CGAL users discussion list

[Monique Teillaud <>]

Le 28/06/13 20:11, Michael Kalygin a écrit :
> Alessandro, ah, I see.
> To get a spherical triangle using triangulation's triangle you can build
> geodesic lines:
> http://en.wikipedia.org/wiki/Geodesic
>
> You can put one dummy point in the center of the sphere and then build
> 3D triangulation of your set of points (with this dummy point). I'm
> assuming that all your points belong to the sphere except the dummy
> point. This will give you a polyhedron.

indeed

> And then for each edge of the
> polyhedron you can build a geodesic line. Hope this will help you.

to do this you can just construct a Circular_arc_3 from its two endpoints
See CGAL chapter 3D Spherical Geometry Kernel

best

--
Monique Teillaud
http://www.inria.fr/sophia/members/Monique.Teillaud/
INRIA Sophia Antipolis - Méditerranée
Institut National de Recherche en Informatique et Automatique

> On Fri, Jun 28, 2013 at 8:33 PM, isscandar [via cgal-discuss] <[hidden
> email] </user/SendEmail.jtp?type=node&node=4657731&i=0>> wrote:
>
>         Michael Kalygin wrote
>         Hi, isscandar, I understand that CGAL has a huge manual. I
>         started from
>         these sections. If you read them, you will understand how to
>         work with
>         triangulation. Take a look at examples too.
>         
> http://www.cgal.org/Manual/3.2/doc_html/cgal_manual/Triangulation_3/Chapter_main.html
>         
> http://www.cgal.org/Manual/latest/doc_html/cgal_manual/TriangulationDS_3_ref/Concept_TriangulationDataStructure_3.html
>         
> http://www.cgal.org/Manual/latest/doc_html/cgal_manual/Triangulation_3_ref/Class_Triangulation_3.html
>
>     Hello Michael,
>     thank you very much for your help!
>     I have read some of the manual but I am still confused: quoting from
>     the manual /The class Triangulation_3 represents a 3-dimensional
>     tetrahedralization of points./ but I think I do not need
>     tetrahedrons in the space because I think I need spherical triangle
>     (http://mathworld.wolfram.com/SphericalTriangle.html), it is not
>     clear to me whether I can get the spherical triangle from the
>     tetrahedrons. What am I missing?
>
>     Alessandro
>
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> --
> Best regards,
> Michael Kalygin.
>
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