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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
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3 changed files with 34 additions and 34 deletions
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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"
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 \

62
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
<center>
<img src="header.png" style="max-width:60%; width=60%;"/>
<img src="header.png" style="max-width:50%; width=50%;"/>
</center>
This package enables the computation of Delaunay triangulations of point sets in the Poincar&eacute;
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 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
@ -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}
<center>
<img src="poincare-disk.svg" style="max-width:35%; width=35%;"/>
<img src="poincare-disk.svg" style="max-width:27%; width=27%;"/>
</center>
\cgalFigureCaptionBegin{Hyperbolic_triangulation_2Poincare_disk}
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
H^2\f$.
</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}
<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>
\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
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}
<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,
are faces of the hyperbolic Delaunay triangulation. The hyperbolic
and Euclidean geometric embeddings of a Delaunay face that exists
in both triangulations are different.
<b>Right:</b> 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:
<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
are described by the concept
`HyperbolicDelaunayTriangulationTraits_2`, which refines
`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
`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> >`.
@ -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
to the Euclidean metric. We insert the same set of points in three triangulations:
<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<>` as traits class;
<li> a Euclidean Delaunay triangulation with `CGAL::Exact_predicates_inexact_constructions_kernel` 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_CK_traits_2` (CK traits) as traits class;
<li> a Euclidean Delaunay triangulation with `CGAL::Exact_predicates_inexact_constructions_kernel` (EPICK) as traits class.
</ul>
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
@ -161,9 +155,9 @@ executed on two machines:
<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><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> 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>
</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;
}