# Re: Overlapping circles - modelling living populations

**URL:** <https://www.ruby-forum.com/t/re-overlapping-circles-modelling-living-populations/68134>\
**Category:** Ruby\
**Created:** [September 9, 2006, 5:42pm UTC](https://www.ruby-forum.com/t/re-overlapping-circles-modelling-living-populations/68134 "2006-09-09T17:42:32Z")\
**Posts on this page:** 1\
**Page:** 1

<div class="post-metadata">

**Author:** ![phrogz](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/p/2acd7d/32.png) [@phrogz](https://www.ruby-forum.com/u/phrogz)\
**Post date:** [September 9, 2006, 5:42pm UTC](https://www.ruby-forum.com/t/re-overlapping-circles-modelling-living-populations/68134/1 "2006-09-09T17:42:32Z")

</div>

From: Philip R. [[mailto:removed\_email\_address@domain.invalid](mailto:removed_email_address@domain.invalid)]

> 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.

Here’s a solution using SVG, assuming you want to visualize the results.  
It’s even easier rolling your own Circle class using matrix/Vector to  
calculate  
distances.

# [http://downloads.sourceforge.jp/ruby-svg/2288/ruby-svg-1.0.3.tar.gz](http://downloads.sourceforge.jp/ruby-svg/2288/ruby-svg-1.0.3.tar.gz)

require ‘svg/svg’

class Array  
def each\_unique\_pair  
self.each\_with\_index{ |a,i|  
self[(i+1)…-1].each{ |b| yield a,b }  
}  
end  
end

class SVG::Circle  
# test (and save) result  
def overlaps?( other\_circle )  
center\_distance = Math.sqrt(  
( cx - other\_circle.cx ) \*\* 2 +  
( cy - other\_circle.cy ) \*\* 2  
)

```
	intersects = center_distance < ( r + other_circle.r )

	# Save the result on both circles
	other_circle.overlaps[self] = intersects
	self.overlaps[other_circle] = intersects
end

def overlaps
	# Make sure we have a hash to save a set of overlappers
	@overlapping_circles ||= {}
end

# An array of all circles this one overlaps
def overlapping_list
	# Make sure we have a hash to save a set of overlappers
	@overlapping_circles ||= {}
	@overlapping_circles.select{ |circle,status|
		status == true
	}.map{ |circle,status|
		circle
	}
end

```

end

# Create/manage your populations

populations = []  
20.times{  
# Randomly add populations  
x = rand 800 + 100  
y = rand 800 + 100  
radius = rand 150 + 10  
populations \<\< SVG::Circle.new( x, y, radius )  
}

# Make sure the overlapping list is valid

populations.each\_unique\_pair{ |a,b|  
a.overlaps?( b )  
}

# Make the picture

svg = SVG.new(‘100%’, ‘100%’, ‘0 0 1000 1000’)

# Your grid here…lots of SVG::Lines

0.step( 1000, 20 ){ |i|  
svg \<\< SVG::Line.new( i, 0, i, 1000 )  
svg \<\< SVG::Line.new( 0, i, 1000, i )  
}

svg \<\< g = SVG::Group.new{  
self.style = SVG::Style.new(  
:fill =\> ‘#ffc’, :stroke =\> ‘red’, :stroke\_width =\> 1.5  
)  
}

low\_opacity = SVG::Style.new( :opacity =\> 0.5 )

populations.each{ |circle|  
circle.style = low\_opacity  
g \<\< circle  
}

File.open( ‘populations.svg’, ‘w’ ){ |file|  
file \<\< svg.to\_s  
}

# view in your favorite SVG viewer, like FF 1.5

# for an example, see [http://phrogz.net/svg/populations.svg](http://phrogz.net/svg/populations.svg)