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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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