Re: Surface Normal

*To*: mathgroup at smc.vnet.net*Subject*: [mg55173] Re: Surface Normal*From*: dh <dh at metrohm.ch>*Date*: Wed, 16 Mar 2005 05:35:49 -0500 (EST)*References*: <d15s2g$9k2$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Hi Rick, here is how you get the normal to a parametrized surface: x = (10 + 5Cos[v])Cos[u] (* your surface *) y = (10 + 5Cos[v])Sin[u] z = 5Sin[v] r = {x, y, z}; (*3D position vecto of your surface*) ru = D[r, u]; (*Tangential vector in direction u*) rv = D[r, v];(*Tangential vector in direction v*) n = Cross[ru, rv]; (* normal *) nn = n/Sqrt[n.n]; (* normalized normal *) Daniel gouqizi.lvcha at gmail.com wrote: > Hi, All: > > If I have a surface in parametric form > > For example, > x = (10 + 5cosv)cosu > y = (10 + 5cosv)sinu > z = 5sinv > > How can I quickly calculate its normal for any (u,v) by mathematica > > Rick >