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Modifications to user manual to account for Mael's lates review; new figures included

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Iordan Iordanov 2018-12-12 15:03:44 +01:00
parent 54353573e5
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2
Hyperbolic_triangulation_2/doc/Hyperbolic_triangulation_2/Doxyfile.in
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@ -6,6 +6,8 @@ EXAMPLE_PATH = ${CGAL_PACKAGE_DIR}/examples
PROJECT_NAME = "CGAL ${CGAL_DOC_VERSION} - 2D Hyperbolic Delaunay Triangulations" 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 \ 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/poincare-disk.svg \
${CGAL_PACKAGE_DOC_DIR}/fig/header.png \ ${CGAL_PACKAGE_DOC_DIR}/fig/header.png \

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Hyperbolic_triangulation_2/doc/Hyperbolic_triangulation_2/Hyperbolic_triangulation_2.txt
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@ -12,11 +12,11 @@ namespace CGAL {
\author Mikhail Bogdanov, Iordan Iordanov, and Monique Teillaud \author Mikhail Bogdanov, Iordan Iordanov, and Monique Teillaud
<center> <center>
<img src="header.png" style="max-width:60%; width=60%;"/> <img src="header.png" style="max-width:50%; width=50%;"/>
</center> </center>
This package enables the computation of Delaunay triangulations of point sets in the Poincar&eacute; This package enables the computation of Delaunay triangulations of
disk model of the hyperbolic plane, as well as their dual objects. point sets in the Poincar&eacute; disk model of the hyperbolic plane.
\section HT2_Poincare_model The Poincar&eacute; Disk Model of the Hyperbolic Plane \section HT2_Poincare_model The Poincar&eacute; Disk Model of the Hyperbolic Plane
The Poincar&eacute; disk model represents the hyperbolic plane The Poincar&eacute; 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 In this model, a hyperbolic line is either an arc of circle
perpendicular to the unit circle or, if it passes through the origin, 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 a diameter of the unit disk. A hyperbolic circle is a Euclidean
contained in the unit disk; however, its hyperbolic center and radius circle contained in the unit disk; however, its hyperbolic center and radius
are not the same as its Euclidean center and radius. are not the same as its Euclidean center and radius.
\cgalFigureAnchor{Hyperbolic_triangulation_2Poincare_disk} \cgalFigureAnchor{Hyperbolic_triangulation_2Poincare_disk}
<center> <center>
<img src="poincare-disk.svg" style="max-width:35%; width=35%;"/> <img src="poincare-disk.svg" style="max-width:27%; width=27%;"/>
</center> </center>
\cgalFigureCaptionBegin{Hyperbolic_triangulation_2Poincare_disk} \cgalFigureCaptionBegin{Hyperbolic_triangulation_2Poincare_disk}
The Poincar&eacute; disk model for the hyperbolic plane. The figure shows The Poincar&eacute; disk model for the hyperbolic plane. The figure shows
@ -58,31 +58,25 @@ are <i>hyperbolic</i>:
P\f$) passing through its endpoints is contained in \f$\mathbb P\f$) passing through its endpoints is contained in \f$\mathbb
H^2\f$. H^2\f$.
</ul> </ul>
See \cgalFigureRef{Hyperbolic_triangulation_2Euclidean_vs_hyperbolic}.
In the Euclidean Delaunay triangulation, there is a bijection between
non-hyperbolic faces and non-hyperbolic edges&nbsp;\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&nbsp;\cgalFigureRef{Hyperbolic_triangulation_2Euclidean_vs_hyperbolic}.
\cgalFigureAnchor{Hyperbolic_triangulation_2Euclidean_vs_hyperbolic} \cgalFigureAnchor{Hyperbolic_triangulation_2Euclidean_vs_hyperbolic}
<center> <center>
<img src="hyperbolic-vs-euclidean.svg" style="max-width:35%; width=35%;"/> <img src="hyperbolic-vs-euclidean.svg" style="max-width:27%; width=27%; display: inline-block; text-align:right;"/>
<img src="ht-empty-disks.svg" style="max-width:30%; width=30%; display: inline-block; text-align:left;"/>
</center> </center>
\cgalFigureCaptionBegin{Hyperbolic_triangulation_2Euclidean_vs_hyperbolic} \cgalFigureCaptionBegin{Hyperbolic_triangulation_2Euclidean_vs_hyperbolic}
The Euclidean (green) and hyperbolic (black) Delaunay triangulations <b>Left:</b> The Euclidean (red) and hyperbolic (black) Delaunay triangulations
of a given set of points in the unit disk. Only the colored faces 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 are faces of the hyperbolic Delaunay triangulation. The hyperbolic
Delaunay face that exists in both triangulations are different. and Euclidean geometric embeddings of a Delaunay face that exists
\cgalFigureCaptionEnd in both triangulations are different.
<b>Right:</b> The shaded face is non-hyperbolic. Its dashed edge is non-hyperbolic,
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}
<center>
<img src="ht-empty-disks.svg" style="max-width:35%; width=35%;"/>
</center>
\cgalFigureCaptionBegin{Hyperbolic_triangulation_2Empty_disks}
The shaded face is non-hyperbolic. Its dashed edge is non-hyperbolic,
as no empty circle through its endpoints is contained in as no empty circle through its endpoints is contained in
\f$\mathbb H^2\f$. Its other two edges are hyperbolic. \f$\mathbb H^2\f$. Its other two edges are hyperbolic.
\cgalFigureCaptionEnd \cgalFigureCaptionEnd
@ -91,20 +85,20 @@ as no empty circle through its endpoints is contained in
\section HT2_Software_design Software Design \section HT2_Software_design Software Design
From what was said above, it is natural that the class From what was said above, it is natural that the class
`Hyperbolic_Delaunay_triangulation_2` privately inherits from the class `Hyperbolic_Delaunay_triangulation_2` privately inherits from the class
`Delaunay_triangulation_2`. So, users are encouraged to look at Chapter `Delaunay_triangulation_2`. Consequently, users are encouraged to look at Chapter
\ref Chapter_2D_Triangulations "2D Triangulation" of the CGAL manual to \ref Chapter_2D_Triangulations "2D Triangulation" of the %CGAL manual to
know more in particular about the representation of triangulations in know more in particular about the representation of triangulations in
CGAL and the flexibility of the design. CGAL and the flexibility of the design.
The class `Hyperbolic_Delaunay_triangulation_2` has two template The class `Hyperbolic_Delaunay_triangulation_2` has two template
parameters: parameters:
<ul> <ul>
<li> A geometric traits class `Gt`, which provides geometric <li> A <b>geometric traits</b> class `Gt`, which provides geometric
primitives. The requirements on this first template parameter primitives. The requirements on this first template parameter
are described by the concept are described by the concept
`HyperbolicDelaunayTriangulationTraits_2`, which refines `HyperbolicDelaunayTriangulationTraits_2`, which refines
`DelaunayTriangulationTraits_2`. `DelaunayTriangulationTraits_2`.
<li> A triangulation data structure parameter, for which the <li> A <b>triangulation data structure</b> parameter, for which the
requirements are described by the concept requirements are described by the concept
`TriangulationDataStructure_2`. The default for this second template parameter `TriangulationDataStructure_2`. The default for this second template parameter
is `Triangulation_data_structure_2< Triangulation_vertex_base_2<Gt>, Hyperbolic_triangulation_face_base_2<Gt> >`. is `Triangulation_data_structure_2< Triangulation_vertex_base_2<Gt>, Hyperbolic_triangulation_face_base_2<Gt> >`.
@ -141,9 +135,9 @@ parameters against the insertion time in a Euclidean \cgal triangulation.
We generate 1 million random points, uniformly distributed in the unit disk with respect We generate 1 million random points, uniformly distributed in the unit disk with respect
to the Euclidean metric. We insert the same set of points in three triangulations: to the Euclidean metric. We insert the same set of points in three triangulations:
<ul> <ul>
<li> a hyperbolic Delaunay triangulation with `CGAL::Hyperbolic_Delaunay_triangulation_CK_traits_2<>` as traits class; <li> a hyperbolic Delaunay triangulation with `CGAL::Hyperbolic_Delaunay_triangulation_traits_2` (%CORE traits) as traits class;
<li> a hyperbolic Delaunay triangulation with `CGAL::Hyperbolic_Delaunay_triangulation_traits_2<>` as traits class; <li> a hyperbolic Delaunay triangulation with `CGAL::Hyperbolic_Delaunay_triangulation_CK_traits_2` (CK traits) as traits class;
<li> a Euclidean Delaunay triangulation with `CGAL::Exact_predicates_inexact_constructions_kernel` as traits class. <li> a Euclidean Delaunay triangulation with `CGAL::Exact_predicates_inexact_constructions_kernel` (EPICK) as traits class.
</ul> </ul>
We create two instances of each type of triangulation. In one instance we insert the points one by one, which causes We create two instances of each type of triangulation. In one instance we insert the points one by one, which causes
non-hyperbolic faces to be filtered out at each insertion. In the other instance we insert the points via iterator non-hyperbolic faces to be filtered out at each insertion. In the other instance we insert the points via iterator
@ -161,9 +155,9 @@ executed on two machines:
<caption>Table 1: Comparison of insertion times of 1 million random points</caption> <caption>Table 1: Comparison of insertion times of 1 million random points</caption>
<tr><th> %Triangulation type <th colspan="2"> Machine 1 <th colspan="2"> Machine 2 <tr><th> %Triangulation type <th colspan="2"> Machine 1 <th colspan="2"> Machine 2
<tr><td> <td> Sequential insertion <td> %Iterator insertion <td> Sequential insertion <td> %Iterator insertion <tr><td> <td> Sequential insertion <td> %Iterator insertion <td> Sequential insertion <td> %Iterator insertion
<tr><td> Hyperbolic (General traits) <td> 955 sec. <td> 23 sec. <td> 884 sec. <td> 20 sec. <tr><td> Hyperbolic (%CORE traits) <td> 955 sec. <td> 23 sec. <td> 884 sec. <td> 20 sec.
<tr><td> Hyperbolic (CK traits) <td> 330 sec. <td> 1 sec. <td> 289 sec. <td> 1 sec. <tr><td> Hyperbolic (CK traits) <td> 330 sec. <td> 1 sec. <td> 289 sec. <td> 1 sec.
<tr><td> Euclidean (%Cartesian traits) <td> 131 sec. <td> < 1 sec. <td> 114 sec. <td> < 1 sec. <tr><td> Euclidean (EPICK) <td> 131 sec. <td> < 1 sec. <td> 114 sec. <td> < 1 sec.
</table> </table>
</center> </center>

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Hyperbolic_triangulation_2/doc/Hyperbolic_triangulation_2/css/customstyle.css Normal file
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@ -0,0 +1,4 @@
.image {
display: inline;
}