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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
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"Weng Boon" <chiaweng@gmail.com> wrote in message <ics6dc$khv$1@fred.mathworks.com>...
> 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.

Bruno