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CGAL 6.0 - 2D Visibility
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#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. |
Visibility_2 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. | |
| 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).
| 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.