PartitionTraits_2 Concept Reference

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.
typedef unspecified_type	Less_xy_2
	Predicate object type that compares 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 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::Comparison_result operator()(Point_2 p, Point_2 q) to compare the \( y\) values of two points.
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 () const
Less_xy_2	less_xy_2_object () const
Left_turn_2	left_turn_2_object () const
Orientation_2	orientation_2_object () const
Compare_y_2	compare_y_2_object () const
Compare_x_2	compare_x_2_object () const

Member Typedef Documentation

Compare_y_2

typedef unspecified_type PartitionTraits_2::Compare_y_2

Predicate object type that provides CGAL::Comparison_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 \( p_y = q_y\).

Less_xy_2

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.

Polygon_2

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().