# Overlapping circles - modelling living populations

**URL:** <https://www.ruby-forum.com/t/overlapping-circles-modelling-living-populations/68116>\
**Category:** Ruby\
**Created:** [September 9, 2006, 10:20am UTC](https://www.ruby-forum.com/t/overlapping-circles-modelling-living-populations/68116 "2006-09-09T10:20:00Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![unebaguettesvp](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/u/47e85d/32.png) [@unebaguettesvp](https://www.ruby-forum.com/u/unebaguettesvp)\
**Post date:** [September 9, 2006, 10:20am UTC](https://www.ruby-forum.com/t/overlapping-circles-modelling-living-populations/68116/1 "2006-09-09T10:20:00Z")

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People,

I have been thinking about how to use Ruby for modelling populations - I  
want to use circles on a grid to represent the size of individual  
populations and determine if there is dispersal between pairs of  
populations by testing whether there is overlap with the two circles.

I need to keep track of:

- all the individual circles (populations) on a grid

- which other circles each circle overlaps with

And I need to:

- iterate through ALL the circles (for each generation of the  
populations)

I thought of using a two dimensional array, each row representing a  
circle. Elements 2-x of each row could point to another array  
representing the other circles that this circle overlaps with - but this  
seems fairly clumsy and was wondering if there is some better  
mechanism . .

Thanks,

## Phil.

Philip R.

Pricom Pty Limited (ACN 003 252 275 ABN 91 003 252 275)  
GPO Box 3411  
Sydney NSW 2001  
Australia  
Mobile: +61:(0)411-185-652  
Fax: +61:(0)2-8221-9599  
E-mail: removed\_email\_address@domain.invalid

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<div class="post-metadata">

**Author:** ![unebaguettesvp](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/u/47e85d/32.png) [@unebaguettesvp](https://www.ruby-forum.com/u/unebaguettesvp)\
**Post date:** [September 9, 2006, 10:52am UTC](https://www.ruby-forum.com/t/overlapping-circles-modelling-living-populations/68116/2 "2006-09-09T10:52:02Z")

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Philip R. wrote:

> People,
> 
> I have been thinking about how to use Ruby for modelling populations - I  
> want to use circles on a grid to represent the size of individual  
> populations and determine if there is dispersal between pairs of  
> populations by testing whether there is overlap with the two circles.

This is, strictly speaking, a math question. It is rather far removed  
from  
Ruby per se.

For two circles (position x,y and radius r) x1,y1,r1 and x2,y2,r2, if:

(x2-x1)^2+(y2-y1)^2 \< (r2+r1)^2

Then the circles overlap. With a little more math, you can compute the  
area  
of the overlapping region.

> I thought of using a two dimensional array, each row representing a  
> circle.

At first glance, there’s no need for a two-dimensional array. You have a  
set  
of circles and you want to find those that overlap. Simply create an  
algorithm that compares every circle with every other circle using the  
relation stated above. The fact that the problem exists in two-space  
doesn’t mean the array needs two dimensions.

> Elements 2-x of each row could point to another array  
> representing the other circles that this circle overlaps with -

This is indeed rather cumbersome. You could create a result array of  
circles  
containing the degree to which they overlap (you can establish the area  
of  
overlap), and you could update this list by repeating the algorithm  
after  
making changes to the positions and sizes of the original circles.

If you really need the specific degree of overlap of each circle with  
each  
of the other circles, then at that point you do need a two-dimensional  
array. If instead you only need the cumulative amount of overlap without  
having to identify the overlapping circles, then a single dimension will  
suffice.

Now to touch on Ruby. The first step would be to create a class  
containing  
the circle descriptions:

class PopCircle  
attr\_accessor :x,:y,:r  
def initialize(x,y,r)  
# read the class variables  
end  
end

Then you would create a list of such class instances by reading a data  
file  
that describes the circles. Then, having created the list, you would  
compare all the circles to each other to find overlaps, and create some  
sort of result array showing the overlaps.

The difficult part will be deciding what the result means.

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<div class="post-metadata">

**Author:** ![unebaguettesvp](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/u/47e85d/32.png) [@unebaguettesvp](https://www.ruby-forum.com/u/unebaguettesvp)\
**Post date:** [September 9, 2006, 7:40pm UTC](https://www.ruby-forum.com/t/overlapping-circles-modelling-living-populations/68116/3 "2006-09-09T19:40:45Z")

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Paul,

On Sat, 2006-09-09 at 17:50 +0900, Paul L. wrote:

> Ruby per se.
> 
> > - all the individual circles (populations) on a grid
> 
> containing the degree to which they overlap (you can establish the area of  
> the circle descriptions:  
> compare all the circles to each other to find overlaps, and create some  
> sort of result array showing the overlaps.
> 
> The difficult part will be deciding what the result means.

Thanks for that! - I know what I want to do with the population  
simulation so this helps.

Regards,

## Phil.

Philip R.

Pricom Pty Limited (ACN 003 252 275 ABN 91 003 252 275)  
GPO Box 3411  
Sydney NSW 2001  
Australia  
Mobile: +61:(0)411-185-652  
Fax: +61:(0)2-8221-9599  
E-mail: removed\_email\_address@domain.invalid