mirror of https://github.com/CGAL/cgal
592 lines
22 KiB
C++
592 lines
22 KiB
C++
#ifndef CGAL_SURFACE_MESH_APPROXIMATION_VSA_METRICS_H
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#define CGAL_SURFACE_MESH_APPROXIMATION_VSA_METRICS_H
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#include <CGAL/Kernel/global_functions.h>
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#include <CGAL/squared_distance_3.h>
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#include <CGAL/linear_least_squares_fitting_3.h>
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#include <boost/graph/graph_traits.hpp>
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#include <map>
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#include <list>
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namespace CGAL
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{
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/*!
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* \ingroup PkgTSMA
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* @brief Plane proxy class for the Variational Shape Approximation algorithm.
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*
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* It is simply a class containing few proxy parameters.
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* It is used as the default proxy for the `L21Metric` and `L2Metric`
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*
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* \cgalModels `Proxy`
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*
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* @tparam GeomTraits geometric traits
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*/
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template <typename GeomTraits>
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class PlaneProxy
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{
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typedef typename GeomTraits::Vector_3 Vector_3;
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typedef typename GeomTraits::Plane_3 Plane_3;
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public:
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// The proxy normal used in the `L21Metric`.
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Vector_3 normal;
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// The fitting plane of the proxy used in the `L2Metric`.
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Plane_3 fit_plane;
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};
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/*!
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* \ingroup PkgTSMA
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* @brief L21 metric class for the Variational Shape Approximation algorithm.
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* It is simply a functor that takes a facet and a proxy, returns the L21 error between them.
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*
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* \cgalModels `ErrorMetric`
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*
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* @tparam TriangleMesh a triangle `FaceGraph`
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* @tparam VertexPointMap a property map containing the vertex points,
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and `boost::graph_traits<TriangleMesh>::%vertex_descriptor` as key type,
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GeomTraits::Point_3 as value type
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* @tparam GeomTraits geometric traits
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* @tparam PlaneProxy a model of `PlaneProxy`
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*/
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template <typename TriangleMesh,
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typename VertexPointMap
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= typename boost::property_map<TriangleMesh, boost::vertex_point_t>::type,
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typename GeomTraits = typename TriangleMesh::Traits,
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typename PlaneProxy = CGAL::PlaneProxy<GeomTraits> >
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class L21Metric
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{
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typedef typename GeomTraits::FT FT;
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typedef typename GeomTraits::Vector_3 Vector_3;
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typedef typename GeomTraits::Point_3 Point_3;
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typedef typename GeomTraits::Construct_scaled_vector_3 Construct_scaled_vector_3;
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typedef typename GeomTraits::Construct_sum_of_vectors_3 Construct_sum_of_vectors_3;
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typedef typename GeomTraits::Compute_scalar_product_3 Compute_scalar_product_3;
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typedef typename boost::graph_traits<TriangleMesh>::face_descriptor face_descriptor;
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typedef typename boost::graph_traits<TriangleMesh>::halfedge_descriptor halfedge_descriptor;
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typedef boost::associative_property_map<std::map<face_descriptor, Vector_3> > FacetNormalMap;
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typedef boost::associative_property_map<std::map<face_descriptor, FT> > FacetAreaMap;
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public:
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// The type define required by the `ErrorMetric` concept
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typedef PlaneProxy Proxy;
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// constructor
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L21Metric(const TriangleMesh &tm, const VertexPointMap &point_pmap)
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: normal_pmap(facet_normals), area_pmap(facet_areas) {
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GeomTraits traits;
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scalar_product_functor = traits.compute_scalar_product_3_object();
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sum_functor = traits.construct_sum_of_vectors_3_object();
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scale_functor = traits.construct_scaled_vector_3_object();
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// construct internal facet normal & area map
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BOOST_FOREACH(face_descriptor f, faces(tm)) {
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const halfedge_descriptor he = halfedge(f, tm);
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const Point_3 &p0 = point_pmap[source(he, tm)];
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const Point_3 &p1 = point_pmap[target(he, tm)];
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const Point_3 &p2 = point_pmap[target(next(he, tm), tm)];
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Vector_3 normal = CGAL::unit_normal(p0, p1, p2);
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facet_normals.insert(std::pair<face_descriptor, Vector_3>(f, normal));
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FT area(std::sqrt(CGAL::to_double(CGAL::squared_area(p0, p1, p2))));
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facet_areas.insert(std::pair<face_descriptor, FT>(f, area));
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}
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}
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// returns L21 error of a facet f to a proxy px.
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FT operator()(const face_descriptor &f, const Proxy &px) const {
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Vector_3 v = sum_functor(normal_pmap[f], scale_functor(px.normal, FT(-1)));
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return area_pmap[f] * scalar_product_functor(v, v);
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}
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private:
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std::map<face_descriptor, Vector_3> facet_normals;
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std::map<face_descriptor, FT> facet_areas;
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const FacetNormalMap normal_pmap;
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const FacetAreaMap area_pmap;
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Construct_scaled_vector_3 scale_functor;
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Compute_scalar_product_3 scalar_product_functor;
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Construct_sum_of_vectors_3 sum_functor;
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};
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// specialization
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template <typename TriangleMesh,
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typename GeomTraits,
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typename PlaneProxy>
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class L21Metric<TriangleMesh,
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typename boost::property_map<TriangleMesh, boost::vertex_point_t>::type,
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GeomTraits,
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PlaneProxy>
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{
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typedef typename GeomTraits::FT FT;
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typedef typename GeomTraits::Vector_3 Vector_3;
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typedef typename GeomTraits::Point_3 Point_3;
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typedef typename GeomTraits::Construct_scaled_vector_3 Construct_scaled_vector_3;
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typedef typename GeomTraits::Construct_sum_of_vectors_3 Construct_sum_of_vectors_3;
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typedef typename GeomTraits::Compute_scalar_product_3 Compute_scalar_product_3;
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typedef typename boost::graph_traits<TriangleMesh>::face_descriptor face_descriptor;
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typedef typename boost::graph_traits<TriangleMesh>::halfedge_descriptor halfedge_descriptor;
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typedef typename boost::property_map<TriangleMesh, boost::vertex_point_t>::type VertexPointMap;
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typedef boost::associative_property_map<std::map<face_descriptor, Vector_3> > FacetNormalMap;
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typedef boost::associative_property_map<std::map<face_descriptor, FT> > FacetAreaMap;
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public:
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// The type define required by the `ErrorMetric` concept
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typedef PlaneProxy Proxy;
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// constructor
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L21Metric(const TriangleMesh &tm)
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: normal_pmap(facet_normals), area_pmap(facet_areas) {
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GeomTraits traits;
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scalar_product_functor = traits.compute_scalar_product_3_object();
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sum_functor = traits.construct_sum_of_vectors_3_object();
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scale_functor = traits.construct_scaled_vector_3_object();
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// construct internal facet normal & area map
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VertexPointMap point_pmap = get(boost::vertex_point, const_cast<TriangleMesh &>(tm));
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BOOST_FOREACH(face_descriptor f, faces(tm)) {
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const halfedge_descriptor he = halfedge(f, tm);
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const Point_3 &p0 = point_pmap[source(he, tm)];
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const Point_3 &p1 = point_pmap[target(he, tm)];
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const Point_3 &p2 = point_pmap[target(next(he, tm), tm)];
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Vector_3 normal = CGAL::unit_normal(p0, p1, p2);
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facet_normals.insert(std::pair<face_descriptor, Vector_3>(f, normal));
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FT area(std::sqrt(CGAL::to_double(CGAL::squared_area(p0, p1, p2))));
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facet_areas.insert(std::pair<face_descriptor, FT>(f, area));
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}
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}
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// returns L21 error of a facet f to a proxy px.
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FT operator()(const face_descriptor &f, const Proxy &px) const {
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Vector_3 v = sum_functor(normal_pmap[f], scale_functor(px.normal, FT(-1)));
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return area_pmap[f] * scalar_product_functor(v, v);
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}
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private:
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std::map<face_descriptor, Vector_3> facet_normals;
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std::map<face_descriptor, FT> facet_areas;
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const FacetNormalMap normal_pmap;
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const FacetAreaMap area_pmap;
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Construct_scaled_vector_3 scale_functor;
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Compute_scalar_product_3 scalar_product_functor;
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Construct_sum_of_vectors_3 sum_functor;
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};
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/*!
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* \ingroup PkgTSMA
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* @brief L21 proxy fitting class for the Variational Shape Approximation algorithm.
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* It is simply a functor that takes a range of facets, fitting the proxy parameters.
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*
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* \cgalModels `ProxyFitting`
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*
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* @tparam TriangleMesh a triangle `FaceGraph`
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* @tparam VertexPointMap a property map containing the vertex points,
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and `boost::graph_traits<TriangleMesh>::%vertex_descriptor` as key type,
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GeomTraits::Point_3 as value type
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* @tparam GeomTraits geometric traits
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* @tparam PlaneProxy a model of `PlaneProxy`
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*/
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template <typename TriangleMesh,
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typename VertexPointMap
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= typename boost::property_map<TriangleMesh, boost::vertex_point_t>::type,
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typename GeomTraits = typename TriangleMesh::Traits,
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typename PlaneProxy = CGAL::PlaneProxy<GeomTraits> >
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class L21ProxyFitting
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{
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typedef typename GeomTraits::FT FT;
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typedef typename GeomTraits::Vector_3 Vector_3;
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typedef typename GeomTraits::Point_3 Point_3;
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typedef typename GeomTraits::Construct_scaled_vector_3 Construct_scaled_vector_3;
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typedef typename GeomTraits::Construct_sum_of_vectors_3 Construct_sum_of_vectors_3;
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typedef typename boost::graph_traits<TriangleMesh>::face_descriptor face_descriptor;
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typedef typename boost::graph_traits<TriangleMesh>::halfedge_descriptor halfedge_descriptor;
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typedef boost::associative_property_map<std::map<face_descriptor, Vector_3> > FacetNormalMap;
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typedef boost::associative_property_map<std::map<face_descriptor, FT> > FacetAreaMap;
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public:
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// The type define required by the `ErrorMetric` concept
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typedef PlaneProxy Proxy;
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// constructor.
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L21ProxyFitting(const TriangleMesh &tm, const VertexPointMap &point_pmap)
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: normal_pmap(facet_normals), area_pmap(facet_areas) {
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GeomTraits traits;
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sum_functor = traits.construct_sum_of_vectors_3_object();
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scale_functor = traits.construct_scaled_vector_3_object();
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// construct internal facet normal & area map
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BOOST_FOREACH(face_descriptor f, faces(tm)) {
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const halfedge_descriptor he = halfedge(f, tm);
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const Point_3 &p0 = point_pmap[source(he, tm)];
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const Point_3 &p1 = point_pmap[target(he, tm)];
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const Point_3 &p2 = point_pmap[target(next(he, tm), tm)];
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Vector_3 normal = CGAL::unit_normal(p0, p1, p2);
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facet_normals.insert(std::pair<face_descriptor, Vector_3>(f, normal));
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FT area(std::sqrt(CGAL::to_double(CGAL::squared_area(p0, p1, p2))));
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facet_areas.insert(std::pair<face_descriptor, FT>(f, area));
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}
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}
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// returns the proxy fitted from the facets from beg to end.
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template <typename FacetIterator>
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Proxy operator()(const FacetIterator beg, const FacetIterator end) const {
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CGAL_assertion(beg != end);
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// fitting normal
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Vector_3 norm = CGAL::NULL_VECTOR;
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for (FacetIterator fitr = beg; fitr != end; ++fitr) {
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norm = sum_functor(norm,
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scale_functor(normal_pmap[*fitr], area_pmap[*fitr]));
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}
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norm = scale_functor(norm,
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FT(1.0 / std::sqrt(CGAL::to_double(norm.squared_length()))));
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// construct proxy
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Proxy px;
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px.normal = norm;
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return px;
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}
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private:
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std::map<face_descriptor, Vector_3> facet_normals;
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std::map<face_descriptor, FT> facet_areas;
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const FacetNormalMap normal_pmap;
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const FacetAreaMap area_pmap;
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Construct_scaled_vector_3 scale_functor;
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Construct_sum_of_vectors_3 sum_functor;
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};
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// specialization
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template <typename TriangleMesh,
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typename GeomTraits,
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typename PlaneProxy>
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class L21ProxyFitting<TriangleMesh,
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typename boost::property_map<TriangleMesh, boost::vertex_point_t>::type,
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GeomTraits,
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PlaneProxy>
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{
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typedef typename GeomTraits::FT FT;
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typedef typename GeomTraits::Vector_3 Vector_3;
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typedef typename GeomTraits::Point_3 Point_3;
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typedef typename GeomTraits::Construct_scaled_vector_3 Construct_scaled_vector_3;
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typedef typename GeomTraits::Construct_sum_of_vectors_3 Construct_sum_of_vectors_3;
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typedef typename boost::graph_traits<TriangleMesh>::face_descriptor face_descriptor;
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typedef typename boost::graph_traits<TriangleMesh>::halfedge_descriptor halfedge_descriptor;
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typedef typename boost::property_map<TriangleMesh, boost::vertex_point_t>::type VertexPointMap;
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typedef boost::associative_property_map<std::map<face_descriptor, Vector_3> > FacetNormalMap;
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typedef boost::associative_property_map<std::map<face_descriptor, FT> > FacetAreaMap;
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public:
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// The type define required by the `ErrorMetric` concept
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typedef PlaneProxy Proxy;
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// constructor.
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L21ProxyFitting(const TriangleMesh &tm)
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: normal_pmap(facet_normals), area_pmap(facet_areas) {
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GeomTraits traits;
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sum_functor = traits.construct_sum_of_vectors_3_object();
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scale_functor = traits.construct_scaled_vector_3_object();
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// construct internal facet normal & area map
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VertexPointMap point_pmap = get(boost::vertex_point, const_cast<TriangleMesh &>(tm));
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BOOST_FOREACH(face_descriptor f, faces(tm)) {
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const halfedge_descriptor he = halfedge(f, tm);
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const Point_3 &p0 = point_pmap[source(he, tm)];
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const Point_3 &p1 = point_pmap[target(he, tm)];
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const Point_3 &p2 = point_pmap[target(next(he, tm), tm)];
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Vector_3 normal = CGAL::unit_normal(p0, p1, p2);
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facet_normals.insert(std::pair<face_descriptor, Vector_3>(f, normal));
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FT area(std::sqrt(CGAL::to_double(CGAL::squared_area(p0, p1, p2))));
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facet_areas.insert(std::pair<face_descriptor, FT>(f, area));
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}
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}
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// returns the proxy fitted from the facets from beg to end.
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template <typename FacetIterator>
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Proxy operator()(const FacetIterator beg, const FacetIterator end) const {
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CGAL_assertion(beg != end);
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// fitting normal
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Vector_3 norm = CGAL::NULL_VECTOR;
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for (FacetIterator fitr = beg; fitr != end; ++fitr) {
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norm = sum_functor(norm,
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scale_functor(normal_pmap[*fitr], area_pmap[*fitr]));
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}
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norm = scale_functor(norm,
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FT(1.0 / std::sqrt(CGAL::to_double(norm.squared_length()))));
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// construct proxy
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Proxy px;
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px.normal = norm;
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return px;
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}
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private:
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std::map<face_descriptor, Vector_3> facet_normals;
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std::map<face_descriptor, FT> facet_areas;
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const FacetNormalMap normal_pmap;
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const FacetAreaMap area_pmap;
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Construct_scaled_vector_3 scale_functor;
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Construct_sum_of_vectors_3 sum_functor;
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};
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/*!
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* \ingroup PkgTSMA
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* @brief L2 metric class for the Variational Shape Approximation algorithm.
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* It is simply a functor that takes a facet and a proxy, returns the L2 error between them.
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*
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* \cgalModels `ErrorMetric`
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*
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* @tparam TriangleMesh a triangle `FaceGraph`
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* @tparam VertexPointMap a property map containing the vertex points,
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and `boost::graph_traits<TriangleMesh>::%vertex_descriptor` as key type,
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GeomTraits::Point_3 as value type
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* @tparam GeomTraits geometric traits
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* @tparam PlaneProxy a model of `PlaneProxy`
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*/
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template <typename TriangleMesh,
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typename VertexPointMap
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= typename boost::property_map<TriangleMesh, boost::vertex_point_t>::type,
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typename GeomTraits = typename TriangleMesh::Traits,
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typename PlaneProxy = CGAL::PlaneProxy<GeomTraits> >
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class L2Metric
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{
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typedef typename GeomTraits::FT FT;
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typedef typename GeomTraits::Point_3 Point_3;
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typedef typename boost::graph_traits<TriangleMesh>::face_descriptor face_descriptor;
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typedef typename boost::graph_traits<TriangleMesh>::halfedge_descriptor halfedge_descriptor;
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typedef boost::associative_property_map<std::map<face_descriptor, FT> > FacetAreaMap;
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public:
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// The type define required by the `ErrorMetric` concept
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typedef PlaneProxy Proxy;
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// constructor
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L2Metric(const TriangleMesh &tm, const VertexPointMap &_point_pmap)
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: mesh(&tm), area_pmap(facet_areas), point_pmap(_point_pmap) {
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BOOST_FOREACH(face_descriptor f, faces(tm)) {
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const halfedge_descriptor he = halfedge(f, tm);
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const Point_3 &p0 = point_pmap[source(he, tm)];
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const Point_3 &p1 = point_pmap[target(he, tm)];
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const Point_3 &p2 = point_pmap[target(next(he, tm), tm)];
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FT area(std::sqrt(CGAL::to_double(CGAL::squared_area(p0, p1, p2))));
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facet_areas.insert(std::pair<face_descriptor, FT>(f, area));
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}
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}
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// returns the l2 fitting error of a facet f to proxy px.
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FT operator()(const face_descriptor &f, const PlaneProxy &px) const {
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halfedge_descriptor he = halfedge(f, *mesh);
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const Point_3 &p0 = point_pmap[source(he, *mesh)];
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const Point_3 &p1 = point_pmap[target(he, *mesh)];
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const Point_3 &p2 = point_pmap[target(next(he, *mesh), *mesh)];
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FT sq_d0 = CGAL::squared_distance(p0, px.fit_plane);
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FT sq_d1 = CGAL::squared_distance(p1, px.fit_plane);
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FT sq_d2 = CGAL::squared_distance(p2, px.fit_plane);
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FT d0(std::sqrt(CGAL::to_double(sq_d0)));
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FT d1(std::sqrt(CGAL::to_double(sq_d1)));
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FT d2(std::sqrt(CGAL::to_double(sq_d2)));
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return (sq_d0 + sq_d1 + sq_d2 + d0 * d1 + d1 * d2 + d2 * d0) * area_pmap[f] / FT(6);
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}
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private:
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const TriangleMesh *mesh;
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std::map<face_descriptor, FT> facet_areas;
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const FacetAreaMap area_pmap;
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const VertexPointMap point_pmap;
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};
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// specialization
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template <typename TriangleMesh,
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typename GeomTraits,
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typename PlaneProxy>
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class L2Metric<TriangleMesh,
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typename boost::property_map<TriangleMesh, boost::vertex_point_t>::type,
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GeomTraits,
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PlaneProxy>
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{
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typedef typename GeomTraits::FT FT;
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typedef typename GeomTraits::Point_3 Point_3;
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typedef typename boost::graph_traits<TriangleMesh>::face_descriptor face_descriptor;
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typedef typename boost::graph_traits<TriangleMesh>::halfedge_descriptor halfedge_descriptor;
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typedef typename boost::property_map<TriangleMesh, boost::vertex_point_t>::type VertexPointMap;
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typedef boost::associative_property_map<std::map<face_descriptor, FT> > FacetAreaMap;
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public:
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// The type define required by the `ErrorMetric` concept
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typedef PlaneProxy Proxy;
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// constructor
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L2Metric(const TriangleMesh &tm)
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: mesh(&tm), area_pmap(facet_areas),
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point_pmap(get(boost::vertex_point, const_cast<TriangleMesh &>(tm))) {
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BOOST_FOREACH(face_descriptor f, faces(tm)) {
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const halfedge_descriptor he = halfedge(f, tm);
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const Point_3 &p0 = point_pmap[source(he, tm)];
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const Point_3 &p1 = point_pmap[target(he, tm)];
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const Point_3 &p2 = point_pmap[target(next(he, tm), tm)];
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FT area(std::sqrt(CGAL::to_double(CGAL::squared_area(p0, p1, p2))));
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facet_areas.insert(std::pair<face_descriptor, FT>(f, area));
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}
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}
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// returns the l2 fitting error of a facet f to proxy px.
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FT operator()(const face_descriptor &f, const PlaneProxy &px) const {
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halfedge_descriptor he = halfedge(f, *mesh);
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const Point_3 &p0 = point_pmap[source(he, *mesh)];
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const Point_3 &p1 = point_pmap[target(he, *mesh)];
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const Point_3 &p2 = point_pmap[target(next(he, *mesh), *mesh)];
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FT sq_d0 = CGAL::squared_distance(p0, px.fit_plane);
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FT sq_d1 = CGAL::squared_distance(p1, px.fit_plane);
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FT sq_d2 = CGAL::squared_distance(p2, px.fit_plane);
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FT d0(std::sqrt(CGAL::to_double(sq_d0)));
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FT d1(std::sqrt(CGAL::to_double(sq_d1)));
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FT d2(std::sqrt(CGAL::to_double(sq_d2)));
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return (sq_d0 + sq_d1 + sq_d2 + d0 * d1 + d1 * d2 + d2 * d0) * area_pmap[f] / FT(6);
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}
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private:
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const TriangleMesh *mesh;
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std::map<face_descriptor, FT> facet_areas;
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const FacetAreaMap area_pmap;
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const VertexPointMap point_pmap;
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};
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/*!
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* \ingroup PkgTSMA
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* @brief L2 proxy fitting class for the Variational Shape Approximation algorithm.
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* It is simply a functor that takes a range of facets, fitting the L2 proxy parameters.
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* It uses the PCA algorithm to fit the proxy parameters.
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*
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* \cgalModels `ProxyFitting`
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*
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* @tparam TriangleMesh a triangle `FaceGraph`
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* @tparam VertexPointMap a property map containing the vertex points,
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and `boost::graph_traits<TriangleMesh>::%vertex_descriptor` as key type,
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GeomTraits::Point_3 as value type
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* @tparam GeomTraits geometric traits
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* @tparam PlaneProxy a model of `PlaneProxy`
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*/
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template <typename TriangleMesh,
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typename VertexPointMap
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= typename boost::property_map<TriangleMesh, boost::vertex_point_t>::type,
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typename GeomTraits = typename TriangleMesh::Traits,
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typename PlaneProxy = CGAL::PlaneProxy<GeomTraits> >
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class L2ProxyFitting
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{
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typedef typename GeomTraits::Point_3 Point_3;
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typedef typename GeomTraits::Triangle_3 Triangle_3;
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typedef typename boost::graph_traits<TriangleMesh>::halfedge_descriptor halfedge_descriptor;
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|
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public:
|
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// The type define required by the `ErrorMetric` concept
|
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typedef PlaneProxy Proxy;
|
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|
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// construct L2 proxy fitting functor from a triangle mesh and the vertex point map.
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L2ProxyFitting(const TriangleMesh &_mesh, const VertexPointMap &_point_pmap)
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: mesh(&_mesh), point_pmap(_point_pmap) {}
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|
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// returns the proxy fitted from a range of facets.
|
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template <typename FacetIterator>
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Proxy operator()(const FacetIterator beg, const FacetIterator end) const {
|
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CGAL_assertion(beg != end);
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|
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std::list<Triangle_3> tris;
|
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for (FacetIterator fitr = beg; fitr != end; ++fitr) {
|
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halfedge_descriptor he = halfedge(*fitr, *mesh);
|
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const Point_3 &p0 = point_pmap[source(he, *mesh)];
|
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const Point_3 &p1 = point_pmap[target(he, *mesh)];
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const Point_3 &p2 = point_pmap[target(next(he, *mesh), *mesh)];
|
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tris.push_back(Triangle_3(p0, p1, p2));
|
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}
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|
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// construct and fit proxy plane
|
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Proxy px;
|
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CGAL::linear_least_squares_fitting_3(
|
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tris.begin(),
|
|
tris.end(),
|
|
px.fit_plane,
|
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CGAL::Dimension_tag<2>());
|
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|
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return px;
|
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}
|
|
|
|
private:
|
|
const TriangleMesh *mesh;
|
|
const VertexPointMap point_pmap;
|
|
};
|
|
|
|
// specialization.
|
|
template <typename TriangleMesh,
|
|
typename GeomTraits,
|
|
typename PlaneProxy>
|
|
class L2ProxyFitting<TriangleMesh,
|
|
typename boost::property_map<TriangleMesh, boost::vertex_point_t>::type,
|
|
GeomTraits,
|
|
PlaneProxy>
|
|
{
|
|
typedef typename GeomTraits::Point_3 Point_3;
|
|
typedef typename GeomTraits::Triangle_3 Triangle_3;
|
|
|
|
typedef typename boost::graph_traits<TriangleMesh>::halfedge_descriptor halfedge_descriptor;
|
|
|
|
typedef typename boost::property_map<TriangleMesh, boost::vertex_point_t>::type VertexPointMap;
|
|
|
|
public:
|
|
// The type define required by the `ErrorMetric` concept
|
|
typedef PlaneProxy Proxy;
|
|
|
|
// construct L2 proxy fitting functor from a triangle mesh.
|
|
L2ProxyFitting(const TriangleMesh &_mesh)
|
|
: mesh(&_mesh),
|
|
point_pmap(get(boost::vertex_point, const_cast<TriangleMesh &>(_mesh))) {}
|
|
|
|
// returns the proxy fitted from a range of facets.
|
|
template <typename FacetIterator>
|
|
Proxy operator()(const FacetIterator beg, const FacetIterator end) const {
|
|
CGAL_assertion(beg != end);
|
|
|
|
std::list<Triangle_3> tris;
|
|
for (FacetIterator fitr = beg; fitr != end; ++fitr) {
|
|
halfedge_descriptor he = halfedge(*fitr, *mesh);
|
|
const Point_3 &p0 = point_pmap[source(he, *mesh)];
|
|
const Point_3 &p1 = point_pmap[target(he, *mesh)];
|
|
const Point_3 &p2 = point_pmap[target(next(he, *mesh), *mesh)];
|
|
tris.push_back(Triangle_3(p0, p1, p2));
|
|
}
|
|
|
|
// construct and fit proxy plane
|
|
Proxy px;
|
|
CGAL::linear_least_squares_fitting_3(
|
|
tris.begin(),
|
|
tris.end(),
|
|
px.fit_plane,
|
|
CGAL::Dimension_tag<2>());
|
|
|
|
return px;
|
|
}
|
|
|
|
private:
|
|
const TriangleMesh *mesh;
|
|
const VertexPointMap point_pmap;
|
|
};
|
|
|
|
} // end namespace CGAL
|
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|
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#endif // CGAL_SURFACE_MESH_APPROXIMATION_VSA_METRICS_H
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