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// Copyright (c) 2003-2004 // Utrecht University (The Netherlands), // ETH Zurich (Switzerland), // INRIA Sophia-Antipolis (France), // Max-Planck-Institute Saarbruecken (Germany), // Copyright (c) 2010 GeometryFactory Sarl (France) // // 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_internal_3.h $ // $Id: include/CGAL/Kernel/global_functions_internal_3.h b26b07a1242 $ // SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial // // // Author(s) : Sylvain Pion #ifndef CGAL_KERNEL_GLOBAL_FUNCTIONS_INTERNAL_3_H #define CGAL_KERNEL_GLOBAL_FUNCTIONS_INTERNAL_3_H // Generic functions calling the kernel functor. // See comments in CGAL/Kernel/global_functions_internal_3.h. #include #include #include #include #include namespace CGAL { namespace internal { template inline typename K::Angle angle(const typename K::Vector_3 &u, const typename K::Vector_3 &v, const K &k) { return k.angle_3_object()(u, v); } template inline typename K::Angle angle(const typename K::Point_3 &p, const typename K::Point_3 &q, const typename K::Point_3 &r, const K &k) { return k.angle_3_object()(p, q, r); } template inline typename K::Angle angle(const typename K::Point_3 &p, const typename K::Point_3 &q, const typename K::Point_3 &r, const typename K::Point_3 &s, const K &k) { return k.angle_3_object()(p, q, r, s); } template inline typename K::Angle angle(const typename K::Point_3 &p, const typename K::Point_3 &q, const typename K::Point_3 &r, const typename K::Vector_3 &v, const K &k) { return k.angle_3_object()(p, q, r, v); } template < class K > inline typename K::FT approximate_angle(const typename K::Vector_3 &u, const typename K::Vector_3 &v , const K& k) { return k.compute_approximate_angle_3_object()(u, v); } template < class K > inline typename K::FT approximate_angle(const typename K::Point_3 &p, const typename K::Point_3 &q, const typename K::Point_3 &r, const K& k) { return k.compute_approximate_angle_3_object()(p, q, r); } template < class K > inline typename K::FT approximate_dihedral_angle(const typename K::Point_3 &p, const typename K::Point_3 &q, const typename K::Point_3 &r, const typename K::Point_3 &s, const K& k) { return k.compute_approximate_dihedral_angle_3_object()(p, q, r, s); } template < class K > inline typename K::Boolean are_ordered_along_line(const typename K::Point_3 &p, const typename K::Point_3 &q, const typename K::Point_3 &r, const K& k) { return k.are_ordered_along_line_3_object()(p, q, r); } template < class K > inline typename K::Boolean are_strictly_ordered_along_line(const typename K::Point_3 &p, const typename K::Point_3 &q, const typename K::Point_3 &r, const K& k) { return k.are_strictly_ordered_along_line_3_object()(p, q, r); } template < class K > inline typename K::Point_3 barycenter(const typename K::Point_3 &p1, const typename K::FT& w1, const typename K::Point_3 &p2, const K& k) { return k.construct_barycenter_3_object()(p1, w1, p2); } template < class K > inline typename K::Point_3 barycenter(const typename K::Point_3 &p1, const typename K::FT& w1, const typename K::Point_3 &p2, const typename K::FT& w2, const K& k) { return k.construct_barycenter_3_object()(p1, w1, p2, w2); } template < class K > inline typename K::Point_3 barycenter(const typename K::Point_3 &p1, const typename K::FT& w1, const typename K::Point_3 &p2, const typename K::FT& w2, const typename K::Point_3 &p3, const K& k) { return k.construct_barycenter_3_object()(p1, w1, p2, w2, p3); } template < class K > inline typename K::Point_3 barycenter(const typename K::Point_3 &p1, const typename K::FT& w1, const typename K::Point_3 &p2, const typename K::FT& w2, const typename K::Point_3 &p3, const typename K::FT& w3, const K& k) { return k.construct_barycenter_3_object()(p1, w1, p2, w2, p3, w3); } template < class K > inline typename K::Point_3 barycenter(const typename K::Point_3 &p1, const typename K::FT& w1, const typename K::Point_3 &p2, const typename K::FT& w2, const typename K::Point_3 &p3, const typename K::FT& w3, const typename K::Point_3 &p4, const K& k) { return k.construct_barycenter_3_object()(p1, w1, p2, w2, p3, w3, p4); } template < class K > inline typename K::Point_3 barycenter(const typename K::Point_3 &p1, const typename K::FT& w1, const typename K::Point_3 &p2, const typename K::FT& w2, const typename K::Point_3 &p3, const typename K::FT& w3, const typename K::Point_3 &p4, const typename K::FT& w4, const K& k) { return k.construct_barycenter_3_object()(p1, w1, p2, w2, p3, w3, p4, w4); } template inline typename K::Plane_3 bisector(const typename K::Point_3 &p, const typename K::Point_3 &q, const K &k) { return k.construct_bisector_3_object()(p, q); } template inline typename K::Plane_3 bisector(const typename K::Plane_3 &h1, const typename K::Plane_3 &h2, const K &k) { return k.construct_bisector_3_object()(h1, h2); } template < class K > inline typename K::Point_3 centroid(const typename K::Point_3 &p, const typename K::Point_3 &q, const typename K::Point_3 &r, const typename K::Point_3 &s, const K &k) { return k.construct_centroid_3_object()(p, q, r, s); } template < class K > inline typename K::Point_3 centroid(const typename K::Point_3 &p, const typename K::Point_3 &q, const typename K::Point_3 &r, const K &k) { return k.construct_centroid_3_object()(p, q, r); } template < class K > inline typename K::Point_3 centroid(const typename K::Tetrahedron_3 &t, const K &k) { return k.construct_centroid_3_object()(t); } template < class K > inline typename K::Point_3 centroid(const typename K::Triangle_3 &t, const K &k) { return k.construct_centroid_3_object()(t); } template < class K > inline typename K::Point_3 circumcenter(const typename K::Point_3 &p, const typename K::Point_3 &q, const K &k) { return k.construct_circumcenter_3_object()(p, q); } template < class K > inline typename K::Point_3 circumcenter(const typename K::Point_3 &p, const typename K::Point_3 &q, const typename K::Point_3 &r, const K &k) { return k.construct_circumcenter_3_object()(p, q, r); } template < class K > inline typename K::Point_3 circumcenter(const typename K::Point_3 &p, const typename K::Point_3 &q, const typename K::Point_3 &r, const typename K::Point_3 &s, const K &k) { return k.construct_circumcenter_3_object()(p, q, r, s); } template < class K > inline typename K::Point_3 circumcenter(const typename K::Tetrahedron_3 &t, const K& k) { return k.construct_circumcenter_3_object()(t); } template < class K > inline typename K::Point_3 circumcenter(const typename K::Triangle_3 &t, const K& k) { return k.construct_circumcenter_3_object()(t); } template < class K > inline typename K::Boolean collinear(const typename K::Point_3 &p, const typename K::Point_3 &q, const typename K::Point_3 &r, const K& k) { return k.collinear_3_object()(p, q, r); } template < class K > inline typename K::Boolean collinear_are_ordered_along_line( const typename K::Point_3 &p, const typename K::Point_3 &q, const typename K::Point_3 &r, const K& k) { return k.collinear_are_ordered_along_line_3_object()(p, q, r); } template < class K > inline typename K::Boolean collinear_are_strictly_ordered_along_line( const typename K::Point_3 &p, const typename K::Point_3 &q, const typename K::Point_3 &r, const K& k) { return k.collinear_are_strictly_ordered_along_line_3_object()(p, q, r); } template < class K > inline typename K::Comparison_result compare_angle(const typename K::Point_3& a, const typename K::Point_3& b, const typename K::Point_3& c, const typename K::FT& cosine, const K& k) { return k.compare_angle_3_object()(a, b, c, cosine); } template < class K > inline typename K::Comparison_result compare_angle(const typename K::Point_3& a1, const typename K::Point_3& b1, const typename K::Point_3& c1, const typename K::Point_3& a2, const typename K::Point_3& b2, const typename K::Point_3& c2, const K& k) { return k.compare_angle_3_object()(a1, b1, c1, a2, b2, c2); } template < class K > inline typename K::Comparison_result compare_angle(const typename K::Vector_3& u1, const typename K::Vector_3& v1, const typename K::Vector_3& u2, const typename K::Vector_3& v2, const K& k) { return k.compare_angle_3_object()(u1, v1, u2, v2); } template < class K > inline typename K::Comparison_result compare_dihedral_angle(const typename K::Point_3& a1, const typename K::Point_3& b1, const typename K::Point_3& c1, const typename K::Point_3& d1, const typename K::Point_3& a2, const typename K::Point_3& b2, const typename K::Point_3& c2, const typename K::Point_3& d2, const K& k) { return k.compare_dihedral_angle_3_object()(a1, b1, c1, d1, a2, b2, c2, d2); } template < class K > inline typename K::Comparison_result compare_dihedral_angle(const typename K::Point_3& a1, const typename K::Point_3& b1, const typename K::Point_3& c1, const typename K::Point_3& d1, const typename K::FT& cosine, const K& k) { return k.compare_dihedral_angle_3_object()(a1, b1, c1, d1, cosine); } template < class K > inline typename K::Comparison_result compare_dihedral_angle(const typename K::Vector_3& ab1, const typename K::Vector_3& ac1, const typename K::Vector_3& ad1, const typename K::Vector_3& ab2, const typename K::Vector_3& ac2, const typename K::Vector_3& ad2, const K& k) { return k.compare_dihedral_angle_3_object()(ab1, ac1, ad1, ab2, ac2, ad2); } template < class K > inline typename K::Comparison_result compare_dihedral_angle(const typename K::Vector_3& ab1, const typename K::Vector_3& ac1, const typename K::Vector_3& ad1, const typename K::FT& cosine, const K& k) { return k.compare_dihedral_angle_3_object()(ab1, ac1, ad1, cosine); } template inline std::enable_if_t< boost::mpl::equal_to::type::value>, boost::mpl::integral_c >::value, typename K::Comparison_result> // boost::mpl::equal_to::type, // boost::mpl::int_<3> >, // typename K::Comparison_result>::type compare_distance(const T1 &o1, const T2 &o2, const T3 &o3, const K& k) { return k.compare_distance_3_object()(o1, o2, o3); } template inline std::enable_if_t< boost::mpl::equal_to::type::value>, boost::mpl::integral_c >::value, typename K::Comparison_result> // boost::mpl::equal_to::type, // boost::mpl::int_<3> >, // typename K::Comparison_result>::type compare_distance(const T1 &o1, const T2 &o2, const T3 &o3, const T4 &o4, const K& k) { return k.compare_distance_3_object()(o1, o2, o3, o4); } template < class K > inline typename K::Comparison_result compare_distance_to_point(const typename K::Point_3 &p, const typename K::Point_3 &q, const typename K::Point_3 &r, const K& k) { return k.compare_distance_3_object()(p, q, r); } template < class K > inline typename K::Comparison_result compare_power_distance(const typename K::Point_3 &r, const typename K::Weighted_point_3 &p, const typename K::Weighted_point_3 &q, const K& k) { return k.compare_power_distance_3_object()(r, p, q); } template < class K > inline typename K::Comparison_result compare_slope(const typename K::Point_3 &p, const typename K::Point_3 &q, const typename K::Point_3 &r, const typename K::Point_3 &s, const K& k) { return k.compare_slope_3_object()(p, q, r, s); } template < class K > inline typename K::Comparison_result compare_squared_distance(const typename K::Point_3 &p, const typename K::Point_3 &q, const typename K::FT &d2, const K& k) { return k.compare_squared_distance_3_object()(p, q, d2); } template < class K > inline typename K::Comparison_result compare_squared_radius(const typename K::Point_3 &p, const typename K::FT &sr, const K& k) { return k.compare_squared_radius_3_object()(p, sr); } template < class K > inline typename K::Comparison_result compare_squared_radius(const typename K::Point_3 &p, const typename K::Point_3 &q, const typename K::FT &sr, const K& k) { return k.compare_squared_radius_3_object()(p, q, sr); } template < class K > inline typename K::Comparison_result compare_squared_radius(const typename K::Point_3 &p, const typename K::Point_3 &q, const typename K::Point_3 &r, const typename K::FT &sr, const K& k) { return k.compare_squared_radius_3_object()(p, q, r, sr); } template < class K > inline typename K::Comparison_result compare_squared_radius(const typename K::Point_3 &p, const typename K::Point_3 &q, const typename K::Point_3 &r, const typename K::Point_3 &s, const typename K::FT &sr, const K& k) { return k.compare_squared_radius_3_object()(p, q, r, s, sr); } template < class K > inline typename K::Comparison_result compare_lexicographically_xyz(const typename K::Point_3 &p, const typename K::Point_3 &q, const K& k) { return k.compare_xyz_3_object()(p, q); } template < class K > inline typename K::Comparison_result compare_signed_distance_to_plane(const typename K::Plane_3 &h, const typename K::Point_3 &p, const typename K::Point_3 &q, const K &k) { if (k.less_signed_distance_to_plane_3_object()(h, p, q)) return SMALLER; if (k.less_signed_distance_to_plane_3_object()(h, q, p)) return LARGER; return EQUAL; } template < class K > inline typename K::Comparison_result compare_signed_distance_to_plane(const typename K::Point_3 &hp, const typename K::Point_3 &hq, const typename K::Point_3 &hr, const typename K::Point_3 &p, const typename K::Point_3 &q, const K &k) { if (k.less_signed_distance_to_plane_3_object()(hp, hq, hr, p, q)) return SMALLER; if (k.less_signed_distance_to_plane_3_object()(hp, hq, hr, q, p)) return LARGER; return EQUAL; } template < class K > inline typename K::Comparison_result compare_weighted_squared_radius(const typename K::Weighted_point_3 &p, const typename K::FT &w, const K &k) { return k.compare_weighted_squared_radius_3_object()(p, w); } template < class K > inline typename K::Comparison_result compare_weighted_squared_radius(const typename K::Weighted_point_3 &p, const typename K::Weighted_point_3 &q, const typename K::FT &w, const K &k) { return k.compare_weighted_squared_radius_3_object()(p, q, w); } template < class K > inline typename K::Comparison_result compare_weighted_squared_radius(const typename K::Weighted_point_3 &p, const typename K::Weighted_point_3 &q, const typename K::Weighted_point_3 &r, const typename K::FT &w, const K &k) { return k.compare_weighted_squared_radius_3_object()(p, q, r, w); } template < class K > inline typename K::Comparison_result compare_weighted_squared_radius(const typename K::Weighted_point_3 &p, const typename K::Weighted_point_3 &q, const typename K::Weighted_point_3 &r, const typename K::Weighted_point_3 &s, const typename K::FT &w, const K &k) { return k.compare_weighted_squared_radius_3_object()(p, q, r, s, w); } template < class K > inline typename K::Comparison_result compare_x(const typename K::Point_3 &p, const typename K::Point_3 &q, const K &k) { return k.compare_x_3_object()(p, q); } template < class K > inline typename K::Comparison_result compare_y(const typename K::Point_3 &p, const typename K::Point_3 &q, const K &k) { return k.compare_y_3_object()(p, q); } template < class K > inline typename K::Comparison_result compare_z(const typename K::Point_3 &p, const typename K::Point_3 &q, const K &k) { return k.compare_z_3_object()(p, q); } template < class K > inline typename K::Comparison_result compare_xyz(const typename K::Point_3 &p, const typename K::Point_3 &q, const K &k) { return k.compare_xyz_3_object()(p, q); } template < class K > inline typename K::Boolean coplanar(const typename K::Point_3 &p, const typename K::Point_3 &q, const typename K::Point_3 &r, const typename K::Point_3 &s, const K& k) { return k.coplanar_3_object()(p, q, r, s); } template < class K > inline typename K::Orientation coplanar_orientation(const typename K::Point_3 &p, const typename K::Point_3 &q, const typename K::Point_3 &r, const typename K::Point_3 &s, const K& k) { return k.coplanar_orientation_3_object()(p, q, r, s); } template < class K > inline typename K::Orientation coplanar_orientation(const typename K::Point_3 &p, const typename K::Point_3 &q, const typename K::Point_3 &r, const K& k) { return k.coplanar_orientation_3_object()(p, q, r); } template < class K > inline typename K::Bounded_side coplanar_side_of_bounded_circle(const typename K::Point_3 &p, const typename K::Point_3 &q, const typename K::Point_3 &r, const typename K::Point_3 &t, const K& k) { return k.coplanar_side_of_bounded_circle_3_object()(p, q, r, t); } template < class K > inline typename K::Vector_3 cross_product(const typename K::Vector_3 &v, const typename K::Vector_3 &w, const K& k) { return k.construct_cross_product_vector_3_object()(v, w); } template < class K > inline typename K::FT determinant(const typename K::Vector_3 &v0, const typename K::Vector_3 &v1, const typename K::Vector_3 &v2, const K &k) { return k.compute_determinant_3_object()(v0, v1, v2); } template < class K > inline typename K::Line_3 equidistant_line(const typename K::Point_3 &p, const typename K::Point_3 &q, const typename K::Point_3 &r, const K& k) { return k.construct_equidistant_line_3_object()(p, q, r); } template < class K > inline typename K::Boolean has_smaller_distance_to_point(const typename K::Point_3 &p, const typename K::Point_3 &q, const typename K::Point_3 &r, const K &k) { return k.less_distance_to_point_3_object()(p, q, r); } template < class K > inline typename K::Boolean has_larger_distance_to_point(const typename K::Point_3 &p, const typename K::Point_3 &q, const typename K::Point_3 &r, const K &k) { return k.compare_distance_3_object()(p, q, r) == LARGER; } template < class K > inline typename K::Boolean has_larger_signed_distance_to_plane(const typename K::Plane_3 &h, const typename K::Point_3 &p, const typename K::Point_3 &q, const K &k) { return k.less_signed_distance_to_plane_3_object()(h, q, p); } template < class K > inline typename K::Boolean has_larger_signed_distance_to_plane(const typename K::Point_3 &hp, const typename K::Point_3 &hq, const typename K::Point_3 &hr, const typename K::Point_3 &p, const typename K::Point_3 &q, const K &k) { return k.less_signed_distance_to_plane_3_object()(hp, hq, hr, q, p); } template < class K > inline typename K::Boolean has_smaller_signed_distance_to_plane(const typename K::Plane_3 &h, const typename K::Point_3 &p, const typename K::Point_3 &q, const K &k) { return k.less_signed_distance_to_plane_3_object()(h, p, q); } template < class K > inline typename K::Boolean has_smaller_signed_distance_to_plane(const typename K::Point_3 &hp, const typename K::Point_3 &hq, const typename K::Point_3 &hr, const typename K::Point_3 &p, const typename K::Point_3 &q, const K &k) { return k.less_signed_distance_to_plane_3_object()(hp, hq, hr, p, q); } template < class K > inline typename K::Boolean less_x(const typename K::Point_3 &p, const typename K::Point_3 &q, const K &k) { return k.less_x_3_object()(p, q); } template < class K > inline typename K::Boolean less_y(const typename K::Point_3 &p, const typename K::Point_3 &q, const K &k) { return k.less_y_3_object()(p, q); } template < class K > inline typename K::Boolean less_z(const typename K::Point_3 &p, const typename K::Point_3 &q, const K &k) { return k.less_z_3_object()(p, q); } template < class K > inline typename K::Boolean lexicographically_xyz_smaller(const typename K::Point_3 &p, const typename K::Point_3 &q, const K &k) { return k.less_xyz_3_object()(p, q); } template < class K > inline typename K::FT l_infinity_distance(const typename K::Point_3 &p, const typename K::Point_3 &q, const K& k) { return k.compute_L_infinity_distance_3_object()(p, q); } template < class K > inline typename K::Point_3 midpoint(const typename K::Point_3 &p, const typename K::Point_3 &q, const K &k) { return k.construct_midpoint_3_object()(p, q); } template < class K > inline typename K::Point_3 midpoint(const typename K::Segment_3 &s, const K &k) { return k.construct_midpoint_3_object()(s); } template < class K > inline typename K::Point_3 max_vertex(const typename K::Iso_cuboid_3 &ic, const K &k) { return k.construct_max_vertex_3_object()(ic); } template < class K > inline typename K::Point_3 min_vertex(const typename K::Iso_cuboid_3 &ic, const K &k) { return k.construct_min_vertex_3_object()(ic); } template < class K > inline typename K::Vector_3 normal(const typename K::Point_3 &p, const typename K::Point_3 &q, const typename K::Point_3 &r, const K &k) { return k.construct_normal_3_object()(p, q, r); } template < class K > inline typename K::Vector_3 unit_normal(const typename K::Point_3 &p, const typename K::Point_3 &q, const typename K::Point_3 &r, const K &k) { return k.construct_unit_normal_3_object()(p, q, r); } template inline typename K::Orientation orientation(const typename K::Point_3 &p, const typename K::Point_3 &q, const typename K::Point_3 &r, const typename K::Point_3 &s, const K &k) { return k.orientation_3_object()(p, q, r, s); } template inline typename K::Orientation orientation(const typename K::Vector_3 &u, const typename K::Vector_3 &v, const typename K::Vector_3 &w, const K &k) { return k.orientation_3_object()(u, v, w); } template < class K > inline typename K::Vector_3 orthogonal_vector(const typename K::Point_3 &p, const typename K::Point_3 &q, const typename K::Point_3 &r, const K &k) { return k.construct_orthogonal_vector_3_object()(p, q, r); } template < class K > inline typename K::Vector_3 orthogonal_vector(const typename K::Plane_3 &p, const K &k) { return k.construct_orthogonal_vector_3_object()(p); } template inline typename K::Boolean parallel(const typename K::Line_3 &l1, const typename K::Line_3 &l2, const K &k) { return k.are_parallel_3_object()(l1, l2); } template inline typename K::Boolean parallel(const typename K::Plane_3 &h1, const typename K::Plane_3 &h2, const K &k) { return k.are_parallel_3_object()(h1, h2); } template inline typename K::Boolean parallel(const typename K::Ray_3 &r1, const typename K::Ray_3 &r2, const K &k) { return k.are_parallel_3_object()(r1, r2); } template inline typename K::Boolean parallel(const typename K::Segment_3 &s1, const typename K::Segment_3 &s2, const K &k) { return k.are_parallel_3_object()(s1, s2); } template inline typename K::FT power_distance_to_power_sphere(const typename K::Weighted_point_3 &p, const typename K::Weighted_point_3 &q, const typename K::Weighted_point_3 &r, const typename K::Weighted_point_3 &s, const typename K::Weighted_point_3 &t, const K &k) { return k.compute_power_distance_to_power_sphere_3_object()(p, q, r, s, t); } template inline typename K::FT power_product(const typename K::Weighted_point_3 &p, const typename K::Weighted_point_3 &q, const K &k) { return k.compute_power_product_3_object()(p, q); } template inline typename K::Bounded_side power_side_of_bounded_power_sphere(const typename K::Weighted_point_3 &p, const typename K::Weighted_point_3 &q, const K &k) { return k.power_side_of_bounded_power_sphere_3_object()(p, q); } template inline typename K::Bounded_side power_side_of_bounded_power_sphere(const typename K::Weighted_point_3 &p, const typename K::Weighted_point_3 &q, const typename K::Weighted_point_3 &r, const K &k) { return k.power_side_of_bounded_power_sphere_3_object()(p, q, r); } template inline typename K::Bounded_side power_side_of_bounded_power_sphere(const typename K::Weighted_point_3 &p, const typename K::Weighted_point_3 &q, const typename K::Weighted_point_3 &r, const typename K::Weighted_point_3 &s, const K &k) { return k.power_side_of_bounded_power_sphere_3_object()(p, q, r, s); } template inline typename K::Bounded_side power_side_of_bounded_power_sphere(const typename K::Weighted_point_3 &p, const typename K::Weighted_point_3 &q, const typename K::Weighted_point_3 &r, const typename K::Weighted_point_3 &s, const typename K::Weighted_point_3 &t, const K &k) { return k.power_side_of_bounded_power_sphere_3_object()(p, q, r, s, t); } template inline typename K::Oriented_side power_side_of_oriented_power_sphere(const typename K::Weighted_point_3 &p, const typename K::Weighted_point_3 &q, const K &k) { return k.power_side_of_oriented_power_sphere_3_object()(p, q); } template inline typename K::Oriented_side power_side_of_oriented_power_sphere(const typename K::Weighted_point_3 &p, const typename K::Weighted_point_3 &q, const typename K::Weighted_point_3 &r, const K &k) { return k.power_side_of_oriented_power_sphere_3_object()(p, q, r); } template inline typename K::Oriented_side power_side_of_oriented_power_sphere(const typename K::Weighted_point_3 &p, const typename K::Weighted_point_3 &q, const typename K::Weighted_point_3 &r, const typename K::Weighted_point_3 &s, const K &k) { return k.power_side_of_oriented_power_sphere_3_object()(p, q, r, s); } template inline typename K::Oriented_side power_side_of_oriented_power_sphere(const typename K::Weighted_point_3 &p, const typename K::Weighted_point_3 &q, const typename K::Weighted_point_3 &r, const typename K::Weighted_point_3 &s, const typename K::Weighted_point_3 &t, const K &k) { return k.power_side_of_oriented_power_sphere_3_object()(p, q, r, s, t); } template inline typename K::Bounded_side side_of_bounded_sphere(const typename K::Point_3 &p, const typename K::Point_3 &q, const typename K::Point_3 &test, const K &k) { return k.side_of_bounded_sphere_3_object()(p, q, test); } template inline typename K::Bounded_side side_of_bounded_sphere(const typename K::Point_3 &p, const typename K::Point_3 &q, const typename K::Point_3 &r, const typename K::Point_3 &test, const K &k) { return k.side_of_bounded_sphere_3_object()(p, q, r, test); } template inline typename K::Bounded_side side_of_bounded_sphere(const typename K::Point_3 &p, const typename K::Point_3 &q, const typename K::Point_3 &r, const typename K::Point_3 &s, const typename K::Point_3 &test, const K &k) { return k.side_of_bounded_sphere_3_object()(p, q, r, s, test); } template inline typename K::Oriented_side side_of_oriented_sphere(const typename K::Point_3 &p, const typename K::Point_3 &q, const typename K::Point_3 &r, const typename K::Point_3 &s, const typename K::Point_3 &test, const K &k) { return k.side_of_oriented_sphere_3_object()(p, q, r, s, test); } template inline typename K::FT squared_area(const typename K::Point_3 &p, const typename K::Point_3 &q, const typename K::Point_3 &r, const K &k) { return k.compute_squared_area_3_object()(p, q, r); } template inline typename K::FT squared_length(const typename K::Vector_3 &v, const K &k) { return k.compute_squared_length_3_object()(v); } template inline typename K::FT squared_length(const typename K::Segment_3 &s, const K &k) { return k.compute_squared_length_3_object()(s); } template < class K > inline typename K::FT squared_radius(const typename K::Point_3 &p, const typename K::Point_3 &q, const typename K::Point_3 &r, const typename K::Point_3 &s, const K &k) { return k.compute_squared_radius_3_object()(p, q, r, s); } template < class K > inline typename K::FT squared_radius(const typename K::Point_3 &p, const typename K::Point_3 &q, const typename K::Point_3 &r, const K &k) { return k.compute_squared_radius_3_object()(p, q, r); } template < class K > inline typename K::FT squared_radius(const typename K::Point_3 &p, const typename K::Point_3 &q, const K &k) { return k.compute_squared_radius_3_object()(p, q); } template < class K > inline typename K::FT squared_radius(const typename K::Point_3 &p, const K &k) { return k.compute_squared_radius_3_object()(p); } template < class K > inline typename K::FT squared_radius_smallest_orthogonal_sphere(const typename K::Weighted_point_3 &p, const K &k) { return k.compute_squared_radius_smallest_orthogonal_sphere_3_object()(p); } template < class K > inline typename K::FT squared_radius_smallest_orthogonal_sphere(const typename K::Weighted_point_3 &p, const typename K::Weighted_point_3 &q, const K &k) { return k.compute_squared_radius_smallest_orthogonal_sphere_3_object()(p, q); } template < class K > inline typename K::FT squared_radius_smallest_orthogonal_sphere(const typename K::Weighted_point_3 &p, const typename K::Weighted_point_3 &q, const typename K::Weighted_point_3 &r, const K &k) { return k.compute_squared_radius_smallest_orthogonal_sphere_3_object()(p, q, r); } template < class K > inline typename K::FT squared_radius_smallest_orthogonal_sphere(const typename K::Weighted_point_3 &p, const typename K::Weighted_point_3 &q, const typename K::Weighted_point_3 &r, const typename K::Weighted_point_3 &s, const K &k) { return k.compute_squared_radius_smallest_orthogonal_sphere_3_object()(p, q, r, s); } template < class K > inline typename K::FT volume(const typename K::Point_3 &p, const typename K::Point_3 &q, const typename K::Point_3 &r, const typename K::Point_3 &s, const K &k) { return k.compute_volume_3_object()(p, q, r, s); } template < class K > inline typename K::Point_3 weighted_circumcenter(const typename K::Weighted_point_3 &p, const typename K::Weighted_point_3 &q, const K &k) { return k.construct_weighted_circumcenter_3_object()(p, q); } template < class K > inline typename K::Point_3 weighted_circumcenter(const typename K::Weighted_point_3 &p, const typename K::Weighted_point_3 &q, const typename K::Weighted_point_3 &r, const K &k) { return k.construct_weighted_circumcenter_3_object()(p, q, r); } template < class K > inline typename K::Point_3 weighted_circumcenter(const typename K::Weighted_point_3 &p, const typename K::Weighted_point_3 &q, const typename K::Weighted_point_3 &r, const typename K::Weighted_point_3 &s, const K &k) { return k.construct_weighted_circumcenter_3_object()(p, q, r, s); } template < class K > inline typename K::Boolean x_equal(const typename K::Point_3 &p, const typename K::Point_3 &q, const K &k) { return k.equal_x_3_object()(p, q); } template < class K > inline typename K::Boolean y_equal(const typename K::Point_3 &p, const typename K::Point_3 &q, const K &k) { return k.equal_y_3_object()(p, q); } template < class K > inline typename K::Boolean z_equal(const typename K::Point_3 &p, const typename K::Point_3 &q, const K &k) { return k.equal_z_3_object()(p, q); } // The following functions only call some of the previous ones. template inline typename K::Boolean are_negative_oriented(const typename K::Point_3 &p, const typename K::Point_3 &q, const typename K::Point_3 &r, const typename K::Point_3 &s, const K &k) { return internal::orientation(p, q, r, s, k) == NEGATIVE; } template inline typename K::Boolean are_positive_oriented(const typename K::Point_3 &p, const typename K::Point_3 &q, const typename K::Point_3 &r, const typename K::Point_3 &s, const K &k) { return internal::orientation(p, q, r, s, k) == POSITIVE; } template < class K > inline typename K::Boolean lexicographically_xyz_smaller_or_equal(const typename K::Point_3 &p, const typename K::Point_3 &q, const K&k) { return internal::compare_lexicographically_xyz(p, q, k) != LARGER; } } // namespace internal } //namespace CGAL #endif // CGAL_KERNEL_GLOBAL_FUNCTIONS_INTERNAL_3_H