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// Copyright (c) 2002 // Utrecht University (The Netherlands), // ETH Zurich (Switzerland), // INRIA Sophia-Antipolis (France), // Max-Planck-Institute Saarbruecken (Germany), // and Tel-Aviv University (Israel). All rights reserved. // // This file is part of CGAL (www.cgal.org) // // $URL: https://github.com/CGAL/cgal/blob/v6.1/Kernel_d/include/CGAL/Kernel_d/intersection_objectsHd.h $ // $Id: include/CGAL/Kernel_d/intersection_objectsHd.h b26b07a1242 $ // SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial // // // Author(s) : ? #ifndef CGAL_INTERSECTION_OBJECTSHD_H #define CGAL_INTERSECTION_OBJECTSHD_H #include namespace CGAL { /*{\Manpage{Line_line_intersectionHd}{R}{intersecting two lines}}*/ template class Line_line_intersectionHd { typedef typename R::RT RT; typedef typename R::FT FT; typedef typename R::LA LA; typedef typename R::Point_d Point_d; public: enum Intersection_result { NO_INTERSECTION, POINT, LINE }; Intersection_result operator()( const Point_d& s1, const Point_d& t1, const Point_d& s2, const Point_d& t2, Point_d& p, FT& l1, FT& l2) /*{\Mfunop returns |NO_INTERSECTION| if the lines which are represented by |s1t1| and |s2t2| don't intersect, returns |POINT| if they intersect in a unique point, and returns LINE if they are identical. In the |POINT| case the point of intersection is assigned to |p|. Then |p = s1 + l1 * t1-s1| and |p = s2 + l2 * t2-s2|. \precond none of the point pairs is degenerate.}*/ { int d = s1.dimension(),i; CGAL_assertion_msg(d==s2.dimension(), "intersection: dimensions disagree!"); typename LA::Matrix M(d,2),S; typename LA::Vector b(d), lambda(2), c; RT D; RT s1w = s1.homogeneous(d); RT t1w = t1.homogeneous(d); RT s2w = s2.homogeneous(d); RT t2w = t2.homogeneous(d); RT g1w = s1w*t1w; RT g2w = s2w*t2w; RT t12w = t1w*t2w; /* init $d \times 2$ - matrix |M| and $d$ - vector |b| */ for (i = 0; i < d; i++) { M(i,0) = g2w * (t1.homogeneous(i) * s1w - s1.homogeneous(i) * t1w); M(i,1) = g1w * (s2.homogeneous(i) * t2w - t2.homogeneous(i) * s2w); b[i] = t12w * (s2.homogeneous(i) * s1w - s1.homogeneous(i) * s2w); } if (LA::linear_solver(M,b,lambda,D,S,c)) { if (S.column_dimension()>0) return LINE; l1 = R::make_FT(lambda[0],D); l2 = R::make_FT(lambda[1],D); p = s1 + l1 * (t1 - s1); return POINT; } return NO_INTERSECTION; } }; /*{\Manpage {Line_hyperplane_intersectionHd}{R} {intersecting a line and a hyperplane}}*/ template class Line_hyperplane_intersectionHd { typedef typename R::RT RT; typedef typename R::FT FT; typedef typename R::LA LA; typedef typename R::Point_d Point_d; typedef typename R::Hyperplane_d Hyperplane_d; public: enum Intersection_result { NO_INTERSECTION, POINT, LINE }; Intersection_result operator()(const Point_d& s, const Point_d& t, const Hyperplane_d& h, Point_d& p, FT& lambda) /*{\Mfunop returns |NO_INTERSECTION| if the line represented by |s1t1| and the hyperplane |h| don't intersect, returns |POINT| if they intersect in a unique point, and returns LINE if the line is part of the hyperplane. In the |POINT| case the point of intersection is assigned to |p|. Then |p = s1 + lambda * t1-s1|. \precond the point pair is not degenerate.}*/ { CGAL_assertion_msg((h.dimension()==s.dimension() && h.dimension()==t.dimension()), "Line_hyperplane_intersection_d: dimensions do not agree."); int d = h.dimension(),i; RT S(0),T(0); for (i=0; i<=d; ++i) { S += h[i]*s.homogeneous(i); T += h[i]*t.homogeneous(i); } bool s_contained = CGAL_NTS is_zero(S), t_contained = CGAL_NTS is_zero(T); if (s_contained && t_contained) { p = s; return LINE; } if (s_contained) { p = s; return POINT; } if (t_contained) { p = t; return POINT; } // now the simple cases are done RT D = S * t.homogeneous(d) - T * s.homogeneous(d); if (CGAL_NTS is_zero(D)) return NO_INTERSECTION; typename LA::Vector homog(d + 1); for (i = 0; i < d; ++i) homog[i] = S * t.homogeneous(i) - T * s.homogeneous(i); homog[d] = D; p = Point_d(d,homog.begin(),homog.end()); lambda = R::make_FT(S * t.homogeneous(d), D); return POINT; } }; } //namespace CGAL #include #endif //CGAL_INTERSECTION_OBJECTSHD_H