\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.13.1 - 2D Visibility
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.
RegularizationCategoryindicates 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). More...
 
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. More...
 

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.