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CGAL::convex_partition_is_valid_2
Definition
Function that determines if a given set of polygons represents
a valid convex partitioning for a given sequence of points that represent a
simple, counterclockwise-oriented polygon.
A convex partition is valid if the
polygons do not overlap, the union of the polygons is the same as the original
polygon given by the sequence of points, and if each partition polygon is
convex.
#include <CGAL/partition_is_valid_2.h>
template<class InputIterator, class ForwardIterator, class Traits>
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bool
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convex_partition_is_valid_2 ( |
InputIterator point_first,
InputIterator point_beyond,
ForwardIterator poly_first,
ForwardIterator poly_beyond,
Traits traits = Default_traits) |
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determines if the polygons in the range [poly_first, poly_beyond)
define a valid convex partition of the polygon defined by the points in the
range [point_first, point_beyond).
The function returns true iff the partition is valid and otherwise
returns false.
Precondition: | The points in the range [point_first, point_beyond)
define a simple, counterclockwise-oriented polygon. |
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Requirements
- Traits is a model of the concept
ConvexPartitionIsValidTraits_2
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- 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::optimal_convex_partition_2
CGAL::partition_is_valid_2
CGAL::is_convex_2
Implementation
This function calls partition_is_valid_2 using the function object
Is_convex_2 to determine the convexity of each partition polygon.
Thus the time required by this function is loglog where
is the total number of vertices in the partition polygons and the
total number of edges.
Example
See the example presented with the function approx_convex_partition_2
for an illustration of the use of this function.
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