Hello all, I am having trouble with a math problem, and I was hoping someone could shed some light or push me in the right direction. The problem is as follows:

Suppose I have a bounding box, which axis-aligned, and lies on the XY plane. I would like to find the minimum z-position at which this object is full visible on screen, with no parts of it intersecting the view frustum planes.

Of course, one could take the naive approach of just continually incrementing the z position of the camera until the frustum test passes, but this seems like a very bad approach. Does anyone have any other ideas for how to solve this problem?

Thanks.