Update documents

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Ning Xu 2014-08-11 23:31:27 -04:00
parent 50af0ffae0
commit f9eee7cc00
5 changed files with 17 additions and 21 deletions

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@ -40,17 +40,17 @@ public:
/// \name Tags /// \name Tags
/// @{ /// @{
/*! /*!
Tag identifying whether the regularized visibility area is computed. Its value is either \ref CGAL::Tag_true or \ref CGAL::Tag_false.
*/ */
typedef RegularizationTag Regularization_tag; typedef RegularizationTag Regularization_tag;
/*! /*!
The class supports general polygons (i.e.\ with holes). Its value is \ref CGAL::Tag_true.
*/ */
typedef ::Tag_true Supports_general_polygon_tag; typedef ::Tag_true Supports_general_polygon_tag;
/*! /*!
The class supports general simple polygons. Its value is \ref CGAL::Tag_true.
*/ */
typedef ::Tag_true Supports_simple_polygon_tag; typedef ::Tag_true Supports_simple_polygon_tag;
/// @} /// @}

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@ -46,16 +46,17 @@ public:
/// @{ /// @{
/*! /*!
Tag identifying whether the regularized visibility area is computed. Tag identifying whether the regularized visibility area is computed.
Its value is either \ref CGAL::Tag_true or \ref CGAL::Tag_false.
*/ */
typedef RegularizationTag Regularization_tag; typedef RegularizationTag Regularization_tag;
/*! /*!
The class does not support general polygons (i.e.\ with holes). Its value is \ref CGAL::Tag_false.
*/ */
typedef ::Tag_false Supports_general_polygon_tag; typedef ::Tag_false Supports_general_polygon_tag;
/*! /*!
The class supports general simple polygons. Its value is \ref CGAL::Tag_true.
*/ */
typedef ::Tag_true Supports_simple_polygon_tag; typedef ::Tag_true Supports_simple_polygon_tag;
/// @} /// @}

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@ -42,17 +42,17 @@ public:
/// \name Tags /// \name Tags
/// @{ /// @{
/*! /*!
Tag identifying whether the regularized visibility area is computed. Its value is either \ref CGAL::Tag_true or \ref CGAL::Tag_false.
*/ */
typedef RegularizationTag Regularization_tag; typedef RegularizationTag Regularization_tag;
/*! /*!
The class supports general polygons (i.e.\ with holes). Its value is \ref CGAL::Tag_true.
*/ */
typedef ::Tag_true Supports_general_polygon_tag; typedef ::Tag_true Supports_general_polygon_tag;
/*! /*!
The class supports general simple polygons. Its value is \ref CGAL::Tag_true.
*/ */
typedef ::Tag_true Supports_simple_polygon_tag; typedef ::Tag_true Supports_simple_polygon_tag;
/// @} /// @}

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@ -20,12 +20,7 @@ public:
/*! /*!
The arrangement type of the input. The arrangement type of the input.
*/ */
typedef Hidden_type Arrangement_2; typedef unspecified_type Arrangement_2;
/*!
The geometry traits class of Arrangement_2.
*/
typedef Arrangement_2::Traits_2 Traits_2;
/*! /*!
The 2D point type used for the queries. The 2D point type used for the queries.
@ -49,17 +44,17 @@ public:
/*! /*!
Tag identifying whether the regularized visibility area is computed (either \ref CGAL::Tag_true or \ref CGAL::Tag_false). Tag identifying whether the regularized visibility area is computed (either \ref CGAL::Tag_true or \ref CGAL::Tag_false).
*/ */
typedef Hidden_type Regularization_tag; typedef unspecified_type Regularization_tag;
/*! /*!
Tag identifying whether general polygons (with holes) are supported (either \ref CGAL::Tag_true or \ref CGAL::Tag_false). Tag identifying whether general polygons (with holes) are supported (either \ref CGAL::Tag_true or \ref CGAL::Tag_false).
*/ */
typedef Hidden_type Supports_general_polygon_tag; typedef unspecified_type Supports_general_polygon_tag;
/*! /*!
Tag identifying whether general simple polygons are supported (either \ref CGAL::Tag_true or \ref CGAL::Tag_false). Tag identifying whether general simple polygons are supported (either \ref CGAL::Tag_true or \ref CGAL::Tag_false).
*/ */
typedef Hidden_type Supports_simple_polygon_tag; typedef unspecified_type Supports_simple_polygon_tag;
/// @} /// @}
/// \name Constructors /// \name Constructors

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@ -22,10 +22,10 @@ region of \f$ q \f$, denoted by \f$ V_q \f$
Definition [Valid Polygon]: Definition [Valid Polygon]:
A polygon \f$ P \f$ is valid if \f$ P \f$ is closed (\f$\partial P \subset P\f$) 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.
and each boundary loop (only one outer boundary loop in case of no holes) is simple.
See \ref PkgBooleanSetOperations2Summary for the complete definition.
Definition [Simple Polygon]
A valid polygon is simple if has no holes, i.e., it has exactly one boundary which is an outer boundary.
\subsection visibility_2_degeneracies Degeneracies and Regularization \subsection visibility_2_degeneracies Degeneracies and Regularization
@ -117,7 +117,7 @@ Complete Cathedral | total preprocessing time | total query time
Thus, in general we recommend to use `Triangular_expansion_visibility_2` even if the polygon is simple. The main advantage Thus, in general we recommend to use `Triangular_expansion_visibility_2` even if the polygon is simple. The main advantage
of the algorithm is its locality. After the triangle that contains the query point is located in the triangulation, of the algorithm is its locality. After the triangle that contains the query point is located in the triangulation,
the algorithm explores neighboring triangles, but only those that are actually seen.In this sense the algorithm can be considered as output sensitive. the algorithm explores neighboring triangles, but only those that are actually seen.In this sense the algorithm can be considered as output sensitive.
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. 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.
However, if the simple polygon is rather convex (i.e., nearly all boundary is seen) or However, if the simple polygon is rather convex (i.e., nearly all boundary is seen) or
if only one (or very little) queries are required, using one of the algorithms that does not require preprocessing is advantageous. if only one (or very little) queries are required, using one of the algorithms that does not require preprocessing is advantageous.