After reading through you post, we need some clarification here.
1) Is your "bounding box" always square (or even rectangular) as in your example?
2) Are you looking for the smallest circle that encompasses all four points?
3) You suggest that the circle might need to be "a bit bigger" to take in the points, how much bigger?
Incidentally, if you are looking for the smallest circle whose radius takes in all four points, your calculated radius should be SqrRt(8).
I guess, as wossname suggested, your needs are a little unclear. Anything you can add will be of help.
This picture should help.
The radius is what I need to find.
The center of the node is easy.
The radius that encompas's past the 4 points....So the entire box is in the sphere.
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