mirror of https://github.com/CGAL/cgal
new thumbnail; new figures; example of empty disk
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@ -11,7 +11,7 @@ namespace CGAL {
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\cgalAutoToc
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\author Monique Teillaud, Mikhail Bogdanov, and Iordan Iordanov
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\image html htriangulation-350px.png
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\image html ht-450px.png
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2D hyperbolic triangulations of \cgal are designed to represent triangulations of
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the hyperbolic plane. The vertices of the triangulation are defined by an input set of points.
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@ -35,6 +35,11 @@ The Delaunay triangulation of a set of points \f$\mathcal P\f$ in \f$\mathbb H^2
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<li> A face is Delaunay hyperbolic if its circumscribing circle is contained in \f$\mathbb H^2\f$.
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</ul>
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\cgalModifEnd
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For an illustration, see \cgalFigureRef{figEmptyDisks}
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\cgalFigureBegin{figEmptyDisks, ht-empty-disks.png}
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A face is Delaunay hyperbolic if its circumscribing disk is empty and is also contained in \f$\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$\mathbb H^2\f$.
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\cgalFigureEnd
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\section HT2_Design Design and Implementation History
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@ -18,7 +18,7 @@
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\addtogroup PkgHyperbolicTriangulation2
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\cgalPkgDescriptionBegin{2D Hyperbolic Triangulations,PkgHyperbolicTriangulation2Summary}
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\cgalPkgPicture{Hyperbolic_triangulation_2/fig/htriangulation-120px.png}
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\cgalPkgPicture{Hyperbolic_triangulation_2/fig/ht-120px.png}
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\cgalPkgSummaryBegin
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\cgalPkgAuthor{Monique Teillaud, Mikhail Bogdanov, and Iordan Iordanov}
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