CGAL Namespace Reference

Namespaces
	cpp11
	cpp98
	Mesh_2

Classes
class	Aff_transformation_2
class	Aff_transformation_3
struct	Algebraic_kernel_for_circles_2_2
struct	Algebraic_kernel_for_spheres_2_3
class	Algebraic_structure_traits
struct	Ambient_dimension
	The class Ambient_dimension allows to retrieve the dimension of the ambient space of a type T in a kernel K. More...
class	Bbox_2
class	Bbox_3
struct	Boolean_tag
struct	Cartesian
class	Cartesian_converter
class	Cartesian_d
struct	Cast_function_object
class	CC_safe_handle
class	Circle_2
class	Circle_3
class	Circular_arc_2
class	Circular_arc_3
class	Circular_arc_point_2
class	Circular_arc_point_3
struct	Circular_kernel_2
struct	Coercion_traits
struct	Compact
class	Compact_container
class	Compact_container_base
struct	Compact_container_traits
class	Compare_to_less
class	Concurrent_compact_container
struct	Concurrent_compact_container_traits
class	Const_oneset_iterator
class	Constrained_Delaunay_triangulation_2
class	Constrained_triangulation_2
class	Constrained_triangulation_face_base_2
class	Constrained_triangulation_plus_2
struct	Construct_array
class	Convex_hull_constructive_traits_2
class	Convex_hull_traits_2
class	Convex_hull_traits_adapter_2
class	Counting_iterator
class	Creator_1
class	Creator_2
class	Creator_3
class	Creator_4
class	Creator_5
class	Creator_uniform_2
class	Creator_uniform_3
class	Creator_uniform_4
class	Creator_uniform_5
class	Creator_uniform_6
class	Creator_uniform_7
class	Creator_uniform_8
class	Creator_uniform_9
class	Creator_uniform_d
struct	Default
class	Delaunay_mesh_criteria_2
class	Delaunay_mesh_face_base_2
class	Delaunay_mesh_size_criteria_2
class	Delaunay_mesh_vertex_base_2
class	Delaunay_mesher_2
class	Delaunay_triangulation_2
struct	Dereference
struct	Dimension_tag
	An object of the class Dimension_tag is an empty object which can be used for dispatching functions based on the dimension of an object, as provided by the dim parameter. More...
class	Direction_2
class	Direction_3
class	Direction_d
class	Dispatch_or_drop_output_iterator
class	Dispatch_output_iterator
struct	Dynamic_dimension_tag
	An object of the class Dynamic_dimension_tag is an empty object which can be used for dispatching functions based on the dimension of an object. More...
struct	Emptyset_iterator
struct	Epeck_d
struct	Epick_d
struct	Euclidean_ring_tag
class	Exact_circular_kernel_2
struct	Exact_intersections_tag
class	Exact_predicates_exact_constructions_kernel
class	Exact_predicates_exact_constructions_kernel_with_kth_root
class	Exact_predicates_exact_constructions_kernel_with_root_of
class	Exact_predicates_exact_constructions_kernel_with_sqrt
class	Exact_predicates_inexact_constructions_kernel
struct	Exact_predicates_tag
class	Exact_spherical_kernel_3
struct	Fast
struct	Feature_dimension
	The class Feature_dimension allows to retrieve the geometric dimension of a type T in a kernel K. More...
struct	Field_tag
struct	Field_with_kth_root_tag
struct	Field_with_root_of_tag
struct	Field_with_sqrt_tag
struct	Filter_iterator
struct	Filtered_kernel
struct	Filtered_kernel_adaptor
	Filtered_kernel_adaptor is a kernel that uses a filtering technique to obtain a kernel with exact and efficient predicate functors. More...
class	Filtered_predicate
class	Fourtuple
class	Fraction_traits
class	General_polygon_with_holes_2
struct	Get_address
class	Gmpfi
class	Gmpfr
class	Gmpq
class	Gmpz
class	Gmpzf
struct	Homogeneous
class	Homogeneous_converter
class	Homogeneous_d
class	Hyperplane_d
struct	Identity
class	Identity_transformation
class	In_place_list
class	In_place_list_base
class	Insert_iterator
struct	Integral_domain_tag
struct	Integral_domain_without_division_tag
class	Interval_nt
class	Inverse_index
class	Is_valid
class	Iso_box_d
class	Iso_cuboid_3
class	Iso_rectangle_2
class	Iterator_range
class	Join_input_iterator_1
class	Join_input_iterator_2
class	Join_input_iterator_3
struct	Kernel_traits
class	Lazy_exact_nt
class	Line_2
class	Line_3
class	Line_arc_2
class	Line_arc_3
class	Line_d
class	Linear_algebraCd
class	Linear_algebraHd
struct	Location_policy
struct	Max
struct	Min
class	MP_Float
struct	Mpzf
class	Multiset
class	N_step_adaptor
struct	No_constraint_intersection_requiring_constructions_tag
struct	No_constraint_intersection_tag
struct	No_intersection_tag
struct	NT_converter
struct	Null_functor
struct	Null_tag
class	Null_vector
class	Number_type_checker
class	Object
class	Oneset_iterator
class	Origin
struct	Parallel_if_available_tag
struct	Parallel_tag
class	Plane_3
class	Point_2
class	Point_3
class	Point_d
class	Polygon_2
class	Polygon_with_holes_2
class	Polyhedron_3
class	Polyhedron_incremental_builder_3
class	Polyhedron_items_3
class	Polyhedron_min_items_3
class	Polyhedron_traits_3
class	Polyhedron_traits_with_normals_3
class	Polynomial_1_2
class	Polynomial_1_3
class	Polynomial_for_circles_2_2
class	Polynomial_for_spheres_2_3
class	Polynomials_for_lines_3
struct	Project_facet
struct	Project_next
struct	Project_next_opposite
struct	Project_normal
struct	Project_opposite_prev
struct	Project_plane
struct	Project_point
struct	Project_prev
struct	Project_vertex
class	Projection_traits_xy_3
class	Projection_traits_xz_3
class	Projection_traits_yz_3
struct	Protect_FPU_rounding
class	Quadruple
class	Quotient
class	Random_access_adaptor
class	Random_access_value_adaptor
class	Rational_traits
class	Ray_2
class	Ray_3
class	Ray_d
class	Real_embeddable_traits
class	Reflection
class	Regular_triangulation_2
class	Regular_triangulation_face_base_2
class	Regular_triangulation_vertex_base_2
class	Root_for_circles_2_2
class	Root_for_spheres_2_3
struct	Root_of_traits
class	Rotation
class	Scaling
class	Segment_2
class	Segment_3
class	Segment_d
struct	Sequential_tag
class	Set_ieee_double_precision
struct	Simple_cartesian
struct	Simple_homogeneous
class	Sixtuple
class	Spatial_lock_grid_3
class	Sphere_3
class	Sphere_d
struct	Spherical_kernel_3
class	Sqrt_extension
class	Tetrahedron_3
class	Threetuple
class	Translation
class	Triangle_2
class	Triangle_3
class	Triangulation_2
class	Triangulation_conformer_2
class	Triangulation_cw_ccw_2
class	Triangulation_face_base_2
class	Triangulation_face_base_with_info_2
class	Triangulation_hierarchy_2
class	Triangulation_hierarchy_vertex_base_2
class	Triangulation_vertex_base_2
class	Triangulation_vertex_base_with_info_2
class	Triple
class	Twotuple
class	Uncertain
struct	Unique_factorization_domain_tag
struct	value_type_traits
struct	value_type_traits< std::back_insert_iterator< Container > >
struct	value_type_traits< std::front_insert_iterator< Container > >
struct	value_type_traits< std::insert_iterator< Container > >
class	Vector_2
class	Vector_3
class	Vector_d
class	Weighted_point_2
class	Weighted_point_3

Typedefs
typedef Interval_nt< false >	Interval_nt_advanced
typedef unspecified_type	Exact_integer
typedef unspecified_type	Exact_rational
typedef Location_policy< Compact >	Compact_location
typedef Location_policy< Fast >	Fast_location
typedef CGAL::Boolean_tag< false >	Tag_false
typedef CGAL::Boolean_tag< true >	Tag_true
typedef void(*	Failure_function) (const char *type, const char *expression, const char *file, int line, const char *explanation)
typedef Sign	Orientation

Enumerations
enum	Mesh_optimization_return_code
enum	Circle_type
enum	Failure_behaviour
enum	Angle { OBTUSE, RIGHT, ACUTE }
enum	Bounded_side { ON_UNBOUNDED_SIDE, ON_BOUNDARY, ON_BOUNDED_SIDE }
enum	Comparison_result { SMALLER, EQUAL, LARGER }
enum	Sign { NEGATIVE, ZERO, POSITIVE }
enum	Oriented_side { ON_NEGATIVE_SIDE, ON_ORIENTED_BOUNDARY, ON_POSITIVE_SIDE }
enum	Box_parameter_space_2 {   LEFT_BOUNDARY = 0, RIGHT_BOUNDARY, BOTTOM_BOUNDARY, TOP_BOUNDARY,   INTERIOR, EXTERIOR }

Functions
Point_d< R >	center_of_sphere (ForwardIterator first, ForwardIterator last)
Point_d< R >	lift_to_paraboloid (const Point_d< R > &p)
OutputIterator	linear_base (ForwardIterator first, ForwardIterator last, OutputIterator result)
Point_d< R >	midpoint (const Point_d< R > &p, const Point_d< R > &q)
Point_d< R >	project_along_d_axis (const Point_d< R > &p)
FT	squared_distance (Point_d< R > p, Point_d< R > q)
bool	do_intersect (Type1< R > obj1, Type2< R > obj2)
cpp11::result_of< R::Intersect_d(Type1< R >, Type2< R >)>::type	intersection (Type1< R > f1, Type2< R > f2)
bool	affinely_independent (ForwardIterator first, ForwardIterator last)
int	affine_rank (ForwardIterator first, ForwardIterator last)
Comparison_result	compare_lexicographically (const Point_d< R > &p, const Point_d< R > &q)
bool	contained_in_affine_hull (ForwardIterator first, ForwardIterator last, const Point_d< R > &p)
bool	contained_in_linear_hull (ForwardIterator first, ForwardIterator last, const Vector_d< R > &v)
bool	contained_in_simplex (ForwardIterator first, ForwardIterator last, const Point_d< R > &p)
bool	lexicographically_smaller (const Point_d< R > &p, const Point_d< R > &q)
bool	lexicographically_smaller_or_equal (const Point_d< R > &p, const Point_d< R > &q)
bool	linearly_independent (ForwardIterator first, ForwardIterator last)
int	linear_rank (ForwardIterator first, ForwardIterator last)
Orientation	orientation (ForwardIterator first, ForwardIterator last)
Bounded_side	side_of_bounded_sphere (ForwardIterator first, ForwardIterator last, const Point_d< R > &p)
Oriented_side	side_of_oriented_sphere (ForwardIterator first, ForwardIterator last, const Point_d< R > &p)
OutputIterator	ch_akl_toussaint (ForwardIterator first, ForwardIterator beyond, OutputIterator result, const Traits &ch_traits=Default_traits())
OutputIterator	ch_bykat (InputIterator first, InputIterator beyond, OutputIterator result, const Traits &ch_traits=Default_traits)
OutputIterator	ch_eddy (InputIterator first, InputIterator beyond, OutputIterator result, const Traits &ch_traits=Default_traits)
OutputIterator	ch_graham_andrew (InputIterator first, InputIterator beyond, OutputIterator result, const Traits &ch_traits=Default_traits)
OutputIterator	ch_graham_andrew_scan (BidirectionalIterator first, BidirectionalIterator beyond, OutputIterator result, const Traits &ch_traits=Default_traits)
OutputIterator	ch_jarvis (ForwardIterator first, ForwardIterator beyond, OutputIterator result, const Traits &ch_traits=Default_traits)
OutputIterator	ch_jarvis_march (ForwardIterator first, ForwardIterator beyond, const Traits::Point_2 &start_p, const Traits::Point_2 &stop_p, OutputIterator result, const Traits &ch_traits=Default_traits)
OutputIterator	ch_melkman (InputIterator first, InputIterator last, OutputIterator result, const Traits &ch_traits=Default_traits)
void	ch_e_point (ForwardIterator first, ForwardIterator beyond, ForwardIterator &e, const Traits &ch_traits=Default_traits)
void	ch_n_point (ForwardIterator first, ForwardIterator beyond, ForwardIterator &n, const Traits &ch_traits=Default_traits)
void	ch_ns_point (ForwardIterator first, ForwardIterator beyond, ForwardIterator &n, ForwardIterator &s, const Traits &ch_traits=Default_traits)
void	ch_nswe_point (ForwardIterator first, ForwardIterator beyond, ForwardIterator &n, ForwardIterator &s, ForwardIterator &w, ForwardIterator &e, const Traits &ch_traits=Default_traits)
void	ch_s_point (ForwardIterator first, ForwardIterator beyond, ForwardIterator &s, const Traits &ch_traits=Default_traits)
void	ch_we_point (ForwardIterator first, ForwardIterator beyond, ForwardIterator &w, ForwardIterator &e, const Traits &ch_traits=Default_traits)
void	ch_w_point (ForwardIterator first, ForwardIterator beyond, ForwardIterator &w, const Traits &ch_traits=Default_traits)
OutputIterator	convex_hull_2 (InputIterator first, InputIterator beyond, OutputIterator result, const Traits &ch_traits)
OutputIterator	convex_hull_2 (InputIterator first, InputIterator beyond, OutputIterator result)
OutputIterator	lower_hull_points_2 (InputIterator first, InputIterator beyond, OutputIterator result, const Traits &ch_traits=Default_traits)
OutputIterator	upper_hull_points_2 (InputIterator first, InputIterator beyond, OutputIterator result, const Traits &ch_traits=Default_traits)
bool	is_ccw_strongly_convex_2 (ForwardIterator first, ForwardIterator beyond, const Traits &ch_traits=Default_traits)
bool	is_cw_strongly_convex_2 (ForwardIterator first, ForwardIterator beyond, const Traits &ch_traits=Default_traits)
void	draw (const T2 &at2)
void	refine_Delaunay_mesh_2 (CDT &t, const Criteria &criteria=Criteria())
void	refine_Delaunay_mesh_2 (CDT &t, InputIterator begin, InputIterator end, const Criteria &criteria=Criteria(), bool mark=false)
void	write_vtu (std::ostream &os, const CDT &tr, IO::Mode mode=IO::BINARY)
CGAL::Mesh_optimization_return_code	lloyd_optimize_mesh_2 (CDT &cdt, double parameters::time_limit=0, std::size_t parameters::max_iteration_number=0, double parameters::convergence=0.001, double parameters::freeze_bound=0.001, PointIterator parameters::seeds_begin=PointIterator(), PointIterator parameters::seeds_end=PointIterator(), bool parameters::mark=false)
void	make_conforming_Delaunay_2 (CDT &t)
void	make_conforming_Gabriel_2 (CDT &t)
bool	is_finite (double x)
bool	is_finite (float x)
bool	is_finite (long double x)
OutputIterator	compute_roots_of_2 (const RT &a, const RT &b, const RT &c, OutputIterator oit)
Root_of_traits< RT >::Root_of_2	make_root_of_2 (const RT &a, const RT &b, const RT &c, bool s)
Root_of_traits< RT >::Root_of_2	make_root_of_2 (RT alpha, RT beta, RT gamma)
Root_of_traits< RT >::Root_of_2	make_sqrt (const RT &x)
Rational	simplest_rational_in_interval (double d1, double d2)
Rational	to_rational (double d)
bool	is_valid (const T &x)
T	max (const T &x, const T &y)
T	min (const T &x, const T &y)
NT	abs (const NT &x)
result_type	compare (const NT &x, const NT &y)
result_type	div (const NT1 &x, const NT2 &y)
void	div_mod (const NT1 &x, const NT2 &y, result_type &q, result_type &r)
result_type	gcd (const NT1 &x, const NT2 &y)
result_type	integral_division (const NT1 &x, const NT2 &y)
NT	inverse (const NT &x)
result_type	is_negative (const NT &x)
result_type	is_one (const NT &x)
result_type	is_positive (const NT &x)
result_type	is_square (const NT &x)
result_type	is_square (const NT &x, NT &y)
result_type	is_zero (const NT &x)
NT	kth_root (int k, const NT &x)
result_type	mod (const NT1 &x, const NT2 &y)
NT	root_of (int k, InputIterator begin, InputIterator end)
result_type	sign (const NT &x)
void	simplify (const NT &x)
NT	sqrt (const NT &x)
NT	square (const NT &x)
double	to_double (const NT &x)
std::pair< double, double >	to_interval (const NT &x)
NT	unit_part (const NT &x)
bool	has_in_x_range (const Circular_arc_2< CircularKernel > &ca, const Circular_arc_point_2< CircularKernel > &p)
bool	has_in_x_range (const Line_arc_2< CircularKernel > &ca, const Circular_arc_point_2< CircularKernel > &p)
bool	has_on (const Circle_2< CircularKernel > &c, const Circular_arc_point_2< CircularKernel > &p)
OutputIterator	make_x_monotone (const Circular_arc_2< CircularKernel > &ca, OutputIterator res)
OutputIterator	make_xy_monotone (const Circular_arc_2< CircularKernel > &ca, OutputIterator res)
Circular_arc_point_2< CircularKernel >	x_extremal_point (const Circle_2< CircularKernel > &c, bool b)
OutputIterator	x_extremal_points (const Circle_2< CircularKernel > &c, OutputIterator res)
Circular_arc_point_2< CircularKernel >	y_extremal_point (const Circle_2< CircularKernel > &c, bool b)
OutputIterator	y_extremal_points (const Circle_2< CircularKernel > &c, OutputIterator res)
CGAL::Comparison_result	compare_y_to_right (const Circular_arc_2< CircularKernel > &ca1, const Circular_arc_2< CircularKernel > &ca2, Circular_arc_point_2< CircularKernel > &p)
CGAL::Circle_type	classify (const CGAL::Circle_3< SphericalKernel > &c, const CGAL::Sphere_3< SphericalKernel > &sphere)
Comparison_result	compare_theta (const CGAL::Circular_arc_point_3< SphericalKernel > &p, const CGAL::Circular_arc_point_3< SphericalKernel > &q, const CGAL::Sphere_3< SphericalKernel > &sphere)
Comparison_result	compare_theta (const CGAL::Circular_arc_point_3< SphericalKernel > &p, const CGAL::Vector_3< SphericalKernel > &m, const CGAL::Sphere_3< SphericalKernel > &sphere)
Comparison_result	compare_theta (const CGAL::Vector_3< SphericalKernel > &m, const CGAL::Circular_arc_point_3< SphericalKernel > &p, const CGAL::Sphere_3< SphericalKernel > &sphere)
bool	compare_theta_z (const CGAL::Circular_arc_point_3< SphericalKernel > &p, const CGAL::Circular_arc_point_3< SphericalKernel > &q, const CGAL::Sphere_3< SphericalKernel > &sphere)
bool	is_theta_monotone (const CGAL::Circular_arc_3< SphericalKernel > &a, const CGAL::Sphere_3< SphericalKernel > &sphere)
CGAL::Circular_arc_point_3< SphericalKernel >	theta_extremal_point (const CGAL::Circle_3< SphericalKernel > &c, const CGAL::Sphere_3< SphericalKernel > sphere, bool b)
OutputIterator	theta_extremal_points (const CGAL::Circle_3< SphericalKernel > &c, const CGAL::Sphere_3< SphericalKernel > &sphere, OutputIterator res)
CGAL::Circular_arc_point_3< SphericalKernel >	x_extremal_point (const CGAL::Sphere_3< SphericalKernel > &c, bool b)
CGAL::Circular_arc_point_3< SphericalKernel >	x_extremal_point (const CGAL::Circle_3< SphericalKernel > &c, bool b)
OutputIterator	x_extremal_points (const CGAL::Sphere_3< SphericalKernel > &c, OutputIterator res)
OutputIterator	x_extremal_points (const CGAL::Circle_3< SphericalKernel > &c, OutputIterator res)
CGAL::Circular_arc_point_3< SphericalKernel >	y_extremal_point (const CGAL::Sphere_3< SphericalKernel > &c, bool b)
CGAL::Circular_arc_point_3< SphericalKernel >	y_extremal_point (const CGAL::Circle_3< SphericalKernel > &c, bool b)
OutputIterator	y_extremal_points (const CGAL::Sphere_3< SphericalKernel > &c, OutputIterator res)
OutputIterator	y_extremal_points (const CGAL::Circle_3< SphericalKernel > &c, OutputIterator res)
CGAL::Circular_arc_point_3< SphericalKernel >	z_extremal_point (const CGAL::Sphere_3< SphericalKernel > &c, bool b)
CGAL::Circular_arc_point_3< SphericalKernel >	z_extremal_point (const CGAL::Circle_3< SphericalKernel > &c, bool b)
OutputIterator	z_extremal_points (const CGAL::Sphere_3< SphericalKernel > &c, OutputIterator res)
OutputIterator	z_extremal_points (const CGAL::Circle_3< SphericalKernel > &c, OutputIterator res)
OutputIterator	copy_n (InputIterator first, Size n, OutputIterator result)
std::pair< ForwardIterator, ForwardIterator >	min_max_element (ForwardIterator first, ForwardIterator last)
std::pair< ForwardIterator, ForwardIterator >	min_max_element (ForwardIterator first, ForwardIterator last, CompareMin comp_min, CompareMax comp_max)
BidirectionalIterator	predecessor (BidirectionalIterator it)
ForwardIterator	successor (ForwardIterator it)
std::array< T, N >	make_array (const T &...)
CC_safe_handle< CC_iterator >	make_cc_safe_handle (CC_iterator iterator)
Compare_to_less< F >	compare_to_less (const F &f)
Iterator_range< T >	make_range (const T &b, const T &e)
T	range_begin (Iterator_range< T > &x)
T	range_end (Iterator_range< T > &x)
T	range_begin (const Iterator_range< T > &x)
T	range_end (const Iterator_range< T > &x)
Failure_function	set_error_handler (Failure_function handler)
Failure_function	set_warning_handler (Failure_function handler)
Failure_behaviour	set_error_behaviour (Failure_behaviour eb)
Failure_behaviour	set_warning_behaviour (Failure_behaviour eb)
void	draw (const POLY &apoly)
template<typename T , typename U >
T	enum_cast (const U &u)
Oriented_side	opposite (const Oriented_side &o)
Bounded_side	opposite (const Bounded_side &o)
bool	do_intersect (Type1< Kernel > obj1, Type2< Kernel > obj2)
	checks whether obj1 and obj2 intersect. More...
template<typename Kernel >
cpp11::result_of< Kernel::Intersect_23(Type1, Type2)>::type	intersection (Type1< Kernel > obj1, Type2< Kernel > obj2)
	Two objects obj1 and obj2 intersect if there is a point p that is part of both obj1 and obj2. More...
template<typename Kernel >
boost::optional< boost::variant< Point_3, Line_3, Plane_3 > >	intersection (const Plane_3< Kernel > &pl1, const Plane_3< Kernel > &pl2, const Plane_3< Kernel > &pl3)
	returns the intersection of 3 planes, which can be a point, a line, a plane, or empty. More...
template<typename Kernel >
Angle	angle (const CGAL::Vector_2< Kernel > &u, const CGAL::Vector_2< Kernel > &v)
	returns CGAL::OBTUSE, CGAL::RIGHT or CGAL::ACUTE depending on the angle formed by the two vectors u and v. More...
template<typename Kernel >
Angle	angle (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const CGAL::Point_2< Kernel > &r)
	returns CGAL::OBTUSE, CGAL::RIGHT or CGAL::ACUTE depending on the angle formed by the three points p, q, r (q being the vertex of the angle). More...
template<typename Kernel >
Angle	angle (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const CGAL::Point_2< Kernel > &r, const CGAL::Point_2< Kernel > &s)
	returns CGAL::OBTUSE, CGAL::RIGHT or CGAL::ACUTE depending on the angle formed by the two vectors pq, rs. More...
template<typename Kernel >
Angle	angle (const CGAL::Vector_3< Kernel > &u, const CGAL::Vector_3< Kernel > &v)
	returns CGAL::OBTUSE, CGAL::RIGHT or CGAL::ACUTE depending on the angle formed by the two vectors u and v. More...
template<typename Kernel >
Angle	angle (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r)
	returns CGAL::OBTUSE, CGAL::RIGHT or CGAL::ACUTE depending on the angle formed by the three points p, q, r (q being the vertex of the angle). More...
template<typename Kernel >
Angle	angle (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r, const CGAL::Point_3< Kernel > &s)
	returns CGAL::OBTUSE, CGAL::RIGHT or CGAL::ACUTE depending on the angle formed by the two vectors pq, rs. More...
template<typename Kernel >
Angle	angle (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r, const CGAL::Vector_3< Kernel > &v)
	returns CGAL::OBTUSE, CGAL::RIGHT or CGAL::ACUTE depending on the angle formed by the normal of the triangle pqr and the vector v. More...
template<typename Kernel >
Kernel::FT	approximate_angle (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r)
	returns an approximation of the angle between p-q and r-q. More...
template<typename Kernel >
Kernel::FT	approximate_angle (const CGAL::Vector_3< Kernel > &u, const CGAL::Vector_3< Kernel > &v)
	returns an approximation of the angle between u and v. More...
template<typename Kernel >
Kernel::FT	approximate_dihedral_angle (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r, const CGAL::Point_3< Kernel > &s)
	returns an approximation of the signed dihedral angle in the tetrahedron pqrs of edge pq. More...
template<typename Kernel >
Kernel::FT	area (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const CGAL::Point_2< Kernel > &r)
	returns the signed area of the triangle defined by the points p, q and r. More...
template<typename Kernel >
bool	are_ordered_along_line (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const CGAL::Point_2< Kernel > &r)
	returns true, iff the three points are collinear and q lies between p and r. More...
template<typename Kernel >
bool	are_ordered_along_line (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r)
	returns true, iff the three points are collinear and q lies between p and r. More...
template<typename Kernel >
bool	are_strictly_ordered_along_line (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const CGAL::Point_2< Kernel > &r)
	returns true, iff the three points are collinear and q lies strictly between p and r. More...
template<typename Kernel >
bool	are_strictly_ordered_along_line (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r)
	returns true, iff the three points are collinear and q lies strictly between p and r. More...
template<typename Kernel >
CGAL::Point_2< Kernel >	barycenter (const CGAL::Point_2< Kernel > &p1, const Kernel::FT &w1, const CGAL::Point_2< Kernel > &p2)
	compute the barycenter of the points p1 and p2 with corresponding weights w1 and 1-w1. More...
template<typename Kernel >
CGAL::Point_2< Kernel >	barycenter (const CGAL::Point_2< Kernel > &p1, const Kernel::FT &w1, const CGAL::Point_2< Kernel > &p2, const Kernel::FT &w2)
	compute the barycenter of the points p1 and p2 with corresponding weights w1 and w2. More...
template<typename Kernel >
CGAL::Point_2< Kernel >	barycenter (const CGAL::Point_2< Kernel > &p1, const Kernel::FT &w1, const CGAL::Point_2< Kernel > &p2, const Kernel::FT &w2, const CGAL::Point_2< Kernel > &p3)
	compute the barycenter of the points p1, p2 and p3 with corresponding weights w1, w2 and 1-w1-w2. More...
template<typename Kernel >
CGAL::Point_2< Kernel >	barycenter (const CGAL::Point_2< Kernel > &p1, const Kernel::FT &w1, const CGAL::Point_2< Kernel > &p2, const Kernel::FT &w2, const CGAL::Point_2< Kernel > &p3, const Kernel::FT &w3)
	compute the barycenter of the points p1, p2 and p3 with corresponding weights w1, w2 and w3. More...
template<typename Kernel >
CGAL::Point_2< Kernel >	barycenter (const CGAL::Point_2< Kernel > &p1, const Kernel::FT &w1, const CGAL::Point_2< Kernel > &p2, const Kernel::FT &w2, const CGAL::Point_2< Kernel > &p3, const Kernel::FT &w3, const CGAL::Point_2< Kernel > &p4)
	compute the barycenter of the points p1, p2, p3 and p4 with corresponding weights w1, w2, w3 and 1-w1-w2-w3. More...
template<typename Kernel >
CGAL::Point_2< Kernel >	barycenter (const CGAL::Point_2< Kernel > &p1, const Kernel::FT &w1, const CGAL::Point_2< Kernel > &p2, const Kernel::FT &w2, const CGAL::Point_2< Kernel > &p3, const Kernel::FT &w3, const CGAL::Point_2< Kernel > &p4, const Kernel::FT &w4)
	compute the barycenter of the points p1, p2, p3 and p4 with corresponding weights w1, w2, w3 and w4. More...
template<typename Kernel >
CGAL::Point_3< Kernel >	barycenter (const CGAL::Point_3< Kernel > &p1, const Kernel::FT &w1, const CGAL::Point_3< Kernel > &p2)
	compute the barycenter of the points p1 and p2 with corresponding weights w1 and 1-w1. More...
template<typename Kernel >
CGAL::Point_3< Kernel >	barycenter (const CGAL::Point_3< Kernel > &p1, const Kernel::FT &w1, const CGAL::Point_3< Kernel > &p2, const Kernel::FT &w2)
	compute the barycenter of the points p1 and p2 with corresponding weights w1 and w2. More...
template<typename Kernel >
CGAL::Point_3< Kernel >	barycenter (const CGAL::Point_3< Kernel > &p1, const Kernel::FT &w1, const CGAL::Point_3< Kernel > &p2, const Kernel::FT &w2, const CGAL::Point_3< Kernel > &p3)
	compute the barycenter of the points p1, p2 and p3 with corresponding weights w1, w2 and 1-w1-w2. More...
template<typename Kernel >
CGAL::Point_3< Kernel >	barycenter (const CGAL::Point_3< Kernel > &p1, const Kernel::FT &w1, const CGAL::Point_3< Kernel > &p2, const Kernel::FT &w2, const CGAL::Point_3< Kernel > &p3, const Kernel::FT &w3)
	compute the barycenter of the points p1, p2 and p3 with corresponding weights w1, w2 and w3. More...
template<typename Kernel >
CGAL::Point_3< Kernel >	barycenter (const CGAL::Point_3< Kernel > &p1, const Kernel::FT &w1, const CGAL::Point_3< Kernel > &p2, const Kernel::FT &w2, const CGAL::Point_3< Kernel > &p3, const Kernel::FT &w3, const CGAL::Point_3< Kernel > &p4)
	compute the barycenter of the points p1, p2, p3 and p4 with corresponding weights w1, w2, w3 and 1-w1-w2-w3. More...
template<typename Kernel >
CGAL::Point_3< Kernel >	barycenter (const CGAL::Point_3< Kernel > &p1, const Kernel::FT &w1, const CGAL::Point_3< Kernel > &p2, const Kernel::FT &w2, const CGAL::Point_3< Kernel > &p3, const Kernel::FT &w3, const CGAL::Point_3< Kernel > &p4, const Kernel::FT &w4)
	compute the barycenter of the points p1, p2, p3 and p4 with corresponding weights w1, w2, w3 and w4. More...
template<typename Kernel >
CGAL::Line_2< Kernel >	bisector (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q)
	constructs the bisector line of the two points p and q. More...
template<typename Kernel >
CGAL::Line_2< Kernel >	bisector (const CGAL::Line_2< Kernel > &l1, const CGAL::Line_2< Kernel > &l2)
	constructs the bisector of the two lines l1 and l2. More...
template<typename Kernel >
CGAL::Plane_3< Kernel >	bisector (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q)
	constructs the bisector plane of the two points p and q. More...
template<typename Kernel >
CGAL::Plane_3< Kernel >	bisector (const CGAL::Plane_3< Kernel > &h1, const CGAL::Plane_3< Kernel > &h2)
	constructs the bisector of the two planes h1 and h2. More...
template<typename Kernel >
CGAL::Point_2< Kernel >	centroid (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const CGAL::Point_2< Kernel > &r)
	compute the centroid of the points p, q, and r. More...
template<typename Kernel >
CGAL::Point_2< Kernel >	centroid (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const CGAL::Point_2< Kernel > &r, const CGAL::Point_2< Kernel > &s)
	compute the centroid of the points p, q, r, and s. More...
template<typename Kernel >
CGAL::Point_2< Kernel >	centroid (const CGAL::Triangle_2< Kernel > &t)
	compute the centroid of the triangle t. More...
template<typename Kernel >
CGAL::Point_3< Kernel >	centroid (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r)
	compute the centroid of the points p, q, and r. More...
template<typename Kernel >
CGAL::Point_3< Kernel >	centroid (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r, const CGAL::Point_3< Kernel > &s)
	compute the centroid of the points p, q, r, and s. More...
template<typename Kernel >
CGAL::Point_3< Kernel >	centroid (const CGAL::Triangle_3< Kernel > &t)
	compute the centroid of the triangle t. More...
template<typename Kernel >
CGAL::Point_3< Kernel >	centroid (const CGAL::Tetrahedron_3< Kernel > &t)
	compute the centroid of the tetrahedron t. More...
template<typename Kernel >
CGAL::Point_2< Kernel >	circumcenter (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q)
	compute the center of the smallest circle passing through the points p and q. More...
template<typename Kernel >
CGAL::Point_2< Kernel >	circumcenter (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const CGAL::Point_2< Kernel > &r)
	compute the center of the circle passing through the points p, q, and r. More...
template<typename Kernel >
CGAL::Point_2< Kernel >	circumcenter (const CGAL::Triangle_2< Kernel > &t)
	compute the center of the circle passing through the vertices of t. More...
template<typename Kernel >
CGAL::Point_3< Kernel >	circumcenter (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q)
	compute the center of the smallest sphere passing through the points p and q. More...
template<typename Kernel >
CGAL::Point_3< Kernel >	circumcenter (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r)
	compute the center of the circle passing through the points p, q, and r. More...
template<typename Kernel >
CGAL::Point_3< Kernel >	circumcenter (const CGAL::Triangle_3< Kernel > &t)
	compute the center of the circle passing through the vertices of t. More...
template<typename Kernel >
CGAL::Point_3< Kernel >	circumcenter (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r, const CGAL::Point_3< Kernel > &s)
	compute the center of the sphere passing through the points p, q, r, and s. More...
template<typename Kernel >
CGAL::Point_3< Kernel >	circumcenter (const CGAL::Tetrahedron_3< Kernel > &t)
	compute the center of the sphere passing through the vertices of t. More...
template<typename Kernel >
bool	collinear_are_ordered_along_line (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const CGAL::Point_2< Kernel > &r)
	returns true, iff q lies between p and r. More...
template<typename Kernel >
bool	collinear_are_ordered_along_line (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r)
	returns true, iff q lies between p and r. More...
template<typename Kernel >
bool	collinear_are_strictly_ordered_along_line (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const CGAL::Point_2< Kernel > &r)
	returns true, iff q lies strictly between p and r. More...
template<typename Kernel >
bool	collinear_are_strictly_ordered_along_line (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r)
	returns true, iff q lies strictly between p and r. More...
template<typename Kernel >
bool	collinear (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const CGAL::Point_2< Kernel > &r)
	returns true, iff p, q, and r are collinear. More...
template<typename Kernel >
bool	collinear (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r)
	returns true, iff p, q, and r are collinear. More...
template<typename Kernel >
Comparison_result	compare_dihedral_angle (const CGAL::Point_3< Kernel > &a1, const CGAL::Point_3< Kernel > &b1, const CGAL::Point_3< Kernel > &c1, const CGAL::Point_3< Kernel > &d1, const Kernel::FT &cosine)
	compares the dihedral angles \( \theta_1\) and \( \theta_2\), where \( \theta_1\) is the dihedral angle, in \( [0, \pi]\), of the tetrahedron (a1, b1, c1, d1) at the edge (a1, b1), and \( \theta_2\) is the angle in \( [0, \pi]\) such that \( cos(\theta_2) = cosine\). More...
template<typename Kernel >
Comparison_result	compare_dihedral_angle (const CGAL::Point_3< Kernel > &a1, const CGAL::Point_3< Kernel > &b1, const CGAL::Point_3< Kernel > &c1, const CGAL::Point_3< Kernel > &d1, const CGAL::Point_3< Kernel > &a2, const CGAL::Point_3< Kernel > &b2, const CGAL::Point_3< Kernel > &c2, const CGAL::Point_3< Kernel > &d2)
	compares the dihedral angles \( \theta_1\) and \( \theta_2\), where \( \theta_i\) is the dihedral angle in the tetrahedron (a_i, b_i, c_i, d_i) at the edge (a_i, b_i). More...
template<typename Kernel >
Comparison_result	compare_dihedral_angle (const CGAL::Vector_3< Kernel > &u1, const CGAL::Vector_3< Kernel > &v1, const CGAL::Vector_3< Kernel > &w1, const Kernel::FT &cosine)
	compares the dihedral angles \( \theta_1\) and \( \theta_2\), where \( \theta_1\) is the dihedral angle, in \( [0, \pi]\), between the vectorial planes defined by (u_1, v_1) and (u_1, w_1), and \( \theta_2\) is the angle in \( [0, \pi]\) such that \( cos(\theta_2) = cosine\). More...
template<typename Kernel >
Comparison_result	compare_dihedral_angle (const CGAL::Vector_3< Kernel > &u1, const CGAL::Vector_3< Kernel > &v1, const CGAL::Vector_3< Kernel > &w1, const CGAL::Vector_3< Kernel > &u2, const CGAL::Vector_3< Kernel > &v2, const CGAL::Vector_3< Kernel > &w2)
	compares the dihedral angles \( \theta_1\) and \( \theta_2\), where \( \theta_i\) is the dihedral angle between the vectorial planes defined by (u_i, v_i) and (u_i, w_i). More...
template<typename Kernel >
Comparison_result	compare_distance_to_point (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const CGAL::Point_2< Kernel > &r)
	compares the distances of points q and r to point p. More...
template<typename Kernel >
Comparison_result	compare_distance_to_point (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r)
	compares the distances of points q and r to point p. More...
template<typename Kernel >
Comparison_result	compare_lexicographically (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q)
	Compares the Cartesian coordinates of points p and q lexicographically in \( xy\) order: first \( x\)-coordinates are compared, if they are equal, \( y\)-coordinates are compared. More...
template<typename Kernel >
Comparison_result	compare_lexicographically (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q)
	Compares the Cartesian coordinates of points p and q lexicographically in \( xyz\) order: first \( x\)-coordinates are compared, if they are equal, \( y\)-coordinates are compared, and if both \( x\)- and \( y\)- coordinate are equal, \( z\)-coordinates are compared. More...
template<typename Kernel >
Comparison_result	compare_signed_distance_to_line (const CGAL::Line_2< Kernel > &l, const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q)
	returns CGAL::LARGER iff the signed distance of p and l is larger than the signed distance of q and l, CGAL::SMALLER, iff it is smaller, and CGAL::EQUAL iff both are equal. More...
template<typename Kernel >
Comparison_result	compare_signed_distance_to_line (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const CGAL::Point_2< Kernel > &r, const CGAL::Point_2< Kernel > &s)
	returns CGAL::LARGER iff the signed distance of r and l is larger than the signed distance of s and l, CGAL::SMALLER, iff it is smaller, and CGAL::EQUAL iff both are equal, where l is the directed line through p and q. More...
template<typename Kernel >
Comparison_result	compare_signed_distance_to_plane (const CGAL::Plane_3< Kernel > &h, const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q)
	returns CGAL::LARGER iff the signed distance of p and h is larger than the signed distance of q and h, CGAL::SMALLER, iff it is smaller, and CGAL::EQUAL iff both are equal. More...
template<typename Kernel >
Comparison_result	compare_signed_distance_to_plane (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r, const CGAL::Point_3< Kernel > &s, const CGAL::Point_3< Kernel > &t)
	returns CGAL::LARGER iff the signed distance of s and h is larger than the signed distance of t and h, CGAL::SMALLER, iff it is smaller, and CGAL::EQUAL iff both are equal, where h is the oriented plane through p, q and r. More...
template<typename Kernel >
Comparison_result	compare_slope (const CGAL::Line_2< Kernel > &l1, const CGAL::Line_2< Kernel > &l2)
	compares the slopes of the lines l1 and l2 More...
template<typename Kernel >
Comparison_result	compare_slope (const CGAL::Segment_2< Kernel > &s1, const CGAL::Segment_2< Kernel > &s2)
	compares the slopes of the segments s1 and s2, where the slope is the variation of the y-coordinate from the left to the right endpoint of the segments. More...
template<typename Kernel >
Comparison_result	compare_slope (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r, const CGAL::Point_3< Kernel > &s)
	compares the slopes of the segments (p,q) and (r,s), where the slope is the variation of the z-coordinate from the first to the second point of the segment divided by the length of the segment. More...
template<typename Kernel >
Comparison_result	compare_squared_distance (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const typename Kernel::FT &d2)
	compares the squared distance of points p and q to d2. More...
template<typename Kernel >
Comparison_result	compare_squared_distance (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const typename Kernel::FT &d2)
	compares the squared distance of points p and q to d2. More...
template<typename Kernel >
Comparison_result	compare_squared_radius (const CGAL::Point_3< Kernel > &p, const typename Kernel::FT &sr)
	compares the squared radius of the sphere of radius 0 centered at p to sr. More...
template<typename Kernel >
Comparison_result	compare_squared_radius (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const typename Kernel::FT &sr)
	compares the squared radius of the sphere defined by the points p and q to sr. More...
template<typename Kernel >
Comparison_result	compare_squared_radius (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r, const typename Kernel::FT &sr)
	compares the squared radius of the sphere defined by the points p, q, and r to sr. More...
template<typename Kernel >
Comparison_result	compare_squared_radius (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r, const CGAL::Point_3< Kernel > &s, const typename Kernel::FT &sr)
	compares the squared radius of the sphere defined by the points p, q, r, and r to sr. More...
template<typename Kernel >
Comparison_result	compare_x (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q)
	compares the \( x\)-coordinates of p and q. More...
template<typename Kernel >
Comparison_result	compare_x (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q)
	compares the \( x\)-coordinates of p and q. More...
template<typename Kernel >
Comparison_result	compare_x (const CGAL::Point_2< Kernel > &p, const CGAL::Line_2< Kernel > &l1, const CGAL::Line_2< Kernel > &l2)
	compares the \( x\)-coordinates of p and the intersection of lines l1 and l2. More...
template<typename Kernel >
Comparison_result	compare_x (const CGAL::Line_2< Kernel > &l, const CGAL::Line_2< Kernel > &h1, const CGAL::Line_2< Kernel > &h2)
	compares the \( x\)-coordinates of the intersection of line l with line h1 and with line h2. More...
template<typename Kernel >
Comparison_result	compare_x (const CGAL::Line_2< Kernel > &l1, const CGAL::Line_2< Kernel > &l2, const CGAL::Line_2< Kernel > &h1, const CGAL::Line_2< Kernel > &h2)
	compares the \( x\)-coordinates of the intersection of lines l1 and l2 and the intersection of lines h1 and h2. More...
template<typename CircularKernel >
Comparison_result	compare_x (const CGAL::Circular_arc_point_2< CircularKernel > &p, const CGAL::Circular_arc_point_2< CircularKernel > &q)
	compares the \( x\)-coordinates of p and q. More...
template<typename CircularKernel >
Comparison_result	compare_x (const CGAL::Circular_arc_point_2< CircularKernel > &p, const CGAL::Point_2< CircularKernel > &q)
	compares the \( x\)-coordinates of p and q. More...
template<typename SphericalKernel >
Comparison_result	compare_x (const CGAL::Circular_arc_point_3< SphericalKernel > &p, const CGAL::Circular_arc_point_3< SphericalKernel > &q)
	compares the \( x\)-coordinates of p and q. More...
template<typename SphericalKernel >
Comparison_result	compare_x (const CGAL::Circular_arc_point_3< SphericalKernel > &p, const CGAL::Point_3< SphericalKernel > &q)
	compares the \( x\)-coordinates of p and q. More...
template<typename Kernel >
Comparison_result	compare_xy (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q)
	Compares the Cartesian coordinates of points p and q lexicographically in \( xy\) order: first \( x\)-coordinates are compared, if they are equal, \( y\)-coordinates are compared. More...
template<typename Kernel >
Comparison_result	compare_xy (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q)
	Compares the Cartesian coordinates of points p and q lexicographically in \( xy\) order: first \( x\)-coordinates are compared, if they are equal, \( y\)-coordinates are compared. More...
template<typename CircularKernel >
Comparison_result	compare_xy (const CGAL::Circular_arc_point_2< CircularKernel > &p, const CGAL::Circular_arc_point_2< CircularKernel > &q)
	Compares the \( x\) and \( y\) Cartesian coordinates of points p and q lexicographically. More...
template<typename CircularKernel >
Comparison_result	compare_xy (const CGAL::Circular_arc_point_2< CircularKernel > &p, const CGAL::Point_2< CircularKernel > &q)
	Compares the \( x\) and \( y\) Cartesian coordinates of points p and q lexicographically. More...
template<typename SphericalKernel >
Comparison_result	compare_xy (const CGAL::Circular_arc_point_3< SphericalKernel > &p, const CGAL::Circular_arc_point_3< SphericalKernel > &q)
	Compares the \( x\) and \( y\) Cartesian coordinates of points p and q lexicographically. More...
template<typename SphericalKernel >
Comparison_result	compare_xy (const CGAL::Circular_arc_point_3< SphericalKernel > &p, const CGAL::Point_3< SphericalKernel > &q)
	Compares the \( x\) and \( y\) Cartesian coordinates of points p and q lexicographically. More...
template<typename Kernel >
Comparison_result	compare_x_at_y (const CGAL::Point_2< Kernel > &p, const CGAL::Line_2< Kernel > &h)
	compares the \( x\)-coordinates of p and the horizontal projection of p on h. More...
template<typename Kernel >
Comparison_result	compare_x_at_y (const CGAL::Point_2< Kernel > &p, const CGAL::Line_2< Kernel > &h1, const CGAL::Line_2< Kernel > &h2)
	This function compares the \( x\)-coordinates of the horizontal projection of p on h1 and on h2. More...
template<typename Kernel >
Comparison_result	compare_x_at_y (const CGAL::Line_2< Kernel > &l1, const CGAL::Line_2< Kernel > &l2, const CGAL::Line_2< Kernel > &h)
	Let p be the intersection of lines l1 and l2. More...
template<typename Kernel >
Comparison_result	compare_x_at_y (const CGAL::Line_2< Kernel > &l1, const CGAL::Line_2< Kernel > &l2, const CGAL::Line_2< Kernel > &h1, const CGAL::Line_2< Kernel > &h2)
	Let p be the intersection of lines l1 and l2. More...
template<typename Kernel >
Comparison_result	compare_y_at_x (const CGAL::Point_2< Kernel > &p, const CGAL::Line_2< Kernel > &h)
	compares the \( y\)-coordinates of p and the vertical projection of p on h. More...
template<typename Kernel >
Comparison_result	compare_y_at_x (const CGAL::Point_2< Kernel > &p, const CGAL::Line_2< Kernel > &h1, const CGAL::Line_2< Kernel > &h2)
	compares the \( y\)-coordinates of the vertical projection of p on h1 and on h2. More...
template<typename Kernel >
Comparison_result	compare_y_at_x (const CGAL::Line_2< Kernel > &l1, const CGAL::Line_2< Kernel > &l2, const CGAL::Line_2< Kernel > &h)
	Let p be the intersection of lines l1 and l2. More...
template<typename Kernel >
Comparison_result	compare_y_at_x (const CGAL::Line_2< Kernel > &l1, const CGAL::Line_2< Kernel > &l2, const CGAL::Line_2< Kernel > &h1, const CGAL::Line_2< Kernel > &h2)
	Let p be the intersection of lines l1 and l2. More...
template<typename Kernel >
Comparison_result	compare_y_at_x (const CGAL::Point_2< Kernel > &p, const CGAL::Segment_2< Kernel > &s)
	compares the \( y\)-coordinates of p and the vertical projection of p on s. More...
template<typename Kernel >
Comparison_result	compare_y_at_x (const CGAL::Point_2< Kernel > &p, const CGAL::Segment_2< Kernel > &s1, const CGAL::Segment_2< Kernel > &s2)
	compares the \( y\)-coordinates of the vertical projection of p on s1 and on s2. More...
template<typename Kernel >
Comparison_result	compare_y (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q)
	compares Cartesian \( y\)-coordinates of p and q. More...
template<typename Kernel >
Comparison_result	compare_y (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q)
	compares Cartesian \( y\)-coordinates of p and q. More...
template<typename Kernel >
Comparison_result	compare_y (const CGAL::Point_2< Kernel > &p, const CGAL::Line_2< Kernel > &l1, const CGAL::Line_2< Kernel > &l2)
	compares the \( y\)-coordinates of p and the intersection of lines l1 and l2. More...
template<typename Kernel >
Comparison_result	compare_y (const CGAL::Line_2< Kernel > &l, const CGAL::Line_2< Kernel > &h1, const CGAL::Line_2< Kernel > &h2)
	compares the \( y\)-coordinates of the intersection of line l with line h1 and with line h2. More...
template<typename Kernel >
Comparison_result	compare_y (const CGAL::Line_2< Kernel > &l1, const CGAL::Line_2< Kernel > &l2, const CGAL::Line_2< Kernel > &h1, const CGAL::Line_2< Kernel > &h2)
	compares the \( y\)-coordinates of the intersection of lines l1 and l2 and the intersection of lines h1 and h2. More...
template<typename CircularKernel >
Comparison_result	compare_y (const CGAL::Circular_arc_point_2< CircularKernel > &p, const CGAL::Circular_arc_point_2< CircularKernel > &q)
	compares the \( y\)-coordinates of p and q. More...
template<typename CircularKernel >
Comparison_result	compare_y (const CGAL::Circular_arc_point_2< CircularKernel > &p, const CGAL::Point_2< CircularKernel > &q)
	compares the \( y\)-coordinates of p and q. More...
template<typename SphericalKernel >
Comparison_result	compare_y (const CGAL::Circular_arc_point_3< SphericalKernel > &p, const CGAL::Circular_arc_point_3< SphericalKernel > &q)
	compares the \( y\)-coordinates of p and q. More...
template<typename SphericalKernel >
Comparison_result	compare_y (const CGAL::Circular_arc_point_3< SphericalKernel > &p, const CGAL::Point_3< SphericalKernel > &q)
	compares the \( y\)-coordinates of p and q. More...
template<typename Kernel >
Comparison_result	compare_xyz (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q)
	Compares the Cartesian coordinates of points p and q lexicographically in \( xyz\) order: first \( x\)-coordinates are compared, if they are equal, \( y\)-coordinates are compared, and if both \( x\)- and \( y\)- coordinate are equal, \( z\)-coordinates are compared. More...
template<typename SphericalKernel >
Comparison_result	compare_xyz (const CGAL::Circular_arc_point_3< SphericalKernel > &p, const CGAL::Circular_arc_point_3< SphericalKernel > &q)
	Compares the Cartesian coordinates of points p and q lexicographically. More...
template<typename SphericalKernel >
Comparison_result	compare_xyz (const CGAL::Circular_arc_point_3< SphericalKernel > &p, const CGAL::Point_3< SphericalKernel > &q)
	Compares the Cartesian coordinates of points p and q lexicographically. More...
template<typename Kernel >
Comparison_result	compare_z (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q)
	compares the \( z\)-coordinates of p and q. More...
template<typename SphericalKernel >
Comparison_result	compare_z (const CGAL::Circular_arc_point_3< SphericalKernel > &p, const CGAL::Circular_arc_point_3< SphericalKernel > &q)
	compares the \( z\)-coordinates of p and q. More...
template<typename SphericalKernel >
Comparison_result	compare_z (const CGAL::Circular_arc_point_3< SphericalKernel > &p, const CGAL::Point_3< SphericalKernel > &q)
	compares the \( z\)-coordinates of p and q. More...
template<typename Kernel >
Comparison_result	compare_yx (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q)
	Compares the Cartesian coordinates of points p and q lexicographically in \( yx\) order: first \( y\)-coordinates are compared, if they are equal, \( x\)-coordinates are compared. More...
template<typename Kernel >
bool	coplanar (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r, const CGAL::Point_3< Kernel > &s)
	returns true, if p, q, r, and s are coplanar. More...
template<typename Kernel >
Orientation	coplanar_orientation (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r, const CGAL::Point_3< Kernel > &s)
	Let P be the plane defined by the points p, q, and r. More...
template<typename Kernel >
Orientation	coplanar_orientation (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r)
	If p,q,r are collinear, then CGAL::COLLINEAR is returned. More...
template<typename Kernel >
Bounded_side	coplanar_side_of_bounded_circle (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r, const CGAL::Point_3< Kernel > &s)
	returns the bounded side of the circle defined by p, q, and r on which s lies. More...
template<typename Kernel >
CGAL::Vector_3< Kernel >	cross_product (const CGAL::Vector_3< Kernel > &u, const CGAL::Vector_3< Kernel > &v)
	returns the cross product of u and v. More...
template<typename Kernel >
Kernel::FT	determinant (const CGAL::Vector_2< Kernel > &v, const CGAL::Vector_2< Kernel > &w)
	returns the determinant of v and w. More...
template<typename Kernel >
Kernel::FT	determinant (const CGAL::Vector_3< Kernel > &u, const CGAL::Vector_3< Kernel > &v, const CGAL::Vector_3< Kernel > &w)
	returns the determinant of u, v and w. More...
template<typename Kernel >
CGAL::Line_3< Kernel >	equidistant_line (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r)
	constructs the line which is at the same distance from the three points p, q and r. More...
template<typename Kernel >
bool	has_larger_distance_to_point (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const CGAL::Point_2< Kernel > &r)
	returns true iff the distance between q and p is larger than the distance between r and p. More...
template<typename Kernel >
bool	has_larger_distance_to_point (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r)
	returns true iff the distance between q and p is larger than the distance between r and p. More...
template<typename Kernel >
bool	has_larger_signed_distance_to_line (const CGAL::Line_2< Kernel > &l, const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q)
	returns true iff the signed distance of p and l is larger than the signed distance of q and l. More...
template<typename Kernel >
bool	has_larger_signed_distance_to_line (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const CGAL::Point_2< Kernel > &r, const CGAL::Point_2< Kernel > &s)
	returns true iff the signed distance of r and l is larger than the signed distance of s and l, where l is the directed line through points p and q. More...
template<typename Kernel >
bool	has_larger_signed_distance_to_plane (const CGAL::Plane_3< Kernel > &h, const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q)
	returns true iff the signed distance of p and h is larger than the signed distance of q and h. More...
template<typename Kernel >
bool	has_larger_signed_distance_to_plane (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r, const CGAL::Point_3< Kernel > &s, const CGAL::Point_3< Kernel > &t)
	returns true iff the signed distance of s and h is larger than the signed distance of t and h, where h is the oriented plane through p, q and r. More...
template<typename Kernel >
bool	has_smaller_distance_to_point (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const CGAL::Point_2< Kernel > &r)
	returns true iff the distance between q and p is smaller than the distance between r and p. More...
template<typename Kernel >
bool	has_smaller_distance_to_point (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r)
	returns true iff the distance between q and p is smaller than the distance between r and p. More...
template<typename Kernel >
bool	has_smaller_signed_distance_to_line (const CGAL::Line_2< Kernel > &l, const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q)
	returns true iff the signed distance of p and l is smaller than the signed distance of q and l. More...
template<typename Kernel >
bool	has_smaller_signed_distance_to_line (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const CGAL::Point_2< Kernel > &r, const CGAL::Point_2< Kernel > &s)
	returns true iff the signed distance of r and l is smaller than the signed distance of s and l, where l is the oriented line through p and q. More...
template<typename Kernel >
bool	has_smaller_signed_distance_to_plane (const CGAL::Plane_3< Kernel > &h, const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q)
	returns true iff the signed distance of p and h is smaller than the signed distance of q and h. More...
template<typename Kernel >
bool	has_smaller_signed_distance_to_plane (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r, const CGAL::Point_3< Kernel > &s, const CGAL::Point_3< Kernel > &t)
	returns true iff the signed distance of p and h is smaller than the signed distance of q and h, where h is the oriented plane through p, q and r. More...
template<typename Kernel >
Kernel::FT	l_infinity_distance (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q)
	returns the distance between p and q in the L-infinity metric. More...
template<typename Kernel >
Kernel::FT	l_infinity_distance (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q)
	returns the distance between p and q in the L-infinity metric. More...
template<typename Kernel >
bool	left_turn (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const CGAL::Point_2< Kernel > &r)
	returns true iff p, q, and r form a left turn. More...
template<typename Kernel >
bool	lexicographically_xy_larger (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q)
	returns true iff p is lexicographically larger than q with respect to \( xy\) order. More...
template<typename Kernel >
bool	lexicographically_xy_larger_or_equal (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q)
	returns true iff p is lexicographically not smaller than q with respect to \( xy\) order. More...
template<typename Kernel >
bool	lexicographically_xy_smaller (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q)
	returns true iff p is lexicographically smaller than q with respect to \( xy\) order. More...
template<typename Kernel >
bool	lexicographically_xy_smaller_or_equal (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q)
	returns true iff p is lexicographically not larger than q with respect to \( xy\) order. More...
template<typename Kernel >
bool	lexicographically_xyz_smaller (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q)
	returns true iff p is lexicographically smaller than q with respect to \( xyz\) order. More...
template<typename Kernel >
bool	lexicographically_xyz_smaller_or_equal (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q)
	returns true iff p is lexicographically not larger than q with respect to \( xyz\) order. More...
template<typename Kernel >
CGAL::Point_2< Kernel >	max_vertex (const CGAL::Iso_rectangle_2< Kernel > &ir)
	computes the vertex with the lexicographically largest coordinates of the iso rectangle ir. More...
template<typename Kernel >
CGAL::Point_3< Kernel >	max_vertex (const CGAL::Iso_cuboid_3< Kernel > &ic)
	computes the vertex with the lexicographically largest coordinates of the iso cuboid ic. More...
template<typename Kernel >
CGAL::Point_2< Kernel >	midpoint (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q)
	computes the midpoint of the segment pq. More...
template<typename Kernel >
CGAL::Point_3< Kernel >	midpoint (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q)
	computes the midpoint of the segment pq. More...
template<typename Kernel >
CGAL::Point_2< Kernel >	min_vertex (const CGAL::Iso_rectangle_2< Kernel > &ir)
	computes the vertex with the lexicographically smallest coordinates of the iso rectangle ir. More...
template<typename Kernel >
CGAL::Point_3< Kernel >	min_vertex (const CGAL::Iso_cuboid_3< Kernel > &ic)
	computes the vertex with the lexicographically smallest coordinates of the iso cuboid ic. More...
template<typename Kernel >
CGAL::Vector_3< Kernel >	normal (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r)
	computes the normal vector for the vectors q-p and r-p. More...
template<typename Kernel >
Orientation	orientation (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const CGAL::Point_2< Kernel > &r)
	returns CGAL::LEFT_TURN, if r lies to the left of the oriented line l defined by p and q, returns CGAL::RIGHT_TURN if r lies to the right of l, and returns CGAL::COLLINEAR if r lies on l. More...
template<typename Kernel >
Orientation	orientation (const CGAL::Vector_2< Kernel > &u, const CGAL::Vector_2< Kernel > &v)
	returns CGAL::LEFT_TURN if u and v form a left turn, returns CGAL::RIGHT_TURN if u and v form a right turn, and returns CGAL::COLLINEAR if u and v are collinear. More...
template<typename Kernel >
Orientation	orientation (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r, const CGAL::Point_3< Kernel > &s)
	returns CGAL::POSITIVE, if s lies on the positive side of the oriented plane h defined by p, q, and r, returns CGAL::NEGATIVE if s lies on the negative side of h, and returns CGAL::COPLANAR if s lies on h. More...
template<typename Kernel >
Orientation	orientation (const CGAL::Vector_3< Kernel > &u, const CGAL::Vector_3< Kernel > &v, const CGAL::Vector_3< Kernel > &w)
	returns CGAL::NEGATIVE if u, v and w are negatively oriented, CGAL::POSITIVE if u, v and w are positively oriented, and CGAL::COPLANAR if u, v and w are coplanar. More...
template<typename Kernel >
CGAL::Vector_3< Kernel >	orthogonal_vector (const CGAL::Plane_3< Kernel > &p)
	computes an orthogonal vector of the plane p, which is directed to the positive side of this plane. More...
template<typename Kernel >
CGAL::Vector_3< Kernel >	orthogonal_vector (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r)
	computes an orthogonal vector of the plane defined by p, q and r, which is directed to the positive side of this plane. More...
template<typename Kernel >
bool	parallel (const CGAL::Line_2< Kernel > &l1, const CGAL::Line_2< Kernel > &l2)
	returns true, if l1 and l2 are parallel or if one of those (or both) is degenerate. More...
template<typename Kernel >
bool	parallel (const CGAL::Ray_2< Kernel > &r1, const CGAL::Ray_2< Kernel > &r2)
	returns true, if r1 and r2 are parallel or if one of those (or both) is degenerate. More...
template<typename Kernel >
bool	parallel (const CGAL::Segment_2< Kernel > &s1, const CGAL::Segment_2< Kernel > &s2)
	returns true, if s1 and s2 are parallel or if one of those (or both) is degenerate. More...
template<typename Kernel >
bool	parallel (const CGAL::Line_3< Kernel > &l1, const CGAL::Line_3< Kernel > &l2)
	returns true, if l1 and l2 are parallel or if one of those (or both) is degenerate. More...
template<typename Kernel >
bool	parallel (const CGAL::Plane_3< Kernel > &h1, const CGAL::Plane_3< Kernel > &h2)
	returns true, if h1 and h2 are parallel or if one of those (or both) is degenerate. More...
template<typename Kernel >
bool	parallel (const CGAL::Ray_3< Kernel > &r1, const CGAL::Ray_3< Kernel > &r2)
	returns true, if r1 and r2 are parallel or if one of those (or both) is degenerate. More...
template<typename Kernel >
bool	parallel (const CGAL::Segment_3< Kernel > &s1, const CGAL::Segment_3< Kernel > &s2)
	returns true, if s1 and s2 are parallel or if one of those (or both) is degenerate. More...
CGAL::Plane_3< Kernel >	radical_plane (const CGAL::Sphere_3< Kernel > &s1, const CGAL::Sphere_3< Kernel > &s2)
	returns the radical plane of the two spheres. More...
template<typename Kernel >
CGAL::Line_2< Kernel >	radical_line (const CGAL::Circle_2< Kernel > &c1, const CGAL::Circle_2< Kernel > &c2)
	returns the radical line of the two circles. More...
template<typename Kernel >
bool	right_turn (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const CGAL::Point_2< Kernel > &r)
	returns true iff p, q, and r form a right turn. More...
template<typename Kernel >
Kernel::FT	scalar_product (const CGAL::Vector_2< Kernel > &u, const CGAL::Vector_2< Kernel > &v)
	returns the scalar product of u and v. More...
template<typename Kernel >
Kernel::FT	scalar_product (const CGAL::Vector_3< Kernel > &u, const CGAL::Vector_3< Kernel > &v)
	returns the scalar product of u and v. More...
template<typename Kernel >
Bounded_side	side_of_bounded_circle (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const CGAL::Point_2< Kernel > &r, const CGAL::Point_2< Kernel > &t)
	returns the relative position of point t to the circle defined by p, q and r. More...
template<typename Kernel >
Bounded_side	side_of_bounded_circle (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const CGAL::Point_2< Kernel > &t)
	returns the position of the point t relative to the circle that has pq as its diameter. More...
template<typename Kernel >
Bounded_side	side_of_bounded_sphere (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r, const CGAL::Point_3< Kernel > &s, const CGAL::Point_3< Kernel > &t)
	returns the relative position of point t to the sphere defined by p, q, r, and s. More...
template<typename Kernel >
Bounded_side	side_of_bounded_sphere (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r, const CGAL::Point_3< Kernel > &t)
	returns the position of the point t relative to the sphere passing through p, q, and r and whose center is in the plane defined by these three points. More...
template<typename Kernel >
Bounded_side	side_of_bounded_sphere (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &t)
	returns the position of the point t relative to the sphere that has pq as its diameter. More...
template<typename Kernel >
Oriented_side	side_of_oriented_circle (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const CGAL::Point_2< Kernel > &r, const CGAL::Point_2< Kernel > &test)
	returns the relative position of point test to the oriented circle defined by p, q and r. More...
template<typename Kernel >
Oriented_side	side_of_oriented_sphere (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r, const CGAL::Point_3< Kernel > &s, const CGAL::Point_3< Kernel > &test)
	returns the relative position of point test to the oriented sphere defined by p, q, r and s. More...
template<typename Kernel >
Kernel::FT	squared_area (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r)
	returns the squared area of the triangle defined by the points p, q and r. More...
template<typename Kernel >
FT	squared_radius (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const CGAL::Point_2< Kernel > &r)
	compute the squared radius of the circle passing through the points p, q, and r. More...
template<typename Kernel >
FT	squared_radius (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q)
	compute the squared radius of the smallest circle passing through p, and q, i.e. one fourth of the squared distance between p and q. More...
template<typename Kernel >
FT	squared_radius (const CGAL::Point_2< Kernel > &p)
	compute the squared radius of the smallest circle passing through p, i.e. \( 0\). More...
template<typename Kernel >
FT	squared_radius (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r, const CGAL::Point_3< Kernel > &s)
	compute the squared radius of the sphere passing through the points p, q, r and s. More...
template<typename Kernel >
FT	squared_radius (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r)
	compute the squared radius of the sphere passing through the points p, q, and r and whose center is in the same plane as those three points. More...
template<typename Kernel >
FT	squared_radius (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q)
	compute the squared radius of the smallest circle passing through p, and q, i.e. one fourth of the squared distance between p and q. More...
template<typename Kernel >
FT	squared_radius (const CGAL::Point_3< Kernel > &p)
	compute the squared radius of the smallest circle passing through p, i.e. \( 0\). More...
CGAL::Vector_3< Kernel >	unit_normal (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r)
	computes the unit normal vector for the vectors q-p and r-p. More...
template<typename Kernel >
Kernel::FT	volume (const CGAL::Point_3< Kernel > &p0, const CGAL::Point_3< Kernel > &p1, const CGAL::Point_3< Kernel > &p2, const CGAL::Point_3< Kernel > &p3)
	Computes the signed volume of the tetrahedron defined by the four points p0, p1, p2 and p3. More...
template<typename Kernel >
bool	x_equal (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q)
	returns true, iff p and q have the same x-coordinate. More...
template<typename Kernel >
bool	x_equal (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q)
	returns true, iff p and q have the same x-coordinate. More...
template<typename Kernel >
bool	y_equal (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q)
	returns true, iff p and q have the same y-coordinate. More...
template<typename Kernel >
bool	y_equal (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q)
	returns true, iff p and q have the same y-coordinate. More...
template<typename Kernel >
bool	z_equal (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q)
	returns true, iff p and q have the same z-coordinate. More...
template<RingNumberType >
void	rational_rotation_approximation (const RingNumberType &dirx, const RingNumberType &diry, RingNumberType &sin_num, RingNumberType &cos_num, RingNumberType &denom, const RingNumberType &eps_num, const RingNumberType &eps_den)
template<typename Kernel >
Kernel::FT	squared_distance (Type1< Kernel > obj1, Type2< Kernel > obj2)
	computes the square of the Euclidean distance between two geometric objects. More...

Variables
	BOUND_REACHED
	TIME_LIMIT_REACHED
	CANT_IMPROVE_ANYMORE
	CONVERGENCE_REACHED
	MAX_ITERATION_NUMBER_REACHED
	ALL_VERTICES_FROZEN
	NORMAL
	THREADED
	POLAR
	BIPOLAR
	ABORT
	EXIT
	EXIT_WITH_SUCCESS
	CONTINUE
	THROW_EXCEPTION
const CGAL::Orientation	CLOCKWISE = NEGATIVE
const CGAL::Orientation	COUNTERCLOCKWISE = POSITIVE
const CGAL::Orientation	COLLINEAR = ZERO
const CGAL::Orientation	LEFT_TURN = POSITIVE
const CGAL::Orientation	RIGHT_TURN = NEGATIVE
const CGAL::Orientation	COPLANAR = ZERO
const CGAL::Orientation	DEGENERATE = ZERO
const CGAL::Null_vector	NULL_VECTOR
const CGAL::Origin	ORIGIN
	A symbolic constant which denotes the point at the origin. More...
template<typename RT >
Point_2< Homogeneous< RT > >	cartesian_to_homogeneous (const Point_2< Cartesian< RT > > &cp)
	converts 2D point cp with Cartesian representation into a 2D point with homogeneous representation with the same number type. More...
template<typename RT >
Point_3< Homogeneous< RT > >	cartesian_to_homogeneous (const Point_3< Cartesian< RT > > &cp)
	converts 3D point cp with Cartesian representation into a 3D point with homogeneous representation with the same number type. More...
template<typename FT >
Point_2< Cartesian< FT > >	homogeneous_to_cartesian (const Point_2< Homogeneous< FT > > &hp)
	converts 2D point hp with homogeneous representation into a 2D point with Cartesian representation with the same number type. More...
template<typename FT >
Point_3< Cartesian< FT > >	homogeneous_to_cartesian (const Point_3< Homogeneous< FT > > &hp)
	converts 3D point hp with homogeneous representation into a 3D point with Cartesian representation with the same number type. More...
template<typename RT >
Point_2< Cartesian< Quotient< RT > > >	homogeneous_to_quotient_cartesian (const Point_2< Homogeneous< RT > > &hp)
	converts the 2D point hp with homogeneous representation with number type RT into a 2D point with Cartesian representation with number type Quotient<RT>. More...
template<typename RT >
Point_3< Cartesian< Quotient< RT > > >	homogeneous_to_quotient_cartesian (const Point_3< Homogeneous< RT > > &hp)
	converts the 3D point hp with homogeneous representation with number type RT into a 3D point with Cartesian representation with number type Quotient<RT>. More...
template<typename RT >
Point_2< Homogeneous< RT > >	quotient_cartesian_to_homogeneous (const Point_2< Cartesian< Quotient< RT > > > &cp)
	converts 2D point cp with Cartesian representation with number type Quotient<RT> into a 2D point with homogeneous representation with number type RT. More...
template<typename RT >
Point_3< Homogeneous< RT > >	quotient_cartesian_to_homogeneous (const Point_3< Cartesian< Quotient< RT > > > &cp)
	converts 3D point cp with Cartesian representation with number type Quotient<RT> into a 3D point with homogeneous representation with number type RT. More...
bool	do_intersect (Type1< CircularKernel > obj1, Type2< CircularKernel > obj2)
	checks whether obj1 and obj2 intersect. More...
template<typename Type1 , typename Type2 , typename OutputIterator >
OutputIterator	intersection (const Type1 &obj1, const Type2 &obj2, OutputIterator intersections)
	Constructs the intersection elements between the two input objects and stores them in the OutputIterator in lexicographic order, where both, Type1 and Type2, can be either. More...

With the 2D Circular Kernel
See 2D Circular Geometry Kernel. #include <CGAL/global_functions_circular_kernel_2.h>
template<typename CircularKernel >
Comparison_result	compare_y_at_x (const CGAL::Circular_arc_point_2< CircularKernel > &p, const CGAL::Circular_arc_2< CircularKernel > &a)
	Same as above, for a point and a circular arc. More...
template<typename CircularKernel >
Comparison_result	compare_y_at_x (const CGAL::Circular_arc_point_2< CircularKernel > &p, const CGAL::Line_arc_2< CircularKernel > &a)
	Same as above, for a point and a line segment. More...
bool	do_intersect (Type1< SphericalKernel > obj1, Type2< SphericalKernel > obj2)
	checks whether obj1 and obj2 intersect. More...
bool	do_intersect (Type1< SphericalKernel > obj1, Type2< SphericalKernel > obj2, Type3< SphericalKernel > obj3)
	checks whether obj1, obj2 and obj3 intersect. More...
template<typename SphericalType1 , typename SphericalType1 , typename OutputIterator >
OutputIterator	intersection (const SphericalType1 &obj1, const SphericalType2 &obj2, OutputIterator intersections)
	Copies in the output iterator the intersection elements between the two objects. More...
template<typename Type1 , typename Type2 , typename Type3 , typename OutputIterator >
OutputIterator	intersection (const Type1 &obj1, const Type2 &obj2, const Type3 &obj3, OutputIterator intersections)
	Copies in the output iterator the intersection elements between the three objects. More...