CGAL::Simple_polygon_visibility_2< Arrangement_2_, RegularizationCategory > Class Template Reference

#include <CGAL/Simple_polygon_visibility_2.h>

Definition

template<typename Arrangement_2_, typename RegularizationCategory = Tag_true>
class CGAL::Simple_polygon_visibility_2< Arrangement_2_, RegularizationCategory >

This class is a model of the concept Visibility_2 can answer visibility queries within a simple polygon with no holes.

This class implements the algorithm of B.Joe and R.B.Simpson [4]. The algorithm is a modification and extension of the linear time algorithm of Lee [5]. It computes the visibility region from a viewpoint that is in the interior or on the boundary of the polygon.

While scanning the boundary the algorithm uses a stack to manipulate the vertices, and ultimately yields the visibility region. For each scanned edge, at most 2 points are pushed onto the stack. Overall, at most 2 \( n \) points are pushed or popped. Thus, the time and space complexities of the algorithm are \(O(n)\)$ even in case of degeneracies such as needles, where \( n \) is the number of the vertices of the polygon.

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::Rotational_sweep_visibility_2

CGAL::Triangular_expansion_visibility_2

Examples

Visibility_2/simple_polygon_visibility_2.cpp.

Types
typedef Arrangement_2	Arrangement_2
	The arrangement type is used for input.

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

Member Typedef Documentation

Regularization_category

template<typename Arrangement_2_ , typename RegularizationCategory = Tag_true>

typedef RegularizationCategory CGAL::Simple_polygon_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::Simple_polygon_visibility_2< Arrangement_2_, RegularizationCategory >::attach

(

const Arrangement_2 &

arr

)

Attaches the given arrangement to the visibility object.

This operation takes \(O(1)\) as the class does no pre-processing.

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