Largest_empty_iso_rectangle

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CGAL::Largest_empty_iso_rectangle_2<T>

Definition

Given a set of points in the plane, the class Largest_empty_iso_rectangle_2<T> is a data structure that maintains an iso-rectangle with the largest area among all iso-rectangles that are inside a given bounding box( iso-rectangle), and that do not contain any point of the point set.

The class Largest_empty_iso_rectangle_2<T> expects a model of the concept LargestEmptyIsoRectangleTraits_2 as its template argument.

#include <CGAL/Largest_empty_iso_rectangle_2.h>

Types

The class Largest_empty_iso_rectangle_2<T> defines the following types:

typedef T	Traits;

typedef Traits::Point_2	Point_2;

typedef Traits::Iso_rectangle_2	Iso_rectangle_2;

The following iterator allows to enumerate the points. It is non mutable, bidirectional and its value type is Point_2. It is invalidated by any insertion or removal of a point.

Largest_empty_iso_rectangle_2<T>::const_iterator
	Iterator over the points.

Creation

Largest_empty_iso_rectangle_2<T> l ( Iso_rectangle_2 b);
	Constructor. The iso-rectangle b is the bounding rectangle.

Largest_empty_iso_rectangle_2<T> l ( const Point_2 p, const Point_2 q);
	Constructor. The iso-rectangle whose lower left and upper right points are p and q respectively is the bounding rectangle.

Largest_empty_iso_rectangle_2<T> l;
	Constructor. The iso-rectangle whose lower left point and upper right points are (0,0) and (1,1) respectively is the bounding rectangle.

Largest_empty_iso_rectangle_2<T> l ( const Largest_empty_iso_rectangle_2<Traits> tr);
	Copy constructor.

Operations

Assignment

Largest_empty_iso_rectangle_2<T>

l = tr

Access Functions

Traits	l.traits () const	Returns a const reference to the traits object.

const_iterator	l.begin () const	Returns an iterator to the beginning of the point set.

const_iterator	l.end () const	Returns a past-the-end iterator for the point set.

Queries

Quadruple<Point_2, Point_2, Point_2, Point_2>
	l.get_left_bottom_right_top ()	Returns the four points that define the largest empty iso-rectangle. (Note that these points are not necessarily on a corner of an iso-rectangle.)
Iso_rectangle_2	l.get_largest_empty_iso_rectangle ()
		Returns the largest empty iso-rectangle. (Note that the two points defining the iso-rectangle are not necessarily part of the point set.)
Iso_rectangle_2	l.get_bounding_box ()	Returns the iso-rectangle passed in the constructor.

Insertion

void	l.insert ( Point_2 p)	Inserts point p in the point set, if it is not already in the set.

void	l.push_back ( Point_2 p)	Inserts point p in the point set, if it is not already in the set.

template < class InputIterator >
int	l.insert ( InputIterator first, InputIterator last)
		Inserts the points in the range [.first, last.). Returns the number of inserted points. Requirements The value_type of first and last is Point.

Removal

bool	l.remove ( Point_2 p)	Removes point p. Returns false iff p is not in the point set.

void	l.clear ()	Removes all points of l.

Implementation

The algorithm is an implementation of [Orl90]. The runtime of an insertion or a removal is O(log n). A query takes O(n²) worst case time and O(n log n) expected time. The working storage is O(n).

Next: LargestEmptyIsoRectangleTraits_2