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Re: Urgent Help needed

• To: mathgroup at smc.vnet.net
• Subject: [mg20419] Re: [mg20390] Urgent Help needed
• From: "Andrzej Kozlowski" <andrzej at tuins.ac.jp>
• Date: Tue, 26 Oct 1999 00:33:04 -0400
• Sender: owner-wri-mathgroup at wolfram.com

The equation F(x,y,z) = 0 does not define a curve but a surface in R^3 (the
level surface corresponding to c). Since curvature is a local invariant
there is no general formula that determines the curvature (Gaussian, mean
etc)at any point of a arbitrary surface given in this way  you need local
coordinates or patches i.e. parametric equations).


--
Andrzej Kozlowski
Toyama International University
JAPAN
http://sigma.tuins.ac.jp
http://eri2.tuins.ac.jp


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>From: "Vladimir Tsyrlin" <vtsyrlin at ozemail.com.au>
To: mathgroup at smc.vnet.net
>To: mathgroup at smc.vnet.net
>Subject: [mg20419] [mg20390] Urgent Help needed
>Date: Mon, Oct 18, 1999, 15:40
>

> Given the implcit form of a curve, i.e. F(x,y,z) = 0, do you know how to
> find the curvature of F at a point in 3D space? All the references I have
> assume F is in parametric form and take the standard differential geometry
> approach.
>
>
> --
> **************************************************
> *************Vladimir Tsyrlin *******************
>  vtsyrlin at cs.rmit.edu.au   vtsyrlin at ozemail.com.au
> ******************************************************
>
>
>
>
>