voronoi polygons

[Curtis Rueden]

Hi Ricardo,

You're right; I was mistaken about the criterion of triangle centers.
It seems it is not so straightforward to convert from Delaunay
triangulation to Voronoi diagram. Looking around a bit, I did find a
piece of CGAL that claims to convert 2D triangulations to the Voronoi
dual:

http://www.cgal.org/Manual/3.2/doc_html/cgal_manual/packages.html#Part:VoronoiDiagrams

You may also be able to glean something from the source code of the
applet you linked.

There is even some C code on Wikipedia that generates a Voronoi
diagram of some random points in 2D:
http://en.wikipedia.org/wiki/Image:Coloured_Voronoi_2D.png

-Curtis

On 1/31/07, Ricardo Mantilla <ricardo at cires.colorado.edu> wrote:
> Curtis,
>
> In my previous email I meant
>
> ... your rule of "voronoi polygons vertex = centroid of triangles" ...
>
> rather than
>
> ... your rule of "voronoi polygons edges = centroid of triangles" ...
>
> I hope this doesn't cause confusions.
>
> Ricardo
>
> Curtis Rueden wrote:
> > Hi Ricardo,
> >
> > VisAD does not contain any code to construct Voronoi polygons, but the
> > Delaunay logic includes everything you need to easily create them
> > yourself. Each Voronoi polygon is computed by finding the center point
> > of each triangle/tetrahedron (average of Tri vertex samples), and
> > connecting those center points across the triangle edges/faces (using
> > the Walk array).
> >
> > Alternately, you could feed the results of a triangulation in VisAD to
> > some external software capable of computing Voronoi diagrams from an
> > input triangulation.
> >
> > -Curtis
> >
> > On 1/31/07, Ricardo Mantilla <ricardo at cires.colorado.edu> wrote:
> >> Hi,
> >>
> >> Has anyone developed methods to obtain the Voronoi polygons from a
> >> Delaunay triangulation?
> >>
> >> I think this question was asked some time ago and at the time there was
> >> no such class implemented.
> >>
> >> Thanks,
> >>    Ricardo
> >>
> >> --
> >> -------------------------------------------------------------
> >> Ricardo Mantilla
> >> Posdoctoral Research Associate
> >>
> >> Department of Earth and Environmental Science
> >> New Mexico Institute of Mining and Technology
> >> 801 Leroy Pl. MSEC 254
> >> Socorro, NM 87801
> >>
> >> Phone: (505) 835-5068
> >> Office: MSEC 254
> >> http://cires.colorado.edu/~ricardo/
> >> -------------------------------------------------------------
> >>
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> >>
> >>
>
> --
> -------------------------------------------------------------
> Ricardo Mantilla
> Posdoctoral Research Associate
>
> Department of Earth and Environmental Science
> New Mexico Institute of Mining and Technology
> 801 Leroy Pl. MSEC 254
> Socorro, NM 87801
>
> Phone: (505) 835-5068
> Office: MSEC 254
> http://cires.colorado.edu/~ricardo/
> -------------------------------------------------------------
>
>

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