CGAL 4.12.1  2D Visibility

#include <CGAL/Triangular_expansion_visibility_2.h>
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 \( n \).
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. 
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 ). More...  
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. More...  
typedef RegularizationCategory CGAL::Triangular_expansion_visibility_2< Arrangement_2_, RegularizationCategory >::Regularization_category 
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. Reattaching forces recomputation.
In case the object is already attached to another arrangement, the visibility object gets detached before being attached to arr
.