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	Vector_3
	a 3D vector
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 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	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_bykat() 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.
typedef unspecified_type	Construct_vector_3
	Function object type that provides Vector_3 operator()(Point_3 p1, Point_3 p2), which constructs and returns the vector p1p2, and Vector_3 operator()(int x,int y,int z) which constructs and returns a vector with integer Cartesian coordinates.
typedef unspecified_type	Orientation_3
	Predicate object type that provides CGAL::Orientation operator()(Vector_3 u, Vector_3 v, Vector_3 w) which 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.

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::Traits_xy_3

A traits class providing the requirements of the template parameter Traits of the 2D convex hull function CGAL::ch_bykat() 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 >.