Definition

Requirements of a traits class that is used by partition_is_valid_2, convex_partition_is_valid_2, and y_monotone_partition_is_valid_2 for testing if a given set of polygons are nonoverlapping and if their union is a polygon that is the same as a polygon represented by a given sequence of points. Note that the traits class for partition_is_valid_2 may have to satisfy additional requirements if each partition polygon is to be tested for having a particular property; see, for example, the descriptions of the function is_convex_2() and the concept YMonotonePartitionTraits_2 for the additional requirements for testing for convexity and $y$ -monotonicity, respectively.

Has Models:: CGAL::Partition_is_valid_traits_2<Traits, PolygonIsValid>

See Also: CGAL::approx_convex_partition_2(); CGAL::greene_approx_convex_partition_2(); CGAL::optimal_convex_partition_2(); CGAL::y_monotone_partition_2()

Types
typedef unspecified_type	Point_2
	The point type on which the partitioning algorithm operates.

typedef unspecified_type	Polygon_2
	The polygon type created by the partitioning function. More...

typedef unspecified_type	Is_valid
	A model of the concept `PolygonIsValid`

typedef unspecified_type	Less_xy_2
	Predicate object type that compares `Point_2`s lexicographically. More...

typedef unspecified_type	Left_turn_2
	Predicate object type that provides `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	Orientation_2
	Predicate object type that provides `CGAL::Orientation operator()(Point_2 p, Point_2 q, Point_2 r)` 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.
	PartitionIsValidTraits_2 (PartitionIsValidTraits_2 tr)

Operations
The following functions that create instances of the above predicate object types must exist.
Orientation_2	is_valid_object ()

Less_xy_2	less_xy_2_object ()

Left_turn_2	left_turn_2_object ()

Orientation_2	orientation_2_object ()

Member Typedef Documentation

typedef unspecified_type PartitionIsValidTraits_2::Less_xy_2

Predicate object type that compares 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 the $x$ and $y$ coordinates of point $p$ , respectively.

typedef unspecified_type PartitionIsValidTraits_2::Polygon_2

The polygon type created by the partitioning function.

This type should provide a nested type Vertex_const_iterator that is the type of the non-mutable iterator over the polygon vertices.

Definition

Types

Creation

Operations

Member Typedef Documentation