Definition

Requirements of the traits class of the function CGAL::convex_hull_3().

CGAL::Convex_hull_traits_3

All models of Kernel

Types
typedef unspecified_type	Point_3
	The point type on which the convex hull algorithm operates. More...

typedef unspecified_type	Plane_3
	a 3D plane More...

typedef unspecified_type	Segment_3
	a 3D segment More...

typedef unspecified_type	Triangle_3
	a 3D triangle More...

typedef unspecified_type	Vector_3
	a 3D vector More...

typedef unspecified_type	Construct_plane_3
	Function object type that provides `Plane_3 operator()(Point_3 p, Point_3 q, Point_3 r)`, which constructs and returns a plane passing through `p`, `q`, and `r` and oriented in a positive sense when seen from the positive side of the plane. More...

typedef unspecified_type	Construct_segment_3
	Function object type that provides `Segment_3 operator()(Point_3 p, Point_3 q)`, which constructs and returns the segment with source `p` and target `q`. More...

typedef unspecified_type	Construct_triangle_3
	Function object type that provides `Triangle_3 operator()(Point_3 p, Point_3 q, Point_3 r)`, which constructs and returns the triangle with vertices `p`, `q`, and `r`. More...

typedef unspecified_type	Construct_vector_3
	Function object type that provides `Vector_3 operator()(Point_3 p, Point_3 q)`, which constructs and returns the vector `q`-`p`. More...

typedef unspecified_type	Equal_3
	Predicate object type that provides `bool operator()(Point_3 p, Point_3 q)`, which determines if points `p` and `q` are equal. More...

typedef unspecified_type	Collinear_3
	Predicate object type that provides `bool operator()(Point_3 p, Point_3 q, Point_3 r)`, which determines if points `p`, `q` and `r` are collinear. More...

typedef unspecified_type	Coplanar_3
	Predicate object type that provides `bool operator()(Point_3 p, Point_3 q, Point_3 r, Point_3 s)`, which determines if points `p`, `q`, `r`, and `s` are coplanar. More...

typedef unspecified_type	Has_on_positive_side_3
	Predicate object type that provides `bool operator()(Plane_3 h, Point_3 q)`, which determines if the point `q` is on the positive side of the halfspace `h`. More...

typedef unspecified_type	Less_distance_to_point_3
	Predicate object type that provides a constructor taking a single `Point_3` object and `bool operator()(Point_3 q, Point_3 r)`, which returns true iff the distance from `q` to `p` is smaller than the distance from `r` to `p`, where `p` is the point passed to the object at construction. More...

typedef unspecified_type	Less_signed_distance_to_plane_3
	Predicate object type that provides `bool operator()(Plane_3 p, Point_3 q, Point_3 r)`, which returns true iff the signed distance from `q` to `p` is smaller than the signed distance from `r` to `p` More...

Creation
Only a copy constructor is required.
	ConvexHullTraits_3 (ConvexHullTraits_3 &ch)

Operations
For each of the above function and predicate object types, `Func_obj_type`, a function must exist with the name `func_obj_type_object` that creates an instance of the function or predicate object type. For example:
Construct_plane_3	construct_plane_3_object ()

Member Typedef Documentation

typedef unspecified_type ConvexHullTraits_3::Collinear_3

Predicate object type that provides bool operator()(Point_3 p, Point_3 q, Point_3 r), which determines if points p, q and r are collinear.

typedef unspecified_type ConvexHullTraits_3::Construct_plane_3

Function object type that provides Plane_3 operator()(Point_3 p, Point_3 q, Point_3 r), which constructs and returns a plane passing through p, q, and r and oriented in a positive sense when seen from the positive side of the plane.

typedef unspecified_type ConvexHullTraits_3::Construct_segment_3

Function object type that provides Segment_3 operator()(Point_3 p, Point_3 q), which constructs and returns the segment with source p and target q.

typedef unspecified_type ConvexHullTraits_3::Construct_triangle_3

Function object type that provides Triangle_3 operator()(Point_3 p, Point_3 q, Point_3 r), which constructs and returns the triangle with vertices p, q, and r.

typedef unspecified_type ConvexHullTraits_3::Construct_vector_3

Function object type that provides Vector_3 operator()(Point_3 p, Point_3 q), which constructs and returns the vector q-p.

typedef unspecified_type ConvexHullTraits_3::Coplanar_3

Predicate object type that provides bool operator()(Point_3 p, Point_3 q, Point_3 r, Point_3 s), which determines if points p, q, r, and s are coplanar.

typedef unspecified_type ConvexHullTraits_3::Equal_3

Predicate object type that provides bool operator()(Point_3 p, Point_3 q), which determines if points p and q are equal.

typedef unspecified_type ConvexHullTraits_3::Has_on_positive_side_3

Predicate object type that provides bool operator()(Plane_3 h, Point_3 q), which determines if the point q is on the positive side of the halfspace h.

typedef unspecified_type ConvexHullTraits_3::Less_distance_to_point_3

Predicate object type that provides a constructor taking a single Point_3 object and bool operator()(Point_3 q, Point_3 r), which returns true iff the distance from q to p is smaller than the distance from r to p, where p is the point passed to the object at construction.

typedef unspecified_type ConvexHullTraits_3::Less_signed_distance_to_plane_3

Predicate object type that provides bool operator()(Plane_3 p, Point_3 q, Point_3 r), which returns true iff the signed distance from q to p is smaller than the signed distance from r to p

typedef unspecified_type ConvexHullTraits_3::Plane_3

a 3D plane

typedef unspecified_type ConvexHullTraits_3::Point_3

The point type on which the convex hull algorithm operates.

typedef unspecified_type ConvexHullTraits_3::Segment_3

a 3D segment

typedef unspecified_type ConvexHullTraits_3::Triangle_3

a 3D triangle

typedef unspecified_type ConvexHullTraits_3::Vector_3

a 3D vector