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// Copyright (c) 2015 Università della Svizzera italiana. // All rights reserved. // // This file is part of CGAL (www.cgal.org). // // $URL: https://github.com/CGAL/cgal/blob/v6.1/Segment_Delaunay_graph_Linf_2/include/CGAL/Orientation_Linf_2.h $ // $Id: include/CGAL/Orientation_Linf_2.h b26b07a1242 $ // SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial // // // Author(s) : Panagiotis Cheilaris, Sandeep Kumar Dey, Evanthia Papadopoulou //philaris@gmail.com, sandeep.kr.dey@gmail.com, evanthia.papadopoulou@usi.ch #ifndef CGAL_ORIENTATION_LINF_2_H #define CGAL_ORIENTATION_LINF_2_H #include #include #include namespace CGAL { typedef Sign OrientationLinf; template class Orientation_Linf_2 { private: typedef typename K::Point_2 Point_2; typedef typename K::Compare_x_2 Compare_x_2; typedef typename K::Compare_y_2 Compare_y_2; typedef typename K::Comparison_result Comparison_result; Compare_x_2 compare_x_2; Compare_y_2 compare_y_2; OrientationLinf predicate(const Point_2& p, const Point_2& q, const Point_2& r) const { Comparison_result cmpxpq = compare_x_2(p, q); Comparison_result cmpypq = compare_y_2(p, q); Comparison_result cmpxpr = compare_x_2(p, r); Comparison_result cmpypr = compare_y_2(p, r); Comparison_result cmpxqr = compare_x_2(q, r); Comparison_result cmpyqr = compare_y_2(q, r); //std::cout << "debug Orientation_Linf_2 (p,q,r)= " // << p << ' ' << q << ' ' << r // << std::endl; if ( cmpxpq == EQUAL ) { if (cmpypq == EQUAL) {//p and q are same points return DEGENERATE; } else {//pq forms a vertical line if (cmpxpr == EQUAL) {//r lies on the vertical line formed by pq return DEGENERATE; } else { return (cmpypq == cmpxpr) ? RIGHT_TURN : LEFT_TURN ; } } } else if ( cmpypq == EQUAL ) {//p and q forms a horizontal line // here: cmpxpq != EQUAL if (cmpypr == EQUAL) {//r lies on the horizontal line formed by pq return DEGENERATE; } else { return (cmpxpq == cmpypr) ? LEFT_TURN : RIGHT_TURN ; } } else { // here both cmpxpq != EQUAL and cmpypq != EQUAL bool is_monotone = ( ( ( cmpxpr == -cmpxqr ) && ( cmpypr == -cmpyqr ) ) || ( ( cmpxpq == cmpxpr) && ( cmpxpr == cmpxqr ) && ( cmpypq == cmpypr) && ( cmpypr == cmpyqr ) ) || ( (-cmpxpq == cmpxpr) && ( cmpxpr == cmpxqr) && (-cmpypq == cmpypr) && ( cmpypr == cmpyqr) ) ) ; //std::cout << "debug is_monotone=" << is_monotone << std::endl; if (is_monotone) { //p, q, r are monotone here //std::cout << "debug Orientation_Linf_2 are monotone" // << std::endl; return DEGENERATE; } else { // p, q, r do not form stair case //std::cout << "debug Orientation_Linf_2 not monotone" // << std::endl; if ( cmpxpq == SMALLER ) { if ( cmpypq == SMALLER ) {//CASE-I q lies in the North East of p return (cmpyqr == SMALLER || cmpxpr == LARGER || (cmpxqr == LARGER && cmpypr == SMALLER)) ? LEFT_TURN : RIGHT_TURN; }//end of CASE-I else { // compare_y_2(p, q) == LARGER -- // CASE-II q lies in the South East of p return (cmpxqr == SMALLER || cmpypr == SMALLER || (cmpxpr == SMALLER && cmpyqr == SMALLER)) ? LEFT_TURN : RIGHT_TURN; }//end of CASE-II } else {//cmpxpq == LARGER case III and case IV //std::cout << "debug Orientation_Linf_2 cmpxpq LARGER" // << std::endl; if ( cmpypq == SMALLER ) {//CASE-III q lies in the North West of p //std::cout << "debug Orientation_Linf_2 cmpypq SMALLER" // << std::endl; return (cmpxpr == SMALLER || cmpyqr == SMALLER || (cmpxqr == SMALLER && cmpypr == SMALLER)) ? RIGHT_TURN : LEFT_TURN; }//end of CASE-III else {//compare_y_2(p, q) == LARGER -- CASE-IV q lies in the South West of p //std::cout << "debug Orientation_Linf_2 cmpypq LARGER" // << std::endl; return (cmpypr == SMALLER || cmpxqr == LARGER || (cmpxpr == LARGER && cmpyqr == SMALLER)) ? RIGHT_TURN : LEFT_TURN; }//end of CASE-IV } } } } public: typedef OrientationLinf result_type; typedef Point_2 argument_type; OrientationLinf operator()(const Point_2& p, const Point_2& q, const Point_2& r) const { return predicate(p, q, r); } }; } //namespace CGAL #endif // CGAL_ORIENTATION_LINF_2_H