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// Copyright (c) 2005 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_3.h $ // $Id: include/CGAL/natural_neighbor_coordinates_3.h b26b07a1242 $ // SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial // // // Author(s) : Raphaelle Chaine #ifndef CGAL_NATURAL_NEIGHBORS_3_H #define CGAL_NATURAL_NEIGHBORS_3_H #include #include #include #include #include #include #include #include //TO DO : to remove #include #include #include #include namespace CGAL { // ====================== Geometric Traits utilities ========================================= // === Declarations template typename Gt::FT signed_area(const typename Gt::Point_3& p, const typename Gt::Point_3& q, const typename Gt::Point_3& r, const typename Gt::Point_3& point_of_view, const Gt& gt = Gt()); // ====================== Delaunay Triangulation utilities ========================== // === Declarations template < class DT> typename DT::Geom_traits::Point_3 construct_circumcenter(const typename DT::Facet& f, const typename DT::Geom_traits::Point_3& Q, const typename DT::Geom_traits& gt = typename DT::Geom_traits()); // ====================== Natural Neighbors Queries ========================== // === Definitions // Given a 3D point Q and a 3D Delaunay triangulation dt, // the next two functions calculate the natural neighbors and coordinates of Q with regard of dt // // OutputIterator has value type // std::pair // Result : // - An OutputIterator providing natural neighbors P_i of Q with unnormalized coordinates a_i associated to them // - The normalizing coefficient (sum over i of the a_i) // - A boolean specifying whether the calculation has succeeded or not template Triple< OutputIterator, // iterator with value type std::pair typename Dt::Geom_traits::FT, // Should provide 0 and 1 bool > laplace_natural_neighbor_coordinates_3(const Dt& dt, const typename Dt::Geom_traits::Point_3& Q, OutputIterator nn_out, typename Dt::Geom_traits::FT& norm_coeff, const typename Dt::Cell_handle start = CGAL_TYPENAME_DEFAULT_ARG Dt::Cell_handle()) { typedef typename Dt::Geom_traits Gt; typedef typename Gt::Point_3 Point; typedef typename Dt::Cell_handle Cell_handle; typedef typename Dt::Vertex_handle Vertex_handle; typedef typename Dt::Facet Facet; typedef typename Dt::Locate_type Locate_type; typedef typename Gt::FT Coord_type; CGAL_precondition (dt.dimension() == 3); Locate_type lt; int li, lj; Cell_handle c = dt.locate( Q, lt, li, lj, start); if ( lt == Dt::VERTEX ) { *nn_out++= std::make_pair(c->vertex(li), Coord_type(1)); return make_triple(nn_out, norm_coeff = Coord_type(1),true); } else if (dt.is_infinite(c)) { //point outside the convex-hull return make_triple(nn_out, Coord_type(1), false); } std::set cells; // To replace the forbidden access to the "in conflict" flag : // std::find operations on this set std::vector bound_facets; bound_facets.reserve(32); // Find the cells in conflict with Q dt.find_conflicts(Q, c, std::back_inserter(bound_facets), std::inserter(cells, cells.begin())); std::map coordinate; typename std::map::iterator coor_it; typename std::vector::iterator bound_it; for (bound_it = bound_facets.begin(); bound_it != bound_facets.end(); ++bound_it) { //for each facet on the boundary Facet f1 = *bound_it; Cell_handle cc1 = f1.first; if (dt.is_infinite(cc1)) return make_triple(nn_out, norm_coeff=Coord_type(1), false);//point outside the convex-hull CGAL_assertion_code(Cell_handle cc2 = cc1->neighbor(f1.second);) CGAL_assertion(std::find(cells.begin(),cells.end(),cc1) != cells.end());//TODO : Delete CGAL_assertion(std::find(cells.begin(),cells.end(),cc2) == cells.end());//TODO : Delete Point C_1 = construct_circumcenter
(f1, Q, dt.geom_traits()); for(int j=1; j<4; j++) { //for each vertex P of the boundary facet Vertex_handle vP = cc1->vertex((f1.second+j)&3); Vertex_handle vR = cc1->vertex(dt.next_around_edge(f1.second,(f1.second+j)&3)); // turn around the oriented edge vR vP Cell_handle cc3 = cc1; int num_next = dt.next_around_edge((f1.second+j)&3,f1.second); Cell_handle next = cc3->neighbor(num_next); while (std::find(cells.begin(),cells.end(),next) != cells.end()) { CGAL_assertion( next != cc1 ); cc3 = next; num_next = dt.next_around_edge(cc3->index(vR),cc3->index(vP)); next = cc3->neighbor(num_next); } Point C_3 = construct_circumcenter
(Facet(cc3,num_next), Q, dt.geom_traits()); Point midPQ = midpoint(vP->point(),Q); Coord_type coor_add = signed_area(C_3,C_1,midPQ, vP->point(), dt.geom_traits()); ((coor_it = coordinate.find(vP)) == coordinate.end())? coordinate[vP] = coor_add : coor_it->second += coor_add; // Replace by a function call } } //end : for each facet on the boundary norm_coeff = 0; for (coor_it=coordinate.begin(); coor_it!=coordinate.end(); ++coor_it) { Coord_type co = coor_it->second / (CGAL_NTS sqrt(dt.geom_traits().compute_squared_distance_3_object()( coor_it->first->point(),Q))); *nn_out++ = std::make_pair(coor_it->first,co); norm_coeff += co; } return make_triple(nn_out, norm_coeff, true); } template Triple< OutputIterator, // iterator with value type std::pair typename Dt::Geom_traits::FT, // Should provide 0 and 1 bool > sibson_natural_neighbor_coordinates_3(const Dt& dt, const typename Dt::Geom_traits::Point_3& Q, OutputIterator nn_out, typename Dt::Geom_traits::FT& norm_coeff, const typename Dt::Cell_handle start = CGAL_TYPENAME_DEFAULT_ARG Dt::Cell_handle()) { typedef typename Dt::Geom_traits Gt; typedef typename Gt::Point_3 Point; typedef typename Dt::Cell_handle Cell_handle; typedef typename Dt::Vertex_handle Vertex_handle; typedef typename Dt::Facet Facet; typedef typename Dt::Locate_type Locate_type; typedef typename Gt::FT Coord_type; CGAL_precondition (dt.dimension()== 3); Locate_type lt; int li, lj; Cell_handle c = dt.locate( Q, lt, li, lj, start); if ( lt == Dt::VERTEX ) { *nn_out++ = std::make_pair(c->vertex(li),Coord_type(1)); return make_triple(nn_out,norm_coeff=Coord_type(1),true); } else if (dt.is_infinite(c)) { //point outside the convex-hull return make_triple(nn_out, Coord_type(1), false); } std::set cells; typename std::set::iterator cit; // To replace the forbidden access to the "in conflict" flag : // std::find operations on this set // Find the cells in conflict with Q dt.find_conflicts(Q, c, Emptyset_iterator(), std::inserter(cells,cells.begin())); std::map coordinate; typename std::map::iterator coor_it; for (cit = cells.begin(); cit != cells.end(); ++cit) { // for each cell cc1 in conflict Cell_handle cc1 = *cit; CGAL_assertion(std::find(cells.begin(),cells.end(),cc1)!=cells.end());//TODO : Delete if (dt.is_infinite(cc1)) return make_triple(nn_out,norm_coeff=Coord_type(1), false);//point outside the convex-hull typename Dt::Geom_traits::Compute_volume_3 vol = dt.geom_traits().compute_volume_3_object(); Point C1 = dt.dual(cc1); for(int i=0; i<4; i++) { //for each neighboring cell cc2 of cc1 Cell_handle cc2 = cc1->neighbor(i); if(std::find(cells.begin(),cells.end(),cc2) == cells.end()) { // cc2 outside the conflict cavity Point C_1 = construct_circumcenter
(Facet(cc1,i), Q, dt.geom_traits()); for(int j=1; j<4; j++) { //for each vertex P of the boundary facet Vertex_handle vP = cc1->vertex((i+j)&3);//&3 in place of %4 Vertex_handle vR = cc1->vertex(dt.next_around_edge(i,(i+j)&3)); // turn around the oriented edge vR vP Cell_handle cc3 = cc1; int num_next = dt.next_around_edge((i+j)&3,i); Cell_handle next = cc3->neighbor(num_next); while (std::find(cells.begin(),cells.end(),next) != cells.end()) { //next is in conflict CGAL_assertion( next != cc1 ); cc3 = next; num_next = dt.next_around_edge(cc3->index(vR),cc3->index(vP)); next = cc3->neighbor(num_next); } if (dt.is_infinite(cc3)) { //point outside the convex-hull return make_triple(nn_out,norm_coeff = Coord_type(1), false); } Point C3 = dt.dual(cc3); Point C_3 = construct_circumcenter
(Facet(cc3,num_next), Q, dt.geom_traits()); Point midPQ = midpoint(vP->point(),Q); Point midPR = midpoint(vP->point(),vR->point()); Coord_type coor_add = vol(C_1,C1,midPR,midPQ); coor_add -= vol(C_1,C_3,midPR,midPQ); coor_add += vol(C3,C_3,midPR,midPQ); ((coor_it = coordinate.find(vP)) == coordinate.end())? coordinate[vP] = coor_add : coor_it->second += coor_add;// Replace by a function call } } else // cc2 in the conflict cavity { CGAL_assertion(std::find(cells.begin(),cells.end(),cc2)!=cells.end());//TODO : Delete if (dt.is_infinite(cc2)) { //point outside the convex-hull return make_triple(nn_out,norm_coeff = Coord_type(1), false); } Point C2 = dt.dual(cc2); for(int j=1;j<4;j++) { //for each vertex P of the internal facet Vertex_handle vP=cc1->vertex((i+j)&3); Vertex_handle vR=cc1->vertex(dt.next_around_edge(i,(i+j)&3)); Point midPQ = midpoint(vP->point(),Q); Point midPR = midpoint(vP->point(),vR->point()); Coord_type coor_add = vol(C2,C1,midPR,midPQ); ((coor_it=coordinate.find(vP))==coordinate.end())? coordinate[vP]=coor_add : coor_it->second+=coor_add;// Replace by a function call } } } } norm_coeff=0; for (coor_it=coordinate.begin(); coor_it!=coordinate.end(); ++coor_it) { *nn_out++ = std::make_pair(coor_it->first,coor_it->second); norm_coeff += coor_it->second; } return make_triple(nn_out,norm_coeff,true); } template bool is_correct_natural_neighborhood(const Dt& /*dt*/, const typename Dt::Geom_traits::Point_3& Q, InputIterator it_begin, InputIterator it_end, const typename Dt::Geom_traits::FT& norm_coeff) { typedef typename Dt::Geom_traits Gt; typedef typename Gt::FT Coord_type; Coord_type sum_x(0); Coord_type sum_y(0); Coord_type sum_z(0); InputIterator it; for(it = it_begin ; it != it_end ; ++it) { sum_x += it->second*(it->first->point().x()); sum_y += it->second*(it->first->point().y()); sum_z += it->second*(it->first->point().z()); } //!!!! to be replaced by a linear combination of points as soon // as it is available in the kernel. std::cout << sum_x/norm_coeff << " " << sum_y/norm_coeff << " " << sum_z/norm_coeff << std::endl; return ((sum_x == norm_coeff*Q.x()) && (sum_y == norm_coeff*Q.y()) && (sum_z == norm_coeff*Q.z())); } // ====================== Geometric Traits utilities ========================================= // === Definitions template typename Gt::FT signed_area(const typename Gt::Point_3& p, const typename Gt::Point_3& q, const typename Gt::Point_3& r, const typename Gt::Point_3& point_of_view, const Gt& gt /* = Gt() */) { // signed area of the triangle p q r return gt.compute_area_3_object()(p,q,r) * (gt.orientation_3_object()(p, q, r, point_of_view) == COUNTERCLOCKWISE?+1:-1); } // ====================== Delaunay Triangulation utilities ========================== // === Definitions template < class DT> typename DT::Geom_traits::Point_3 construct_circumcenter(const typename DT::Facet& f, const typename DT::Geom_traits::Point_3& Q, const typename DT::Geom_traits& gt /* = typename DT::Geom_traits() */ ) { CGAL_precondition(//&3 in place of %4 !gt.coplanar_3_object()( f.first->vertex((f.second+1)&3)->point(), f.first->vertex((f.second+2)&3)->point(), f.first->vertex((f.second+3)&3)->point(), Q)); // else the facet is not on the envelope of the conflict cavity associated to P return gt.construct_circumcenter_3_object()( f.first->vertex((f.second+1)&3)->point(), f.first->vertex((f.second+2)&3)->point(), f.first->vertex((f.second+3)&3)->point(), Q); } } //namespace CGAL #endif // CGAL_NATURAL_NEIGHBORS_3_H