OptimalConvexPartitionTraits_2 Concept Reference

Definition

Requirements of a traits class to be used with the function optimal_convex_partition_2() that computes an optimal convex partition of a polygon.

Refines:

PartitionTraits_2

Has Models:

CGAL::Partition_traits_2<R>

See also

CGAL::convex_partition_is_valid_2()

CGAL::Partition_is_valid_traits_2<Traits, PolygonIsValid>

Types
In addition to the types listed with the concept PartitionTraits_2, the following types are required:
typedef unspecified_type	Segment_2
	A segment type.
typedef unspecified_type	Ray_2
	A ray type.
typedef unspecified_type	Object_2
	A general object type that can be either a point or a segment.
typedef unspecified_type	Construct_segment_2
	Function object type that provides Segment_2 operator()(Point_2 p, Point_2 q), which constructs and returns the segment defined by the points \( p\) and \( q\).
typedef unspecified_type	Construct_ray_2
	Function object type that provides Ray_2 operator()(Point_2 p, Point_2 q), which constructs and returns the ray from point \( p\) through point \( q\).
typedef unspecified_type	Collinear_are_ordered_along_line_2
	Predicate object type that determines orderings of Point_2 's on a line. More...
typedef unspecified_type	Are_stritcly_ordered_along_line_2
	Predicate object type that determines orderings of Point_2 's. More...
typedef unspecified_type	Intersect_2
	Function object type that provides Object_2 operator()(Segment_2 s1, Segment_2 s2) that returns the intersection of two segments (which may be either a segment or a point).
typedef unspecified_type	Assign_2
	Function object type that provides bool operator()(Segment_2 s1, Object_2 o) that returns true if o is a segment and assigns the value of o to s1; returns false otherwise.

Creation
Only a copy constructor is required.
	OptimalConvexPartitionTraits_2 (OptimalConvexPartitionTraits_2 tr)

Operations
In addition to the functions required by PartitionTraits_2, the following functions that create instances of the above function object types must exist:
Collinear_are_ordered_along_line_2	collinear_are_ordered_along_line_2_object () const
Construct_segment_2	construct_segment_2_object () const
Construct_ray_2	construct_ray_2_object () const
Are_strictly_ordered_along_line_2	are_strictly_ordered_along_line_2_object () const

Member Typedef Documentation

Are_stritcly_ordered_along_line_2

typedef unspecified_type OptimalConvexPartitionTraits_2::Are_stritcly_ordered_along_line_2

Predicate object type that determines orderings of Point_2 's.

Must provide bool operator()(Point_2 p, Point_2 q, Point_2 r) that returns true, iff the three points are collinear and q lies strictly between p and r. Note that false should be returned if q==p or q==r.

Collinear_are_ordered_along_line_2

typedef unspecified_type OptimalConvexPartitionTraits_2::Collinear_are_ordered_along_line_2

Predicate object type that determines orderings of Point_2 's on a line.

Must provide bool operator()(Point_2 p, Point_2 q, Point_2 r) that returns true, iff q lies between p and r and p, q, and r satisfy the precondition that they are collinear.