> OK, taking a very quick look at that paper and what you say, I see I
> misunderstood your original question. My bad. However, I think the answer
> may be easier than what I was getting at, in that a polynomial curve is a
> $C^\{infty}$ structure already, so there is no problem at all.
> Or am I missing something?
Hmm.. For polynomial curves and polynomial surfaces, the theorem is satisfied,
of course. But for general NURBS surfaces used in BRL-CAD, can we make use of
this property (which may require C-infinity) so as to simplify surface-surface
intersections?
Theorem 3 in that paper: Given two polynomial surfaces, if they overlap over a
region, then the overlap region must be bounded by parts of the boundaries of
the two surfaces. That is to say, the overlap region cannot end in the middle
of both surfaces. In other words, the two polynomial surfaces can be considered
as two trimmed surfaces trimmed from a common polynomial surface.
Cheers!
Wu
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