721 lines
24 KiB
C++
Executable File
721 lines
24 KiB
C++
Executable File
// Copyright (c) 2000, 2016
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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); you can redistribute it and/or
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// modify it under the terms of the GNU Lesser General Public License as
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// published by the Free Software Foundation; either version 3 of the License,
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// or (at your option) any later version.
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//
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// Licensees holding a valid commercial license may use this file in
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// accordance with the commercial license agreement provided with the software.
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//
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// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
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// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
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//
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// $URL$
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// $Id$
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// SPDX-License-Identifier: LGPL-3.0+
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//
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//
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// Author(s) : Herve Bronnimann, Sylvain Pion, Olivier Devillers
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//
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#ifndef CGAL_PREDICATES_KERNEL_FTC2_H
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#define CGAL_PREDICATES_KERNEL_FTC2_H
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#include <CGAL/algorithm.h>
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#include <CGAL/number_utils.h>
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#include <CGAL/predicates/sign_of_determinant.h>
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#include <CGAL/constructions/kernel_ftC2.h>
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namespace CGAL {
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template < class FT >
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inline
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typename Equal_to<FT>::result_type
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parallelC2(const FT &l1a, const FT &l1b,
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const FT &l2a, const FT &l2b)
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{
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return sign_of_determinant(l1a, l1b, l2a, l2b) == ZERO;
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}
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template < class FT >
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typename Equal_to<FT>::result_type
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parallelC2(const FT &s1sx, const FT &s1sy,
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const FT &s1tx, const FT &s1ty,
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const FT &s2sx, const FT &s2sy,
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const FT &s2tx, const FT &s2ty)
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{
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return sign_of_determinant(s1tx - s1sx, s1ty - s1sy,
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s2tx - s2sx, s2ty - s2sy) == ZERO;
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}
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template < class FT >
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CGAL_KERNEL_MEDIUM_INLINE
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typename Equal_to<FT>::result_type
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equal_lineC2(const FT &l1a, const FT &l1b, const FT &l1c,
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const FT &l2a, const FT &l2b, const FT &l2c)
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{
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if (sign_of_determinant(l1a, l1b, l2a, l2b) != ZERO)
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return false; // Not parallel.
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typename Sgn<FT>::result_type s1a = CGAL_NTS sign(l1a);
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if (s1a != ZERO)
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return s1a == CGAL_NTS sign(l2a)
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&& sign_of_determinant(l1a, l1c, l2a, l2c) == ZERO;
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return CGAL_NTS sign(l1b) == CGAL_NTS sign(l2b)
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&& sign_of_determinant(l1b, l1c, l2b, l2c) == ZERO;
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}
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template < class FT >
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CGAL_KERNEL_MEDIUM_INLINE
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typename Compare<FT>::result_type
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compare_xC2(const FT &px,
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const FT &la, const FT &lb, const FT &lc,
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const FT &ha, const FT &hb, const FT &hc)
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{
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// The abscissa of the intersection point is num/den.
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FT num = determinant( lb, lc, hb, hc);
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FT den = determinant( la, lb, ha, hb);
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typename Sgn<FT>::result_type s = CGAL_NTS sign(den);
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CGAL_kernel_assertion( s != ZERO );
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return s * CGAL_NTS compare(px * den, num);
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}
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template < class FT >
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CGAL_KERNEL_MEDIUM_INLINE
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typename Compare<FT>::result_type
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compare_xC2(const FT &la, const FT &lb, const FT &lc,
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const FT &h1a, const FT &h1b, const FT &h1c,
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const FT &h2a, const FT &h2b, const FT &h2c)
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{
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/*
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FT num1 = determinant( lb, lc, h1b, h1c);
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FT den1 = determinant( la, lb, h1a, h1b);
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FT num2 = determinant( lb, lc, h2b, h2c);
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FT den2 = determinant( la, lb, h2a, h2b);
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Sign s = Sign (CGAL_NTS sign(den1) * CGAL_NTS sign(den2));
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CGAL_kernel_assertion( s != ZERO );
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return s * sign_of_determinant(num1, num2, den1, den2);
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*/
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FT num1 = determinant( la, lc, h1a, h1c);
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FT num2 = determinant( la, lc, h2a, h2c);
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FT num = determinant(h1a,h1c,h2a,h2c)*lb
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+ determinant(num1,num2,h1b,h2b);
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FT den1 = determinant( la, lb, h1a, h1b);
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FT den2 = determinant( la, lb, h2a, h2b);
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return CGAL_NTS sign(lb) *
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CGAL_NTS sign(num) *
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CGAL_NTS sign(den1) *
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CGAL_NTS sign(den2);
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}
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template < class FT >
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CGAL_KERNEL_MEDIUM_INLINE
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typename Compare<FT>::result_type
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compare_xC2(const FT &l1a, const FT &l1b, const FT &l1c,
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const FT &h1a, const FT &h1b, const FT &h1c,
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const FT &l2a, const FT &l2b, const FT &l2c,
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const FT &h2a, const FT &h2b, const FT &h2c)
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{
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FT num1 = determinant( l1b, l1c, h1b, h1c);
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FT den1 = determinant( l1a, l1b, h1a, h1b);
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FT num2 = determinant( l2b, l2c, h2b, h2c);
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FT den2 = determinant( l2a, l2b, h2a, h2b);
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typename Sgn<FT>::result_type s = CGAL_NTS sign(den1) * CGAL_NTS sign(den2);
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CGAL_kernel_assertion( s != ZERO );
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return s * sign_of_determinant(num1, num2, den1, den2);
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}
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template < class FT >
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CGAL_KERNEL_MEDIUM_INLINE
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typename Compare<FT>::result_type
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compare_y_at_xC2(const FT &px, const FT &py,
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const FT &la, const FT &lb, const FT &lc)
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{
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typename Sgn<FT>::result_type s = CGAL_NTS sign(lb);
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CGAL_kernel_assertion( s != ZERO );
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return s * CGAL_NTS sign(la*px + lb*py + lc);
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}
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template < class FT >
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CGAL_KERNEL_MEDIUM_INLINE
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typename Compare<FT>::result_type
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compare_y_at_xC2(const FT &px,
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const FT &l1a, const FT &l1b, const FT &l1c,
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const FT &l2a, const FT &l2b, const FT &l2c)
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{
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typename Sgn<FT>::result_type s = CGAL_NTS sign(l1b) * CGAL_NTS sign(l2b);
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CGAL_kernel_assertion( s != ZERO );
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return s * sign_of_determinant<FT>(l2a*px+l2c, l2b,
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l1a*px+l1c, l1b);
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}
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template < class FT >
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CGAL_KERNEL_LARGE_INLINE
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typename Compare<FT>::result_type
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compare_y_at_xC2(const FT &l1a, const FT &l1b, const FT &l1c,
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const FT &l2a, const FT &l2b, const FT &l2c,
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const FT &ha, const FT &hb, const FT &hc)
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{
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typename Sgn<FT>::result_type s = CGAL_NTS sign(hb) *
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sign_of_determinant(l1a, l1b, l2a, l2b);
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CGAL_kernel_assertion( s != ZERO );
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return s * sign_of_determinant(l1a, l1b, l1c,
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l2a, l2b, l2c,
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ha, hb, hc);
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}
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template < class FT >
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CGAL_KERNEL_LARGE_INLINE
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typename Compare<FT>::result_type
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compare_y_at_xC2(const FT &l1a, const FT &l1b, const FT &l1c,
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const FT &l2a, const FT &l2b, const FT &l2c,
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const FT &h1a, const FT &h1b, const FT &h1c,
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const FT &h2a, const FT &h2b, const FT &h2c)
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{
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// The abscissa of the intersection point is num/den.
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FT num = determinant( l1b, l1c, l2b, l2c);
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FT den = determinant( l1a, l1b, l2a, l2b);
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typename Sgn<FT>::result_type s = CGAL_NTS sign(h1b) *
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CGAL_NTS sign(h2b) *
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CGAL_NTS sign(den);
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CGAL_kernel_assertion( s != ZERO );
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return s * sign_of_determinant<FT>(h2a*num+h2c*den, h2b,
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h1a*num+h1c*den, h1b);
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}
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// forward-declaration of orientationC2, used in compare_y_at_xC2
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template < class FT >
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inline
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typename Same_uncertainty_nt<Orientation, FT>::type
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orientationC2(const FT &px, const FT &py,
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const FT &qx, const FT &qy,
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const FT &rx, const FT &ry);
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template < class FT >
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CGAL_KERNEL_LARGE_INLINE
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typename Compare<FT>::result_type
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compare_y_at_xC2(const FT &px, const FT &py,
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const FT &ssx, const FT &ssy,
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const FT &stx, const FT &sty)
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{
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// compares the y-coordinates of p and the vertical projection of p on s.
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// Precondition : p is in the x-range of s.
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CGAL_kernel_precondition(are_ordered(ssx, px, stx));
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if (ssx < stx)
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return orientationC2(px, py, ssx, ssy, stx, sty);
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else if (ssx > stx)
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return orientationC2(px, py, stx, sty, ssx, ssy);
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else {
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if (py < (CGAL::min)(sty, ssy))
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return SMALLER;
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if (py > (CGAL::max)(sty, ssy))
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return LARGER;
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return EQUAL;
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}
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}
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template < class FT >
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CGAL_KERNEL_LARGE_INLINE
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typename Compare<FT>::result_type
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compare_y_at_x_segment_C2(const FT &px,
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const FT &s1sx, const FT &s1sy,
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const FT &s1tx, const FT &s1ty,
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const FT &s2sx, const FT &s2sy,
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const FT &s2tx, const FT &s2ty)
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{
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// compares the y-coordinates of the vertical projections of p on s1 and s2
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// Precondition : p is in the x-range of s1 and s2.
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// - if one or two segments are vertical :
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// - if the segments intersect, return EQUAL
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// - if not, return the obvious SMALLER/LARGER.
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CGAL_kernel_precondition(are_ordered(s1sx, px, s1tx));
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CGAL_kernel_precondition(are_ordered(s2sx, px, s2tx));
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if (s1sx != s1tx && s2sx != s2tx) {
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FT s1stx = s1sx-s1tx;
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FT s2stx = s2sx-s2tx;
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return CGAL_NTS compare(s1sx, s1tx) *
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CGAL_NTS compare(s2sx, s2tx) *
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CGAL_NTS compare(-(s1sx-px)*(s1sy-s1ty)*s2stx,
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(s2sy-s1sy)*s2stx*s1stx
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-(s2sx-px)*(s2sy-s2ty)*s1stx );
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}
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else {
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if (s1sx == s1tx) { // s1 is vertical
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typename Compare<FT>::result_type c1, c2;
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c1 = compare_y_at_xC2(px, s1sy, s2sx, s2sy, s2tx, s2ty);
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c2 = compare_y_at_xC2(px, s1ty, s2sx, s2sy, s2tx, s2ty);
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if (c1 == c2)
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return c1;
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return EQUAL;
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}
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// s2 is vertical
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typename Compare<FT>::result_type c3, c4;
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c3 = compare_y_at_xC2(px, s2sy, s1sx, s1sy, s1tx, s1ty);
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c4 = compare_y_at_xC2(px, s2ty, s1sx, s1sy, s1tx, s1ty);
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if (c3 == c4)
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return -c3;
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return EQUAL;
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}
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}
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template < class FT >
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CGAL_KERNEL_MEDIUM_INLINE
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typename Equal_to<FT>::result_type
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equal_directionC2(const FT &dx1, const FT &dy1,
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const FT &dx2, const FT &dy2)
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{
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return CGAL_NTS sign(dx1) == CGAL_NTS sign(dx2)
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&& CGAL_NTS sign(dy1) == CGAL_NTS sign(dy2)
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&& sign_of_determinant(dx1, dy1, dx2, dy2) == ZERO;
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}
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template < class FT >
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CGAL_KERNEL_MEDIUM_INLINE
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typename Compare<FT>::result_type
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compare_angle_with_x_axisC2(const FT &dx1, const FT &dy1,
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const FT &dx2, const FT &dy2)
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{
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// angles are in [-pi,pi], and the angle between Ox and d1 is compared
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// with the angle between Ox and d2
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int quadrant_1 = (dx1 >= 0) ? (dy1 >= 0 ? 1 : 4)
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: (dy1 >= 0 ? 2 : 3);
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int quadrant_2 = (dx2 >= 0) ? (dy2 >= 0 ? 1 : 4)
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: (dy2 >= 0 ? 2 : 3);
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// We can't use CGAL_NTS compare(quadrant_1,quadrant_2) because in case
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// of tie, we need additional computation
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if (quadrant_1 > quadrant_2)
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return LARGER;
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else if (quadrant_1 < quadrant_2)
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return SMALLER;
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return -sign_of_determinant(dx1,dy1,dx2,dy2);
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}
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template < class FT >
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CGAL_KERNEL_MEDIUM_INLINE
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typename Compare<FT>::result_type
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compare_slopesC2(const FT &l1a, const FT &l1b, const FT &l2a, const FT &l2b)
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{
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typedef typename Compare<FT>::result_type result_type;
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if (CGAL_NTS is_zero(l1a)) // l1 is horizontal
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return CGAL_NTS is_zero(l2b) ? result_type(SMALLER)
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: CGAL_NTS sign(l2a) * CGAL_NTS sign(l2b);
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if (CGAL_NTS is_zero(l2a)) // l2 is horizontal
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return CGAL_NTS is_zero(l1b) ? result_type(LARGER)
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: - CGAL_NTS sign(l1a) * CGAL_NTS sign(l1b);
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if (CGAL_NTS is_zero(l1b)) return CGAL_NTS is_zero(l2b) ? EQUAL : LARGER;
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if (CGAL_NTS is_zero(l2b)) return SMALLER;
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result_type l1_sign = - CGAL_NTS sign(l1a) * CGAL_NTS sign(l1b);
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result_type l2_sign = - CGAL_NTS sign(l2a) * CGAL_NTS sign(l2b);
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if (l1_sign < l2_sign) return SMALLER;
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if (l1_sign > l2_sign) return LARGER;
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if (l1_sign > ZERO)
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return CGAL_NTS compare ( CGAL_NTS abs(l1a * l2b),
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CGAL_NTS abs(l2a * l1b) );
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return CGAL_NTS compare ( CGAL_NTS abs(l2a * l1b),
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CGAL_NTS abs(l1a * l2b) );
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}
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template < class FT >
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CGAL_KERNEL_MEDIUM_INLINE
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typename Compare<FT>::result_type
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compare_slopesC2(const FT &s1_src_x, const FT &s1_src_y, const FT &s1_tgt_x,
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const FT &s1_tgt_y, const FT &s2_src_x, const FT &s2_src_y,
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const FT &s2_tgt_x, const FT &s2_tgt_y)
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{
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typedef typename Compare<FT>::result_type Cmp;
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typedef typename Sgn<FT>::result_type Sg;
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Cmp cmp_y1 = CGAL_NTS compare(s1_src_y, s1_tgt_y);
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if (cmp_y1 == EQUAL) // horizontal
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{
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Cmp cmp_x2 = CGAL_NTS compare(s2_src_x, s2_tgt_x);
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if (cmp_x2 == EQUAL) return SMALLER;
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return - CGAL_NTS sign(s2_src_y - s2_tgt_y) * CGAL_NTS sign(s2_src_x - s2_tgt_x);
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}
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Cmp cmp_y2 = CGAL_NTS compare(s2_src_y, s2_tgt_y);
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if (cmp_y2 == EQUAL)
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{
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Cmp cmp_x1 = CGAL_NTS compare(s1_src_x, s1_tgt_x);
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if (cmp_x1 == EQUAL) return LARGER;
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return CGAL_NTS sign(s1_src_y - s1_tgt_y) * CGAL_NTS sign(s1_src_x - s1_tgt_x);
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}
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Cmp cmp_x1 = CGAL_NTS compare(s1_src_x, s1_tgt_x);
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Cmp cmp_x2 = CGAL_NTS compare(s2_src_x, s2_tgt_x);
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if (cmp_x1 == EQUAL) return cmp_x2 == EQUAL ? EQUAL : LARGER;
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if (cmp_x2 == EQUAL) return SMALLER;
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FT s1_xdiff = s1_src_x - s1_tgt_x;
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FT s1_ydiff = s1_src_y - s1_tgt_y;
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FT s2_xdiff = s2_src_x - s2_tgt_x;
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FT s2_ydiff = s2_src_y - s2_tgt_y;
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Sg s1_sign = CGAL_NTS sign(s1_ydiff) * CGAL_NTS sign(s1_xdiff);
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Sg s2_sign = CGAL_NTS sign(s2_ydiff) * CGAL_NTS sign(s2_xdiff);
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if (s1_sign < s2_sign) return SMALLER;
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if (s1_sign > s2_sign) return LARGER;
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if (s1_sign > ZERO)
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return CGAL_NTS compare( CGAL_NTS abs(s1_ydiff * s2_xdiff),
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CGAL_NTS abs(s2_ydiff * s1_xdiff));
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return CGAL_NTS compare( CGAL_NTS abs(s2_ydiff * s1_xdiff),
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CGAL_NTS abs(s1_ydiff * s2_xdiff));
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}
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#if 0
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// Unused, undocumented, un-functorized.
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template < class FT >
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inline
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typename Compare<FT>::result_type
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compare_deltax_deltayC2(const FT &px, const FT &qx,
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const FT &ry, const FT &sy)
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{
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return CGAL_NTS compare(CGAL_NTS abs(px-qx), CGAL_NTS abs(ry-sy));
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}
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#endif
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template < class FT >
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inline
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typename Compare<FT>::result_type
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compare_lexicographically_xyC2(const FT &px, const FT &py,
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const FT &qx, const FT &qy)
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{
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typename Compare<FT>::result_type c = CGAL_NTS compare(px,qx);
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|
return (c != EQUAL) ? c : CGAL_NTS compare(py,qy);
|
|
}
|
|
|
|
template < class FT >
|
|
inline
|
|
typename Same_uncertainty_nt<Orientation, FT>::type
|
|
orientationC2(const FT &px, const FT &py,
|
|
const FT &qx, const FT &qy,
|
|
const FT &rx, const FT &ry)
|
|
{
|
|
return sign_of_determinant(qx-px, qy-py, rx-px, ry-py);
|
|
}
|
|
|
|
template < class FT >
|
|
inline
|
|
typename Same_uncertainty_nt<Orientation, FT>::type
|
|
orientationC2(const FT &ux, const FT &uy, const FT &vx, const FT &vy)
|
|
{
|
|
return sign_of_determinant(ux, uy, vx, vy);
|
|
}
|
|
|
|
template < class FT >
|
|
inline
|
|
typename Same_uncertainty_nt<Angle, FT>::type
|
|
angleC2(const FT &ux, const FT &uy,
|
|
const FT &vx, const FT &vy)
|
|
{
|
|
return enum_cast<Angle>(CGAL_NTS sign(ux*vx + uy*vy));
|
|
}
|
|
|
|
template < class FT >
|
|
inline
|
|
typename Same_uncertainty_nt<Angle, FT>::type
|
|
angleC2(const FT &px, const FT &py,
|
|
const FT &qx, const FT &qy,
|
|
const FT &rx, const FT &ry)
|
|
{
|
|
return enum_cast<Angle>(CGAL_NTS sign((px-qx)*(rx-qx)+(py-qy)*(ry-qy)));
|
|
}
|
|
|
|
template < class FT >
|
|
inline
|
|
typename Same_uncertainty_nt<Angle, FT>::type
|
|
angleC2(const FT &px, const FT &py,
|
|
const FT &qx, const FT &qy,
|
|
const FT &rx, const FT &ry,
|
|
const FT &sx, const FT &sy)
|
|
{
|
|
return enum_cast<Angle>(CGAL_NTS sign((px-qx)*(rx-sx)+(py-qy)*(ry-sy)));
|
|
}
|
|
|
|
template < class FT >
|
|
CGAL_KERNEL_MEDIUM_INLINE
|
|
typename Equal_to<FT>::result_type
|
|
collinear_are_ordered_along_lineC2(const FT &px, const FT &py,
|
|
const FT &qx, const FT &qy,
|
|
const FT &rx, const FT &ry)
|
|
{
|
|
if (px < qx) return !(rx < qx);
|
|
if (qx < px) return !(qx < rx);
|
|
if (py < qy) return !(ry < qy);
|
|
if (qy < py) return !(qy < ry);
|
|
return true; // p==q
|
|
}
|
|
|
|
template < class FT >
|
|
CGAL_KERNEL_MEDIUM_INLINE
|
|
typename Equal_to<FT>::result_type
|
|
collinear_are_strictly_ordered_along_lineC2(const FT &px, const FT &py,
|
|
const FT &qx, const FT &qy,
|
|
const FT &rx, const FT &ry)
|
|
{
|
|
if (px < qx) return (qx < rx);
|
|
if (qx < px) return (rx < qx);
|
|
if (py < qy) return (qy < ry);
|
|
if (qy < py) return (ry < qy);
|
|
return false;
|
|
}
|
|
|
|
template < class FT >
|
|
CGAL_KERNEL_LARGE_INLINE
|
|
typename Same_uncertainty_nt<Oriented_side, FT>::type
|
|
side_of_oriented_circleC2(const FT &px, const FT &py,
|
|
const FT &qx, const FT &qy,
|
|
const FT &rx, const FT &ry,
|
|
const FT &tx, const FT &ty)
|
|
{
|
|
// sign_of_determinant(px, py, px*px + py*py, 1,
|
|
// qx, qy, qx*qx + qy*qy, 1,
|
|
// rx, ry, rx*rx + ry*ry, 1,
|
|
// tx, ty, tx*tx + ty*ty, 1);
|
|
// We first translate so that p is the new origin.
|
|
FT qpx = qx-px;
|
|
FT qpy = qy-py;
|
|
FT rpx = rx-px;
|
|
FT rpy = ry-py;
|
|
FT tpx = tx-px;
|
|
FT tpy = ty-py;
|
|
// The usual 3x3 formula can be simplified a little bit to a 2x2.
|
|
// - sign_of_determinant(qpx, qpy, square(qpx) + square(qpy),
|
|
// rpx, rpy, square(rpx) + square(rpy),
|
|
// tpx, tpy, square(tpx) + square(tpy)));
|
|
return sign_of_determinant<FT>( qpx*tpy - qpy*tpx, tpx*(tx-qx) + tpy*(ty-qy),
|
|
qpx*rpy - qpy*rpx, rpx*(rx-qx) + rpy*(ry-qy));
|
|
}
|
|
|
|
template < class FT >
|
|
CGAL_KERNEL_LARGE_INLINE
|
|
typename Same_uncertainty_nt<Bounded_side, FT>::type
|
|
side_of_bounded_circleC2(const FT &px, const FT &py,
|
|
const FT &qx, const FT &qy,
|
|
const FT &rx, const FT &ry,
|
|
const FT &tx, const FT &ty)
|
|
{
|
|
return enum_cast<Bounded_side>( side_of_oriented_circleC2(px,py,qx,qy,rx,ry,tx,ty)
|
|
* orientationC2(px,py,qx,qy,rx,ry) );
|
|
}
|
|
|
|
template < class FT >
|
|
CGAL_KERNEL_LARGE_INLINE
|
|
typename Same_uncertainty_nt<Bounded_side, FT>::type
|
|
side_of_bounded_circleC2(const FT &px, const FT &py,
|
|
const FT &qx, const FT &qy,
|
|
const FT &tx, const FT &ty)
|
|
{
|
|
// Returns whether T lies inside or outside the circle which diameter is PQ.
|
|
return enum_cast<Bounded_side>(
|
|
CGAL_NTS compare((tx-px)*(qx-tx), (ty-py)*(ty-qy)) );
|
|
}
|
|
|
|
template < class FT >
|
|
inline
|
|
typename Compare<FT>::result_type
|
|
cmp_dist_to_pointC2(const FT &px, const FT &py,
|
|
const FT &qx, const FT &qy,
|
|
const FT &rx, const FT &ry)
|
|
{
|
|
return CGAL_NTS compare(squared_distanceC2(px,py,qx,qy),
|
|
squared_distanceC2(px,py,rx,ry));
|
|
}
|
|
|
|
template < class FT >
|
|
inline
|
|
typename Equal_to<FT>::result_type
|
|
has_larger_dist_to_pointC2(const FT &px, const FT &py,
|
|
const FT &qx, const FT &qy,
|
|
const FT &rx, const FT &ry)
|
|
{
|
|
return cmp_dist_to_pointC2(px,py,qx,qy,rx,ry) == LARGER;
|
|
}
|
|
|
|
template < class FT >
|
|
inline
|
|
typename Equal_to<FT>::result_type
|
|
has_smaller_dist_to_pointC2(const FT &px, const FT &py,
|
|
const FT &qx, const FT &qy,
|
|
const FT &rx, const FT &ry)
|
|
{
|
|
return cmp_dist_to_pointC2(px,py,qx,qy,rx,ry) == SMALLER;
|
|
}
|
|
|
|
template < class FT >
|
|
inline
|
|
typename Compare<FT>::result_type
|
|
cmp_signed_dist_to_directionC2(const FT &la, const FT &lb,
|
|
const FT &px, const FT &py,
|
|
const FT &qx, const FT &qy)
|
|
{
|
|
return CGAL_NTS compare(scaled_distance_to_directionC2(la,lb,px,py),
|
|
scaled_distance_to_directionC2(la,lb,qx,qy));
|
|
}
|
|
|
|
template < class FT >
|
|
inline
|
|
typename Equal_to<FT>::result_type
|
|
has_larger_signed_dist_to_directionC2(const FT &la, const FT &lb,
|
|
const FT &px, const FT &py,
|
|
const FT &qx, const FT &qy)
|
|
{
|
|
return cmp_signed_dist_to_directionC2(la,lb,px,py,qx,qy) == LARGER;
|
|
}
|
|
|
|
template < class FT >
|
|
inline
|
|
typename Equal_to<FT>::result_type
|
|
has_smaller_signed_dist_to_directionC2(const FT &la, const FT &lb,
|
|
const FT &px, const FT &py,
|
|
const FT &qx, const FT &qy)
|
|
{
|
|
return cmp_signed_dist_to_directionC2(la,lb,px,py,qx,qy) == SMALLER;
|
|
}
|
|
|
|
template <class FT>
|
|
inline
|
|
typename Compare<FT>::result_type
|
|
cmp_signed_dist_to_lineC2(const FT &px, const FT &py,
|
|
const FT &qx, const FT &qy,
|
|
const FT &rx, const FT &ry,
|
|
const FT &sx, const FT &sy)
|
|
{
|
|
return CGAL_NTS compare(scaled_distance_to_lineC2(px,py,qx,qy,rx,ry),
|
|
scaled_distance_to_lineC2(px,py,qx,qy,sx,sy));
|
|
}
|
|
|
|
template <class FT>
|
|
inline
|
|
typename Equal_to<FT>::result_type
|
|
has_larger_signed_dist_to_lineC2(const FT &px, const FT &py,
|
|
const FT &qx, const FT &qy,
|
|
const FT &rx, const FT &ry,
|
|
const FT &sx, const FT &sy)
|
|
{
|
|
return cmp_signed_dist_to_lineC2(px,py,qx,qy,rx,ry,sx,sy) == LARGER;
|
|
}
|
|
|
|
template <class FT>
|
|
inline
|
|
typename Equal_to<FT>::result_type
|
|
has_smaller_signed_dist_to_lineC2(const FT &px, const FT &py,
|
|
const FT &qx, const FT &qy,
|
|
const FT &rx, const FT &ry,
|
|
const FT &sx, const FT &sy)
|
|
{
|
|
return cmp_signed_dist_to_lineC2(px,py,qx,qy,rx,ry,sx,sy) == SMALLER;
|
|
}
|
|
|
|
template <class FT>
|
|
inline
|
|
typename Same_uncertainty_nt<Oriented_side, FT>::type
|
|
side_of_oriented_lineC2(const FT &a, const FT &b, const FT &c,
|
|
const FT &x, const FT &y)
|
|
{
|
|
return CGAL_NTS sign(a*x+b*y+c);
|
|
}
|
|
|
|
template <class FT>
|
|
Comparison_result
|
|
compare_power_distanceC2(const FT& px, const FT& py, const FT& pwt,
|
|
const FT& qx, const FT& qy, const FT& qwt,
|
|
const FT& rx, const FT& ry)
|
|
{
|
|
// returns SMALLER if r is closer to p w.r.t. the power metric
|
|
FT d1 = CGAL_NTS square(rx - px) + CGAL_NTS square(ry - py) - pwt;
|
|
FT d2 = CGAL_NTS square(rx - qx) + CGAL_NTS square(ry - qy) - qwt;
|
|
return CGAL_NTS compare(d1, d2);
|
|
}
|
|
|
|
template <class FT>
|
|
CGAL_KERNEL_MEDIUM_INLINE
|
|
Bounded_side
|
|
power_side_of_bounded_power_circleC2(const FT &px, const FT &py, const FT &pw,
|
|
const FT &qx, const FT &qy, const FT &qw,
|
|
const FT &tx, const FT &ty, const FT &tw)
|
|
{
|
|
FT dpx = px - qx;
|
|
FT dpy = py - qy;
|
|
FT dtx = tx - qx;
|
|
FT dty = ty - qy;
|
|
FT dpz = CGAL_NTS square(dpx) + CGAL_NTS square(dpy);
|
|
|
|
return enum_cast<Bounded_side>
|
|
(CGAL_NTS sign(-(CGAL_NTS square(dtx) + CGAL_NTS square(dty)-tw+qw)*dpz
|
|
+(dpz-pw+qw)*(dpx*dtx+dpy*dty)));
|
|
}
|
|
|
|
template <class FT>
|
|
Oriented_side
|
|
power_side_of_oriented_power_circleC2(const FT &px, const FT &py, const FT &pwt,
|
|
const FT &qx, const FT &qy, const FT &qwt,
|
|
const FT &rx, const FT &ry, const FT &rwt,
|
|
const FT &tx, const FT &ty, const FT &twt)
|
|
{
|
|
// Note: maybe this can be further optimized like the usual in_circle() ?
|
|
|
|
// We translate the 4 points so that T becomes the origin.
|
|
FT dpx = px - tx;
|
|
FT dpy = py - ty;
|
|
FT dpz = CGAL_NTS square(dpx) + CGAL_NTS square(dpy) - pwt + twt;
|
|
FT dqx = qx - tx;
|
|
FT dqy = qy - ty;
|
|
FT dqz = CGAL_NTS square(dqx) + CGAL_NTS square(dqy) - qwt + twt;
|
|
FT drx = rx - tx;
|
|
FT dry = ry - ty;
|
|
FT drz = CGAL_NTS square(drx) + CGAL_NTS square(dry) - rwt + twt;
|
|
|
|
return sign_of_determinant(dpx, dpy, dpz,
|
|
dqx, dqy, dqz,
|
|
drx, dry, drz);
|
|
}
|
|
|
|
template <class FT>
|
|
Oriented_side
|
|
power_side_of_oriented_power_circleC2(const FT &px, const FT &py, const FT &pwt,
|
|
const FT &qx, const FT &qy, const FT &qwt,
|
|
const FT &tx, const FT &ty, const FT &twt)
|
|
{
|
|
// Same translation as above.
|
|
FT dpx = px - tx;
|
|
FT dpy = py - ty;
|
|
FT dpz = CGAL_NTS square(dpx) + CGAL_NTS square(dpy) - pwt + twt;
|
|
FT dqx = qx - tx;
|
|
FT dqy = qy - ty;
|
|
FT dqz = CGAL_NTS square(dqx) + CGAL_NTS square(dqy) - qwt + twt;
|
|
|
|
// We do an orthogonal projection on the (x) axis, if possible.
|
|
Comparison_result cmpx = CGAL_NTS compare(px, qx);
|
|
if (cmpx != EQUAL)
|
|
return cmpx * sign_of_determinant(dpx, dpz, dqx, dqz);
|
|
|
|
// If not possible, then on the (y) axis.
|
|
Comparison_result cmpy = CGAL_NTS compare(py, qy);
|
|
return cmpy * sign_of_determinant(dpy, dpz, dqy, dqz);
|
|
}
|
|
|
|
} //namespace CGAL
|
|
|
|
#endif // CGAL_PREDICATES_KERNEL_FTC2_H
|