137 lines
4.0 KiB
C
137 lines
4.0 KiB
C
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// Copyright (c) 2002
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// Utrecht University (The Netherlands),
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// ETH Zurich (Switzerland),
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// INRIA Sophia-Antipolis (France),
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// Max-Planck-Institute Saarbruecken (Germany),
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// and Tel-Aviv University (Israel). 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/Kernel_d/include/CGAL/Kernel_d/intersection_objectsCd.h $
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// $Id: intersection_objectsCd.h 0779373 2020-03-26T13:31:46+01:00 Sébastien Loriot
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// SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial
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//
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//
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// Author(s) : ?
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#ifndef CGAL_INTERSECTION_OBJECTSCD_H
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#define CGAL_INTERSECTION_OBJECTSCD_H
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#include <CGAL/basic.h>
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#include <CGAL/Kernel_d/debug.h>
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namespace CGAL {
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/*{\Manpage{Line_line_intersectionCd}{R}{intersecting two lines}}*/
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template <class R>
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class Line_line_intersectionCd {
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typedef typename R::FT FT;
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typedef typename R::LA LA;
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typedef typename R::Point_d Point_d;
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typedef typename R::Line_d Line_d;
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public:
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enum Intersection_result { NO_INTERSECTION, POINT, LINE };
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Intersection_result operator()(
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const Point_d& s1, const Point_d& t1,
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const Point_d& s2, const Point_d& t2,
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Point_d& p, FT& l1, FT& l2)
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/*{\Mfunop returns |NO_INTERSECTION| if the lines which are represented by |s1t1|
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and |s2t2| don't intersect, returns |POINT| if they intersect in a
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unique point, and returns LINE if they are identical. In the |POINT|
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case the point of intersection is assigned to |p|. Then |p = s1 + l1
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* t1-s1| and |p = s2 + l2 * t2-s2|. \precond none of the point pairs
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is degenerate.}*/
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{
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int d = s1.dimension(),i;
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CGAL_assertion_msg(d==s2.dimension(),
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"intersection: dimensions disagree!");
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typename LA::Matrix M(d,2),S;
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typename LA::Vector b(d), lambda(2), c;
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FT D;
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/* init $d \times 2$ - matrix |M| and $d$ - vector |b| */
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for (i = 0; i < d; i++) {
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M(i,0) = t1.cartesian(i) - s1.cartesian(i);
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M(i,1) = s2.cartesian(i) - t2.cartesian(i);
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b[i] = s2.cartesian(i) - s1.cartesian(i);
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}
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if (LA::linear_solver(M,b,lambda,D,S,c)) {
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if ( S.column_dimension()>0 ) return LINE;
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l1 = lambda[0]; l2 = lambda[1];
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p = s1 + l1 * (t1 - s1);
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#ifdef CGAL_CHECK_EXACTNESS
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Line_d L1(s1,t1), L2(s2,t2);
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CGAL_assertion(L1.has_on(p)&&L2.has_on(p));
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#endif
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return POINT;
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}
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return NO_INTERSECTION;
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}
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};
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/*{\Manpage {Line_hyperplane_intersectionCd}{R}
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{intersecting a line and a hyperplane}}*/
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template <class R>
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class Line_hyperplane_intersectionCd {
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typedef typename R::FT FT;
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typedef typename R::LA LA;
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typedef typename R::Point_d Point_d;
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typedef typename R::Hyperplane_d Hyperplane_d;
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public:
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enum Intersection_result { NO_INTERSECTION, POINT, LINE };
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Intersection_result operator()(const Point_d& s, const Point_d& t,
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const Hyperplane_d& h, Point_d& p, FT& lambda)
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/*{\Mfunop returns |NO_INTERSECTION| if the line represented by |s1t1| and the
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hyperplane |h| don't intersect, returns |POINT| if they intersect in a
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unique point, and returns LINE if the line is part of the
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hyperplane. In the |POINT| case the point of intersection is assigned
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to |p|. Then |p = s1 + lambda * t1-s1|. \precond the point pair is
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not degenerate.}*/
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{
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CGAL_assertion_msg((h.dimension()==s.dimension() &&
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h.dimension()==t.dimension()),
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"Line_hyperplane_intersection_d: dimensions do not agree.");
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int d = h.dimension(),i;
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FT S = h.value_at(s), T = h.value_at(t);
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bool s_contained = CGAL_NTS is_zero(S),
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t_contained = CGAL_NTS is_zero(T);
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if (s_contained && t_contained) { p = s; return LINE; }
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if (s_contained) { p = s; return POINT; }
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if (t_contained) { p = t; return POINT; }
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// now the simple cases are done
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FT D = S - T;
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if ( CGAL_NTS is_zero(D) ) return NO_INTERSECTION;
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typename LA::Vector v(d);
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for (i = 0; i < d; ++i)
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v[i] = (S * t.cartesian(i) - T * s.cartesian(i))/D;
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p = Point_d(d,v.begin(),v.end()); lambda = S/D;
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#ifdef CGAL_CHECK_EXACTNESS
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Line_d l(s,t);
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CGAL_assertion(h.has_on(p)&&l.has_on(p));
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#endif
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return POINT;
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}
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};
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} //namespace CGAL
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#include <CGAL/Kernel_d/intersection_objects_d.h>
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#endif //CGAL_INTERSECTION_OBJECTSCD_H
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