For a game, I'm drawing dense clusters of several thousand randomly-distributed circles with varying radii, defined by a sequence of (x,y,r) triples. Here's an example image consisting of 14,000 circles:
I have some dynamic effects in mind, such as merging clusters, but for this to be possible I'll need to redraw all the circles every frame.
Many (maybe 80-90%) of the circles that are drawn are covered over by subsequent draws. Therefore I suspect that with preprocessing I can significantly speed up my draw loop by eliminating covered circles. Is there an algorithm that can identify them with reasonable efficiency?
I can tolerate a fairly large number of false negatives (ie draw some circles that are actually covered), as long as it's not so many that drawing efficiency suffers. I can also tolerate false positives as long as they're almost positive (eg remove some circles that are only 99% covered). I'm also amenable to changes in the way the circles are distributed, as long as it still looks okay.