Code covered by the BSD License

### Highlights from Arbitrary Square Bounded Voronoi Diagram

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# Arbitrary Square Bounded Voronoi Diagram

### Meng Sang Ong (view profile)

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

File Information
Description

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)

MATLAB release MATLAB 7.8 (R2009a)
09 Oct 2014 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!

16 May 2014 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?

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27 Mar 2014 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.

15 Feb 2012 Simon Arame

### Simon Arame (view profile)

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

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15 Feb 2012 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])

Comment only
07 Feb 2012 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.

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18 Aug 2011 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.

21 Jul 2011 Egor Bogatinskiy