ConvexHullTraits_2 Concept Reference

Definition

All convex hull and extreme point algorithms provided in CGAL are parameterized with a traits class Traits, which defines the primitives (objects and predicates) that the convex hull algorithms use. ConvexHullTraits_2 defines the complete set of primitives required in these functions. The specific subset of these primitives required by each function is specified with each function.

Has Models:

CGAL::Convex_hull_constructive_traits_2<R>

CGAL::Convex_hull_traits_2<R>

CGAL::Convex_hull_traits_adapter_2<R>

CGAL::Projection_traits_xy_3<K>

CGAL::Projection_traits_yz_3<K>

CGAL::Projection_traits_xz_3<K>

Types
typedef unspecified_type	Point_2
	The point type on which the convex hull functions operate.
typedef unspecified_type	Equal_2
	Binary predicate object type comparing Point_2s.
typedef unspecified_type	Less_xy_2
	Binary predicate object type comparing Point_2s lexicographically.
typedef unspecified_type	Less_yx_2
	Same as Less_xy_2 with the roles of \( x\) and \( y\) interchanged.
typedef unspecified_type	Left_turn_2
	Predicate object type that must provide bool operator()(Point_2 p,Point_2 q,Point_2 r), which returns true iff r lies to the left of the oriented line through p and q.
typedef unspecified_type	Compare_signed_distance_to_line_2
	Predicate object type that must provide bool operator()(Point_2 p, Point_2 q, Point_2 r,Point_2 s), which compares the signed distance of \( r\) and \( s\) to the directed line \( l_{pq}\) through \( p\) and \( q\).
typedef unspecified_type	Less_rotate_ccw_2
	Predicate object type that must provide bool operator()(Point_2 e, Point_2 p,Point_2 q), where true is returned iff a tangent at \( e\) to the point set \( \{e,p,q\}\) hits \( p\) before \( q\) when rotated counterclockwise around \( e\).
typedef unspecified_type	Orientation_2
	Predicate object type that must provide Orientation operator()(Point_2 e, Point_2 p,Point_2 q), that 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.

Creation
Only a copy constructor is required.
	ConvexHullTraits_2 (ConvexHullTraits_2 &t)

Operations
The following member functions to create instances of the above predicate object types must exist.
Equal_2	equal_2_object ()
Less_xy_2	less_xy_2_object ()
Less_yx_2	less_yx_2_object ()
Compare_signed_distance_to_line_2	compare_signed_distance_to_line_2_object ()
Less_rotate_ccw_2	less_rotate_ccw_2_object ()
Left_turn_2	left_turn_2_object ()
Orientation_2	orientation_2_object ()

Member Typedef Documentation

Compare_signed_distance_to_line_2

typedef unspecified_type ConvexHullTraits_2::Compare_signed_distance_to_line_2

Predicate object type that must provide bool operator()(Point_2 p, Point_2 q, Point_2 r,Point_2 s), which compares the signed distance of \( r\) and \( s\) to the directed line \( l_{pq}\) through \( p\) and \( q\).

It is used to compute the point right of a line with maximum unsigned distance to the line.

Equal_2

typedef unspecified_type ConvexHullTraits_2::Equal_2

Binary predicate object type comparing Point_2s.

Must provide bool operator()(Point_2 p, Point_2 q) where true is returned iff \( p ==_{xy} q\), false otherwise.

Less_rotate_ccw_2

typedef unspecified_type ConvexHullTraits_2::Less_rotate_ccw_2

Predicate object type that must provide bool operator()(Point_2 e, Point_2 p,Point_2 q), where true is returned iff a tangent at \( e\) to the point set \( \{e,p,q\}\) hits \( p\) before \( q\) when rotated counterclockwise around \( e\).

Ties are broken such that the point with larger distance to \( e\) is smaller!

Less_xy_2

typedef unspecified_type ConvexHullTraits_2::Less_xy_2

Binary predicate object type comparing Point_2s lexicographically.

Must provide bool operator()(Point_2 p, Point_2 q) where true is returned iff \( p <_{xy} q\). We have \( p<_{xy}q\), iff \( p_x < q_x\) or \( p_x = q_x\) and \( p_y < q_y\), where \( p_x\) and \( p_y\) denote \( x\) and \( y\) coordinate of point \( p\), respectively.