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From: jp@Apple.COM (John Peterson)
Newsgroups: comp.graphics
Subject: Re: Bezier Curves (really adding knots)
Message-ID: <34676@apple.Apple.COM>
Date: 12 Sep 89 19:02:23 GMT
Organization: Apple Computer Inc., Cupertino, CA
Lines: 20


> You can convert a B-spline to a (sequence of) Bezier curve(s) by
> expanding each knot parameter to multiplicity 4 (for cubic curves).
> The control points for the (concatenated) Bezier segment(s) are the new
> knot vertices, 4 for each Bezier curve.  The t parameter ranges
> between the two knot parameter values at either end.

Actually, to convert B-Spline to Bezier curves making the internal
knots have a multiplicity of 3 is sufficient (for the cubic case).

For doing knot inseration on curves, Boehm's method is much faster
than the Oslo algorithm.  (Boehm, "Inserting new knots into B-Spline
Curves,"  CAD, July 1980).

If you want to learn all about splines and knot vectors, the classic
reference is:  "An Introduction to Splines for use in Computer Graphics
and Geometric Modeling", by Bartels, Beatty and Barsky (Morgan Kaufman, 1987).

Cheers,
jp