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## ConvexHullTraits_2

### 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.

### Types

ConvexHullTraits_2::Point_2
| The point type on which the convex hull functions operate.
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.
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<xyq, iff px < qx or px = qx and py < qy, where px and py denote x and y coordinate of point p, respectively.
ConvexHullTraits_2::Less_yx_2
| Same as Less_xy_2 with the roles of x and y interchanged.
ConvexHullTraits_2::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.
ConvexHullTraits_2::Less_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 returns true iff the signed distance from r to the line lpq through p and q is smaller than the distance from s to lpq. It is used to compute the point right of a line with maximum unsigned distance to the line. The predicate must provide a total order compatible with convexity, i.e., for any line segment s one of the endpoints of s is the smallest point among the points on s, with respect to the order given by Less_signed_distance_to_line_2.
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!

### Creation

Only a copy constructor is required.

ConvexHullTraits_2 traits ( & t);

### Operations

The following member functions to create instances of the above predicate object types must exist.

Equal_2 | traits.equal_2_object ()
Less_xy_2 | traits.less_xy_2_object ()
Less_yx_2 | traits.less_yx_2_object ()
Less_signed_distance_to_line_2
| traits.less_signed_distance_to_line_2_object ()
Less_rotate_ccw_2 | traits.less_rotate_ccw_2_object ()
Left_turn_2 | traits.left_turn_2_object ()

### Has Models

CGAL::Convex_hull_constructive_traits_2<R>
CGAL::Convex_hull_projective_xy_traits_2<Point_3>
CGAL::Convex_hull_projective_xz_traits_2<Point_3>
CGAL::Convex_hull_projective_yz_traits_2<Point_3>
CGAL::Convex_hull_traits_2<R>

### See Also

IsStronglyConvexTraits_3

Next: Convex_hull_constructive_traits_2<R>

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The CGAL Project . Tue, December 21, 2004 .