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Normal vector on a surface

• To: mathgroup at smc.vnet.net
• Subject: [mg29269] Normal vector on a surface
• From: Matthias.Bode at oppenheim.de
• Date: Sat, 9 Jun 2001 03:08:58 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

Dear Colleagues,

I have a function in the variables x1 and y1:

Out[27]=
19.74211746962547 - 61.78321746073334*
   x1 + 70.84823523445556*x1^2 - 
  34.64681309362152*x1^3 + 
  5.822595947190386*x1^4 - 
  61.783217460733795*y1 + 
  188.56171712734522*x1*y1 - 
  208.7457484391798*x1^2*y1 + 
  99.21114279328117*x1^3*y1 - 
  16.223098505477388*x1^4*y1 + 
  70.8482352344551*y1^2 - 
  208.7457484391805*x1*y1^2 + 
  225.08774661852397*x1^2*y1^2 - 
  103.5151716236312*x1^3*y1^2 + 
  16.351931921608763*x1^4*y1^2 - 
  34.64681309362163*y1^3 + 
  99.21114279328117*x1*y1^3 - 
  103.51517162363109*x1^2*y1^3 + 
  45.654124756950296*x1^3*y1^3 - 
  6.928857192755963*x1^4*y1^3 + 
  5.822595947190411*y1^4 - 
  16.22309850547743*x1*y1^4 + 
  16.351931921608763*x1^2*y1^4 - 
  6.928857192755952*x1^3*y1^4 + 
  1.0137658500940734*x1^4*y1^4


This function yields a surface very similar to Sin[x1*y1] for 1<x1<3 and
1<y1<3.

Now I want to calculate (how?) and draw (how?) several "Normalenvektors"
(sorry, I do not know the English termini technici) which should sit smugly
- like palisades - on the plane tangential to the surface.

The "Normalenvektor" N in point P - according to Bronstein-Semendjajew - is
a unity vector perpendicular to the tangential plane; its accompanying
vectors e1 and e2 on the plane form a "right-handed system". N, e1 and e2
are referred to as the "accompanying tripod". - I understand the words but
not their meaning.

My attempts with Calculus`VectorAnalysis` and PlotVectorField3D &c. failed
dismally. 

Thank you for your assistance,

Matthias Bode
Sal. Oppenheim jr. & Cie. KGaA
Koenigsberger Strasse 29
D-60487 Frankfurt am Main
GERMANY
Tel.: +49(0)69 71 34 53 80
Mobile: +49(0)172 6 74 95 77
Fax: +49(0)69 71 34 6380
E-mail: matthias.bode at oppenheim.de
Internet: http://www.oppenheim.de

• Follow-Ups:
  • Re: Normal vector on a surface
    • From: Daniel Lichtblau <danl@wolfram.com>
  • Re: Normal vector on a surface
    • From: jmt <jmt@agat.net>