sphere is cheapest, so...

which is cheaper, capsule or box shape?

Box as there is less to calculate.

I'd say capsule, it's just simple radius checking, where as box is checking for all 6 vertices.

If that is the case, it means a capsule isn't very accurate if you specify say 6 sides?

But doesn't a radius check involve a square root? I can understand why a sphere shapes single calculation would be faster than a box shape, but for three radius checks? Plus however they include the length in that.

Honestly I would have guessed a box to be faster than a capsule

No. From what I remember capsule is the fastest, but isn't most of the "common" square roots in a table somewhere?

ah good point. Well, thanks for the tip!