The formula for a squircle has an exponent in it. When this value is 0 you get a square. When it is 1, a circle. In between 0 and 1, you get the squircle shapes I've been showing.

But what if you go past 1? Fascinating. At 2 you get a diamond. (Which is still a square, but rotated 45 degrees.)

And at 3, a new shape which is called an astroid. It is a diamond with circles cut out of its sides. Of course you can dial in any in-between values you want.

Past 3 it just becomes a narrower astroid - a diamond with squircles cut out of it.

Left to right, squircle + circle, astroid + circle, astroid + astroid.

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Renderosity forum reply notifications are wonky. If I read a follow-up in a thread, but I don't myself reply, then notifications no longer happen AT ALL on that thread. So if I seem to be ignoring a question, that's why. (Updated September 23, 2019)