```Path: news.mathworks.com!not-for-mail
From: <HIDDEN>
Newsgroups: comp.soft-sys.matlab
Subject: Re: Curvature of a 3D implicit function
Date: Sun, 28 Nov 2010 04:10:05 +0000 (UTC)
Organization: The MathWorks, Inc.
Lines: 19
Message-ID: <icskmt\$no3\$1@fred.mathworks.com>
References: <ics6dc\$khv\$1@fred.mathworks.com>
NNTP-Posting-Host: webapp-05-blr.mathworks.com
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
X-Trace: fred.mathworks.com 1290917405 24323 172.30.248.35 (28 Nov 2010 04:10:05 GMT)
X-Complaints-To: news@mathworks.com
NNTP-Posting-Date: Sun, 28 Nov 2010 04:10:05 +0000 (UTC)
Xref: news.mathworks.com comp.soft-sys.matlab:690567

"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?
>
> Yours,
> Weng
- - - - - - - - - -
Your implicit function will define a surface in three dimensions.  Curvature at a point on a surface is only defined in terms of curves that follow the surface through the point.  The maximum and the minimum such curvatures on a surface are called its "principal curvatures".  There are some methods of determining these for a point on a surface in terms of various of its derivatives.

You might get a start on the subject by looking at the Wikepedia website at:

http://en.wikipedia.org/wiki/Curvature

It has a number of links to further discussions of the subject.  This subject is taught in differential geometry classes at universities.

I'm afraid my last class in differential geometry was some six decades ago, so the subject would require some extensive work on my part before I could discuss it intelligently.

Roger Stafford
```