diff --git a/Hyperbolic_triangulation_2/doc/Hyperbolic_triangulation_2/Doxyfile.in b/Hyperbolic_triangulation_2/doc/Hyperbolic_triangulation_2/Doxyfile.in index 4f7caf97a84..8d17ef5c0b8 100644 --- a/Hyperbolic_triangulation_2/doc/Hyperbolic_triangulation_2/Doxyfile.in +++ b/Hyperbolic_triangulation_2/doc/Hyperbolic_triangulation_2/Doxyfile.in @@ -6,6 +6,8 @@ EXAMPLE_PATH = ${CGAL_PACKAGE_DIR}/examples PROJECT_NAME = "CGAL ${CGAL_DOC_VERSION} - 2D Hyperbolic Delaunay Triangulations" +HTML_EXTRA_STYLESHEET = ${CGAL_PACKAGE_DOC_DIR}/css/customstyle.css + HTML_EXTRA_FILES = ${CGAL_PACKAGE_DOC_DIR}/fig/ht-empty-disks.svg \ ${CGAL_PACKAGE_DOC_DIR}/fig/poincare-disk.svg \ ${CGAL_PACKAGE_DOC_DIR}/fig/header.png \ diff --git a/Hyperbolic_triangulation_2/doc/Hyperbolic_triangulation_2/Hyperbolic_triangulation_2.txt b/Hyperbolic_triangulation_2/doc/Hyperbolic_triangulation_2/Hyperbolic_triangulation_2.txt index e435a5dac2c..7121b66d62d 100644 --- a/Hyperbolic_triangulation_2/doc/Hyperbolic_triangulation_2/Hyperbolic_triangulation_2.txt +++ b/Hyperbolic_triangulation_2/doc/Hyperbolic_triangulation_2/Hyperbolic_triangulation_2.txt @@ -12,11 +12,11 @@ namespace CGAL { \author Mikhail Bogdanov, Iordan Iordanov, and Monique Teillaud
- +
-This package enables the computation of Delaunay triangulations of point sets in the Poincaré -disk model of the hyperbolic plane, as well as their dual objects. +This package enables the computation of Delaunay triangulations of +point sets in the Poincaré disk model of the hyperbolic plane. \section HT2_Poincare_model The Poincaré Disk Model of the Hyperbolic Plane The Poincaré disk model represents the hyperbolic plane @@ -26,13 +26,13 @@ H_\infty\f$ of points at infinity. In this model, a hyperbolic line is either an arc of circle perpendicular to the unit circle or, if it passes through the origin, -a diameter of the unit disk. A hyperbolic circle is a Euclidean circle -contained in the unit disk; however, its hyperbolic center and radius +a diameter of the unit disk. A hyperbolic circle is a Euclidean +circle contained in the unit disk; however, its hyperbolic center and radius are not the same as its Euclidean center and radius. \cgalFigureAnchor{Hyperbolic_triangulation_2Poincare_disk}
- +
\cgalFigureCaptionBegin{Hyperbolic_triangulation_2Poincare_disk} The Poincaré disk model for the hyperbolic plane. The figure shows @@ -58,31 +58,25 @@ are hyperbolic: P\f$) passing through its endpoints is contained in \f$\mathbb H^2\f$. -See \cgalFigureRef{Hyperbolic_triangulation_2Euclidean_vs_hyperbolic}. + +In the Euclidean Delaunay triangulation, there is a bijection between +non-hyperbolic faces and non-hyperbolic edges \cgalCite{cgal:bdt-hdcvd-14}. +For an example of a hyperbolic Delaunay triangulation and the underlying Euclidean +Delaunay triangulation, as well as for an example of a non-hyperbolic Delaunay +edge, see \cgalFigureRef{Hyperbolic_triangulation_2Euclidean_vs_hyperbolic}. \cgalFigureAnchor{Hyperbolic_triangulation_2Euclidean_vs_hyperbolic}
- + +
\cgalFigureCaptionBegin{Hyperbolic_triangulation_2Euclidean_vs_hyperbolic} -The Euclidean (green) and hyperbolic (black) Delaunay triangulations +Left: The Euclidean (red) and hyperbolic (black) Delaunay triangulations of a given set of points in the unit disk. Only the colored faces -are faces of the hyperbolic Delaunay triangulation. The hyperbolic and Euclidean geometric embeddings of a -Delaunay face that exists in both triangulations are different. -\cgalFigureCaptionEnd - - -In the Euclidean Delaunay triangulation, there is a bijection between -non-hyperbolic faces and non-hyperbolic edges -\cgalCite{cgal:bdt-hdcvd-14}. See -\cgalFigureRef{Hyperbolic_triangulation_2Empty_disks} - -\cgalFigureAnchor{Hyperbolic_triangulation_2Empty_disks} -
- -
-\cgalFigureCaptionBegin{Hyperbolic_triangulation_2Empty_disks} -The shaded face is non-hyperbolic. Its dashed edge is non-hyperbolic, +are faces of the hyperbolic Delaunay triangulation. The hyperbolic +and Euclidean geometric embeddings of a Delaunay face that exists +in both triangulations are different. +Right: The shaded face is non-hyperbolic. Its dashed edge is non-hyperbolic, as no empty circle through its endpoints is contained in \f$\mathbb H^2\f$. Its other two edges are hyperbolic. \cgalFigureCaptionEnd @@ -91,20 +85,20 @@ 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 Chapter -\ref Chapter_2D_Triangulations "2D Triangulation" of the CGAL manual to +`Delaunay_triangulation_2`. Consequently, 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. The class `Hyperbolic_Delaunay_triangulation_2` has two template parameters: