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@ -40,17 +40,17 @@ public:
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/// \name Tags
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/// @{
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/*!
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Tag identifying whether the regularized visibility area is computed.
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Its value is either \ref CGAL::Tag_true or \ref CGAL::Tag_false.
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*/
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typedef RegularizationTag Regularization_tag;
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/*!
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The class supports general polygons (i.e.\ with holes).
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Its value is \ref CGAL::Tag_true.
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*/
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typedef ::Tag_true Supports_general_polygon_tag;
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/*!
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The class supports general simple polygons.
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Its value is \ref CGAL::Tag_true.
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*/
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typedef ::Tag_true Supports_simple_polygon_tag;
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/// @}
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@ -46,16 +46,17 @@ public:
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/// @{
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/*!
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Tag identifying whether the regularized visibility area is computed.
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Its value is either \ref CGAL::Tag_true or \ref CGAL::Tag_false.
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*/
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typedef RegularizationTag Regularization_tag;
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/*!
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The class does not support general polygons (i.e.\ with holes).
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Its value is \ref CGAL::Tag_false.
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*/
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typedef ::Tag_false Supports_general_polygon_tag;
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/*!
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The class supports general simple polygons.
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Its value is \ref CGAL::Tag_true.
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*/
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typedef ::Tag_true Supports_simple_polygon_tag;
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/// @}
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@ -42,17 +42,17 @@ public:
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/// \name Tags
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/// @{
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/*!
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Tag identifying whether the regularized visibility area is computed.
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Its value is either \ref CGAL::Tag_true or \ref CGAL::Tag_false.
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*/
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typedef RegularizationTag Regularization_tag;
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/*!
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The class supports general polygons (i.e.\ with holes).
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Its value is \ref CGAL::Tag_true.
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*/
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typedef ::Tag_true Supports_general_polygon_tag;
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/*!
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The class supports general simple polygons.
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Its value is \ref CGAL::Tag_true.
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*/
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typedef ::Tag_true Supports_simple_polygon_tag;
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/// @}
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@ -20,12 +20,7 @@ public:
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/*!
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The arrangement type of the input.
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*/
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typedef Hidden_type Arrangement_2;
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/*!
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The geometry traits class of Arrangement_2.
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*/
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typedef Arrangement_2::Traits_2 Traits_2;
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typedef unspecified_type Arrangement_2;
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/*!
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The 2D point type used for the queries.
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@ -49,17 +44,17 @@ public:
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/*!
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Tag identifying whether the regularized visibility area is computed (either \ref CGAL::Tag_true or \ref CGAL::Tag_false).
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*/
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typedef Hidden_type Regularization_tag;
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typedef unspecified_type Regularization_tag;
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/*!
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Tag identifying whether general polygons (with holes) are supported (either \ref CGAL::Tag_true or \ref CGAL::Tag_false).
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*/
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typedef Hidden_type Supports_general_polygon_tag;
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typedef unspecified_type Supports_general_polygon_tag;
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/*!
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Tag identifying whether general simple polygons are supported (either \ref CGAL::Tag_true or \ref CGAL::Tag_false).
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*/
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typedef Hidden_type Supports_simple_polygon_tag;
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typedef unspecified_type Supports_simple_polygon_tag;
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/// @}
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/// \name Constructors
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@ -22,10 +22,10 @@ region of \f$ q \f$, denoted by \f$ V_q \f$
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Definition [Valid Polygon]:
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A polygon \f$ P \f$ is valid if \f$ P \f$ is closed (\f$\partial P \subset P\f$)
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and each boundary loop (only one outer boundary loop in case of no holes) is simple.
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See \ref PkgBooleanSetOperations2Summary for the complete definition.
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A polygon \f$ P \f$ is valid if \f$ P \f$ is closed (\f$\partial P \subset P\f$) and each boundary loop is simple. Namely, \f$ P \f$ has exactly one outer boundary (it may have some inner boundaires), and the edges in each boundary loop are only allowed to intersect at vertices. Note that a vertex may appear multiple times in one boundary loop. See \ref PkgBooleanSetOperations2Summary for the complete definition.
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Definition [Simple Polygon]
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A valid polygon is simple if has no holes, i.e., it has exactly one boundary which is an outer boundary.
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\subsection visibility_2_degeneracies Degeneracies and Regularization
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@ -117,7 +117,7 @@ Complete Cathedral | total preprocessing time | total query time
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Thus, in general we recommend to use `Triangular_expansion_visibility_2` even if the polygon is simple. The main advantage
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of the algorithm is its locality. After the triangle that contains the query point is located in the triangulation,
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the algorithm explores neighboring triangles, but only those that are actually seen.In this sense the algorithm can be considered as output sensitive.
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Note that the `Triangular_expansion_visibility_2` algorithm performs better on the full cathedral by the fact that the additional pillars block the view early in many cases.
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Note that the `Triangular_expansion_visibility_2` algorithm performs better on the full cathedral since the additional pillars block the view early in many cases.
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However, if the simple polygon is rather convex (i.e., nearly all boundary is seen) or
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if only one (or very little) queries are required, using one of the algorithms that does not require preprocessing is advantageous.
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