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

> 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!!!!

Hello Kenneth,

Making a mistake is surely allowed. In any forum, there will always be
others who are ready to correct you :)

Your post regarding the trace macro gave me an idea: to re-write the
TS_Macros to use custom envelopes.

IE:

// ******************************************************************
// macro TS_Intersect
// ------------------------------------------------------------------
// Shoots ray from origin to vector _v and calculates intersection
// point with _ts_envelope.
#macro TS_Intersect( _v )
    trace( _usr_Envelope, <0, 0, 0>, _v, _ts_Normal );
#end
// ******************************************************************

This means geodesic grid data can now be projected onto any POV object.
So, you see, whatever you do - even in error - the butterfly effect is
always there.

Regards,

N.Shea

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