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Thread Subject:
delaunay from voronoi

Subject: delaunay from voronoi

From: Dave Brackett

Date: 11 Feb, 2011 19:38:04

Message: 1 of 5

Hi,

I know that delaunay and voronoi tesselations are duals, so if i have a voronoi how can I convert this to a delaunay? I have seen a lot of posts about how to generate a voronoi from a delaunay but not the other way around.

Can someone advise me how I could do this please? I guess the method would be the same in 2d and 3d.

Thanks very much

Subject: delaunay from voronoi

From: Bruno Luong

Date: 11 Feb, 2011 19:59:05

Message: 2 of 5

"Dave Brackett" wrote in message <ij436r$g0e$1@fred.mathworks.com>...
> Hi,
>
> I know that delaunay and voronoi tesselations are duals, so if i have a voronoi how can I convert this to a delaunay? I have seen a lot of posts about how to generate a voronoi from a delaunay but not the other way around.
>
> Can someone advise me how I could do this please? I guess the method would be the same in 2d and 3d.

For every cell there corresponds one seed. Link two seeds if their cells share a common edge, then you'll get the delaunay triangulation.

Bruno

Subject: delaunay from voronoi

From: Dave Brackett

Date: 14 Feb, 2011 10:56:03

Message: 3 of 5

"Bruno Luong" <b.luong@fogale.findmycountry> wrote in message <ij44e9$5u6$1@fred.mathworks.com>...
> "Dave Brackett" wrote in message <ij436r$g0e$1@fred.mathworks.com>...
> > Hi,
> >
> > I know that delaunay and voronoi tesselations are duals, so if i have a voronoi how can I convert this to a delaunay? I have seen a lot of posts about how to generate a voronoi from a delaunay but not the other way around.
> >
> > Can someone advise me how I could do this please? I guess the method would be the same in 2d and 3d.
>
> For every cell there corresponds one seed. Link two seeds if their cells share a common edge, then you'll get the delaunay triangulation.
>
> Bruno

thanks for your reply. is that the same for both 2d and 3d voronoi?

Subject: delaunay from voronoi

From: Bruno Luong

Date: 14 Feb, 2011 11:08:03

Message: 4 of 5

>
> thanks for your reply. is that the same for both 2d and 3d voronoi?

Yes, to be precise, in 3D

For every cell there corresponds one seed. Link two seeds if their cells share a common *face*, then you'll get the delaunay *tetrahedron*.

Bruno

Subject: delaunay from voronoi

From: Dave Brackett

Date: 15 Feb, 2011 10:27:04

Message: 5 of 5

"Bruno Luong" <b.luong@fogale.findmycountry> wrote in message <ijb2ej$ht1$1@fred.mathworks.com>...
> >
> > thanks for your reply. is that the same for both 2d and 3d voronoi?
>
> Yes, to be precise, in 3D
>
> For every cell there corresponds one seed. Link two seeds if their cells share a common *face*, then you'll get the delaunay *tetrahedron*.
>
> Bruno

ah yeah thanks.

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