#include <Concepts/ConvexHullTraits_3.h>

Definition

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

CGAL::Convex_hull_traits_3<K>

CGAL::Extreme_points_traits_adapter_3<PPM, GT>

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	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	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 `bool operator()(Point_3 p, 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`. 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...

typedef unspecified_type	Traits_xy_3
	A traits class providing the requirements of the template parameter `Traits` of the 2D convex hull function `CGAL::ch_akl_toussaint()` such that `Traits::Point_2` is `Point_3`, and the 2D points considered in the algorithm are the projections of the 3D points in the `xy`-plane. More...

typedef unspecified_type	Traits_yz_3
	Same as above but in the `yz`-plane. More...

typedef unspecified_type	Traits_xz_3
	Same as above but in the `xz`-plane. 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

◆ Collinear_3

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.

◆ Construct_plane_3

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.

◆ Construct_segment_3

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.

◆ Construct_triangle_3

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.

◆ Coplanar_3

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.

◆ Equal_3

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.

◆ Has_on_positive_side_3

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.

◆ Less_distance_to_point_3

typedef unspecified_type ConvexHullTraits_3::Less_distance_to_point_3

Predicate object type that provides bool operator()(Point_3 p, 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.

◆ Less_signed_distance_to_plane_3

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

◆ Plane_3

typedef unspecified_type ConvexHullTraits_3::Plane_3

a 3D plane

◆ Point_3

typedef unspecified_type ConvexHullTraits_3::Point_3

The point type on which the convex hull algorithm operates.

◆ Segment_3

typedef unspecified_type ConvexHullTraits_3::Segment_3

a 3D segment

◆ Traits_xy_3

typedef unspecified_type ConvexHullTraits_3::Traits_xy_3

A traits class providing the requirements of the template parameter Traits of the 2D convex hull function CGAL::ch_akl_toussaint() such that Traits::Point_2 is Point_3, and the 2D points considered in the algorithm are the projections of the 3D points in the xy-plane.

If this type is not available, the function CGAL::convex_hull_3() will automatically use CGAL::Projection_traits_xy< CGAL::Kernel_traits<Point_3>::Kernel >. Otherwise, a function must exist with the name construct_traits_xy_3_object() that creates an instance of Traits_xy_3.

◆ Traits_xz_3

typedef unspecified_type ConvexHullTraits_3::Traits_xz_3

Same as above but in the xz-plane.

◆ Traits_yz_3

typedef unspecified_type ConvexHullTraits_3::Traits_yz_3

Same as above but in the yz-plane.

◆ Triangle_3

typedef unspecified_type ConvexHullTraits_3::Triangle_3

a 3D triangle

Constructor & Destructor Documentation

◆ ConvexHullTraits_3()

ConvexHullTraits_3::ConvexHullTraits_3 ( ConvexHullTraits_3 & ch )

Member Function Documentation

◆ construct_plane_3_object()

Construct_plane_3 ConvexHullTraits_3::construct_plane_3_object ( )