advanced 
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 $$ymonotonicity, respectively.
 
The point type on which the partitioning algorithm operates.
 
 
The polygon type created by the partitioning
function. This type should provide a nested type Vertex_const_iterator
that is the type of the nonmutable iterator over the polygon vertices.
 
 
A model of the concept PolygonIsValid
 
 
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.
 
 
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.
 
 
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.

The following functions that create instances of the above predicate object types must exist.

 

 

 


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
advanced 