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