Path: utzoo!news-server.csri.toronto.edu!cs.utexas.edu!uwm.edu!spool.mu.edu!snorkelwacker.mit.edu!stanford.edu!msi.umn.edu!umeecs!zip!spencer From: spencer@eecs.umich.edu (Spencer W. Thomas) Newsgroups: comp.graphics Subject: Re: Bezier Surface Patches -> NURBS ?? Message-ID: Date: 15 Mar 91 21:25:34 GMT References: <1991Mar14.225606.26325@news.nd.edu> Sender: news@zip.eecs.umich.edu Organization: University of Michigan EECS Dept Lines: 16 In-Reply-To: kellow@rockne.helios.nd.edu's message of 14 Mar 91 22:56:06 GMT A Bezier patch is a "degenerate" NURBS already. You just need a knot vector and a few 1's in the "rational" part. To wit, consider the curve case for a cubic Bezier curve: { (x0,y0,z0), (x1,y1,z1), (x2,y2,z2), (x3,y3,z3) } Use the knot vector { 0, 0, 0, 0, 1, 1, 1, 1 }, and add a 1 to each control point as its weight: { (x0,y0,z0,1), (x1,y1,z1,1), (x2,y2,z2,1), (x3,y3,z3,1) } Voila! You've now got a NURBS curve. The surface case is analogous, except you need a knot vector for each parametric direction. -- =Spencer W. Thomas EECS Dept, U of Michigan, Ann Arbor, MI 48109 spencer@eecs.umich.edu 313-936-2616 (8-6 E[SD]T M-F)