new thumbnail; new figures; example of empty disk

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Iordan Iordanov 2018-08-24 15:35:55 +02:00
parent 5df23fe935
commit 751508cc48
2 changed files with 7 additions and 2 deletions

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@ -11,7 +11,7 @@ namespace CGAL {
\cgalAutoToc
\author Monique Teillaud, Mikhail Bogdanov, and Iordan Iordanov
\image html htriangulation-350px.png
\image html ht-450px.png
2D hyperbolic triangulations of \cgal are designed to represent triangulations of
the hyperbolic plane. The vertices of the triangulation are defined by an input set of points.
@ -35,6 +35,11 @@ The Delaunay triangulation of a set of points \f$\mathcal P\f$ in \f$\mathbb H^2
<li> A face is Delaunay hyperbolic if its circumscribing circle is contained in \f$\mathbb H^2\f$.
</ul>
\cgalModifEnd
For an illustration, see \cgalFigureRef{figEmptyDisks}
\cgalFigureBegin{figEmptyDisks, ht-empty-disks.png}
A face is Delaunay hyperbolic if its circumscribing disk is empty and is also contained in \f$\mathbb H^2\f$ (shaded face). An edge is hyperbolic if there exists at least one disk that passes through its endpoints and is contained in \f$\mathbb H^2\f$. An example of non-hyperbolic edge is the dashed segment: the disks that pass through its endpoints and are contained in \f$\mathbb H^2\f$ are not empty; on the other hand, the disks that pass through its endpoint and are empty, are not contained in \f$\mathbb H^2\f$.
\cgalFigureEnd
\section HT2_Design Design and Implementation History

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@ -18,7 +18,7 @@
\addtogroup PkgHyperbolicTriangulation2
\cgalPkgDescriptionBegin{2D Hyperbolic Triangulations,PkgHyperbolicTriangulation2Summary}
\cgalPkgPicture{Hyperbolic_triangulation_2/fig/htriangulation-120px.png}
\cgalPkgPicture{Hyperbolic_triangulation_2/fig/ht-120px.png}
\cgalPkgSummaryBegin
\cgalPkgAuthor{Monique Teillaud, Mikhail Bogdanov, and Iordan Iordanov}