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// Copyright (c) 2003-2004 // 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_23/include/CGAL/Kernel/global_functions_2.h $ // $Id: include/CGAL/Kernel/global_functions_2.h b26b07a1242 $ // SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial // // // Author(s) : Sylvain Pion #ifndef CGAL_KERNEL_GLOBAL_FUNCTIONS_2_H #define CGAL_KERNEL_GLOBAL_FUNCTIONS_2_H // Generic functions taking "user classes" as parameters, calling the // internal functions (in *_internal*.h, namespace internal) taking a kernel as // additional parameter, which themselves call the corresponding kernel // functors. #include #include #include namespace CGAL { template < class K > inline typename K::Angle angle(const Vector_2 &u, const Vector_2 &v) { return internal::angle(u, v, K()); } template < class K > inline typename K::Angle angle(const Point_2 &p, const Point_2 &q, const Point_2 &r) { return internal::angle(p, q, r, K()); } template < class K > inline typename K::Angle angle(const Point_2 &p, const Point_2 &q, const Point_2 &r, const Point_2 &s) { return internal::angle(p, q, r, s, K()); } template < class K > inline typename K::Boolean are_ordered_along_line(const Point_2 &p, const Point_2 &q, const Point_2 &r) { return internal::are_ordered_along_line(p, q, r, K()); } template < class K > inline typename K::Boolean are_strictly_ordered_along_line(const Point_2 &p, const Point_2 &q, const Point_2 &r) { return internal::are_strictly_ordered_along_line(p, q, r, K()); } template < class K > inline typename K::FT area(const Point_2 &p, const Point_2 &q, const Point_2 &r) { return internal::area(p, q, r, K()); } template < class K > inline typename K::Point_2 barycenter(const Point_2 &p1, const typename K::FT& w1, const Point_2 &p2) { return internal::barycenter(p1, w1, p2, K()); } template < class K > inline typename K::Point_2 barycenter(const Point_2 &p1, const typename K::FT& w1, const Point_2 &p2, const typename K::FT& w2) { return internal::barycenter(p1, w1, p2, w2, K()); } template < class K > inline typename K::Point_2 barycenter(const Point_2 &p1, const typename K::FT& w1, const Point_2 &p2, const typename K::FT& w2, const Point_2 &p3) { return internal::barycenter(p1, w1, p2, w2, p3, K()); } template < class K > inline typename K::Point_2 barycenter(const Point_2 &p1, const typename K::FT& w1, const Point_2 &p2, const typename K::FT& w2, const Point_2 &p3, const typename K::FT& w3) { return internal::barycenter(p1, w1, p2, w2, p3, w3, K()); } template < class K > inline typename K::Point_2 barycenter(const Point_2 &p1, const typename K::FT& w1, const Point_2 &p2, const typename K::FT& w2, const Point_2 &p3, const typename K::FT& w3, const Point_2 &p4) { return internal::barycenter(p1, w1, p2, w2, p3, w3, p4, K()); } template < class K > inline typename K::Point_2 barycenter(const Point_2 &p1, const typename K::FT& w1, const Point_2 &p2, const typename K::FT& w2, const Point_2 &p3, const typename K::FT& w3, const Point_2 &p4, const typename K::FT& w4) { return internal::barycenter(p1, w1, p2, w2, p3, w3, p4, w4, K()); } template inline typename K::Line_2 bisector(const Point_2 &p, const Point_2 &q) { return internal::bisector(p, q, K()); } template inline typename K::Line_2 bisector(const Line_2 &l1, const Line_2 &l2) { return internal::bisector(l1, l2, K()); } template < class K > inline typename K::Point_2 centroid(const Point_2 &p, const Point_2 &q, const Point_2 &r) { return internal::centroid(p, q, r, K()); } template < class K > inline typename K::Point_2 centroid(const Triangle_2 &t) { return internal::centroid(t, K()); } template < class K > inline typename K::Point_2 centroid(const Point_2 &p, const Point_2 &q, const Point_2 &r, const Point_2 &s) { return internal::centroid(p, q, r, s, K()); } template < class K > inline typename K::Point_2 circumcenter(const Point_2 &p, const Point_2 &q) { return internal::circumcenter(p, q, K()); } template < class K > inline typename K::Point_2 circumcenter(const Point_2 &p, const Point_2 &q, const Point_2 &r) { return internal::circumcenter(p, q, r, K()); } template < class K > inline typename K::Point_2 circumcenter(const Triangle_2 &t) { return internal::circumcenter(t, K()); } template < class K > inline typename K::Boolean collinear(const Point_2 &p, const Point_2 &q, const Point_2 &r) { return internal::collinear(p, q, r, K()); } template < class K > inline typename K::Boolean collinear_are_ordered_along_line(const Point_2 &p, const Point_2 &q, const Point_2 &r) { return internal::collinear_are_ordered_along_line(p, q, r, K()); } template < class K > inline typename K::Boolean collinear_are_strictly_ordered_along_line(const Point_2 &p, const Point_2 &q, const Point_2 &r) { return internal::collinear_are_strictly_ordered_along_line(p, q, r, K()); } template < typename K > inline typename K::Comparison_result compare_angle_with_x_axis(const Direction_2& d1, const Direction_2& d2) { return internal::compare_angle_with_x_axis(d1, d2, K()); } template inline typename K::Comparison_result compare_distance_to_point(const Point_2& p, const Point_2& q, const Point_2& r) { return internal::compare_distance_to_point(p, q, r, K()); } template inline typename K::Comparison_result compare_power_distance(const Point_2 &r, const Weighted_point_2 &p, const Weighted_point_2 &q) { return internal::compare_power_distance(r, p, q, K()); } template inline typename K::Comparison_result compare_squared_distance(const Point_2& p, const Point_2& q, const typename K::FT& d2) { return internal::compare_squared_distance(p, q, d2, K()); } template inline typename K::Comparison_result compare_signed_distance_to_line(const Point_2& p, const Point_2& q, const Point_2& r, const Point_2& s) { return internal::compare_signed_distance_to_line(p, q, r, s, K()); } template inline typename K::Comparison_result compare_signed_distance_to_line(const Line_2& l, const Point_2& p, const Point_2& q) { return internal::compare_signed_distance_to_line(l, p, q, K()); } /* FIXME : Undocumented, obsolete... template < class K > inline typename K::Comparison_result compare_lexicographically_xy(const Point_2 &p, const Point_2 &q) { return K().compare_xy_2_object()(p, q); } */ template < class K > inline typename K::Comparison_result compare_slope(const Line_2 &l1, const Line_2 &l2) { return internal::compare_slope(l1, l2, K()); } template < class K > inline typename K::Comparison_result compare_slope(const Segment_2 &s1, const Segment_2 &s2) { return internal::compare_slope(s1, s2, K()); } template < class K > inline typename K::Comparison_result compare_slope(const Point_2 &s1s, const Point_2 &s1t, const Point_2 &s2s, const Point_2 &s2t) { return internal::compare_slope(s1s, s1t, s2s, s2t, K()); } #ifndef CGAL_NO_DEPRECATED_CODE // kept for backward compatibility template < class K > CGAL_DEPRECATED_MSG("This function is deprecated. CGAL::compare_slope() should be used instead") inline typename K::Comparison_result compare_slopes(const Line_2 &l1, const Line_2 &l2) { return internal::compare_slope(l1, l2, K()); } // kept for backward compatibility template < class K > CGAL_DEPRECATED_MSG("This function is deprecated. CGAL::compare_slope() should be used instead") inline typename K::Comparison_result compare_slopes(const Segment_2 &s1, const Segment_2 &s2) { return internal::compare_slope(s1, s2, K()); } #endif template < class K > inline typename K::Comparison_result compare_x(const Point_2 &p, const Point_2 &q) { return internal::compare_x(p, q, K()); } template < class K > inline typename K::Comparison_result compare_x(const Point_2& p, const Line_2& l1, const Line_2& l2) { return internal::compare_x(p, l1, l2, K()); } template < class K > inline typename K::Comparison_result compare_x(const Line_2 &l, const Line_2 &h1, const Line_2 &h2) { return internal::compare_x(l, h1, h2, K()); } template < class K > inline typename K::Comparison_result compare_x(const Line_2 &l1, const Line_2 &h1, const Line_2 &l2, const Line_2 &h2) { return internal::compare_x(l1, h1, l2, h2, K()); } template < class K > inline typename K::Comparison_result compare_x_at_y(const Point_2& p, const Line_2& h) { return internal::compare_x_at_y(p, h, K()); } /* Undocumented template < class K > inline typename K::Comparison_result compare_x_at_y(const Point_2& p, const Segment_2& s) { return internal::compare_x_at_y(p, s, K()); } */ template < class K > inline typename K::Comparison_result compare_x_at_y(const Point_2 &p, const Line_2 &h1, const Line_2 &h2) { return internal::compare_x_at_y(p, h1, h2, K()); } template < class K > inline typename K::Comparison_result compare_x_at_y(const Line_2 &l1, const Line_2 &l2, const Line_2 &h) { return internal::compare_x_at_y(l1, l2, h, K()); } template < class K > inline typename K::Comparison_result compare_x_at_y(const Line_2 &l1, const Line_2 &l2, const Line_2 &h1, const Line_2 &h2) { return internal::compare_x_at_y(l1, l2, h1, h2, K()); } template < class K > inline typename K::Comparison_result compare_xy(const Point_2 &p, const Point_2 &q) { return internal::compare_xy(p, q, K()); } template < class K > inline typename K::Comparison_result compare_lexicographically(const Point_2 &p, const Point_2 &q) { return internal::compare_xy(p, q, K()); } template < class K > inline typename K::Comparison_result compare_y(const Point_2 &p, const Point_2 &q) { return internal::compare_y(p, q, K()); } template < class K > inline typename K::Comparison_result compare_y(const Point_2 &p, const Line_2 &l1, const Line_2 &l2) { return internal::compare_y(p, l1, l2, K()); } template < class K > inline typename K::Comparison_result compare_y(const Line_2 &l1, const Line_2 &l2, const Line_2 &h1, const Line_2 &h2) { return internal::compare_y(l1, l2, h1, h2, K()); } template < class K > inline typename K::Comparison_result compare_y(const Line_2 &l, const Line_2 &h1, const Line_2 &h2) { return internal::compare_y(l, h1, h2, K()); } template < class K > inline typename K::Comparison_result compare_y_at_x(const Point_2 &p, const Segment_2 &s) { return internal::compare_y_at_x(p, s, K()); } template < class K > inline typename K::Comparison_result compare_y_at_x(const Point_2 &p, const Segment_2 &s1, const Segment_2 &s2) { return internal::compare_y_at_x(p, s1, s2, K()); } template < class K > inline typename K::Comparison_result compare_y_at_x(const Point_2 &p, const Line_2 &h) { return internal::compare_y_at_x(p, h, K()); } template < class K > inline typename K::Comparison_result compare_y_at_x(const Point_2 &p, const Line_2 &h1, const Line_2 &h2) { return internal::compare_y_at_x(p, h1, h2, K()); } template < class K > inline typename K::Comparison_result compare_y_at_x(const Line_2 &l1, const Line_2 &l2, const Line_2 &h) { return internal::compare_y_at_x(l1, l2, h, K()); } template < class K > inline typename K::Comparison_result compare_y_at_x(const Line_2 &l1, const Line_2 &l2, const Line_2 &h1, const Line_2 &h2) { return internal::compare_y_at_x(l1, l2, h1, h2, K()); } template < class K > inline typename K::Comparison_result compare_yx(const Point_2 &p, const Point_2 &q) { return internal::compare_yx(p, q, K()); } template < class K > inline typename K::FT determinant(const Vector_2 &v0, const Vector_2 &v1) { return internal::determinant(v0, v1, K()); } template inline typename K::Boolean has_larger_distance_to_point(const Point_2& p, const Point_2& q, const Point_2& r) { return internal::has_larger_distance_to_point(p, q, r, K()); } template inline typename K::Boolean has_smaller_distance_to_point(const Point_2& p, const Point_2& q, const Point_2& r) { return internal::has_smaller_distance_to_point(p, q, r, K()); } template inline typename K::Boolean has_smaller_signed_distance_to_line(const Line_2& l, const Point_2& p, const Point_2& q) { return internal::has_smaller_signed_distance_to_line(l, p, q, K()); } template inline typename K::Boolean has_larger_signed_distance_to_line(const Line_2& l, const Point_2& p, const Point_2& q) { return internal::has_larger_signed_distance_to_line(l, p, q, K()); } template inline typename K::Boolean has_larger_signed_distance_to_line(const Point_2& p, const Point_2& q, const Point_2& r, const Point_2& s) { return internal::has_larger_signed_distance_to_line(p, q, r, s, K()); } template inline typename K::Boolean has_smaller_signed_distance_to_line(const Point_2& p, const Point_2& q, const Point_2& r, const Point_2& s) { return internal::has_smaller_signed_distance_to_line(p, q, r, s, K()); } template < class K > inline typename K::Boolean left_turn(const Point_2 &p, const Point_2 &q, const Point_2 &r) { return internal::left_turn(p, q, r, K()); } template < class K > inline typename K::Boolean less_x(const Point_2 &p, const Point_2 &q) { return internal::less_x(p, q, K()); } template < class K > inline typename K::Boolean less_y(const Point_2 &p, const Point_2 &q) { return internal::less_y(p, q, K()); } template < class K > inline typename K::Boolean lexicographically_xy_larger(const Point_2 &p, const Point_2 &q) { return internal::lexicographically_xy_larger(p, q, K()); } template < class K > inline typename K::Boolean lexicographically_xy_larger_or_equal(const Point_2 &p, const Point_2 &q) { return internal::lexicographically_xy_larger_or_equal(p, q, K()); } template < class K > inline typename K::Boolean lexicographically_xy_smaller(const Point_2 &p, const Point_2 &q) { return internal::lexicographically_xy_smaller(p, q, K()); } template < class K > inline typename K::Boolean lexicographically_xy_smaller_or_equal(const Point_2 &p, const Point_2 &q) { return internal::lexicographically_xy_smaller_or_equal(p, q, K()); } template < class K > inline typename K::Boolean lexicographically_yx_smaller(const Point_2 &p, const Point_2 &q) { return internal::lexicographically_yx_smaller(p, q, K()); } template < class K > inline typename K::Boolean lexicographically_yx_smaller_or_equal(const Point_2 &p, const Point_2 &q) { return internal::lexicographically_yx_smaller_or_equal(p, q, K()); } // FIXME : Undocumented template < class K > inline typename K::Boolean lexicographically_yx_larger(const Point_2 &p, const Point_2 &q) { return internal::lexicographically_yx_larger(p, q, K()); } // FIXME : Undocumented template < class K > inline typename K::Boolean lexicographically_yx_larger_or_equal(const Point_2 &p, const Point_2 &q) { return internal::lexicographically_yx_larger_or_equal(p, q, K()); } template < class K > typename K::FT l_infinity_distance(const Point_2 &p, const Point_2 &q) { return internal::l_infinity_distance(p,q, K()); } template < class K > inline typename K::Point_2 midpoint(const Point_2 &p, const Point_2 &q) { return internal::midpoint(p, q, K()); } template < class K > inline typename K::Point_2 midpoint(const Segment_2 &s) { return internal::midpoint(s, K()); } template < class K > inline typename K::Point_2 max_vertex(const Iso_rectangle_2 &ir) { return internal::max_vertex(ir, K()); } template < class K > inline typename K::Point_2 min_vertex(const Iso_rectangle_2 &ir) { return internal::min_vertex(ir, K()); } // FIXME TODO : What do we do with the operators ? // They have no counter part with the kernel argument... template < class K > inline typename K::Boolean operator==(const Point_2& p, const Point_2& q) { return K().equal_2_object()(p, q); } template < class K > inline typename K::Boolean operator!=(const Point_2& p, const Point_2& q) { return ! (p == q); } template < class K > typename K::Boolean operator==(const Point_2 &p, const Origin& o) { return p == Point_2(o); } template < class K > typename K::Boolean operator==(const Origin& o, const Point_2 &p) { return (p == o); } template < class K > typename K::Boolean operator!=(const Point_2 &p, const Origin& o) { return ! (p == o); } template < class K > typename K::Boolean operator!=(const Origin& o, const Point_2 &p) { return ! (p == o); } template < class K > inline typename K::Boolean operator==(const Origin& o, const Weighted_point_2& p) { return p == o; } template < class K > inline typename K::Boolean operator!=(const Origin& o, const Weighted_point_2& p) { return p != o; } template < class K > inline typename K::Boolean operator==(const Point_2& bp, const Weighted_point_2& p) { return bp == p.point(); } template < class K > inline typename K::Boolean operator!=(const Point_2& bp, const Weighted_point_2& p) { return bp != p.point(); } template < class K > inline typename K::Boolean operator==(const Weighted_point_2& p, const Point_2& bp) { return bp == p.point(); } template < class K > inline typename K::Boolean operator!=(const Weighted_point_2& p, const Point_2& bp) { return bp != p.point(); } template < class K > inline typename K::Boolean operator==(const Weighted_point_2& p, const Weighted_point_2& p2) { return p.point() == p2.point(); } template < class K > inline typename K::Boolean operator!=(const Weighted_point_2& p, const Weighted_point_2& p2) { return p.point() != p2.point(); } template < class K > inline typename K::Boolean operator==(const Vector_2& v, const Vector_2& w) { return K().equal_2_object()(v, w); } template < class K > inline typename K::Boolean operator!=(const Vector_2& v, const Vector_2& w) { return ! (v == w); } template < class K > inline typename K::Boolean operator==(const Vector_2& v, const Null_vector& n) { return K().equal_2_object()(v, n); } template < class K > inline typename K::Boolean operator==(const Null_vector& n, const Vector_2& v) { return v == n; } template < class K > inline typename K::Boolean operator!=(const Vector_2& v, const Null_vector& n) { return ! (v == n); } template < class K > inline typename K::Boolean operator!=(const Null_vector& n, const Vector_2& v) { return ! (v == n); } template < class K > inline typename K::Boolean operator==(const Circle_2& p, const Circle_2& q) { return K().equal_2_object()(p, q); } template < class K > inline typename K::Boolean operator!=(const Circle_2& p, const Circle_2& q) { return ! (p == q); } template < class K > inline typename K::Boolean operator==(const Direction_2& p, const Direction_2& q) { return K().equal_2_object()(p, q); } template < class K > inline typename K::Boolean operator!=(const Direction_2& p, const Direction_2& q) { return ! (p == q); } template < class K > inline typename K::Boolean operator==(const Iso_rectangle_2& p, const Iso_rectangle_2& q) { return K().equal_2_object()(p, q); } template < class K > inline typename K::Boolean operator!=(const Iso_rectangle_2& p, const Iso_rectangle_2& q) { return ! (p == q); } template < class K > inline typename K::Boolean operator==(const Line_2& p, const Line_2& q) { return K().equal_2_object()(p, q); } template < class K > inline typename K::Boolean operator!=(const Line_2& p, const Line_2& q) { return ! (p == q); } template < class K > inline typename K::Boolean operator==(const Ray_2& p, const Ray_2& q) { return K().equal_2_object()(p, q); } template < class K > inline typename K::Boolean operator!=(const Ray_2& p, const Ray_2& q) { return ! (p == q); } template < class K > inline typename K::Boolean operator==(const Segment_2& p, const Segment_2& q) { return K().equal_2_object()(p, q); } template < class K > inline typename K::Boolean operator!=(const Segment_2& p, const Segment_2& q) { return ! (p == q); } template < class K > inline typename K::Boolean operator==(const Triangle_2& p, const Triangle_2& q) { return K().equal_2_object()(p, q); } template < class K > inline typename K::Boolean operator!=(const Triangle_2& p, const Triangle_2& q) { return ! (p == q); } template < class K > inline typename K::Boolean operator<(const Point_2& p, const Point_2& q) { return K().less_xy_2_object()(p, q); } template < class K > inline typename K::Boolean operator<(const Weighted_point_2& p, const Weighted_point_2& q) { return p.point() < q.point(); } template < class K > inline typename K::Boolean operator<(const Direction_2& d1, const Direction_2& d2) { return compare_angle_with_x_axis(d1, d2) == SMALLER; } template < class K > inline typename K::Boolean operator>(const Direction_2& d1, const Direction_2& d2) { return compare_angle_with_x_axis(d1, d2) == LARGER; } template < class K > inline typename K::Boolean operator>=(const Direction_2& d1, const Direction_2& d2) { return compare_angle_with_x_axis(d1, d2) != SMALLER; } template < class K > inline typename K::Boolean operator<=(const Direction_2& d1, const Direction_2& d2) { return compare_angle_with_x_axis(d1, d2) != LARGER; } template < class K > inline typename K::Boolean operator>(const Point_2& p, const Point_2& q) { return K().less_xy_2_object()(q, p); } template < class K > inline typename K::Boolean operator<=(const Point_2& p, const Point_2& q) { return ! K().less_xy_2_object()(q, p); } template < class K > inline typename K::Boolean operator>=(const Point_2& p, const Point_2& q) { return ! K().less_xy_2_object()(p, q); } template < class K > inline typename K::Vector_2 operator*(const typename K::FT &c, const Vector_2 &w) { return K().construct_scaled_vector_2_object()(w, c); } template < class K > inline typename K::Vector_2 operator*(const Vector_2 &w, const typename K::FT &c) { return K().construct_scaled_vector_2_object()(w, c); } template < class K > inline typename K::Vector_2 operator*(const typename First_if_different::Type &c, const Vector_2 &w) { return K().construct_scaled_vector_2_object()(w, c); } template < class K > inline typename K::Vector_2 operator*(const Vector_2 &w, const typename First_if_different::Type &c) { return K().construct_scaled_vector_2_object()(w, c); } template < class K > inline typename K::FT operator*(const Vector_2 &v, const Vector_2 &w) { return K().compute_scalar_product_2_object()(v, w); } template < class K > inline typename K::Point_2 operator+(const Point_2 &p, const Vector_2 &v) { return K().construct_translated_point_2_object()(p, v); } template < class K > inline typename K::Point_2 operator+(const Origin &o, const Vector_2 &v) { return K().construct_translated_point_2_object()(o, v); } template < class K > inline typename K::Point_2 operator-(const Point_2 &p, const Vector_2 &v) { return K().construct_translated_point_2_object() (p, K().construct_opposite_vector_2_object()(v)); } template < class K > inline typename K::Point_2 operator-(const Origin &o, const Vector_2 &v) { return K().construct_translated_point_2_object() (o, K().construct_opposite_vector_2_object()(v)); } template < class K > inline typename K::Vector_2 operator-(const Point_2 &p, const Point_2 &q) { return K().construct_vector_2_object()(q, p); } template < class K > inline typename K::Vector_2 operator-(const Point_2 &p, const Origin &o) { return K().construct_vector_2_object()(o, p); } template < class K > inline typename K::Vector_2 operator-(const Origin &o, const Point_2 &q) { return K().construct_vector_2_object()(q, o); } template inline typename K::Orientation orientation(const Point_2 &p, const Point_2 &q, const Point_2 &r) { return internal::orientation(p, q, r, K()); } template inline typename K::Orientation orientation(const Vector_2 &u, const Vector_2 &v) { return internal::orientation(u, v, K()); } // parallel() functions are in global_functions.h template inline typename K::FT power_product(const Weighted_point_2 &p, const Weighted_point_2 &q) { return internal::power_product(p, q, K()); } template inline typename K::Bounded_side power_side_of_bounded_power_circle(const Weighted_point_2 &p, const Weighted_point_2 &q) { return internal::power_side_of_bounded_power_circle(p, q, K()); } template inline typename K::Bounded_side power_side_of_bounded_power_circle(const Weighted_point_2 &p, const Weighted_point_2 &q, const Weighted_point_2 &r) { return internal::power_side_of_bounded_power_circle(p, q, r, K()); } template inline typename K::Bounded_side power_side_of_bounded_power_circle(const Weighted_point_2 &p, const Weighted_point_2 &q, const Weighted_point_2 &r, const Weighted_point_2 &s) { return internal::power_side_of_bounded_power_circle(p, q, r, s, K()); } template inline typename K::Orientation power_side_of_oriented_power_circle(const Weighted_point_2 &p, const Weighted_point_2 &q) { return internal::power_side_of_oriented_power_circle(p, q, K()); } template inline typename K::Orientation power_side_of_oriented_power_circle(const Weighted_point_2 &p, const Weighted_point_2 &q, const Weighted_point_2 &r) { return internal::power_side_of_oriented_power_circle(p, q, r, K()); } template inline typename K::Orientation power_side_of_oriented_power_circle(const Weighted_point_2 &p, const Weighted_point_2 &q, const Weighted_point_2 &r, const Weighted_point_2 &s) { return internal::power_side_of_oriented_power_circle(p, q, r, s, K()); } template inline typename K::Line_2 radical_axis(const Weighted_point_2 &p, const Weighted_point_2 &q) { return internal::radical_axis(p, q, K()); } template inline typename K::Line_2 radical_line(const Circle_2 &s1, const Circle_2 &s2) { return K().construct_radical_line_2_object()(s1,s2); } template inline typename K::Boolean right_turn(const Point_2 &p, const Point_2 &q, const Point_2 &r) { return internal::right_turn(p, q, r, K()); } template < class K > inline typename K::FT scalar_product(const Vector_2 &v, const Vector_2 &w) { return K().compute_scalar_product_2_object()(v, w); } template inline typename K::Bounded_side side_of_bounded_circle(const Point_2 &p, const Point_2 &q, const Point_2 &r, const Point_2 &t) { return internal::side_of_bounded_circle(p, q, r, t, K()); } template inline typename K::Bounded_side side_of_bounded_circle(const Point_2 &p, const Point_2 &q, const Point_2 &r) { return internal::side_of_bounded_circle(p, q, r, K()); } template inline typename K::Oriented_side side_of_oriented_circle(const Point_2 &p, const Point_2 &q, const Point_2 &r, const Point_2 &t) { return internal::side_of_oriented_circle(p, q, r, t, K()); } template < class K > inline typename K::FT squared_length(const Vector_2 &v) { return internal::squared_length(v, K()); } template < class K > inline typename K::FT squared_length(const Segment_2 &s) { return internal::squared_length(s, K()); } template < class K > inline typename K::FT squared_radius(const Point_2 &p) { return internal::squared_radius(p, K()); } template < class K > inline typename K::FT squared_radius(const Point_2 &p, const Point_2 &q) { return internal::squared_radius(p, q, K()); } template < class K > CGAL_KERNEL_INLINE typename K::FT squared_radius(const Point_2& p, const Point_2& q, const Point_2& r) { return internal::squared_radius(p, q, r, K()); } template < class K > inline typename K::FT squared_radius_smallest_orthogonal_circle(const Weighted_point_2 &p) { return internal::squared_radius_smallest_orthogonal_circle(p, K()); } template < class K > inline typename K::FT squared_radius_smallest_orthogonal_circle(const Weighted_point_2 &p, const Weighted_point_2 &q) { return internal::squared_radius_smallest_orthogonal_circle(p, q, K()); } template < class K > inline typename K::FT squared_radius_smallest_orthogonal_circle(const Weighted_point_2 &p, const Weighted_point_2 &q, const Weighted_point_2 &r) { return internal::squared_radius_smallest_orthogonal_circle(p, q, r, K()); } template < class K > inline typename K::Point_2 weighted_circumcenter(const Weighted_point_2 &p, const Weighted_point_2 &q, const Weighted_point_2 &r) { return internal::weighted_circumcenter(p, q, r, K()); } template < class K > inline typename K::Boolean x_equal(const Point_2 &p, const Point_2 &q) { return internal::x_equal(p, q, K()); } template < class K > inline typename K::Boolean y_equal(const Point_2 &p, const Point_2 &q) { return internal::y_equal(p, q, K()); } } //namespace CGAL #endif // CGAL_KERNEL_GLOBAL_FUNCTIONS_2_H