CGAL::Triangular_expansion_visibility_2< Arrangement_2_, RegularizationCategory > Class Template Reference

#include <CGAL/Triangular_expansion_visibility_2.h>

Definition

template<typename Arrangement_2_, typename RegularizationCategory = Tag_true>
class CGAL::Triangular_expansion_visibility_2< Arrangement_2_, RegularizationCategory >

This class is a model of the concept Visibility_2 can answer visibility queries within a polygon that may have holes.

The algorithm obtains a constrained triangulation from the input arrangement, then computes visibility by expanding the triangle that contains the query point. Preprocessing takes \(O(n)\) time and \(O(n)\)$ space, where \( n \) is the number of vertices of input polygon. The query time is \(O(nh)\), where \( h \) is the number of holes+1 of input polygon. Thus, for simple polygons (or a polygon with a constant number of holes) the algorithm complexity is linear, but it is \(O(n^2)\) in the worst case, as the number of holes can be linear in \( n \).

Template Parameters

Arrangement_2_	is the type used to represent the input environment. It must be an instance of CGAL::Arrangement_2, where its CGAL::Arrangement_2::Traits_2 must be an instance of CGAL::Arr_segment_traits_2, or of CGAL::Arr_non_caching_segment_traits_2.
RegularizationCategory	indicates whether the output should be regularized. It can be specified by one of the following: #Tag_true or #Tag_false, where #Tag_false is the default value.

Is model of

Visibility_2

See also

CGAL::Simple_polygon_visibility_2

CGAL::Rotational_sweep_visibility_2

Examples

Visibility_2/general_polygon_example.cpp.

Types
typedef Arrangement_2_	Arrangement_2
	The type of the input arrangement.

Tags
typedef RegularizationCategory	Regularization_category
	identifies whether the regularized visibility area is computed (either #Tag_true or #Tag_false).
typedef Tag_true	Supports_general_polygon_category
	See Visibility_2::Supports_general_polygon_category.
typedef Tag_true	Supports_simple_polygon_category
	See Visibility_2::Supports_simple_polygon_category.

Functions
void	attach (const Arrangement_2 &arr)
	Attaches the given arrangement to the visibility object and computes the restricted triangulation.

Member Typedef Documentation

Regularization_category

template<typename Arrangement_2_ , typename RegularizationCategory = Tag_true>

typedef RegularizationCategory CGAL::Triangular_expansion_visibility_2< Arrangement_2_, RegularizationCategory >::Regularization_category

identifies whether the regularized visibility area is computed (either #Tag_true or #Tag_false).

Member Function Documentation

attach()

template<typename Arrangement_2_ , typename RegularizationCategory = Tag_true>

void CGAL::Triangular_expansion_visibility_2< Arrangement_2_, RegularizationCategory >::attach

(

const Arrangement_2 &

arr

)

Attaches the given arrangement to the visibility object and computes the restricted triangulation.

This takes \(O(n)\)$ time, where \( n \) is the number of vertices.

From this moment on the class observes changes in the arrangement. If the arrangement changes a new restricted triangulation is computed. Re-attaching forces re-computation.

In case the object is already attached to another arrangement, the visibility object gets detached before being attached to arr.