CGAL 5.5.2 - 2D Polygon Partitioning
PartitionIsValidTraits_2 Concept Reference

## Definition

Requirements of a traits class that is used by CGAL::partition_is_valid_2(), CGAL::convex_partition_is_valid_2(), and CGAL::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 CGAL::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 CGAL::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>
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_2s 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 ()

## ◆ 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

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.