"Kenneth" <kdw### [at] earthlinknet> wrote:

>
> Here's my simple (??) scene for creating a sphere, TRACED with (imaginary)
> rays that
> "orbit" the sphere. This scene graphically demonstrates how the <x,y,z>
> components of the NORMAL vector go about creating a unit-length.

I have an embarassing admission to make: Upon thinking about my own code
more deeply, I see that it does NOT, in fact, "prove" that TRACE returns a
unit-length vector.  All it does is show that the many returned normal
vectors are all the SAME LENGTH. (Yes, by scaling my sphere down, you would
"see" that they are all one unit in length; but, alas, that's not quite the
"proof" I was looking for.) There is, generally speaking, a fundamental
difference between a VISUAL proof and a CONCEPTUAL one. So my own code is
really no different from POV's own example code (except to show the
individual directional components  making up the vector length.)  My
apologies for misleading anyone.

Time to do some more thinking!!!!

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