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MathGroup Archive 2005

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Re: Normal Disappear Problem

  • To: mathgroup at smc.vnet.net
  • Subject: [mg55315] Re: Normal Disappear Problem
  • From: "Valeri Astanoff" <astanoff at yahoo.fr>
  • Date: Sat, 19 Mar 2005 04:45:16 -0500 (EST)
  • References: <d1ecv2$evi$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Rick,

In parametric mode there are often troublesome points.

Notice your normal is not normalized :

normal[u_, v_] := {Sin[v]^2 Cos[u], Sin[v]^2 Sin[u],
      Cos[u]^2 Cos[v] Sin[v]+Sin[u]^2 Cos[v] Sin[v]};

normal[u,v].normal[u,v]//Simplify

	Sin[v]^2


My way to tackle the exception (0,0) :


unitNormal[u_, v_] := normal[u,v] / Sqrt[normal[u,v].normal[u,v]];


unitNormal[0,0]

	{Indeterminate,Indeterminate,Indeterminate}

Series[unitNormal[u,v],{u,0,1},{v,0,1}]//Normal

	{v, u v, 1}

% /. u -> 0 /. v -> 0

	{0, 0, 1}

Then let :
unitNormal[0,0] = {0,0,1}
and you're done.


hth

Valeri


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