Zhichu Chen wrote:

What I want exactly is how to determine if there's anything on
some region of the picture. I need this to test if the random
point I picked is useful.

That is easy to answer: you can't (well, not unless you invest a *lot*
of effort into creating a bitmap edge structure).

However what you can do is ask metapost to calculate intersectionpoints
with (the most likely ones of) the already existing objects. This may
be the easiest solution (even though it will be so slow that for large
numbers of items you may be forced to start a division tree).

The core trick is that you randomly place a circle with random radius
inside an x-y field, and you keep those paths/pictures in an array. For
each newlyt generated circle, you look for an intersection with all the
already existing ones (and the rectangle borders) and keep trying
to re-place it until there are no more collisions.

I can't come up with a solution that is both elegant and fast at the
moment, sorry.

Best wishes,
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