Definition

The polygon partitioning functions are each parameterized by a traits class that defines the primitives used in the algorithms. Many requirements are common to all traits classes. The concept PartitionTraits_2 defines this common set of requirements.

Has Models:: CGAL::Partition_traits_2<R>

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 to be created by the partitioning algorithm. More...

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

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 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 $l$ .

typedef unspecified_type	Compare_y_2
	Predicate object type that provides `CGAL::Comparision_result operator()(Point_2 p, Point_2 q)` to compare the $y$ values of two points. More...

typedef unspecified_type	Compare_x_2
	The same as `Compare_y_2`, except that $x$ coordinates are compared instead of $y$ .

Creation
A copy constructor and default constructor are required.
	PartitionTraits_2 ()

	PartitionTraits_2 (PartitionTraits_2 tr)

Operations
The following functions that create instances of the above predicate object types must exist.
Less_yx_2	less_yx_2_object ()

Less_xy_2	less_xy_2_object ()

Left_turn_2	left_turn_2_object ()

Orientation_2	orientation_2_object ()

Compare_y_2	compare_y_2_object ()

Compare_x_2	compare_x_2_object ()

Member Typedef Documentation

typedef unspecified_type PartitionTraits_2::Compare_y_2

Predicate object type that provides CGAL::Comparision_result operator()(Point_2 p, Point_2 q) to compare the $y$ values of two points.

The operator must return CGAL::SMALLER if $p_y < q_y$ , CGAL::LARGER if $p_y > q_y$ and CGAL::EQUAL if $p_y = q_y$ .

typedef unspecified_type PartitionTraits_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 PartitionTraits_2::Polygon_2

The polygon type to be created by the partitioning algorithm.

For testing the validity postcondition of the partition, this type should provide a nested type Vertex_const_iterator that is the type of the iterator over the polygon vertices and member functions Vertex_const_iterator vertices_begin() and Vertex_const_iterator vertices_end().

Definition

Types

Creation

Operations

Member Typedef Documentation