CGAL 6.0 - 2D Convex Hulls and Extreme Points
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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 | |
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_2 s. | |
typedef unspecified_type | Less_xy_2 |
Binary predicate object type comparing Point_2 s 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 () |
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.
Binary predicate object type comparing Point_2
s.
Must provide bool operator()(Point_2 p, Point_2 q)
where true
is returned iff \( p ==_{xy} q\), false otherwise.
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!
Binary predicate object type comparing Point_2
s 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.