How to pack circles of different sizes in a rectangle?

I am curious to see how I can pack circles with different sizes in a rectangle. The desired filling fraction is an input and circles cannot overlap. Any hint?

Thanks in advance!

Answer 1

[Image Analyst]

See the FAQ: http://matlab.wikia.com/wiki/FAQ#How_do_I_create_a_circle.3F. That, combined with the rand() function to get center locations and radii, will allow you to do this.

Using rand you can randomly place or reject new circles in a Monte Carlo fashion. If you want to fill the rectangle more systematically and completely , you'll have to use the Euclidean Distance Transform to figure out the size of the largest circle than can be placed and where the largest circle can be placed. Keep going until the circles become smaller than what you care about.

[Sunstar]

Thank you. And how to satisfy the non-overlapping condition?

[Image Analyst]

Keep track of all centers and radii. Compare the tentative new circle against past circles. If the distance between the centers is more than the sum of the two radii, then they don't overlap and you're okay to accept it.

if sqrt((x2-x1)^2+(y2-y1)^2) > (r1+r2)
  % Then it's acceptable.

[Sunstar]

Thank you so much!