Overlapping circles - modelling living populations

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
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

···

From: Philip Rhoades [mailto:phil@pricom.com.au]