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Thread Subject:
about bounded region using voronoi command

Subject: about bounded region using voronoi command

From: gtechnical@gmail.com

Date: 23 Jan, 2009 17:34:40

Message: 1 of 7

I am a newbie to this algorithm, I am wondering anyone with experience
could help me out this, I am trying on this subject for several days
and made no progress.
I have several points, and a bounded region (rectangular or triangle)
with known vertexes, how could I using voronoi algorithm to generate
the voronoi cells in this region, and also derive the vertexes for
each cell in this region, so the vertexes of the region could be the
vertexes for the cell too.
I shall appreciate it very much, if anyone could offer me a suggestion
on this matter.

Subject: about bounded region using voronoi command

From: gtechnical@gmail.com

Date: 23 Jan, 2009 17:46:02

Message: 2 of 7

For example, given region determined by
r0=[x0 y0]; r1=[x1 y1]; r2=[x2 y2]; r3=[x3 y3]; r4=[x4 y4];
given points:
a1, a2, a3, a4
how to generate voronoi cell for each point in the given region, and
know each cell's vertexes and area as well.

Subject: about bounded region using voronoi command

From: Damian Sheehy

Date: 23 Jan, 2009 18:50:06

Message: 3 of 7

The functions in MATLAB (voronoi/voronoin) are restricted to the computation
of the voronoi diagram of point sites. You are trying to construct the
voronoi diagram of points and straight line segments; straight line segments
are not supported by the MATLAB functions. I have filed an enhancement
request to capture this requirement.

Tackling this problem will require a good understanding of computational
geometry; you may wish to consider searching the web for alternative
programs you could possibly use.

Regards,

Damian


<gtechnical@gmail.com> wrote in message
news:91bcc4e0-c12a-48d7-8086-a656359ecd7c@r37g2000prr.googlegroups.com...
> For example, given region determined by
> r0=[x0 y0]; r1=[x1 y1]; r2=[x2 y2]; r3=[x3 y3]; r4=[x4 y4];
> given points:
> a1, a2, a3, a4
> how to generate voronoi cell for each point in the given region, and
> know each cell's vertexes and area as well.

Subject: about bounded region using voronoi command

From: gtechnical@gmail.com

Date: 24 Jan, 2009 22:04:10

Message: 4 of 7

On Jan 23, 1:50=A0pm, "Damian Sheehy" <Damian.She...@mathworks.com>
wrote:
> The functions in MATLAB (voronoi/voronoin) are restricted to the computat=
ion
> of thevoronoidiagram of point sites. You are trying to construct thevoron=
oidiagram of points and straight line segments; straight line segments
> are not supported by the MATLAB functions. I have filed an enhancement
> request to capture this requirement.
>
> Tackling this problem will require a good understanding of computational
> geometry; you may wish to consider searching the web for alternative
> programs you could possibly use.
>
> Regards,
>
> Damian
>
> <gtechni...@gmail.com> wrote in message
>
> news:91bcc4e0-c12a-48d7-8086-a656359ecd7c@r37g2000prr.googlegroups.com...
>
>
>
> > For example, given region determined by
> > r0=3D[x0 y0]; r1=3D[x1 y1]; r2=3D[x2 y2]; r3=3D[x3 y3]; r4=3D[x4 y4];
> > given points:
> > a1, a2, a3, a4
> > how to generatevoronoicell for each point in the given region, and
> > know each cell's vertexes and area as well.- Hide quoted text -
>
> - Show quoted text -

Thanks! Damian

Subject: Voronoi diagram of points and straight line segments

From: Rikard

Date: 4 Jan, 2011 14:53:05

Message: 5 of 7

"Damian Sheehy" <Damian.Sheehy@mathworks.com> wrote in message <gld3h0$eps$1@fred.mathworks.com>...
> The functions in MATLAB (voronoi/voronoin) are restricted to the computation
> of the voronoi diagram of point sites. You are trying to construct the
> voronoi diagram of points and straight line segments; straight line segments
> are not supported by the MATLAB functions. I have filed an enhancement
> request to capture this requirement.
>
> Tackling this problem will require a good understanding of computational
> geometry; you may wish to consider searching the web for alternative
> programs you could possibly use.
>
> Regards,
>
> Damian

I have a similar problem where I need to calculate Voronoi diagram of points and straight line segments.
Anybody know of Matlab software that does this?

Regards
Rikard

Subject: about bounded region using voronoi command

From: Meng Sang Ong

Date: 11 Feb, 2011 09:05:08

Message: 6 of 7

These may be of some help to your problem.

http://www.mathworks.com/matlabcentral/fileexchange/30353-arbitrary-square-bounded-voronoi-diagram
http://www.mathworks.com/matlabcentral/fileexchange/30345-circle-bounded-voronoi-diagram

Comments/suggestions are welcomed.

regards,
MS


gtechnical@gmail.com wrote in message <7cf32f09-081d-4175-baa7-7cecf285cc42@n33g2000pri.googlegroups.com>...
> I am a newbie to this algorithm, I am wondering anyone with experience
> could help me out this, I am trying on this subject for several days
> and made no progress.
> I have several points, and a bounded region (rectangular or triangle)
> with known vertexes, how could I using voronoi algorithm to generate
> the voronoi cells in this region, and also derive the vertexes for
> each cell in this region, so the vertexes of the region could be the
> vertexes for the cell too.
> I shall appreciate it very much, if anyone could offer me a suggestion
> on this matter.

Subject: about bounded region using voronoi command

From: Richard Garner

Date: 2 Feb, 2012 20:18:14

Message: 7 of 7

gtechnical@gmail.com wrote in message <7cf32f09-081d-4175-baa7-7cecf285cc42@n33g2000pri.googlegroups.com>...
> I am a newbie to this algorithm, I am wondering anyone with experience
> could help me out this, I am trying on this subject for several days
> and made no progress.
> I have several points, and a bounded region (rectangular or triangle)
> with known vertexes, how could I using voronoi algorithm to generate
> the voronoi cells in this region, and also derive the vertexes for
> each cell in this region, so the vertexes of the region could be the
> vertexes for the cell too.
> I shall appreciate it very much, if anyone could offer me a suggestion
> on this matter.

There is a very nice library of Matlab functions devoted to computational geometry and related stuff (the so-called MPT (multi parametric toolbox). One can download, free of charge, here: http://control.ee.ethz.ch/research/software.en.html (click on "MPT toolbox" and then "downloads" tab at the top). One of the functions in the library is called mpt_voronoi, which takes options, one of which can be a boundary for the desired voronoi diagram. But be aware that you should probably get familiar with the concept of polytopes and H and V representations and so on, if you are not already familar. They have some nice tutorials and demos which discusses it fairly well. You can learn about it in a relatively short amount of time (i.e., minutes to hours, not days to weeks). Note also, the bounded voronoi diagram which the function determines will be bounded by a convex polygon (a polytope).
 If you think you are specifying a non-convex boundary, then you will find that it uses the convex hull of that thing you specify as the boundary. It seems like bounded voronoi diagrams with arbitrary boundaries (nonconvex, possibly with holes) is a very difficult problem. Not alot of stuff out there about that.

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