From: "Bruno Luong" <b.luong@fogale.findmycountry>
Newsgroups: comp.soft-sys.matlab
Subject: Re: Curvature of a 3D implicit function
Date: Sun, 28 Nov 2010 08:50:06 +0000 (UTC)
Organization: FOGALE nanotech
Lines: 14
Message-ID: <ict53u$bdh$>
References: <ics6dc$khv$>
Reply-To: "Bruno Luong" <b.luong@fogale.findmycountry>
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
X-Trace: 1290934206 11697 (28 Nov 2010 08:50:06 GMT)
NNTP-Posting-Date: Sun, 28 Nov 2010 08:50:06 +0000 (UTC)
X-Newsreader: MATLAB Central Newsreader 390839
Xref: comp.soft-sys.matlab:690589

"Weng Boon" <> wrote in message <ics6dc$khv$>...
> Hi,
> Given an implicit function f (x,y,z) = 0 , is there a formula that I can use to calculate the curvature at a point?

At any point on the surface, The implicit can be easily transformed to explicit form

Z = F(X,Y)

simply by choosing the orthonormal basis such that the Z coordinate parallel to gradient f at the point under consideration.

Then take the Hessian of F, the two eigen values of the Hessian are the two principal curvatures.