|
CGAL 6.1 - 2D Convex Hulls and Extreme Points
|
Loading...
Searching...
No Matches
|
CGAL 6.1 - 2D Convex Hulls and Extreme Points
|
#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.
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 () |
| 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.
| 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.
| typedef unspecified_type 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.
| 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!
| 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.
| typedef unspecified_type ConvexHullTraits_2::Less_yx_2 |
Same as Less_xy_2 with the roles of \( x\) and \( y\) interchanged.
| typedef unspecified_type ConvexHullTraits_2::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.
| typedef unspecified_type ConvexHullTraits_2::Point_2 |
The point type on which the convex hull functions operate.
| ConvexHullTraits_2::ConvexHullTraits_2 | ( | ConvexHullTraits_2 & | t | ) |
| Compare_signed_distance_to_line_2 ConvexHullTraits_2::compare_signed_distance_to_line_2_object | ( | ) |
| Equal_2 ConvexHullTraits_2::equal_2_object | ( | ) |
| Left_turn_2 ConvexHullTraits_2::left_turn_2_object | ( | ) |
| Less_rotate_ccw_2 ConvexHullTraits_2::less_rotate_ccw_2_object | ( | ) |
| Less_xy_2 ConvexHullTraits_2::less_xy_2_object | ( | ) |
| Less_yx_2 ConvexHullTraits_2::less_yx_2_object | ( | ) |
| Orientation_2 ConvexHullTraits_2::orientation_2_object | ( | ) |
1.10.0