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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 |
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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().
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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.
See Also
CGAL::approx_convex_partition_2
CGAL::greene_approx_convex_partition_2
CGAL::is_y_monotone_2
CGAL::optimal_convex_partition_2
CGAL::Partition_is_valid_traits_2<Traits, PolygonIsValid>
CGAL::y_monotone_partition_2
CGAL::is_convex_2
Implementation
This function requires O(n log n + e log e + Σi=1p mi) 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 mi is the time required by Traits::Is_valid() to test if partition polygon pi is valid.
Example
See the example presented with the function optimal_convex_partition_2 for an illustration of the use of this function.