CGAL 5.0 - 3D Convex Hulls
ConvexHullTraits_3 Concept Reference

Definition

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

Has Models:

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.

typedef unspecified_type Plane_3
a 3D plane

typedef unspecified_type Segment_3
a 3D segment

typedef unspecified_type Triangle_3
a 3D triangle

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.

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.

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.

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.

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.

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.

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.

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.

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

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.

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

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 ()

◆ 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.