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// Copyright (c) 2014 INRIA Sophia-Antipolis (France). // All rights reserved. // // This file is part of CGAL (www.cgal.org). // // $URL: https://github.com/CGAL/cgal/blob/v6.1/Convex_hull_3/include/CGAL/Convex_hull_3/dual/predicates.h $ // $Id: include/CGAL/Convex_hull_3/dual/predicates.h b26b07a1242 $ // SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial // // // Author(s) : Jocelyn Meyron // #ifndef CGAL_CH3_DUAL_PREDICATES_H #define CGAL_CH3_DUAL_PREDICATES_H #include #include // Predicates used during the computation of the dual convex hull // The dual point associated to the plane which does not contain the origin // and whose equation is // a x + b y + c z + d = 0 // is the point (- a / d, - b / d, - c / d) // The predicates are the ones required by the ConvexHullTraits_3 concept namespace CGAL { namespace Convex_hull_3 { // Plane in the dual space : 3 dual points = 3 planes template struct Plane_dual { typedef typename K::Plane_3 Plane_3; Plane_3 p1; Plane_3 p2; Plane_3 p3; Plane_dual (Plane_3 p1, Plane_3 p2, Plane_3 p3) : p1(p1), p2(p2), p3(p3) {} Plane_dual () {} }; // Segment in the dual space : 2 dual points = 2 planes template struct Segment_dual { typedef typename K::Plane_3 Plane_3; Plane_3 p; Plane_3 q; Segment_dual (Plane_3 p, Plane_3 q) : p(p), q(q) {} }; // Predicates for dual points // Equal template < typename K > struct Equal_3_dual_point { typedef typename K::RT RT; typedef typename K::Plane_3 Plane_3; typedef typename K::Point_3 Point_3; typedef typename K::Boolean result_type; Equal_3_dual_point (Point_3 const& o = Point_3(0, 0, 0)) : origin(o) {} result_type operator()(const Plane_3 &p, const Plane_3 &q) const { RT dp = p.d() + origin.x() * p.a() + origin.y() * p.b() + origin.z() * p.c(); RT dq = q.d() + origin.x() * q.a() + origin.y() * q.b() + origin.z() * q.c(); RT diffa = p.a() * dq - dp * q.a(); RT diffb = p.b() * dq - dp * q.b(); RT diffc = p.c() * dq - dp * q.c(); return CGAL_AND_3(CGAL::is_zero(diffa), CGAL::is_zero(diffb), CGAL::is_zero(diffc)); } private: Point_3 origin; }; // Collinear template < typename K > struct Collinear_3_dual_point { typedef typename K::RT RT; typedef typename K::Plane_3 Plane_3; typedef typename K::Point_3 Point_3; typedef typename K::Boolean result_type; Collinear_3_dual_point (Point_3 const& o = Point_3(0, 0, 0)) : origin(o) {} result_type operator()(const Plane_3 &p, const Plane_3 &q, const Plane_3 &r) const { RT dp = p.d() + origin.x() * p.a() + origin.y() * p.b() + origin.z() * p.c(); RT dq = q.d() + origin.x() * q.a() + origin.y() * q.b() + origin.z() * q.c(); RT dr = r.d() + origin.x() * r.a() + origin.y() * r.b() + origin.z() * r.c(); RT diffapq = dp * q.a() - dq * p.a(); RT diffbpq = dp * q.b() - dq * p.b(); RT diffcpq = dp * q.c() - dq * p.c(); RT diffapr = dp * r.a() - dr * p.a(); RT diffbpr = dp * r.b() - dr * p.b(); RT diffcpr = dp * r.c() - dr * p.c(); // Cross product RT cross1 = diffbpq * diffcpr - diffcpq * diffbpr; RT cross2 = diffcpq * diffapr - diffapq * diffcpr; RT cross3 = diffapq * diffbpr - diffbpq * diffapr; return CGAL_AND_3(CGAL::is_zero(cross1), CGAL::is_zero(cross2), CGAL::is_zero(cross3)); } private: Point_3 origin; }; // Coplanar template < typename K > struct Coplanar_3_dual_point { typedef typename K::RT RT; typedef typename K::Plane_3 Plane_3; typedef typename K::Point_3 Point_3; typedef typename K::Boolean result_type; Coplanar_3_dual_point (Point_3 const& o = Point_3(0, 0, 0)) : origin(o) {} result_type operator()(const Plane_3 &p, const Plane_3 &q, const Plane_3 &r, const Plane_3 &s) const { RT dp = p.d() + origin.x() * p.a() + origin.y() * p.b() + origin.z() * p.c(); RT dq = q.d() + origin.x() * q.a() + origin.y() * q.b() + origin.z() * q.c(); RT dr = r.d() + origin.x() * r.a() + origin.y() * r.b() + origin.z() * r.c(); RT ds = s.d() + origin.x() * s.a() + origin.y() * s.b() + origin.z() * s.c(); RT diffapq = dp * q.a() - dq * p.a(); RT diffbpq = dp * q.b() - dq * p.b(); RT diffcpq = dp * q.c() - dq * p.c(); RT diffapr = dp * r.a() - dr * p.a(); RT diffbpr = dp * r.b() - dr * p.b(); RT diffcpr = dp * r.c() - dr * p.c(); RT diffaps = dp * s.a() - ds * p.a(); RT diffbps = dp * s.b() - ds * p.b(); RT diffcps = dp * s.c() - ds * p.c(); return (CGAL::sign_of_determinant(diffapq, diffapr, diffaps, diffbpq, diffbpr, diffbps, diffcpq, diffcpr, diffcps) == CGAL::ZERO); } private: Point_3 origin; }; // Has on positive side template < typename K > struct Has_on_positive_side_3_dual_point { typedef typename K::RT RT; typedef typename K::Plane_3 Plane_3; typedef typename K::Point_3 Point_3; typedef typename K::Boolean result_type; Has_on_positive_side_3_dual_point (Point_3 const& o = Point_3(0, 0, 0)) : origin(o) {} result_type operator()(const Plane_dual p, const Plane_3 &q) const { Plane_3 p1 = p.p1; Plane_3 p2 = p.p2; Plane_3 p3 = p.p3; RT dp1 = p1.d() + origin.x() * p1.a() + origin.y() * p1.b() + origin.z() * p1.c(); RT dp2 = p2.d() + origin.x() * p2.a() + origin.y() * p2.b() + origin.z() * p2.c(); RT dp3 = p3.d() + origin.x() * p3.a() + origin.y() * p3.b() + origin.z() * p3.c(); RT dq = q.d() + origin.x() * q.a() + origin.y() * q.b() + origin.z() * q.c(); // Compute the normal to the plane RT alpha = (dp1 * p2.b() - dp2 * p1.b()) * (dp1 * p3.c() - dp3 * p1.c()) - (dp1 * p2.c() - dp2 * p1.c()) * (dp1 * p3.b() - dp3 * p1.b()); RT beta = (dp1 * p2.c() - dp2 * p1.c()) * (dp1 * p3.a() - dp3 * p1.a()) - (dp1 * p2.a() - dp2 * p1.a()) * (dp1 * p3.c() - dp3 * p1.c()); RT gamma = (dp1 * p2.a() - dp2 * p1.a()) * (dp1 * p3.b() - dp3 * p1.b()) - (dp1 * p2.b() - dp2 * p1.b()) * (dp1 * p3.a() - dp3 * p1.a()); // Test if q is on the positive side of p RT prod = alpha * (p1.a() * dq - q.a() * dp1) + beta * (p1.b() * dq - q.b() * dp1) + gamma * (p1.c() * dq - q.c() * dp1); if (CGAL::is_positive(dp1 * dq)) { return CGAL::is_positive(prod); } else { return CGAL::is_negative(prod); } } private: Point_3 origin; }; // Less distance to point template < typename K > struct Less_distance_to_point_3_dual_point { typedef typename K::RT RT; typedef typename K::Plane_3 Plane_3; typedef typename K::Point_3 Point_3; typedef typename K::Boolean result_type; Less_distance_to_point_3_dual_point (Point_3 const& o = Point_3(0, 0, 0)) : origin(o) {} result_type operator()(const Plane_3 &p, const Plane_3 &q, const Plane_3 &r) const { RT dp = p.d() + origin.x() * p.a() + origin.y() * p.b() + origin.z() * p.c(); RT dq = q.d() + origin.x() * q.a() + origin.y() * q.b() + origin.z() * q.c(); RT dr = r.d() + origin.x() * r.a() + origin.y() * r.b() + origin.z() * r.c(); RT diffapq = p.a() * dq - q.a() * dp; RT diffbpq = p.b() * dq - q.b() * dp; RT diffcpq = p.c() * dq - q.c() * dp; RT diffapr = p.a() * dr - r.a() * dp; RT diffbpr = p.b() * dr - r.b() * dp; RT diffcpr = p.c() * dr - r.c() * dp; RT distpq = diffapq * diffapq + diffbpq * diffbpq + diffcpq * diffcpq; RT distpr = diffapr * diffapr + diffbpr * diffbpr + diffcpr * diffcpr; return CGAL::is_positive(dq * dq * distpr - dr * dr * distpq); } private: Point_3 origin; }; // Less signed distance to plane template < typename K > struct Less_signed_distance_to_plane_3_dual_point { typedef typename K::RT RT; typedef typename K::Plane_3 Plane_3; typedef typename K::Point_3 Point_3; typedef typename K::Boolean result_type; Less_signed_distance_to_plane_3_dual_point (Point_3 const& o = Point_3(0, 0, 0)) : origin(o) {} result_type operator()(const Plane_dual &p, const Plane_3 &q, const Plane_3 &r) const { Plane_3 p1 = p.p1; Plane_3 p2 = p.p2; Plane_3 p3 = p.p3; RT dp1 = p1.d() + origin.x() * p1.a() + origin.y() * p1.b() + origin.z() * p1.c(); RT dp2 = p2.d() + origin.x() * p2.a() + origin.y() * p2.b() + origin.z() * p2.c(); RT dp3 = p3.d() + origin.x() * p3.a() + origin.y() * p3.b() + origin.z() * p3.c(); RT dq = q.d() + origin.x() * q.a() + origin.y() * q.b() + origin.z() * q.c(); RT dr = r.d() + origin.x() * r.a() + origin.y() * r.b() + origin.z() * r.c(); // Compute the normal to the plane RT alpha = (dp1 * p2.b() - dp2 * p1.b()) * (dp1 * p3.c() - dp3 * p1.c()) - (dp1 * p2.c() - dp2 * p1.c()) * (dp1 * p3.b() - dp3 * p1.b()); RT beta = (dp1 * p2.c() - dp2 * p1.c()) * (dp1 * p3.a() - dp3 * p1.a()) - (dp1 * p2.a() - dp2 * p1.a()) * (dp1 * p3.c() - dp3 * p1.c()); RT gamma = (dp1 * p2.a() - dp2 * p1.a()) * (dp1 * p3.b() - dp3 * p1.b()) - (dp1 * p2.b() - dp2 * p1.b()) * (dp1 * p3.a() - dp3 * p1.a()); RT sumpq = alpha * q.a() + beta * q.b() + gamma * q.c(); RT sumpr = alpha * r.a() + beta * r.b() + gamma * r.c(); RT diff = dr * sumpq - dq * sumpr; if (CGAL::is_positive(dq * dr)) { return CGAL::is_positive(diff); } else { return CGAL::is_negative(diff); } } private: Point_3 origin; }; // Oriented side template < typename K > struct Oriented_side_3_dual_point { typedef typename K::RT RT; typedef typename K::Plane_3 Plane_3; typedef typename K::Point_3 Point_3; typedef CGAL::Oriented_side result_type; Oriented_side_3_dual_point (Point_3 const& o = Point_3(0, 0, 0)) : origin(o) {} result_type operator()(const Plane_dual p, const Plane_3 &q) const { Plane_3 p1 = p.p1; Plane_3 p2 = p.p2; Plane_3 p3 = p.p3; RT dp1 = p1.d() + origin.x() * p1.a() + origin.y() * p1.b() + origin.z() * p1.c(); RT dp2 = p2.d() + origin.x() * p2.a() + origin.y() * p2.b() + origin.z() * p2.c(); RT dp3 = p3.d() + origin.x() * p3.a() + origin.y() * p3.b() + origin.z() * p3.c(); RT dq = q.d() + origin.x() * q.a() + origin.y() * q.b() + origin.z() * q.c(); // Compute the normal to the plane RT alpha = (dp1 * p2.b() - dp2 * p1.b()) * (dp1 * p3.c() - dp3 * p1.c()) - (dp1 * p2.c() - dp2 * p1.c()) * (dp1 * p3.b() - dp3 * p1.b()); RT beta = (dp1 * p2.c() - dp2 * p1.c()) * (dp1 * p3.a() - dp3 * p1.a()) - (dp1 * p2.a() - dp2 * p1.a()) * (dp1 * p3.c() - dp3 * p1.c()); RT gamma = (dp1 * p2.a() - dp2 * p1.a()) * (dp1 * p3.b() - dp3 * p1.b()) - (dp1 * p2.b() - dp2 * p1.b()) * (dp1 * p3.a() - dp3 * p1.a()); // Test if q is on the positive side of p RT prod = alpha * (p1.a() * dq - q.a() * dp1) + beta * (p1.b() * dq - q.b() * dp1) + gamma * (p1.c() * dq - q.c() * dp1); if (CGAL::is_positive(dp1 * dq)) { if (CGAL::is_positive(prod)) { return CGAL::ON_POSITIVE_SIDE; } else if (CGAL::is_negative(prod)) { return CGAL::ON_NEGATIVE_SIDE; } else { return CGAL::ON_ORIENTED_BOUNDARY; } } else { if (CGAL::is_negative(prod)) { return CGAL::ON_POSITIVE_SIDE; } else if (CGAL::is_positive(prod)) { return CGAL::ON_NEGATIVE_SIDE; } else { return CGAL::ON_ORIENTED_BOUNDARY; } } } private: Point_3 origin; }; } // namespace Convex_hull_3 } // namespace CGAL #endif // CGAL_CH3_DUAL_PREDICATES_H