Path: news.mathworks.com!newsfeed-00.mathworks.com!news.kjsl.com!usenet.stanford.edu!elk.ncren.net!newsflash.concordia.ca!canopus.cc.umanitoba.ca!not-for-mail From: Walter Roberson <roberson@hushmail.com> Newsgroups: comp.soft-sys.matlab Subject: Re: Quadric approximation and Date: Thu, 22 Jul 2010 11:34:49 -0500 Organization: Canada Eat The Cookie Foundation Lines: 23 Message-ID: <i29s6c$1oe$1@canopus.cc.umanitoba.ca> References: <i29qu2$g1$1@fred.mathworks.com> NNTP-Posting-Host: ibd-nat.ibd.nrc.ca Mime-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 7bit X-Trace: canopus.cc.umanitoba.ca 1279816716 1806 132.246.133.10 (22 Jul 2010 16:38:36 GMT) X-Complaints-To: abuse@cc.umanitoba.ca NNTP-Posting-Date: Thu, 22 Jul 2010 16:38:36 +0000 (UTC) User-Agent: Thunderbird 2.0.0.24 (X11/20100317) In-Reply-To: <i29qu2$g1$1@fred.mathworks.com> Xref: news.mathworks.com comp.soft-sys.matlab:655302 Alexander Petrov wrote: > Application of Matlab fit function under 2d-matrix give me an quadratic > function: sf(x,y) = p00 + p10*x + p01*y + p20*x^2 + p11*x*y + p02*y^2 > > But what I want is an general equation of quadric surface, like on that > webpage - http://mathworld.wolfram.com/QuadraticSurface.html > > I've know, that this is a stupid question, but could I really rewrite > matlab result as: > > let z= sf(x,y); > p00 + p10*x + p01*y + p20*x^2 + p11*x*y + p02*y^2 - z = 0 > > Does such a "trick" give me an general equation of quadric surface ? No. If z = sf(x,y) and the overall surface is to remain quadradic, then sf(x,y) would have to be a multinomial in x and y in which the "total power" of each term did not exceed 2. Such a multinomial, when substituted into the proposed expression, would be of identical form to the p00 <etc> expression except with different coefficients. This would not be sufficient to express the general quadratic surfaces as described on Wolfram's page, which require polynomials in x, y, and z.