y_monotone_partition_is_valid

advanced

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

Traits is a model of the concept YMonotonePartitionIsValidTraits_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.
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 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 logn + e loge) 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.