Given an object:

• With the bounds [x, y, z, width, height, depth]
• And an orthographic projection [left, right, bottom, top, near, far]

I want to determine the radius of a sphere which allows me to randomly place my camera on so that:

1. The object is fully visible from all positions on this sphere
2. The sphere radius is the smallest possible value while still satisfying 1.

Assume the object is centered around the origin.
How can I find this radius?

I'm currently using sqrt(width^2 + height^2 + depth^2) but I'm not sure that's the correct value, as it doesn't take the camera into account.

Thanks for any advice.

I'm sorry for confusing a few things here. My comments below should clarify what I'm trying to do actually.