You can think of it like this:
A ray is first tested against the bounding object (manual or automatic). If the
bounding object is hit, the ray is tested against the actual object. The main
purpose of this is to speed up rendering, since it's much faster to check an
intersection with a box or sphere than with, say, a quartic. What you describe
sounds more like clipping. Bounded_by and clipped_by should not be confused,
they work quite differently.
Bounding is viewpoint dependent: for an object to be rendered, its volume does
_not_ have to be inside the bounding object. Its 2D _projection_ from the
current viewpoint has to be in the 2D projection of the bounding object.
Basically, you can think of bounded_by as working in 2D screen space, as opposed
to the 3D space of your scene.
Clipping works similarly to the difference CSG operation. But clipping leaves a
hole in the cut object where difference leaves the surface of the cutting
object. Clipping is not viewpoint dependant.

Margus

Darcy Johnston wrote:
> 
> I'm curious. Can someone explain how this works? I was always under the
> impression that the manual bounding was used to define the size of an object
> and any part of the object that was outside of the bounding object was
> essentially clipped. I guess this is either only partly correct or a
> misinterpretation of what actually happens. I more complete explanation
> would be great.
> 
> Thanks,
> Darcy

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