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
>

```

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