33 KiB
C++
829 lines
33 KiB
C++
// Copyright (c) 2015 GeometryFactory (France).
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// All rights reserved.
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//
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// This file is part of CGAL (www.cgal.org).
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//
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// $URL: https://github.com/CGAL/cgal/blob/v5.1/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/measure.h $
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// $Id: measure.h 80f6f65 2020-04-05T17:56:50+02:00 Mael Rouxel-Labbé
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// SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
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//
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//
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// Author(s) : Andreas Fabri
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#ifndef CGAL_POLYGON_MESH_PROCESSING_MEASURE_H
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#define CGAL_POLYGON_MESH_PROCESSING_MEASURE_H
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#include <CGAL/license/Polygon_mesh_processing/measure.h>
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#include <CGAL/disable_warnings.h>
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#include <CGAL/assertions.h>
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#include <CGAL/boost/graph/iterator.h>
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#include <CGAL/boost/graph/helpers.h>
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#include <CGAL/boost/graph/properties.h>
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#include <CGAL/Polygon_mesh_processing/internal/named_function_params.h>
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#include <CGAL/Polygon_mesh_processing/internal/named_params_helper.h>
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#include <CGAL/squared_distance_3.h>
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#include <CGAL/Kernel/global_functions_3.h>
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#include <CGAL/Lazy.h> // needed for CGAL::exact(FT)/CGAL::exact(Lazy_exact_nt<T>)
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#include <boost/unordered_set.hpp>
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#include <boost/graph/graph_traits.hpp>
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#include <utility>
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#ifdef DOXYGEN_RUNNING
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#define CGAL_PMP_NP_TEMPLATE_PARAMETERS NamedParameters
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#define CGAL_PMP_NP_CLASS NamedParameters
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#endif
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namespace CGAL {
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// workaround for area(face_range, tm) overload
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template<typename CGAL_PMP_NP_TEMPLATE_PARAMETERS, typename NP>
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class GetGeomTraits<CGAL_PMP_NP_CLASS, NP>
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{
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public:
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struct type{};
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};
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namespace Polygon_mesh_processing {
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/**
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* \ingroup measure_grp
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* computes the length of an edge of a given polygon mesh.
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* The edge is given by one of its halfedges, or the edge itself.
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*
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* @tparam PolygonMesh a model of `HalfedgeGraph`
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* @tparam NamedParameters a sequence of \ref bgl_namedparameters "Named Parameters"
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*
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* @param h one halfedge of the edge to compute the length
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* @param pmesh the polygon mesh to which `h` belongs
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* @param np an optional sequence of \ref bgl_namedparameters "Named Parameters" among the ones listed below
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*
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* \cgalNamedParamsBegin
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* \cgalParamNBegin{vertex_point_map}
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* \cgalParamDescription{a property map associating points to the vertices of `pmesh`}
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* \cgalParamType{a class model of `ReadablePropertyMap` with `boost::graph_traits<PolygonMesh>::%vertex_descriptor`
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* as key type and `%Point_3` as value type}
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* \cgalParamDefault{`boost::get(CGAL::vertex_point, pmesh)`}
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* \cgalParamNEnd
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*
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* \cgalParamNBegin{geom_traits}
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* \cgalParamDescription{an instance of a geometric traits class}
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* \cgalParamType{a class model of `Kernel`}
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* \cgalParamDefault{a \cgal Kernel deduced from the point type, using `CGAL::Kernel_traits`}
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* \cgalParamExtra{The geometric traits class must be compatible with the vertex point type.}
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* \cgalParamNEnd
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* \cgalNamedParamsEnd
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*
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* @return the length of `h`. The return type `FT` is a number type. It is
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* either deduced from the `geom_traits` \ref bgl_namedparameters "Named Parameters" if provided,
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* or the geometric traits class deduced from the point property map
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* of `pmesh`.
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*
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* \warning This function involves a square root computation.
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* If `FT` does not have a `sqrt()` operation, the square root computation
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* will be done approximately.
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*
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* @sa `face_border_length()`
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*/
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template<typename PolygonMesh,
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typename NamedParameters>
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#ifdef DOXYGEN_RUNNING
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FT
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#else
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typename GetGeomTraits<PolygonMesh, NamedParameters>::type::FT
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#endif
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edge_length(typename boost::graph_traits<PolygonMesh>::halfedge_descriptor h,
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const PolygonMesh& pmesh,
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const NamedParameters& np)
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{
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using parameters::choose_parameter;
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using parameters::get_parameter;
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typename GetVertexPointMap<PolygonMesh, NamedParameters>::const_type
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vpm = choose_parameter(get_parameter(np, internal_np::vertex_point),
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get_const_property_map(CGAL::vertex_point, pmesh));
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return CGAL::approximate_sqrt(CGAL::squared_distance(get(vpm, source(h, pmesh)),
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get(vpm, target(h, pmesh))));
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}
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template<typename PolygonMesh>
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typename CGAL::Kernel_traits<typename property_map_value<PolygonMesh,
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CGAL::vertex_point_t>::type>::Kernel::FT
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edge_length(typename boost::graph_traits<PolygonMesh>::halfedge_descriptor h,
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const PolygonMesh& pmesh)
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{
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return edge_length(h, pmesh, CGAL::Polygon_mesh_processing::parameters::all_default());
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}
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// edge overloads
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template<typename PolygonMesh,
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typename NamedParameters>
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typename GetGeomTraits<PolygonMesh, NamedParameters>::type::FT
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edge_length(typename boost::graph_traits<PolygonMesh>::edge_descriptor e,
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const PolygonMesh& pmesh,
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const NamedParameters& np)
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{
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return edge_length(halfedge(e, pmesh), pmesh, np);
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}
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template<typename PolygonMesh>
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typename CGAL::Kernel_traits<typename property_map_value<PolygonMesh,
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CGAL::vertex_point_t>::type>::Kernel::FT
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edge_length(typename boost::graph_traits<PolygonMesh>::edge_descriptor e,
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const PolygonMesh& pmesh)
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{
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return edge_length(halfedge(e, pmesh), pmesh);
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}
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/**
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* \ingroup measure_grp
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* computes the length of the border polyline
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* that contains a given halfedge.
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*
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* @tparam PolygonMesh a model of `HalfedgeGraph`
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* @tparam NamedParameters a sequence of \ref bgl_namedparameters "Named Parameters"
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*
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* @param h a halfedge of the border polyline of which the length is computed
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* @param pmesh the polygon mesh to which `h` belongs
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* @param np an optional sequence of \ref bgl_namedparameters "Named Parameters" among the ones listed below
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*
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* \cgalNamedParamsBegin
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* \cgalParamNBegin{vertex_point_map}
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* \cgalParamDescription{a property map associating points to the vertices of `pmesh`}
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* \cgalParamType{a class model of `ReadablePropertyMap` with `boost::graph_traits<PolygonMesh>::%vertex_descriptor`
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* as key type and `%Point_3` as value type}
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* \cgalParamDefault{`boost::get(CGAL::vertex_point, pmesh)`}
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* \cgalParamNEnd
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*
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* \cgalParamNBegin{geom_traits}
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* \cgalParamDescription{an instance of a geometric traits class}
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* \cgalParamType{a class model of `Kernel`}
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* \cgalParamDefault{a \cgal Kernel deduced from the point type, using `CGAL::Kernel_traits`}
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* \cgalParamExtra{The geometric traits class must be compatible with the vertex point type.}
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* \cgalParamNEnd
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* \cgalNamedParamsEnd
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*
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* @return the length of the sequence of border edges of `face(h, pmesh)`.
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* The return type `FT` is a number type. It is
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* either deduced from the `geom_traits` \ref bgl_namedparameters "Named Parameters" if provided,
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* or the geometric traits class deduced from the point property map
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* of `pmesh`.
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*
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* \warning This function involves a square root computation.
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* If `Kernel::FT` does not have a `sqrt()` operation, the square root computation
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* will be done approximately.
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*
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* @sa `edge_length()`
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*/
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template<typename PolygonMesh,
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typename NamedParameters>
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#ifdef DOXYGEN_RUNNING
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FT
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#else
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typename GetGeomTraits<PolygonMesh, NamedParameters>::type::FT
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#endif
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face_border_length(typename boost::graph_traits<PolygonMesh>::halfedge_descriptor h,
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const PolygonMesh& pmesh,
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const NamedParameters& np)
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{
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typename GetGeomTraits<PolygonMesh, NamedParameters>::type::FT result = 0;
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for(typename boost::graph_traits<PolygonMesh>::halfedge_descriptor haf : halfedges_around_face(h, pmesh))
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{
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result += edge_length(haf, pmesh, np);
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exact(result);
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}
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return result;
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}
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template<typename PolygonMesh>
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typename CGAL::Kernel_traits<typename property_map_value<PolygonMesh,
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CGAL::vertex_point_t>::type>::Kernel::FT
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face_border_length(typename boost::graph_traits<PolygonMesh>::halfedge_descriptor h,
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const PolygonMesh& pmesh)
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{
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return face_border_length(h, pmesh, CGAL::Polygon_mesh_processing::parameters::all_default());
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}
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/**
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* \ingroup measure_grp
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* finds the longest border of a given triangulated surface and returns
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* a halfedge that is part of this border and the length of this border.
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*
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* @tparam PolygonMesh a model of `HalfedgeGraph`
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* @tparam NamedParameters a sequence of \ref bgl_namedparameters "Named Parameters"
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*
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* @param pmesh the polygon mesh
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* @param np an optional sequence of \ref bgl_namedparameters "Named Parameters" among the ones listed below
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*
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* \cgalNamedParamsBegin
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* \cgalParamNBegin{vertex_point_map}
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* \cgalParamDescription{a property map associating points to the vertices of `pmesh`}
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* \cgalParamType{a class model of `ReadablePropertyMap` with `boost::graph_traits<PolygonMesh>::%vertex_descriptor`
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* as key type and `%Point_3` as value type}
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* \cgalParamDefault{`boost::get(CGAL::vertex_point, pmesh)`}
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* \cgalParamNEnd
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*
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* \cgalParamNBegin{geom_traits}
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* \cgalParamDescription{an instance of a geometric traits class}
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* \cgalParamType{a class model of `Kernel`}
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* \cgalParamDefault{a \cgal Kernel deduced from the point type, using `CGAL::Kernel_traits`}
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* \cgalParamExtra{The geometric traits class must be compatible with the vertex point type.}
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* \cgalParamNEnd
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* \cgalNamedParamsEnd
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*
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* @return a pair composed of two members:
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* - `first`: a halfedge on the longest border.
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* The return type `halfedge_descriptor` is a halfedge descriptor. It is
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* deduced from the graph traits corresponding to the type `PolygonMesh`.
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* - `second`: the length of the longest border
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* The return type `FT` is a number type. It is
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* either deduced from the `geom_traits` \ref bgl_namedparameters "Named Parameters" if provided,
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* or the geometric traits class deduced from the point property map
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* of `pmesh`
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*
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*/
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template<typename PolygonMesh,
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typename NamedParameters>
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#ifdef DOXYGEN_RUNNING
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std::pair<halfedge_descriptor, FT>
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#else
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std::pair<typename boost::graph_traits<PolygonMesh>::halfedge_descriptor,
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typename GetGeomTraits<PolygonMesh, NamedParameters>::type::FT>
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#endif
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longest_border(const PolygonMesh& pmesh,
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const NamedParameters& np)
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{
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typedef typename CGAL::Kernel_traits<
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typename property_map_value<PolygonMesh, CGAL::vertex_point_t>::type>::Kernel::FT FT;
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typedef typename boost::graph_traits<PolygonMesh>::halfedge_descriptor halfedge_descriptor;
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boost::unordered_set<halfedge_descriptor> visited;
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halfedge_descriptor result_halfedge = boost::graph_traits<PolygonMesh>::null_halfedge();
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FT result_len = 0;
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for(halfedge_descriptor h : halfedges(pmesh))
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{
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if(visited.find(h)== visited.end())
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{
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if(is_border(h, pmesh))
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{
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FT len = 0;
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for(halfedge_descriptor haf : halfedges_around_face(h, pmesh))
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{
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len += edge_length(haf, pmesh, np);
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visited.insert(haf);
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}
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if(result_len < len)
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{
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result_len = len;
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result_halfedge = h;
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}
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}
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}
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}
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return std::make_pair(result_halfedge, result_len);
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}
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template<typename PolygonMesh>
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std::pair<typename boost::graph_traits<PolygonMesh>::halfedge_descriptor,
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typename CGAL::Kernel_traits<typename property_map_value<PolygonMesh,
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CGAL::vertex_point_t>::type>::Kernel::FT>
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longest_border(const PolygonMesh& pmesh)
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{
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return longest_border(pmesh, CGAL::Polygon_mesh_processing::parameters::all_default());
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}
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/**
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* \ingroup measure_grp
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* computes the area of a face of a given
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* triangulated surface mesh.
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*
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* @tparam TriangleMesh a model of `HalfedgeGraph`
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* @tparam NamedParameters a sequence of \ref bgl_namedparameters "Named Parameters"
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*
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* @param f the face of which the area is computed
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* @param tmesh the triangulated surface mesh to which `f` belongs
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* @param np an optional sequence of \ref bgl_namedparameters "Named Parameters" among the ones listed below
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*
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* \cgalNamedParamsBegin
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* \cgalParamNBegin{vertex_point_map}
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* \cgalParamDescription{a property map associating points to the vertices of `tmesh`}
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* \cgalParamType{a class model of `ReadablePropertyMap` with `boost::graph_traits<TriangleMesh>::%vertex_descriptor`
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* as key type and `%Point_3` as value type}
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* \cgalParamDefault{`boost::get(CGAL::vertex_point, tmesh)`}
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* \cgalParamNEnd
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*
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* \cgalParamNBegin{geom_traits}
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* \cgalParamDescription{an instance of a geometric traits class}
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* \cgalParamType{a class model of `Kernel`}
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* \cgalParamDefault{a \cgal Kernel deduced from the point type, using `CGAL::Kernel_traits`}
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* \cgalParamExtra{The geometric traits class must be compatible with the vertex point type.}
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* \cgalParamNEnd
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* \cgalNamedParamsEnd
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*
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* @pre `f != boost::graph_traits<TriangleMesh>::%null_face()`
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*
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* @return the area of `f`.
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* The return type `FT` is a number type. It is
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* either deduced from the `geom_traits` \ref bgl_namedparameters "Named Parameters" if provided,
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* or the geometric traits class deduced from the point property map
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* of `tmesh`.
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*
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* @sa `area()`
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*/
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template<typename TriangleMesh,
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typename CGAL_PMP_NP_TEMPLATE_PARAMETERS>
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#ifdef DOXYGEN_RUNNING
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FT
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#else
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typename GetGeomTraits<TriangleMesh, CGAL_PMP_NP_CLASS>::type::FT
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#endif
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face_area(typename boost::graph_traits<TriangleMesh>::face_descriptor f,
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const TriangleMesh& tmesh,
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const CGAL_PMP_NP_CLASS& np)
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{
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using parameters::choose_parameter;
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using parameters::get_parameter;
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typedef typename boost::graph_traits<TriangleMesh>::halfedge_descriptor halfedge_descriptor;
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CGAL_precondition(boost::graph_traits<TriangleMesh>::null_face() != f);
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typename GetVertexPointMap<TriangleMesh, CGAL_PMP_NP_CLASS>::const_type
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vpm = choose_parameter(get_parameter(np, internal_np::vertex_point),
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get_const_property_map(CGAL::vertex_point, tmesh));
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halfedge_descriptor hd = halfedge(f, tmesh);
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halfedge_descriptor nhd = next(hd, tmesh);
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typedef typename GetGeomTraits<TriangleMesh, CGAL_PMP_NP_CLASS>::type GT;
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GT traits = choose_parameter<GT>(get_parameter(np, internal_np::geom_traits));
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return approximate_sqrt(traits.compute_squared_area_3_object()(get(vpm, source(hd, tmesh)),
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get(vpm, target(hd, tmesh)),
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get(vpm, target(nhd, tmesh))));
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}
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template<typename TriangleMesh>
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typename CGAL::Kernel_traits<typename property_map_value<TriangleMesh,
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CGAL::vertex_point_t>::type>::Kernel::FT
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face_area(typename boost::graph_traits<TriangleMesh>::face_descriptor f,
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const TriangleMesh& tmesh)
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{
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return face_area(f, tmesh, CGAL::Polygon_mesh_processing::parameters::all_default());
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}
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/**
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* \ingroup measure_grp
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* computes the area of a range of faces of a given
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* triangulated surface mesh.
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*
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* @tparam FaceRange range of `boost::graph_traits<PolygonMesh>::%face_descriptor`,
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model of `Range`.
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Its iterator type is `InputIterator`.
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* @tparam TriangleMesh a model of `HalfedgeGraph`
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* @tparam NamedParameters a sequence of \ref bgl_namedparameters "Named Parameters"
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*
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* @param face_range the range of faces of which the area is computed
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* @param tmesh the triangulated surface mesh to which the faces of `face_range` belong
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* @param np an optional sequence of \ref bgl_namedparameters "Named Parameters" among the ones listed below
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*
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* \cgalNamedParamsBegin
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* \cgalParamNBegin{vertex_point_map}
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* \cgalParamDescription{a property map associating points to the vertices of `tmesh`}
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* \cgalParamType{a class model of `ReadablePropertyMap` with `boost::graph_traits<TriangleMesh>::%vertex_descriptor`
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* as key type and `%Point_3` as value type}
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* \cgalParamDefault{`boost::get(CGAL::vertex_point, tmesh)`}
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* \cgalParamNEnd
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*
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* \cgalParamNBegin{geom_traits}
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* \cgalParamDescription{an instance of a geometric traits class}
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* \cgalParamType{a class model of `Kernel`}
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* \cgalParamDefault{a \cgal Kernel deduced from the point type, using `CGAL::Kernel_traits`}
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* \cgalParamExtra{The geometric traits class must be compatible with the vertex point type.}
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* \cgalParamNEnd
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* \cgalNamedParamsEnd
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*
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* @return sum of face areas of `faces`.
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* The return type `FT` is a number type. It is
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* either deduced from the `geom_traits` \ref bgl_namedparameters "Named Parameters" if provided,
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* or the geometric traits class deduced from the point property map
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* of `tmesh`.
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*
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* \warning This function involves a square root computation.
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* If `Kernel::FT` does not have a `sqrt()` operation, the square root computation
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* will be done approximately.
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*
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* @sa `face_area()`
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*/
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template<typename FaceRange,
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typename TriangleMesh,
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typename CGAL_PMP_NP_TEMPLATE_PARAMETERS>
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#ifdef DOXYGEN_RUNNING
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FT
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#else
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typename GetGeomTraits<TriangleMesh, CGAL_PMP_NP_CLASS>::type::FT
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#endif
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area(FaceRange face_range,
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const TriangleMesh& tmesh,
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const CGAL_PMP_NP_CLASS& np)
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{
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typedef typename boost::graph_traits<TriangleMesh>::face_descriptor face_descriptor;
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typename GetGeomTraits<TriangleMesh, CGAL_PMP_NP_CLASS>::type::FT result = 0;
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for(face_descriptor f : face_range)
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{
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result += face_area(f, tmesh, np);
|
|
exact(result);
|
|
}
|
|
|
|
return result;
|
|
}
|
|
|
|
template<typename FaceRange, typename TriangleMesh>
|
|
typename GetGeomTraits<TriangleMesh>::type::FT
|
|
area(FaceRange face_range, const TriangleMesh& tmesh)
|
|
{
|
|
return area(face_range, tmesh, CGAL::Polygon_mesh_processing::parameters::all_default());
|
|
}
|
|
|
|
/**
|
|
* \ingroup measure_grp
|
|
* computes the surface area of a triangulated surface mesh.
|
|
*
|
|
* @tparam TriangleMesh a model of `HalfedgeGraph`
|
|
* @tparam NamedParameters a sequence of \ref bgl_namedparameters "Named Parameters"
|
|
*
|
|
* @param tmesh the triangulated surface mesh
|
|
* @param np an optional sequence of \ref bgl_namedparameters "Named Parameters" among the ones listed below
|
|
*
|
|
* \cgalNamedParamsBegin
|
|
* \cgalParamNBegin{vertex_point_map}
|
|
* \cgalParamDescription{a property map associating points to the vertices of `tmesh`}
|
|
* \cgalParamType{a class model of `ReadablePropertyMap` with `boost::graph_traits<TriangleMesh>::%vertex_descriptor`
|
|
* as key type and `%Point_3` as value type}
|
|
* \cgalParamDefault{`boost::get(CGAL::vertex_point, tmesh)`}
|
|
* \cgalParamNEnd
|
|
*
|
|
* \cgalParamNBegin{geom_traits}
|
|
* \cgalParamDescription{an instance of a geometric traits class}
|
|
* \cgalParamType{a class model of `Kernel`}
|
|
* \cgalParamDefault{a \cgal Kernel deduced from the point type, using `CGAL::Kernel_traits`}
|
|
* \cgalParamExtra{The geometric traits class must be compatible with the vertex point type.}
|
|
* \cgalParamNEnd
|
|
* \cgalNamedParamsEnd
|
|
*
|
|
* @return the surface area of `tmesh`.
|
|
* The return type `FT` is a number type. It is
|
|
* either deduced from the `geom_traits` \ref bgl_namedparameters "Named Parameters" if provided,
|
|
* or the geometric traits class deduced from the point property map
|
|
* of `tmesh`.
|
|
*
|
|
* \warning This function involves a square root computation.
|
|
* If `Kernel::FT` does not have a `sqrt()` operation, the square root computation
|
|
* will be done approximately.
|
|
*
|
|
* @sa `face_area()`
|
|
*/
|
|
template<typename TriangleMesh,
|
|
typename CGAL_PMP_NP_TEMPLATE_PARAMETERS>
|
|
#ifdef DOXYGEN_RUNNING
|
|
FT
|
|
#else
|
|
typename GetGeomTraits<TriangleMesh, CGAL_PMP_NP_CLASS>::type::FT
|
|
#endif
|
|
area(const TriangleMesh& tmesh, const CGAL_PMP_NP_CLASS& np)
|
|
{
|
|
return area(faces(tmesh), tmesh, np);
|
|
}
|
|
|
|
template<typename TriangleMesh>
|
|
typename CGAL::Kernel_traits<typename property_map_value<TriangleMesh,
|
|
CGAL::vertex_point_t>::type>::Kernel::FT
|
|
area(const TriangleMesh& tmesh)
|
|
{
|
|
return area(faces(tmesh), tmesh, CGAL::Polygon_mesh_processing::parameters::all_default());
|
|
}
|
|
|
|
/**
|
|
* \ingroup measure_grp
|
|
* computes the volume of the domain bounded by
|
|
* a closed triangulated surface mesh.
|
|
*
|
|
* @tparam TriangleMesh a model of `HalfedgeGraph`
|
|
* @tparam NamedParameters a sequence of \ref bgl_namedparameters "Named Parameters"
|
|
*
|
|
* @param tmesh the closed triangulated surface mesh bounding the volume
|
|
* @param np an optional sequence of \ref bgl_namedparameters "Named Parameters" among the ones listed below
|
|
*
|
|
* @pre `tmesh` is closed
|
|
*
|
|
* \cgalNamedParamsBegin
|
|
* \cgalParamNBegin{vertex_point_map}
|
|
* \cgalParamDescription{a property map associating points to the vertices of `tmesh`}
|
|
* \cgalParamType{a class model of `ReadablePropertyMap` with `boost::graph_traits<TriangleMesh>::%vertex_descriptor`
|
|
* as key type and `%Point_3` as value type}
|
|
* \cgalParamDefault{`boost::get(CGAL::vertex_point, tmesh)`}
|
|
* \cgalParamNEnd
|
|
*
|
|
* \cgalParamNBegin{geom_traits}
|
|
* \cgalParamDescription{an instance of a geometric traits class}
|
|
* \cgalParamType{a class model of `Kernel`}
|
|
* \cgalParamDefault{a \cgal Kernel deduced from the point type, using `CGAL::Kernel_traits`}
|
|
* \cgalParamExtra{The geometric traits class must be compatible with the vertex point type.}
|
|
* \cgalParamNEnd
|
|
* \cgalNamedParamsEnd
|
|
*
|
|
* @return the volume bounded by `tmesh`.
|
|
* The return type `FT` is a number type. It is
|
|
* either deduced from the `geom_traits` \ref bgl_namedparameters "Named Parameters" if provided,
|
|
* or the geometric traits class deduced from the point property map
|
|
* of `tmesh`.
|
|
*/
|
|
template<typename TriangleMesh,
|
|
typename CGAL_PMP_NP_TEMPLATE_PARAMETERS>
|
|
#ifdef DOXYGEN_RUNNING
|
|
FT
|
|
#else
|
|
typename GetGeomTraits<TriangleMesh, CGAL_PMP_NP_CLASS>::type::FT
|
|
#endif
|
|
volume(const TriangleMesh& tmesh,
|
|
const CGAL_PMP_NP_CLASS& np)
|
|
{
|
|
CGAL_assertion(is_triangle_mesh(tmesh));
|
|
CGAL_assertion(is_closed(tmesh));
|
|
|
|
using parameters::choose_parameter;
|
|
using parameters::get_parameter;
|
|
|
|
typename GetVertexPointMap<TriangleMesh, CGAL_PMP_NP_CLASS>::const_type
|
|
vpm = choose_parameter(get_parameter(np, internal_np::vertex_point),
|
|
get_const_property_map(CGAL::vertex_point, tmesh));
|
|
typename GetGeomTraits<TriangleMesh, CGAL_PMP_NP_CLASS>::type::Point_3 origin(0, 0, 0);
|
|
|
|
typedef typename boost::graph_traits<TriangleMesh>::face_descriptor face_descriptor;
|
|
|
|
typename GetGeomTraits<TriangleMesh, CGAL_PMP_NP_CLASS>::type::FT volume = 0;
|
|
typename CGAL::Kernel_traits<typename property_map_value<TriangleMesh,
|
|
CGAL::vertex_point_t>::type>::Kernel::Compute_volume_3 cv3;
|
|
|
|
for(face_descriptor f : faces(tmesh))
|
|
{
|
|
volume += cv3(origin,
|
|
get(vpm, target(halfedge(f, tmesh), tmesh)),
|
|
get(vpm, target(next(halfedge(f, tmesh), tmesh), tmesh)),
|
|
get(vpm, target(prev(halfedge(f, tmesh), tmesh), tmesh)));
|
|
exact(volume);
|
|
}
|
|
|
|
return volume;
|
|
}
|
|
|
|
template<typename TriangleMesh>
|
|
typename CGAL::Kernel_traits<typename property_map_value<TriangleMesh,
|
|
CGAL::vertex_point_t>::type>::Kernel::FT
|
|
volume(const TriangleMesh& tmesh)
|
|
{
|
|
return volume(tmesh, CGAL::Polygon_mesh_processing::parameters::all_default());
|
|
}
|
|
|
|
/**
|
|
* \ingroup measure_grp
|
|
* computes the aspect ratio of a face of a given triangulated surface mesh.
|
|
*
|
|
* @tparam TriangleMesh a model of `HalfedgeGraph`
|
|
* @tparam NamedParameters a sequence of \ref bgl_namedparameters "Named Parameters"
|
|
*
|
|
* @param f the face of which the aspect ratio is computed
|
|
* @param tmesh the triangulated surface mesh to which `f` belongs
|
|
* @param np an optional sequence of \ref bgl_namedparameters "Named Parameters" among the ones listed below
|
|
*
|
|
* \cgalNamedParamsBegin
|
|
* \cgalParamNBegin{vertex_point_map}
|
|
* \cgalParamDescription{a property map associating points to the vertices of `tmesh`}
|
|
* \cgalParamType{a class model of `ReadablePropertyMap` with `boost::graph_traits<TriangleMesh>::%vertex_descriptor`
|
|
* as key type and `%Point_3` as value type}
|
|
* \cgalParamDefault{`boost::get(CGAL::vertex_point, tmesh)`}
|
|
* \cgalParamNEnd
|
|
*
|
|
* \cgalParamNBegin{geom_traits}
|
|
* \cgalParamDescription{an instance of a geometric traits class}
|
|
* \cgalParamType{a class model of `Kernel`}
|
|
* \cgalParamDefault{a \cgal Kernel deduced from the point type, using `CGAL::Kernel_traits`}
|
|
* \cgalParamExtra{The geometric traits class must be compatible with the vertex point type.}
|
|
* \cgalParamNEnd
|
|
* \cgalNamedParamsEnd
|
|
*
|
|
* @pre `f != boost::graph_traits<TriangleMesh>::%null_face()`
|
|
*
|
|
* @return the aspect ratio of `f`. The return type `FT` is a number type. It is
|
|
* either deduced from the `geom_traits` \ref bgl_namedparameters "Named Parameters" if provided,
|
|
* or the geometric traits class deduced from the point property map of `tmesh`.
|
|
*
|
|
*/
|
|
template<typename TriangleMesh,
|
|
typename CGAL_PMP_NP_TEMPLATE_PARAMETERS>
|
|
#ifdef DOXYGEN_RUNNING
|
|
FT
|
|
#else
|
|
typename GetGeomTraits<TriangleMesh, CGAL_PMP_NP_CLASS>::type::FT
|
|
#endif
|
|
face_aspect_ratio(typename boost::graph_traits<TriangleMesh>::face_descriptor f,
|
|
const TriangleMesh& tmesh,
|
|
const CGAL_PMP_NP_CLASS& np)
|
|
{
|
|
CGAL_precondition(is_triangle(f, tmesh));
|
|
|
|
typedef typename boost::graph_traits<TriangleMesh>::halfedge_descriptor halfedge_descriptor;
|
|
|
|
typedef typename GetGeomTraits<TriangleMesh, CGAL_PMP_NP_CLASS>::type Geom_traits;
|
|
typedef typename Geom_traits::FT FT;
|
|
|
|
using parameters::choose_parameter;
|
|
using parameters::get_parameter;
|
|
|
|
typename GetVertexPointMap<TriangleMesh, CGAL_PMP_NP_CLASS>::const_type
|
|
vpm = choose_parameter(get_parameter(np, internal_np::vertex_point),
|
|
get_const_property_map(CGAL::vertex_point, tmesh));
|
|
|
|
halfedge_descriptor h = halfedge(f, tmesh);
|
|
|
|
Geom_traits gt = choose_parameter<Geom_traits>(get_parameter(np, internal_np::geom_traits));
|
|
|
|
#if 0
|
|
const FT sq_triangle_area = gt.compute_squared_area_3_object()(get(vpm, source(h, tmesh)),
|
|
get(vpm, target(h, tmesh)),
|
|
get(vpm, target(next(h, tmesh), tmesh)));
|
|
const FT sq_d12 = gt.compute_squared_distance_2_object()(get(vpm, source(h, tmesh)),
|
|
get(vpm, target(h, tmesh)));
|
|
const FT sq_d13 = gt.compute_squared_distance_2_object()(get(vpm, source(h, tmesh)),
|
|
get(vpm, target(next(h, tmesh), tmesh)));
|
|
const FT sq_d23 = gt.compute_squared_distance_2_object()(get(vpm, target(h, tmesh)),
|
|
get(vpm, target(next(h, tmesh), tmesh)));
|
|
|
|
const FT min_sq_d123 = (std::min)(sq_d12, (std::min)(sq_d13, sq_d23));
|
|
|
|
const FT aspect_ratio = 4*sq_triangle_area*min_sq_d123 / (sq_d12*sq_d13*sq_d23);
|
|
#else // below requires SQRT
|
|
typedef typename Geom_traits::Line_3 Line_3;
|
|
|
|
FT sq_max_edge_length = gt.compute_squared_distance_3_object()(get(vpm, source(h, tmesh)),
|
|
get(vpm, target(h, tmesh)));
|
|
FT sq_min_alt = gt.compute_squared_distance_3_object()(get(vpm, target(next(h, tmesh), tmesh)),
|
|
Line_3(get(vpm, source(h, tmesh)),
|
|
get(vpm, target(h, tmesh))));
|
|
h = next(h, tmesh);
|
|
|
|
for(int i=1; i<3; ++i)
|
|
{
|
|
FT sq_edge_length = gt.compute_squared_distance_3_object()(get(vpm, source(h, tmesh)),
|
|
get(vpm, target(h, tmesh)));
|
|
FT sq_alt = gt.compute_squared_distance_3_object()(get(vpm, target(next(h, tmesh), tmesh)),
|
|
Line_3(get(vpm, source(h, tmesh)),
|
|
get(vpm, target(h, tmesh))));
|
|
|
|
if(sq_alt < sq_min_alt)
|
|
sq_min_alt = sq_alt;
|
|
if(sq_edge_length > sq_max_edge_length)
|
|
sq_max_edge_length = sq_edge_length;
|
|
|
|
h = next(h, tmesh);
|
|
}
|
|
|
|
CGAL_assertion(sq_min_alt > 0);
|
|
const FT aspect_ratio = CGAL::approximate_sqrt(sq_max_edge_length / sq_min_alt);
|
|
#endif
|
|
|
|
return aspect_ratio;
|
|
}
|
|
|
|
template<typename TriangleMesh>
|
|
typename CGAL::Kernel_traits<typename property_map_value<TriangleMesh,
|
|
CGAL::vertex_point_t>::type>::Kernel::FT
|
|
face_aspect_ratio(typename boost::graph_traits<TriangleMesh>::face_descriptor f,
|
|
const TriangleMesh& tmesh)
|
|
{
|
|
return face_aspect_ratio(f, tmesh, CGAL::Polygon_mesh_processing::parameters::all_default());
|
|
}
|
|
|
|
/**
|
|
* \ingroup measure_grp
|
|
* computes the centroid of a volume bounded by
|
|
* a closed triangulated surface mesh.
|
|
*
|
|
* @tparam TriangleMesh a model of `FaceListGraph`
|
|
* @tparam NamedParameters a sequence of \ref bgl_namedparameters "Named Parameters"
|
|
*
|
|
* @param tmesh the closed triangulated surface mesh bounding the volume
|
|
* @param np an optional sequence of \ref bgl_namedparameters "Named Parameters" among the ones listed below
|
|
*
|
|
* @pre `tmesh` is closed
|
|
*
|
|
* \cgalNamedParamsBegin
|
|
* \cgalParamNBegin{vertex_point_map}
|
|
* \cgalParamDescription{a property map associating points to the vertices of `tmesh`}
|
|
* \cgalParamType{a class model of `ReadablePropertyMap` with `boost::graph_traits<TriangleMesh>::%vertex_descriptor`
|
|
* as key type and `%Point_3` as value type}
|
|
* \cgalParamDefault{`boost::get(CGAL::vertex_point, tmesh)`}
|
|
* \cgalParamNEnd
|
|
*
|
|
* \cgalParamNBegin{geom_traits}
|
|
* \cgalParamDescription{an instance of a geometric traits class}
|
|
* \cgalParamType{a class model of `Kernel`}
|
|
* \cgalParamDefault{a \cgal Kernel deduced from the point type, using `CGAL::Kernel_traits`}
|
|
* \cgalParamExtra{The geometric traits class must be compatible with the vertex point type.}
|
|
* \cgalParamNEnd
|
|
* \cgalNamedParamsEnd
|
|
*
|
|
* @return the centroid of the domain bounded by `tmesh`.
|
|
*/
|
|
template<typename TriangleMesh, typename CGAL_PMP_NP_TEMPLATE_PARAMETERS>
|
|
#ifdef DOXYGEN_RUNNING
|
|
Point_3
|
|
#else
|
|
typename GetGeomTraits<TriangleMesh, CGAL_PMP_NP_CLASS>::type::Point_3
|
|
#endif
|
|
centroid(const TriangleMesh& tmesh, const CGAL_PMP_NP_CLASS& np)
|
|
{
|
|
// See: http://www2.imperial.ac.uk/~rn/centroid.pdf
|
|
|
|
CGAL_assertion(is_triangle_mesh(tmesh));
|
|
CGAL_assertion(is_closed(tmesh));
|
|
|
|
using parameters::choose_parameter;
|
|
using parameters::get_parameter;
|
|
|
|
typedef typename GetVertexPointMap<TriangleMesh, CGAL_PMP_NP_CLASS>::const_type Vpm;
|
|
Vpm vpm = choose_parameter(get_parameter(np, internal_np::vertex_point),
|
|
get_const_property_map(CGAL::vertex_point, tmesh));
|
|
|
|
typedef typename GetGeomTraits<TriangleMesh, CGAL_PMP_NP_CLASS>::type Kernel;
|
|
typedef typename Kernel::Point_3 Point_3;
|
|
typedef typename Kernel::Vector_3 Vector_3;
|
|
typedef typename Kernel::Construct_translated_point_3 Construct_translated_point_3;
|
|
typedef typename Kernel::Construct_vector_3 Construct_vector_3;
|
|
typedef typename Kernel::Construct_normal_3 Construct_normal_3;
|
|
typedef typename Kernel::Compute_scalar_product_3 Scalar_product;
|
|
typedef typename Kernel::Construct_scaled_vector_3 Scale;
|
|
typedef typename Kernel::Construct_sum_of_vectors_3 Sum;
|
|
typedef typename boost::graph_traits<TriangleMesh>::face_descriptor face_descriptor;
|
|
typedef typename Kernel::FT FT;
|
|
|
|
FT volume = 0;
|
|
|
|
Vector_3 centroid(NULL_VECTOR);
|
|
|
|
Construct_translated_point_3 point;
|
|
Construct_vector_3 vector;
|
|
Construct_normal_3 normal;
|
|
Scalar_product scalar_product;
|
|
Scale scale;
|
|
Sum sum;
|
|
|
|
for(face_descriptor fd : faces(tmesh))
|
|
{
|
|
const Point_3& p = get(vpm, target(halfedge(fd, tmesh), tmesh));
|
|
const Point_3& q = get(vpm, target(next(halfedge(fd, tmesh), tmesh), tmesh));
|
|
const Point_3& r = get(vpm, target(prev(halfedge(fd, tmesh), tmesh), tmesh));
|
|
Vector_3 vp = vector(ORIGIN, p),
|
|
vq = vector(ORIGIN, q),
|
|
vr = vector(ORIGIN, r);
|
|
Vector_3 n = normal(p, q, r);
|
|
volume += (scalar_product(n,vp))/FT(6);
|
|
n = scale(n, FT(1)/FT(24));
|
|
|
|
Vector_3 v2 = sum(vp, vq);
|
|
Vector_3 v3 = Vector_3(square(v2.x()), square(v2.y()), square(v2.z()));
|
|
v2 = sum(vq, vr);
|
|
v3 = sum(v3, Vector_3(square(v2.x()), square(v2.y()), square(v2.z())));
|
|
v2 = sum(vp, vr);
|
|
v3 = sum(v3, Vector_3(square(v2.x()), square(v2.y()), square(v2.z())));
|
|
|
|
centroid = sum(centroid, Vector_3(n.x() * v3.x(), n.y() * v3.y(), n.z() * v3.z()));
|
|
}
|
|
|
|
centroid = scale(centroid, FT(1)/(FT(2)*volume));
|
|
return point(ORIGIN, centroid);
|
|
}
|
|
|
|
template<typename TriangleMesh>
|
|
typename CGAL::Kernel_traits<typename property_map_value<TriangleMesh,
|
|
CGAL::vertex_point_t>::type>::Kernel::Point_3
|
|
centroid(const TriangleMesh& tmesh)
|
|
{
|
|
return centroid(tmesh, CGAL::Polygon_mesh_processing::parameters::all_default());
|
|
}
|
|
|
|
} // namespace Polygon_mesh_processing
|
|
} // namespace CGAL
|
|
|
|
#include <CGAL/enable_warnings.h>
|
|
|
|
#endif // CGAL_POLYGON_MESH_PROCESSING_MEASURE_H
|