       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

```

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