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// Copyright (c) 2003 INRIA Sophia-Antipolis (France). // All rights reserved. // // This file is part of CGAL (www.cgal.org). // // $URL: https://github.com/CGAL/cgal/blob/v6.1/Interpolation/include/CGAL/natural_neighbor_coordinates_2.h $ // $Id: include/CGAL/natural_neighbor_coordinates_2.h b26b07a1242 $ // SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial // // Author(s) : Frank Da, Julia Floetotto #ifndef CGAL_NATURAL_NEIGHBOR_COORDINATES_2_H #define CGAL_NATURAL_NEIGHBOR_COORDINATES_2_H #include #include #include #include #include #include #include #include #include #include #include #include #include namespace CGAL { // The following natural_neighbor_coordinate_2 functions fix the // traits class to be Dt::Geom_traits. The following signatures could // be used if one wants to pass a traits class as argument: // // template // Triple< OutputIterator, typename Traits::FT, bool > // natural_neighbor_coordinates_2(const Dt& dt, // const typename Traits::Point_2& p, // OutputIterator out, const Traits& traits, // typename Dt::Face_handle start // = typename Dt::Face_handle()) //template //Triple< OutputIterator, typename Traits::FT, bool > //natural_neighbor_coordinates_2(const Dt& dt, // typename Dt::Vertex_handle vh, // OutputIterator out, const Traits& traits) //the following two functions suppose that // OutputIterator has value type `pair` //!!!they are not documented!!! template < class Dt, class OutputIterator > Triple< OutputIterator, typename Dt::Geom_traits::FT, bool > natural_neighbors_2(const Dt& dt, const typename Dt::Geom_traits::Point_2& p, OutputIterator out, typename Dt::Face_handle start = typename Dt::Face_handle()) { typedef typename Dt::Geom_traits Traits; typedef typename Traits::FT Coord_type; typedef typename Traits::Point_2 Point_2; typedef typename Dt::Face_handle Face_handle; typedef typename Dt::Vertex_handle Vertex_handle; typedef typename Dt::Edge Edge; typedef typename Dt::Locate_type Locate_type; typedef typename Traits::Equal_x_2 Equal_x_2; CGAL_precondition(dt.dimension() == 2); Locate_type lt; int li; Face_handle fh = dt.locate(p, lt, li, start); if (lt == Dt::OUTSIDE_AFFINE_HULL || lt == Dt::OUTSIDE_CONVEX_HULL) { return make_triple(out, Coord_type(1), false); } if ((lt == Dt::EDGE && (dt.is_infinite(fh) || dt.is_infinite(fh->neighbor(li))))) { Vertex_handle v1 = fh->vertex(dt.cw(li)); Vertex_handle v2 = fh->vertex(dt.ccw(li)); Point_2 p1(v1->point()), p2(v2->point()); Coord_type coef1(0); Equal_x_2 equal_x_2; if(!equal_x_2(p1,p2)) coef1 = (p.x() - p2.x()) / (p1.x() - p2.x()); else coef1 = (p.y() - p2.y()) / (p1.y() - p2.y()); if(coef1 == 0) { *out++ = std::make_pair(v2, Coord_type(1)); return make_triple(out, Coord_type(1), true); } Coord_type coef2 = 1 - coef1; if(coef2 == 0) { *out++ = std::make_pair(v1, Coord_type(1)); return make_triple(out, Coord_type(1), true); } *out++ = std::make_pair(v1,coef1); *out++ = std::make_pair(v2,coef2); return { out, coef1+coef2, true }; } if (lt == Dt::VERTEX) { *out++= std::make_pair(fh->vertex(li), Coord_type(1)); return make_triple(out, Coord_type(1), true); } std::list hole; dt.get_boundary_of_conflicts(p, std::back_inserter(hole), fh); return natural_neighbors_2(dt, p, out, hole.begin(), hole.end()); } // This function is called when the conflict zone is known. // OutputIterator has value type `pair` // // \pre p must lie inside the hole (=^ inside convex hull of neighbors) template < class Dt, class OutputIterator, class EdgeIterator > Triple< OutputIterator, typename Dt::Geom_traits::FT, bool > natural_neighbors_2(const Dt& dt, const typename Dt::Geom_traits::Point_2& p, OutputIterator out, EdgeIterator hole_begin, EdgeIterator hole_end) { CGAL_precondition(dt.dimension() == 2); typedef typename Dt::Geom_traits Traits; typedef typename Traits::FT Coord_type; typedef typename Traits::Point_2 Point_2; typedef typename Dt::Vertex_handle Vertex_handle; typedef typename Dt::Face_circulator Face_circulator; std::vector vor(3); Coord_type area_sum(0); EdgeIterator hit = hole_end; --hit; // At the beginning, `prev` is the "last" vertex of the hole. // Later, `prev` is the last vertex processed (previously). Vertex_handle prev = hit->first->vertex(dt.cw(hit->second)); hit = hole_begin; while (hit != hole_end) { Coord_type area(0); Vertex_handle current = hit->first->vertex(dt.cw(hit->second)); vor[0] = dt.geom_traits().construct_circumcenter_2_object()( current->point(), hit->first->vertex(dt.ccw(hit->second))->point(), p); Face_circulator fc = dt.incident_faces(current, hit->first); ++fc; vor[1] = dt.dual(fc); while(!fc->has_vertex(prev)) { ++fc; vor[2] = dt.dual(fc); area += polygon_area_2(vor.begin(), vor.end(), dt.geom_traits()); vor[1] = vor[2]; } vor[2] = dt.geom_traits().construct_circumcenter_2_object()(prev->point(), current->point(), p); area += polygon_area_2(vor.begin(), vor.end(), dt.geom_traits()); if(area > 0) { *out++ = std::make_pair(current,area); area_sum += area; } //update prev and hit: prev = current; ++hit; } return make_triple(out, area_sum, true); } /////////////////////////////////////////////////////////////////////////////// /////////////////////////////////////////////////////////////////////////////// // This function is called when the conflict zone is known. // OutputIterator has value type `pair< Dt::Geom_traits::Point_2, Dt::Geom_traits::FT>` template < class Dt, class OutputIterator, class OutputFunctor, class EdgeIterator > Triple< OutputIterator, typename Dt::Geom_traits::FT, bool > natural_neighbor_coordinates_2(const Dt& dt, const typename Dt::Geom_traits::Point_2& p, OutputIterator out, OutputFunctor fct, EdgeIterator hole_begin, EdgeIterator hole_end) { CGAL_precondition(dt.dimension() == 2); typedef Interpolation::internal:: Project_vertex_output_iterator OutputIteratorWithFunctor; typedef typename Dt::Geom_traits::FT FT; OutputIteratorWithFunctor op(out, fct); Triple result = natural_neighbors_2(dt, p, op, hole_begin, hole_end); return make_triple(result.first.base(), result.second, result.third); } // Same as above but without OutputFunctor. Default to extracting the point, for backward compatibility. template < class Dt, class OutputIterator, class EdgeIterator > Triple< OutputIterator, typename Dt::Geom_traits::FT, bool > natural_neighbor_coordinates_2(const Dt& dt, const typename Dt::Geom_traits::Point_2& p, OutputIterator out, EdgeIterator hole_begin, EdgeIterator hole_end) { typedef typename Dt::Geom_traits::FT FT; typedef Interpolation::internal::Extract_point_in_pair OutputFunctor; return natural_neighbor_coordinates_2(dt, p, out, OutputFunctor(), hole_begin, hole_end); } /////////////////////////////////////////////////////////////////////////////// /////////////////////////////////////////////////////////////////////////////// // Function with a point. Can take a default starting face. template < class Dt, class OutputIterator, class OutputFunctor > Triple< OutputIterator, typename Dt::Geom_traits::FT, bool > natural_neighbor_coordinates_2(const Dt& dt, const typename Dt::Geom_traits::Point_2& p, OutputIterator out, OutputFunctor fct, typename Dt::Face_handle start = CGAL_TYPENAME_DEFAULT_ARG Dt::Face_handle(), std::enable_if_t< !is_iterator::value >* = 0) { CGAL_precondition(dt.dimension() == 2); typedef Interpolation::internal:: Project_vertex_output_iterator OutputIteratorWithFunctor; typedef typename Dt::Geom_traits::FT FT; OutputIteratorWithFunctor op(out, fct); Triple result = natural_neighbors_2(dt, p, op, start); return make_triple(result.first.base(), result.second, result.third); } // Same as above but without OutputFunctor. Default to extracting the point, for backward compatibility. template < class Dt, class OutputIterator > Triple< OutputIterator, typename Dt::Geom_traits::FT, bool > natural_neighbor_coordinates_2(const Dt& dt, const typename Dt::Geom_traits::Point_2& p, OutputIterator out, typename Dt::Face_handle start = CGAL_TYPENAME_DEFAULT_ARG Dt::Face_handle()) { typedef typename Dt::Geom_traits::FT FT; typedef Interpolation::internal::Extract_point_in_pair OutputFunctor; return natural_neighbor_coordinates_2(dt, p, out, OutputFunctor(), start); } //////////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////////// // Function with a Vertex_handle template Triple< OutputIterator, typename Dt::Geom_traits::FT, bool > natural_neighbor_coordinates_2(const Dt& dt, typename Dt::Vertex_handle vh, OutputIterator out, OutputFunctor fct) { // This function creates a small triangulation of the incident vertices of this vertex // and computes the natural neighbor coordinates of ch->point() w.r.t. it. typedef typename Dt::Vertex_circulator Vertex_circulator; typedef typename Dt::Vertex_handle Vertex_handle; CGAL_precondition(dt.dimension() == 2); Dt t2; Vertex_circulator vc = dt.incident_vertices(vh), done(vc); typedef std::map Correspondence_map; Correspondence_map cm; do { if(dt.is_infinite(vc)) continue; Vertex_handle t2_vh = t2.insert(vc->point()); cm[t2_vh] = vc; } while(++vc != done); // Before applying the output functor, we need to switch back from vertices of `t2` // to the vertices of `dt` typedef typename Dt::Geom_traits::FT FT; typedef Interpolation::internal::Pair_mapper Mapper; Mapper pair_mapper(cm); CGAL::Unary_compose_1 composed_fct(fct, pair_mapper); return natural_neighbor_coordinates_2(t2, vh->point(), out, composed_fct); } // Same as above but without OutputFunctor. Default to extracting the point, for backward compatibility. template Triple< OutputIterator, typename Dt::Geom_traits::FT, bool > natural_neighbor_coordinates_2(const Dt& dt, typename Dt::Vertex_handle vh, OutputIterator out) { typedef typename Dt::Geom_traits::FT FT; typedef Interpolation::internal::Extract_point_in_pair OutputFunctor; return natural_neighbor_coordinates_2(dt, vh, out, OutputFunctor()); } //////////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////////// // OutputIterator has value type `std::pair< Dt::Geom_traits::Point_2, Dt::Geom_traits::FT>` template < class Dt, class OutputIterator, class OutputFunctor > class natural_neighbor_coordinates_2_object { public: typedef OutputFunctor Function; Triple< OutputIterator, typename Dt::Geom_traits::FT, bool > operator()(const Dt& dt, typename Dt::Vertex_handle vh, OutputIterator out, OutputFunctor fct) const { return natural_neighbor_coordinates_2(dt, vh, out, fct); } }; } //namespace CGAL #endif // CGAL_NATURAL_NEIGHBOR_COORDINATES_2_H