Position N circles of different radii inside a larger circle without overlapping

Question

Given n circles with radii r1 ... rn, position them in such a way that no circles are overlapping and the bounding circle is of \"small\" radius.

The program takes a lis

Answer 1

I have a pretty naive one pass (over the radii) solution that produces alright results, although there is definitely room for improvement. I do have some ideas in that direction but figure I might as well share what I have in case anybody else wants to hack on it too.

It looks like they intersect at the center, but they don't. I decorated the placement function with a nested loop that checks every circle against every other circle (twice) and raises an AssertionError if there is an intersection.

Also, I can get the edge close to perfect by simply reverse sorting the list but I don't think the center looks good that way. It's (pretty much the only thing ;) discussed in the comments to the code.

The idea is to only look at discrete points that a circle might live at and iterate over them using the following generator:

def base_points(radial_res, angular_res):
    circle_angle = 2 * math.pi
    r = 0
    while 1:
        theta = 0
        while theta <= circle_angle:
            yield (r * math.cos(theta), r * math.sin(theta))
            r_ = math.sqrt(r) if r > 1 else 1
            theta += angular_res/r_
        r += radial_res

This just starts at the origin and traces out points along concentric circles around it. We process the radii by sorting them according to some parameters to keep the large circles near the center (beginning of list) but enough small ones near the beginning to fill in spaces. We then iterate over the radii. within the main loop, we first loop over points that we have already looked at and saved away. If none of those are suitable, we start pulling new points out of the generator and saving them (in order) until we find a suitable spot. We then place the circle and go through our list of saved points pulling out all of the ones that fall within the new circle. We then repeat. on the next radius.

I'll put some ideas I have into play and make it mo`bettah. This might serve as a good first step for a physics based idea because you get to start with no overlaps. Of course it might already be tight enough so that you wouldn't have much room.

Also, I've never played with numpy or matplotlib so I write just vanilla python. There might be something in there that will make it run much faster, I'll have to look.