songsenand
/
cgal
mirror of https://github.com/CGAL/cgal
1
0
Fork 0
Code Issues Packages Projects Releases Wiki Activity

added example of non-simplicial decompisition of the Bolza surface

This commit is contained in:
Iordan Iordanov 2018-09-04 11:52:55 +02:00
parent 958f1190ac
commit 10f7ad2c54
2 changed files with 15 additions and 1 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

3
Periodic_4_hyperbolic_triangulation_2/doc/Periodic_4_hyperbolic_triangulation_2/Doxyfile.in
View File

@ -12,7 +12,8 @@ HTML_EXTRA_FILES = ${CGAL_PACKAGE_DOC_DIR}/fig/octagon_identification.svg \
${CGAL_PACKAGE_DOC_DIR}/fig/dt-construction.svg \ ${CGAL_PACKAGE_DOC_DIR}/fig/dt-construction.svg \
${CGAL_PACKAGE_DOC_DIR}/fig/periodic_face.svg \ ${CGAL_PACKAGE_DOC_DIR}/fig/periodic_face.svg \
${CGAL_PACKAGE_DOC_DIR}/fig/ds_cgal.svg \ ${CGAL_PACKAGE_DOC_DIR}/fig/ds_cgal.svg \
${CGAL_PACKAGE_DOC_DIR}/fig/dummy-points.png ${CGAL_PACKAGE_DOC_DIR}/fig/dummy-points.png \
${CGAL_PACKAGE_DOC_DIR}/fig/non-triangulation.svg \
HTML_EXTRA_STYLESHEET = ${CGAL_PACKAGE_DOC_DIR}/css/customstyle.css HTML_EXTRA_STYLESHEET = ${CGAL_PACKAGE_DOC_DIR}/css/customstyle.css

13
Periodic_4_hyperbolic_triangulation_2/doc/Periodic_4_hyperbolic_triangulation_2/Periodic_4_hyperbolic_triangulation_2.txt
View File

@ -237,6 +237,19 @@ Some point sets do not admit a triangulation of \f$\mathcal M\f$.
For instance, a single point does not define a triangulation of \f$\mathcal M\f$, as the result For instance, a single point does not define a triangulation of \f$\mathcal M\f$, as the result
would not be a simplicial complex. would not be a simplicial complex.
\cgalModifEnd \cgalModifEnd
\cgalFigureAnchor{P4HNonSimplicialExample}
<center>
<img src="non-triangulation.svg" style="max-width:45%; width=45%; display: inline-block;"/>
</center>
\cgalFigureCaptionBegin{P4HNonSimplicialExample}
Example of a non-simplicial decomposition of the Bolza surface. Note that with the three
points in the central octagon, we obtain a decomposition that is <b>not</b> a triangulation,
since it is non-simplicial. On the figure a few cycles of length 2 are shown in color. Such
cycles are double edges in the triangulation. Note also the pink edge between the two blue
vertices: it corresponds to a loop on the surface.
\cgalFigureCaptionEnd
For this reason, we initialize a triangulation of \f$\mathcal M\f$ with a predetermined set of For this reason, we initialize a triangulation of \f$\mathcal M\f$ with a predetermined set of
14 points, called <i>dummy points</i>, whose triangulation in \f$\mathcal M\f$ is a simplicial 14 points, called <i>dummy points</i>, whose triangulation in \f$\mathcal M\f$ is a simplicial
complex and has the empty circle property. The set of dummy points has been proposed in complex and has the empty circle property. The set of dummy points has been proposed in