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## Arbitrary Square Bounded Voronoi Diagram

version 1.0 (8.7 KB) by

Compute individual Voronoi cell area of 2D point sets bounded in an arbitrary square

Updated

This function compute the individual Voronoi cell area of point sets bounded in an arbitrary square.

Inputs:
x : M x 1 array of x-coordinates
y : M x 1 array of y-coordinates
toggleplot : 1 to turn on figures, 0 to turn off figures;
[x1,x2,y1,y2] : 1 x 4 array of square edges

Outputs:
CellArea : M x 1 array of Voronoi cell area bounded in an arbitrary square

Usage:
CellArea=SquareBV(x,y,toggleplot,[x1,x2,y1,y2])
CellArea=SquareBV(x,y,toggleplot)

Rik van der Vlist

Ignacio Bordeu

### Ignacio Bordeu (view profile)

Sorry, wrong file.

Ignacio Bordeu

### Ignacio Bordeu (view profile)

Hey guys, I have found an issue when considering certain sets of points. When trying the following example:

xc = [25.0362, 619.2890, 137.8061, 387.3650, 2.7294, 85.5450]

yc = [643.6328, 8.6653, 621.3243, 55.4894, 545.6431, 193.8842]

r = 500;
VoronoiLimit(xc,yc,'bs_ext',[0,r;r,r;r,0;0,0],'figure','on');

You can see that the limits are not drawn correctly, this issue disappears for smaller values of r.. any ideas on how to fix it?

Juan Nogues

### Juan Nogues (view profile)

I am getting the following error:
Error using qhullmx
QH6019 qhull input error: can not scale last coordinate. Input is cocircular
or cospherical. Use option 'Qz' to add a point at infinity.

My command line looks something like this

>> x1=-10;
>> x2=10;
>> y1=-10;
>> y2=10;
>> x=[-5 5 5 -5]';
>> y=[-5 -5 5 5]';
>> CellArea=SquareBV(x',y',1);

Any help on this ?

Charles

### Charles (view profile)

I only used it for a very simple rectangle bounding an area with four "precipitation gage" points, but it worked well. The figures come out looking odd and confusing, but the calculation of areas, which is the basic point, was correct. Thanks!

Tom

### Tom (view profile)

By a "partial solution," what did Simon mean (on 15 Feb 2012)?

After I edit SquareBV line 66 to add the qhull option QJ, SquareBV now runs, but reports an (incorrect) area of zero for each of four Voronoi cells.

Any ideas on how to fix this?

Dikun

### Dikun (view profile)

I think I have found in some cases this code doesn't work properly.

Try examples:

SquareBV([56.01 188.01 47.01],[6 9 4],0,[-450 450 -750 750])

or

SquareBV([56.01 188.01 47.01],[6 9 4],0,[-450 450 0 750])

PS: toggleplot=1 doesn't plot sensible figures.

Simon Arame

### Simon Arame (view profile)

I found a partial solution to my enquiry, voronoin has to be called with the option 'QJ'

Simon Arame

### Simon Arame (view profile)

Greetings,

This file is great, however there seem to be a problem with colinear points. I got an error message while testing for :
x = [0.25; 0.75; 0.25; 0.75];
y = [0.25; 0.25; 0.75; 0.75];
SquareBV(x,y,0,[0,1,0,1])

Meng Sang Ong

### Meng Sang Ong (view profile)

Hi Oscar,
To answer your question, the function aims to compute the individual Voronoi cell area of point sets BOUNDED in an arbitrary square.

However, from your inputs, you have a x-input (5.0000,5.0000) which lies outside of your square boundary [0 1 0 1], hence will result in incorrect cell area computation.

You can either opt to have all your x and y points inside the square [0 1 0 1] or introduce a larger boundary, e.g. [0 5 0 5], so that it encapsulates your third point (5.0000, 5.0000).

Hope it helps.

Oscar

### Oscar (view profile)

It seems this function has some bugs in it. With input
x = 0.5000 y= 0.3333
0.5010 0.6666
5.0000 5.0000

and corners = [0 1 0 1] it gives me [4997 0 0]. This, clearly is not correct, as the two first points should have roughly half each of the specified area. Or perhaps I don't understand the interface correctly. Also, the documentation is rather sparse for this code. Thanks, though for a great effort. This is the only code I could find that attempts this.

Egor Bogatinskiy

### Egor Bogatinskiy (view profile)

##### MATLAB Release
MATLAB 7.8 (R2009a)