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Re: Normal vector on a surface

• To: mathgroup at smc.vnet.net
• Subject: [mg29289] Re: [mg29269] Normal vector on a surface
• From: jmt <jmt at agat.net>
• Date: Mon, 11 Jun 2001 04:38:30 -0400 (EDT)
• References: <200106090708.DAA29328@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

There is no built-in "normal vector" function, but you can use this :

Needs["Calculus`VectorAnalysis`"]

n[u_, v_] := Module[{dx, dy, p},
    dx[x_, y_] = {1, 0, D[f[x, y], {x, 1}]};
    dy[x_, y_] = {0, 1, D[f[x, y], {y, 1}]};
    p[x_, y_] = CrossProduct[dx[x, y], dy[x, y]];
    With[{m = p[u, v]}, m/Sqrt[m.m]]
    ]


On Saturday 09 June 2001 09:08, Matthias.Bode at oppenheim.de wrote:
> 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

• References:
  • Normal vector on a surface
    • From: Matthias.Bode@oppenheim.de