Xref: utzoo comp.graphics:16695 sci.math.num-analysis:1671 Path: utzoo!utgpu!news-server.csri.toronto.edu!rpi!usc!samsung!umich!umeecs!zip!spencer From: spencer@eecs.umich.edu (Spencer W. Thomas) Newsgroups: comp.graphics,sci.math.num-analysis Subject: Re: Degenerate surfaces Message-ID: Date: 19 Mar 91 15:57:12 GMT References: <1991Mar18.213610.18736@silma.com> Sender: news@zip.eecs.umich.edu Distribution: usa Organization: University of Michigan EECS Dept Lines: 18 In-Reply-To: reddy@silma.com's message of 18 Mar 91 21:36:10 GMT In article <1991Mar18.213610.18736@silma.com> reddy@silma.com (Reddy) writes: Does anybody out there know a better way to approximate partial derivatives (specifically normal - du X dv) on parametric surface S(u,v) at a degenerate point. At the degenerate point S(u0,v0) either du=0 or dv=0 or du=dv=0. Assuming the tangent plane exists, then if dS/du is 0, use (d^2 S)/du^2, (or the lowest n such that (d^n S)/du^n is non-zero). At a point such that dS/du is parallel to dS/dv, you need to evaluate a directional derivative in another direction. If you choose the vector (u,v)=(1,1) then you can just evaluate (d S(u,u))/du. Again, assuming the tangent plane exists, this should not be parallel to dS/du (although I'm sure I could come up with a pathological case where it was, and a higher-order derivative was required.) -- =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)