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MathGroup Archive 2005

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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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