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// Copyright (c) 1997-2002 Max-Planck-Institute Saarbruecken (Germany). // All rights reserved. // // This file is part of CGAL (www.cgal.org). // // $URL: https://github.com/CGAL/cgal/blob/v6.1/Nef_3/include/CGAL/normal_vector_newell_3.h $ // $Id: include/CGAL/normal_vector_newell_3.h b26b07a1242 $ // SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial // // // Author(s) : Michael Seel // Miguel Granados // Susan Hert // Lutz Kettner #ifndef CGAL_NORMAL_VECTOR_NEWELL_3_H #define CGAL_NORMAL_VECTOR_NEWELL_3_H 1 #include #include #undef CGAL_NEF_DEBUG #define CGAL_NEF_DEBUG 79 #include #include #include namespace CGAL { namespace internal_nef { template CGAL_MEDIUM_INLINE void newell_single_step_3( const Handle& p, const Handle& q, Vector& n, const Homogeneous_tag&) { typedef typename Kernel_traits::Kernel::RT RT; const RT& phw = p.hw(); const RT& qhw = q.hw(); const RT& nhw = n.hw(); const RT& sq = square(phw) * square(qhw); const RT& phyqhw = p.hy() * qhw; const RT& qhyphw = q.hy() * phw; const RT& phxqhw = p.hx() * qhw; const RT& qhxphw = q.hx() * phw; const RT& phzqhw = p.hz() * qhw; const RT& qhzphw = q.hz() * phw; n = Vector( n.hx() * sq + nhw * ( phyqhw - qhyphw ) * ( phzqhw + qhzphw ), n.hy() * sq + nhw * ( phzqhw - qhzphw ) * ( phxqhw + qhxphw ), n.hz() * sq + nhw * ( phxqhw - qhxphw ) * ( phyqhw + qhyphw ), n.hw() * sq ); } template CGAL_MEDIUM_INLINE void newell_single_step_3( const Handle& p, const Handle& q, Vector& n, const Cartesian_tag&) { typedef typename Kernel_traits::Kernel::FT FT; const FT& py = p.y(); const FT& qy = q.y(); const FT& px = p.x(); const FT& qx = q.x(); const FT& pz = p.z(); const FT& qz = q.z(); n = Vector( n.x() + ( py - qy ) * ( pz + qz ), n.y() + ( pz - qz ) * ( px + qx ), n.z() + ( px - qx ) * ( py + qy ) ); } template bool is_triangle_3( const IC& first ) { return std::next(first,3) == first; } } template void normal_vector_newell_3( IC first, IC last, Vector& n ) // compute a facet normal n via the Newell-method for the facet // surrounded by the points in the range [`h', `last'), where `IC' // denotes either an iterator or a circulator with a point type as // value type. The Newell-method computes for non-planar facets the // best least-square-fit normal of the plane equation. Precondition: // The numbertype for the points and the vector n must be compatible // with `double'. The points and the vector n must have dimension // three. { CGAL_assertion( !CGAL::is_empty_range( first, last)); if(internal_nef::is_triangle_3(first)) { n = orthogonal_vector(*first,*(std::next(first)),*(std::next(first,2))); return; } typedef typename Kernel_traits::Kernel R; // Compute facet normals via the Newell-method as described in // Filippo Tampieri: Newell's Method for Computing the Plane // Equation of a Polygon. Graphics Gems III, David Kirk, // AP Professional, 1992. // The code works with cartesian and with semi-rational points. n = Vector( 0, 0, 0); // init current normal to 0 IC start_point = first; IC prev = first; ++first; while( first != last) { internal_nef::newell_single_step_3( *prev, *first, n, typename R::Kernel_tag()); prev = first; ++first; } internal_nef::newell_single_step_3( *prev, *start_point, n, typename R::Kernel_tag()); CGAL_NEF_TRACEN("newell normal vector "< void normal_vector_newell_3( IC first, IC last, VertexPointMap vpm, Vector& n ) { CGAL_assertion( !CGAL::is_empty_range( first, last)); if(internal_nef::is_triangle_3(first)) { n = orthogonal_vector(get(vpm,*first),get(vpm,*(std::next(first))),get(vpm,*(std::next(first,2)))); return; } typedef typename Kernel_traits::Kernel R; // Compute facet normals via the Newell-method as described in // Filippo Tampieri: Newell's Method for Computing the Plane // Equation of a Polygon. Graphics Gems III, David Kirk, // AP Professional, 1992. // The code works with cartesian and with semi-rational points. n = Vector( 0, 0, 0); // init current normal to 0 IC start_point = first; IC prev = first; ++first; while( first != last) { internal_nef::newell_single_step_3( get(vpm,*prev), get(vpm,*first), n, typename R::Kernel_tag()); prev = first; ++first; } internal_nef::newell_single_step_3( get(vpm,*prev), get(vpm,*start_point), n, typename R::Kernel_tag()); CGAL_NEF_TRACEN("newell normal vector "<