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