diff --git a/Hyperbolic_triangulation_2/doc/Hyperbolic_triangulation_2/Hyperbolic_triangulation_2.txt b/Hyperbolic_triangulation_2/doc/Hyperbolic_triangulation_2/Hyperbolic_triangulation_2.txt index 9be7ec92ea9..b17e1d24b38 100644 --- a/Hyperbolic_triangulation_2/doc/Hyperbolic_triangulation_2/Hyperbolic_triangulation_2.txt +++ b/Hyperbolic_triangulation_2/doc/Hyperbolic_triangulation_2/Hyperbolic_triangulation_2.txt @@ -9,7 +9,7 @@ namespace CGAL { \anchor chapterHTriangulation2 \cgalAutoToc -\author Mikhail Bogdanov, and Iordan Iordanov, and Monique Teillaud +\author Mikhail Bogdanov, Iordan Iordanov, and Monique Teillaud
@@ -46,22 +46,8 @@ As hyperbolic circles coincide with Euclidean circles contained in the unit disk, the combinatorial structure of the hyperbolic Delaunay triangulation of a set \f$\mathcal P\f$ of points in \f$\mathbb H^2\f$ is a subset of the Euclidean Delaunay triangulation of \f$\mathcal -P\f$. Of course, the hyperbolic and Euclidean geometric embeddings of a -given Delaunay face are different. See -\cgalFigureRef{Hyperbolic_triangulation_2Euclidean_vs_hyperbolic}. - -\cgalFigureAnchor{Hyperbolic_triangulation_2Euclidean_vs_hyperbolic} -
- -
-\cgalFigureCaptionBegin{Hyperbolic_triangulation_2Euclidean_vs_hyperbolic} -Comparison of the Euclidean (green) and hyperbolic (black) Delaunay triangulations -of a given set of points in the unit disk. Note that only the colored faces -are faces of the hyperbolic Delaunay triangulation. -\cgalFigureCaptionEnd - -More precisely, the hyperbolic Delaunay triangulation of \f$\mathcal -P\f$ is a connected simplicial complex. It only +P\f$. More precisely, the hyperbolic Delaunay triangulation of \f$\mathcal +P\f$ is a connected simplicial complex that only contains the simplices of the Euclidean Delaunay triangulation that are hyperbolic: +See \cgalFigureRef{Hyperbolic_triangulation_2Euclidean_vs_hyperbolic}. + +\cgalFigureAnchor{Hyperbolic_triangulation_2Euclidean_vs_hyperbolic} +
+ +
+\cgalFigureCaptionBegin{Hyperbolic_triangulation_2Euclidean_vs_hyperbolic} +Comparison of the Euclidean (green) and hyperbolic (black) Delaunay triangulations +of a given set of points in the unit disk. Only the colored faces +are faces of the hyperbolic Delaunay triangulation. The hyperbolic and Euclidean geometric embeddings of a +Delaunay face that exists in both triangulations are different. +\cgalFigureCaptionEnd + + In the Euclidean Delaunay triangulation, there is a bijection between non-hyperbolic faces and non-hyperbolic edges \cgalCite{cgal:bdt-hdcvd-14}. See @@ -91,7 +91,7 @@ as no empty circle through its endpoints is contained in \section HT2_Software_design Software Design From what was said above, it is natural that the class `Hyperbolic_Delaunay_triangulation_2` privately inherits from the class -`Delaunay_triangulation_2`. So, users are encouraged to look at the chapter +`Delaunay_triangulation_2`. So, users are encouraged to look at Chapter \ref Chapter_2D_Triangulations "2D Triangulation" of the CGAL manual to know more in particular about the representation of triangulations in CGAL and the flexibility of the design.