Margus Ramst wrote:
> 
> Upon furter meditation, this is not quite right. Ken's 4D argument is
> correct. The sphere has normals pointing in all directions, but all normals
> point to the same side of it's surface, by default the "outside". For an
> object to have it's "inside" and "outside" on the same surface, it wold have
> to be twisted in 4D (e.g. the Klein bottle, the 4D equivalent of the Moebius
> band). This also happens when a smooth triangle's normals go from "up" at
> one corner to "down" in the other.
> The ambiguity problem I still applies, but a clearer definition is: when a
> corner normal differs more than 90 degrees from the general normal (defined
> by the corners of the triangle), POV cannot tell which way to do the
> interpolation - is the surface concave? Or convex?
> 
> Margus

  I was taking a shot in the dark with that reply but it just so happens
that I was reading up on the klien bottle last night before I responded
and that is what prompted me to think that it might be a case of twisting
it being twisted in a "4th" dimension. I can't think of any other way to
have two opposing sides of a flat surface connected to each other. Looks
like I got lucky this time.

-- 
Ken Tyler

mailto://tylereng@pacbell.net

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