Path: utzoo!utgpu!news-server.csri.toronto.edu!cs.utexas.edu!sun-barr!apple!jp
From: jp@Apple.COM (John Peterson)
Newsgroups: comp.graphics
Subject: Re: Bezier Surface Patches -> NURBS ??
Keywords: NURBS Bezier, conversion
Message-ID: <50301@apple.Apple.COM>
Date: 15 Mar 91 20:14:17 GMT
Organization: Apple Computer Inc., Cupertino, CA
Lines: 37


John Kellow (kellow@ndcheg.cheg.nd.edu) writes:

> I am trying to convert some bezier surface patch data to NURB surface
> patches and I was wondering if someone could point me to a good reference
> on doing this (or even some examples of source code).

R Victor Klassen (klassen@gvax.cs.cornell.edu) writes:

> This is a special case of a non-uniform b-spline, (NURBS) so you're there.
> In order to do this conversion, find the matrix BZ that takes Bezier control
> points to monomial form, and the matrix B that takes Bspline control points to
> monomial form, then apply B BZ^-1 to the control points...
>
> [stuff about matrices and Macsyma deleted...]


It's really straightforward to convert Bezier patches to NURBS -
there's no need to do the basis matrix stuff.  Just assign the Bezier
control points to the NURB control points (if the Bezier control
points don't have a rational ("W") component, set the NURB W's to
1.0).  Set the NURB orders to the degree+1 of the Bezier patch. 

Then create the knot vectors with N zeros followed by N ones, where 
N = degree + 1 of the Bezier patch.  For example, a cubic knot vector
would be:

        0 0 0 0 1 1 1 1

and for a degree seven Bezier patch use knot vectors like:

	0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 

That's all there is to it.

Cheers,
jp