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2D Voronoi diagram adaptor


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  • From: Vicente Helano <>
  • To:
  • Subject: 2D Voronoi diagram adaptor
  • Date: Mon, 23 Jul 2007 06:17:29 -0800

Dears,

When we construct a Delaunay triangulation with three distinct vertices we get
the following graph:

|
|
o
/ \
/ \
/ \
o-------o
/ \
/ \

There, we have 4 vertices (3 finite plus 1 infinite), 6 edges and 4 faces.
I thought that its dual would have 4 vertices, 6 edges and 3 faces,
as illustrated in the following figure.

e'
t----------------,t
\`\ ,/ /
\ `\ e2 e1 ,/ /
\ `\ ,/ /
\ `\ / /
e''' \ o /e''
\ |e3 /
\ | /
\ | /
\|/
t

However, when I instantiate a 2D Voronoi diagram with an identity
adaption policy, the resulting dual graph has only 1 vertex, 3 edges (half the
halfedges) and 3 faces.
How could I access the "target" vertices ('t' vertices) of these 3 edges (e1,
e2, e3)?
And do the edges e', e'', e''' exist? How could I access them?

Thanks in advance,
Vicente Helano.

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  • 2D Voronoi diagram adaptor, Vicente Helano, 07/23/2007

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