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 >