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CGAL::y_monotone_partition_is_valid_2

Definition

Function that determines if a given set of polygons represents a valid $$y-monotone partitioning for a given sequence of points that define a simple, counterclockwise-oriented polygon. A valid partition is one in which the polygons are nonoverlapping and the union of the polygons is the same as the original polygon and each polygon is $$y-monotone

#include <CGAL/partition_is_valid_2.h>

template<class InputIterator, class ForwardIterator, class Traits>
bool	y_monotone_partition_is_valid_2 ( InputIterator point_first, InputIterator point_beyond, ForwardIterator poly_first, ForwardIterator poly_beyond, Traits traits = Default_traits)
		determines if the polygons in the range [poly_first, poly_beyond) define a valid $$y-monotone partition of the polygon represented by the points in the range [point_first, point_beyond). The function returns true iff the partition is valid and otherwise returns false. Precondition: Points in the range [point_first, point_beyond) define a simple, counterclockwise-oriented polygon.

Requirements

1. Traits is a model of the concept YMonotonePartitionIsValidTraits_2 .
2. InputIterator::value_type should be Traits::Point_2, which should also be the type of the points stored in an object of type Traits::Polygon_2.
3. ForwardIterator::value_type should be Traits::Polygon_2.

The default traits class Default_traits is Partition_traits_2, with the representation type determined by InputIterator::value_type.

See Also

CGAL::y_monotone_partition_2
CGAL::is_y_monotone_2
CGAL::partition_is_valid_2
CGAL::Partition_is_valid_traits_2<Traits, PolygonIsValid>

Implementation

This function uses the function partition_is_valid_2 together with the function object Is_y_monotone_2 to determine if each polygon is $$y-monotone or not. Thus the time required is $$O(n log$$n + e log$$e) where $$n is the total number of vertices of the partition polygons and $$e is the total number of edges.

Example

See the example presented with the function y_monotone_partition_2 for an illustration of the use of this function.

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