> However, mine still shows a slight discontinuity.  My brain is too fuzzy
> right now to dive into the calculus, but it seems that what POV-Ray's
> formula and mine have in common is that they both have a discontinuity
> (probably at the 2nd derivative level) where the field of one component
> intersects the surface of another.  The massive Photoshop engine in our
> visual cortex is sensitive to this discontinuity, although you cannot
> see it by looking at a silhouette of the object.

Yes, if you have a reflective finish at all then it will show up any 
discontinuities at the 2nd derivative level very obviously. For example 
if you make a simple rounded box with cylinders and spheres there is a 
step change in the rate of change of normal direction (2nd derivative of 
position) at the join between the flat faces and the cylinders. It won't 
be so visible with a diffuse finish, but any specular or reflective 
finish will show up a definite "edge" that your eye will easily pick up 
as a "join" or "crease".

I don't remember for sure, but even 3rd level discontinuities might be 
noticeable on reflective surfaces too. You better ask someone who 
designs car body panels :-)

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