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MathGroup Archive 2005

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Re: Normal Disappear Problem

  • To: mathgroup at smc.vnet.net
  • Subject: [mg55310] Re: Normal Disappear Problem
  • From: "Jens-Peer Kuska" <kuska at informatik.uni-leipzig.de>
  • Date: Sat, 19 Mar 2005 04:45:11 -0500 (EST)
  • Organization: Uni Leipzig
  • References: <d1ecv2$evi$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,

surf = {Cos[u]*Sin[v], Sin[u]*Sin[v], Cos[v]};

notUnitLength = Cross[D[surf, u], D[surf, v]] // 
Simplify;

normal = 
notUnitLength/Sqrt[notUnitLength.notUnitLength] // 
FullSimplify;

Limit[normal /. u -> 0 , v -> 0]

{0,0,-1}

and so

you have to *normalize* the normal and you have to 
take the limit.

Regards

  Jens

<gouqizi.lvcha at gmail.com> schrieb im Newsbeitrag 
news:d1ecv2$evi$1 at smc.vnet.net...
> Hi, All:
>
> I have the following parametric equation for an 
> unit sphere:
>
> x = cos(u)sin(v)
> y = sin(u)sin(v)
> z = cos(v)
>
> 0<=u<2*Pi ; 0<=v<=Pi
>
> Then I use
>
> normal = (Dx/Du, Dy/Du, Dz/Du) CROSS (Dx/Dv, 
> Dy/Dv, Dz/Dv) to get the
> normal vector.
>
> I get the follwoing after calculation (with 
> normalization):
>
> normal =  [sin(v) ^2 cos(u), sin(v)^2  sin(u), 
> cos(u)^2  cos(v) sin(v)
> +  sin(u)^2  cos(v) sin(v)]
>
> Now when u=0, v=0 , Normal = (0,0,0)! How can it 
> be? We know the fact
> that a sphere should have normal everywhere.
>
> Rick
> 



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