#include <Concepts/ConvexHullTraits_2.h>
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>
- See also
IsStronglyConvexTraits_3
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typedef unspecified_type | Point_2 |
| The point type on which the convex hull functions operate. More...
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typedef unspecified_type | Equal_2 |
| Binary predicate object type comparing Point_2 s. More...
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typedef unspecified_type | Less_xy_2 |
| Binary predicate object type comparing Point_2 s lexicographically. More...
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typedef unspecified_type | Less_yx_2 |
| Same as Less_xy_2 with the roles of \( x\) and \( y\) interchanged. More...
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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 . More...
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typedef unspecified_type | 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 \( l_{pq}\) through \( p\) and \( q\) is smaller than the distance from \( s\) to \( l_{pq}\). More...
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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 \( e\). More...
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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 . More...
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◆ Equal_2
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.
◆ 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
.
◆ 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_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 \( l_{pq}\) through \( p\) and \( q\) is smaller than the distance from \( s\) to \( l_{pq}\).
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
.
◆ Less_xy_2
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.
◆ Less_yx_2
Same as Less_xy_2
with the roles of \( x\) and \( y\) interchanged.
◆ 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
.
◆ Point_2
The point type on which the convex hull functions operate.
◆ ConvexHullTraits_2()
◆ equal_2_object()
Equal_2 ConvexHullTraits_2::equal_2_object |
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◆ left_turn_2_object()
◆ less_rotate_ccw_2_object()
◆ less_signed_distance_to_line_2_object()
◆ less_xy_2_object()
Less_xy_2 ConvexHullTraits_2::less_xy_2_object |
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◆ less_yx_2_object()
Less_yx_2 ConvexHullTraits_2::less_yx_2_object |
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◆ orientation_2_object()