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// All rights reserved.
//
// This file is part of CGAL (www.cgal.org).
// You can redistribute it and/or modify it under the terms of the GNU
// General Public License as published by the Free Software Foundation,
// either version 3 of the License, or (at your option) any later version.
//
// Licensees holding a valid commercial license may use this file in
// accordance with the commercial license agreement provided with the software.
//
// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
//
// $URL$
// $Id$
//
//
// Author(s) : Peter Hachenberger <hachenberger@mpi-sb.mpg.de>
#ifndef CGAL_MINKOWSKI_SUM_3_H
#define CGAL_MINKOWSKI_SUM_3_H
#include <CGAL/convex_decomposition_3.h>
#include <CGAL/Minkowski_sum_3/bipartite_nary_union_sorted_combined.h>
#include <CGAL/Is_extended_kernel.h>
/// \file minkowski_sum_3.h
namespace CGAL {
/*!
\ingroup PkgMinkowskiSum3
The function `minkowski_sum_3()` computes the Minkowski sum of two
given 3D Nef polyhedra \f$ N0\f$ and \f$ N1\f$. Note that the function runs in
\f$ O(n^3m^3)\f$ time in the worst case, where \f$ n\f$ and
\f$ m\f$ are the complexities of the two input polyhedra (the complexity of
a `Nef_polyhedron_3` is the sum of its `Vertices`,
`Halfedges` and `SHalfedges`).
An input polyhedron may consist of:
<OL>
<LI>singular vertices
<LI>singular edges
<LI>singular convex facets without holes
<LI>surfaces with convex facets that have no holes.
<LI>three-dimensional features, whose coplanar facets have
common selection marks (this includes open and closed solids)
</OL>
Taking a different viewpoint, the implementation is restricted as
follows:
<OL>
<LI>The input polyhedra must be bounded (selected outer volume is ignored).
<LI>All sets of coplanar facets of a full-dimensional
feature must have the same selection mark (in case of different
selection marks, unselected is assumed).
<LI>All facets of lower-dimensional features need to be convex and
must not have holes (non-convex facets and holes are ignored).
</OL>
\post If either of the input polyhedra is non-convex, it is modified during the computation, i.e., it is decomposed into convex pieces.
\sa `CGAL::Nef_polyhedron_3<Traits>`
\sa \link CGAL::convex_decomposition_3 `CGAL::convex_decomposition_3()`\endlink
*/
template<typename Nef_polyhedron_3>
Nef_polyhedron_3
minkowski_sum_3(Nef_polyhedron_3& N0, Nef_polyhedron_3& N1)
{
typedef typename Nef_polyhedron_3::Kernel Kernel;
typedef typename Is_extended_kernel<Kernel>::value_type Is_extended_kernel;
if(check_tag(Is_extended_kernel())) {
std::cerr << "extended kernel is not supported" << std::endl;
return N0;
}
if(N0.volumes_begin()->mark()) {
std::cerr << "first parameter is an infinite point set" << std::endl;
return N0;
}
if(N1.volumes_begin()->mark()) {
std::cerr << "second parameter is an infinite point set" << std::endl;
return N1;
}
CGAL::convex_decomposition_3<Nef_polyhedron_3>(N0);
CGAL::convex_decomposition_3<Nef_polyhedron_3>(N1);
CGAL_assertion(N0.is_valid());
CGAL_assertion(N1.is_valid());
Nef_polyhedron_3 result =
CGAL::bipartite_nary_union_sorted_combined(N0, N1);
CGAL_assertion(result.is_valid());
return result;
}
} //namespace CGAL
#endif // CGAL_MINKOWSKI_SUM_3_H
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