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Michael Hemmer 2014-09-18 16:30:10 +02:00
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Visibility_2/doc/Visibility_2/visibility_2.txt
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@ -14,7 +14,7 @@ namespace CGAL {
This package provides functionality to compute the visibility region within polygons in two dimensions. This package provides functionality to compute the visibility region within polygons in two dimensions.
The package is based on the package \ref PkgArrangement2Summary and uses CGAL::Arrangement_2 The package is based on the package \ref PkgArrangement2Summary and uses CGAL::Arrangement_2
as the fundamental class to specify the input as well as the output. as the fundamental class to specify the input as well as the output.
Hence, a polygon \f$ P \f$ is represented by an bounded arrangement face \f$ f \f$ Hence, a polygon \f$ P \f$ is represented by a bounded arrangement face \f$ f \f$
that does not have any isolated vertices and any edge that is adjacent to \f$ f \f$ separates \f$ f \f$ from another face. that does not have any isolated vertices and any edge that is adjacent to \f$ f \f$ separates \f$ f \f$ from another face.
Note that \f$ f \f$ may contain holes. Note that \f$ f \f$ may contain holes.
Similarly, a simple polygon is represented by a face without holes. Similarly, a simple polygon is represented by a face without holes.
@ -50,7 +50,7 @@ For more information about regularization, refer to Chapter \ref PkgBooleanSetOp
\section visibility_2_classes Classes and Algorithms \section visibility_2_classes Classes and Algorithms
Answering visibility queries is, in many ways, similar to answering point-location queries. Answering visibility queries is, in many ways, similar to answering point-location queries.
Thus, we use the same design used to implement point location. Thus, we use the same design used to implement \ref PkgArrangement2Summary point location.
Each of the various visibility class templates employs a different Each of the various visibility class templates employs a different
algorithm or \em strategy for answering algorithm or \em strategy for answering
queries\cgalFootnote{The term \em strategy is borrowed from the queries\cgalFootnote{The term \em strategy is borrowed from the
@ -91,7 +91,7 @@ The left hand side of Figure \cgalFigureRef{cathedral-fig} depicts the outer bou
which is a simple polygon with 565 vertices. which is a simple polygon with 565 vertices.
The right hand side shows the cathedral also with its inner pillars, which is a polygon (with holes) The right hand side shows the cathedral also with its inner pillars, which is a polygon (with holes)
with 1153 vertices. with 1153 vertices.
The following table shows the total runtime consumption of the computation of The following table shows the total running time consumption of the computation of
all visibility polygons for all vertices of the cathedral. all visibility polygons for all vertices of the cathedral.
<CENTER> <CENTER>
@ -137,8 +137,8 @@ The visibility region of \f$ q \f$ in a simple polygon: (1) non-regularized visi
\section general_polygon_example Example of Visibility in a Polygon with Holes \section general_polygon_example Example of Visibility in a Polygon with Holes
The following example shows how to obtain the regularized visibility region using the model The following example shows how to obtain the regularized visibility region using the model
`Triangular_expansion_visibility_2`, see \cgalFigureRef{general_polygon}. `Triangular_expansion_visibility_2`, see \cgalFigureRef{general_polygon}.
The arrangement has six bounded faces and an unbounded face. T The arrangement has six bounded faces and an unbounded face.
he query point \f$ q \f$ is on a vertex. The query point \f$ q \f$ is on a vertex.
The red arrow denotes the halfedge \f$ \overrightarrow{pq} \f$, The red arrow denotes the halfedge \f$ \overrightarrow{pq} \f$,
which also identifies the face in which the visibility region is computed. which also identifies the face in which the visibility region is computed.
\cgalFigureBegin{general_polygon, general_polygon_example.png} \cgalFigureBegin{general_polygon, general_polygon_example.png}