Re: Surface Normal

*To*: mathgroup at smc.vnet.net*Subject*: [mg55176] Re: Surface Normal*From*: D Herring <dherring at at.uiuc.dot.edu>*Date*: Wed, 16 Mar 2005 05:35:52 -0500 (EST)*References*: <d15s2g$9k2$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

> 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 Why does this sound like a homework problem? An intro differential geometry class? Anyway... - cross product of the gradients wrt u and v - simplify and normalize as desired This is rather simple to do symbolically in Mathematica. Use a list of {x,y,z} with D[], Cross[], and optionally Simplify[]. Your particular example is just as easily done by hand. If this is homework, do it first by hand and then check by Mathematica; computers are rarely allowed for exams. If it isn't homework, please list the steps you want to perform; the replies will tend to be of a higher quality. Later, Daniel