partition_is_valid

advanced

CGAL::partition_is_valid_2

Definition

Function that determines if a given set of polygons represents a valid partition 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.

#include <CGAL/partition_is_valid_2.h>

template<class InputIterator, class ForwardIterator, class Traits>

bool

partition_is_valid_2 ( InputIterator point_first,
InputIterator point_beyond,
ForwardIterator poly_first,
ForwardIterator poly_beyond,
Traits traits = Default_traits)

returns true iff the polygons in the range [poly_first, poly_beyond) define a valid partition of the polygon defined by the points in the range [point_first, point_beyond) and false otherwise. Each polygon must also satisfy the property tested by Traits::Is_valid().

Precondition:

Points in the range [point_first, point_beyond) define a simple, counterclockwise-oriented polygon.

Requirements

Traits is a model of the concept PartitionIsValidTraits_2 and the concept defining the requirements for the validity test implemented by Traits::Is_valid().
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.
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.

Implementation

This function requires O(n logn + e loge + _i=1^p m_i) where n is the total number of vertices of the p partition polygons, e is the total number of edges of the partition polygons and m_i is the time required by Traits::Is_valid() to test if partition polygon p_i is valid.

Example

See the example presented with the function optimal_convex_partition_2 for an illustration of the use of this function.