On Tue, Jul 16, 2013 at 8:49 AM, phoenix <284281...@qq.com> wrote:
>
> 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?
>
If I'm interpreting the bottom part of p.624 and the top of p.625 in that
paper correctly, we cannot assume this property holds for general NURBS or
B-Spline surfaces (intuitively I wouldn't expect it to) but if the paper is
correct we *can* assume this is true for Bezier patches. Therefore, if the
NURBS surface in question is converted to a set of Bezier patches via knot
insertion or knot refinement the test may be possible for the resulting
Bezier patches. Of course, the challenge is then to take that information
and relate it back to the NURBS surfaces, since multiple patches will
potentially need to be "stitched" into the final NURBS overlap boundary
curve.
CY
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