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 ---------- >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 > ****************************************************** > > > > >