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

Margus Ramst wrote:
> 
> I'm not a programmer type and I might be wrong, but there seems to be a
> problem of ambiguity. This is how I envision it: the normals of a smooth
> triangle are calculated via interpolation of its 3 corner normals. When one
> normal is rotated more than 180 degrees in relation to the others, how
> should POV know which way to do the interpolated rotation? Bad ASCII art:
> 
>  |   /
> --- --- ---
>          \
> 
>  |   \
> --- --- --- ---
>          /   \
> 
> The end result is the same, but the intermediate normals are different. As
> long as the angle difference is less than 180 degrees there is no ambiguity.
> 
> Margus
>

Post a reply to this message