CGAL 5.5.1 - 2D Polygon Partitioning
PartitionIsValidTraits_2 Concept Reference


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>
See also


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 \( l\).


Only a copy constructor is required.

 PartitionIsValidTraits_2 (PartitionIsValidTraits_2 tr)


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

◆ 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.