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> distSq < radius1Sq + radius2Sq + 2 * max( radius1Sq, radius2Sq )
>
> So now we have a test that doesn't require taking any square roots, but it
> isn't as "tight" as it could be - it will return true sometimes when the
> circles aren't intersecting.
>
> Can this be improved?
How about more simply:
distSq < 4 * max( radius1Sq, radius2Sq )
Followed by the expensive square root operation to check if they really
intersect?
Obviously the benefits will depend on many factors, like how similarly sized
your circles are, and what % of them intersect.
Is there any history to the comparisons that you could make use of? Eg a
large number of circles that are being repeatedly tested for intersection
after they move a small amount? If so you can get much bigger speed-ups
using other methods (eg keeping the list of circles ordered by x
coordinate).
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