98 lines
3.1 KiB
C
98 lines
3.1 KiB
C
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// Copyright (c) 2005-2008 Max-Planck-Institute Saarbruecken (Germany).
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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/Minkowski_sum_3/include/CGAL/minkowski_sum_3.h $
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// $Id: minkowski_sum_3.h 0779373 2020-03-26T13:31:46+01:00 Sébastien Loriot
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// SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
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//
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//
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// Author(s) : Peter Hachenberger <hachenberger@mpi-sb.mpg.de>
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#ifndef CGAL_MINKOWSKI_SUM_3_H
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#define CGAL_MINKOWSKI_SUM_3_H
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#include <CGAL/license/Minkowski_sum_3.h>
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#include <CGAL/convex_decomposition_3.h>
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#include <CGAL/Minkowski_sum_3/bipartite_nary_union_sorted_combined.h>
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#include <CGAL/Is_extended_kernel.h>
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/// \file minkowski_sum_3.h
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namespace CGAL {
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/*!
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\ingroup PkgMinkowskiSum3Ref
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The function `minkowski_sum_3()` computes the Minkowski sum of two
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given 3D Nef polyhedra \f$ N0\f$ and \f$ N1\f$. Note that the function runs in
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\f$ O(n^3m^3)\f$ time in the worst case, where \f$ n\f$ and
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\f$ m\f$ are the complexities of the two input polyhedra (the complexity of
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a `Nef_polyhedron_3` is the sum of its `Vertices`,
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`Halfedges` and `SHalfedges`).
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An input polyhedron may consist of:
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<OL>
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<LI>singular vertices
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<LI>singular edges
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<LI>singular convex facets without holes
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<LI>surfaces with convex facets that have no holes.
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<LI>three-dimensional features, whose coplanar facets have
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common selection marks (this includes open and closed solids)
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</OL>
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Taking a different viewpoint, the implementation is restricted as
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follows:
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<OL>
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<LI>The input polyhedra must be bounded (selected outer volume is ignored).
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<LI>All sets of coplanar facets of a full-dimensional
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feature must have the same selection mark (in case of different
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selection marks, unselected is assumed).
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<LI>All facets of lower-dimensional features need to be convex and
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must not have holes (non-convex facets and holes are ignored).
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</OL>
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\post If either of the input polyhedra is non-convex, it is modified during the computation, i.e., it is decomposed into convex pieces.
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\sa `CGAL::Nef_polyhedron_3<Traits>`
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\sa \link CGAL::convex_decomposition_3 `CGAL::convex_decomposition_3()`\endlink
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*/
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template<typename Nef_polyhedron_3>
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Nef_polyhedron_3
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minkowski_sum_3(Nef_polyhedron_3& N0, Nef_polyhedron_3& N1)
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{
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typedef typename Nef_polyhedron_3::Kernel Kernel;
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typedef typename Is_extended_kernel<Kernel>::value_type Is_extended_kernel;
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if(check_tag(Is_extended_kernel())) {
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std::cerr << "extended kernel is not supported" << std::endl;
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return N0;
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}
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if(N0.volumes_begin()->mark()) {
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std::cerr << "first parameter is an infinite point set" << std::endl;
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return N0;
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}
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if(N1.volumes_begin()->mark()) {
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std::cerr << "second parameter is an infinite point set" << std::endl;
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return N1;
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}
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CGAL::convex_decomposition_3<Nef_polyhedron_3>(N0);
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CGAL::convex_decomposition_3<Nef_polyhedron_3>(N1);
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CGAL_assertion(N0.is_valid());
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CGAL_assertion(N1.is_valid());
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Nef_polyhedron_3 result =
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CGAL::bipartite_nary_union_sorted_combined(N0, N1);
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CGAL_assertion(result.is_valid());
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return result;
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}
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} //namespace CGAL
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#endif // CGAL_MINKOWSKI_SUM_3_H
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