>> Typically, the perspective transform is defined such that the resulting 
>> z-coordinates fall in a suitable range (e.g. [0,1]). Clipping can then be 
>> performed without knowledge about the original clipping planes.
>
> I see. So there's extra information, but it might be implicit. Interesting 
> approach.

Yes, the 3D hardware is usually programmed to clip when Z is outside a 
certain range.  It is then up to you (the programmer) to decide how you map 
real world coordinates to this range, and yes you can do it with just a 4x4 
matrix.

DirectX has a helper function to create such a matrix for you:

http://tinyurl.com/yg5z9t7

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