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Re: [cgal-discuss] triangulate points in a 3d plane


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  • From: Manuel Caroli <>
  • To:
  • Subject: Re: [cgal-discuss] triangulate points in a 3d plane
  • Date: Thu, 02 Oct 2008 10:38:26 +0200

Hi Shi Yan and Jens,

just to clean up a bit:
There is the Triangulation_2 package that computes triangulations in 2d and so needs 2d points.
Then there is the Triangulation_3 package that normally computes triangulations in 3d (also called tetrahedralization). However, if you give the Triangulation_3 a set of points that all lie in one plane then this is considered a degenerate case and a two dimensional triangulation is computed. You can find in the manual how to extract it from the Triangulation_data_structure_3 then.

Note that it might be slower to compute a 2d Triangulation with the Triangulation_3 package than converting the points into a 2d coordiate system and use Triangulation_2.

Regarding the infinite vertex, there is always exactly one and it is adjacent to exactly all convex hull vertices.

best

Manuel


Shi Yan wrote:
really? i thought the 3D triangulation is for tetrahedrons, not for
triangles. i need definitely check the manual again.

and i'm sorry, i don't quite understand what the infinite points are.

thank you very much.

On Thu, Oct 2, 2008 at 1:12 AM, Jens K. Becker
<>
wrote:
Hi Shi,

I am not an expert with CGAL (yet), but I had the same problem. There are
plenty
of triangulation methods in 3D (all of them work in 3d if I am not
mistaken).
The resulting triangulation will be in 3D because infinite points will be
added
to your point set. If you just check for these points
(T.is_infinite(vertex))
and eliminating them should leave you with a triangulation in the plane.

Greetings,

Jens

--
Dr. J.K. Becker
University of Tuebingen - Institute for Geoscience
Sigwartst. 10 - 72076 Tuebingen (Germany)
Tel.: ++49 7071 29 73139 Fax: +49 7071 5059
web: http://www.jkbecker.de


Quoting Shi Yan
<>:

hello guys,

i need to do triangulation inside a 3d triangle. the triangulation
method provided by CGAL seems to be for 2D. so instead of me
converting the 3D points into a 2D coordinate system, is there any
convenient CGAL function that can do this for me?

thank you very much.
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