Space filling with circles of unequal size

Question

Here is my problem:

• I have a bunch of circles that I need to display inside a canvas.
• There are an arbitrary number of circles, each with a predefined ra

Answer 1

Since your goal is just to "achieve a pleasing effect", not solve a math problem, you should try the simplest algorithm which could work first and see if it looks good. There should be no need to use very complex math.

I understand that you want the spheres to "fill" the available space, not leaving large empty areas while other areas are crowded. You also want the layout to appear random -- not lined up on a grid or anything like that.

The obvious, dead-simple way to achieve that is simply to place the spheres one by one, in random locations. If one lands on top of an already-placed sphere, generate another random location until you find one where it fits.

It appears there are about 40 spheres in the image shown. The chances of 40 spheres all landing in the same area of the image, leaving the rest of the image empty, is very, very small. As the number of spheres increases, the chances of getting a very unbalanced layout will become close to zero.

Try that first and see if it meets your needs. If it is not "even" enough, you should be able to use some very simple math to bias the randomly chosen locations in favor of choosing empty areas. There should be no need to use complex algorithms.