diff --git a/Visibility_2/doc/Visibility_2/visibility_2.txt b/Visibility_2/doc/Visibility_2/visibility_2.txt index 54881336abb..3e6ba84946c 100644 --- a/Visibility_2/doc/Visibility_2/visibility_2.txt +++ b/Visibility_2/doc/Visibility_2/visibility_2.txt @@ -14,7 +14,7 @@ namespace CGAL { 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 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. Note that \f$ f \f$ may contain 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 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 algorithm or \em strategy for answering 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. The right hand side shows the cathedral also with its inner pillars, which is a polygon (with holes) 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.
@@ -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 The following example shows how to obtain the regularized visibility region using the model `Triangular_expansion_visibility_2`, see \cgalFigureRef{general_polygon}. -The arrangement has six bounded faces and an unbounded face. T -he query point \f$ q \f$ is on a vertex. +The arrangement has six bounded faces and an unbounded face. +The query point \f$ q \f$ is on a vertex. The red arrow denotes the halfedge \f$ \overrightarrow{pq} \f$, which also identifies the face in which the visibility region is computed. \cgalFigureBegin{general_polygon, general_polygon_example.png}