CGAL users discussion list

[Monique Teillaud <>]

The Voronoi diagram is the dual of the Delaunay triangulation.
For instance, the dual of a Delaunay tetrahedron is a Voronoi vertex.

Szymon Stoma wrote:
> maybe my question is trivial, but.. from what i understand Delaunay 
> triangulations work on triangles/tetrahedron. My question is about 
> compartments described by polygons/polyhedron. can it be easly performed 
> using the CGAL? thanks and sorry if i am asking about sth. obvious. 
>
> 2009/2/19 Monique Teillaud < 
> <mailto:>>
>
>     Hi Szymon,
>
>     CGAL provides computation of Delaunay triangulations in both 2D and 3D.
>
>     you can have a look at the package overview
>     
> http://www.cgal.org/Manual/3.4/doc_html/cgal_manual/packages.html#part_VIII
>
>     The Delaunay triangulation classes offer some dual functions to
>     compute features of the Voronoi diagram. This is described in the
>     manual of the corresponding classes.
>
>     Best regards,
>            Monique Teillaud
>
>
>     Szymon Stoma wrote:
>
>         hello,
>
>         i have a general question. i would like to discretize the
>         continous, convex subset S of r2/r3 into smaller compartments
>         (such as their intersection is empty, and sum is equal to S).
>         since i would like to have some influence on the comparments, i
>         am preparing the editor allowing for manual manipulation of the
>         compartments. to make the editing easier (especially in 3D) i
>         would like to use a cloud of points representing implicitely the
>         compartments. to get the exact geometry of each compartment i
>         would like to use voronoi concept. i hope i am clear at this point.
>
>         1. will i find routines allowing me to calculate the edges (and
>         their geometry) of each compartment in 2D in CGAL library?
>         2. will i find routines allowing me to calculate the faces (and
>         their geometry) of each compartment in 3D in CGAL library?
>         3. what other library might be good for this task (it should be
>         something i could use from C/C++/Python).
>
>         thank you very much for any answer and suggestion.
>
>         cheers,
>         szymon stoma.
>
>
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