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Dynamic tangential plane - how?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg92909] Dynamic tangential plane - how?
  • From: "m.g." <mg at michaelgamer.de>
  • Date: Sat, 18 Oct 2008 06:24:40 -0400 (EDT)

Hello Group,

  I=B4m trying to visualize the tangential plane to a function f(x,y). I
=B4ve done various attemps -  none of them was successfull. Here an
extract of my attempts:

f[x_, y_] := (1 - x^2) (2 x - y^3)
grad[x_, y_] := {2 (1 - x^2) - 2 x (2 x - y^3), -3 (1 - x^2) y^2}

DynamicModule[{a = 1, b = 1, p, q, punkt},
 {Slider2D[Dynamic[{a, b}], {{-2, -2}, {2, 2}}],
  p = Plot3D[f[x, y], {x, -2, 2}, {y, -2, 2}],
  punkt = Dynamic @ Graphics3D[{PointSize[Large], Red, Point[{a, b,
f[a, b]}]}],
  q = Dynamic @ Plot3D[f[a, b] + grad[a, b].{x - a, y - b}, {x, -2,
2}, {y, -2, 2}]
  }
 ]

Here the three parts I need (the surface of f, the tangential plane
and the point "punkt" where the plane touches the surface) are shown,
side by side.How can I manage it, that this three graphics are put
together in ONE Graphics.

The attempt

DynamicModule[{a = 1, b = 1, p, q, punkt},
 {Slider2D[Dynamic[{a, b}], {{-2, -2}, {2, 2}}],
  punkt = Dynamic @ Graphics3D[{PointSize[Large], Red, Point[{a, b,
f[a, b]}]}],
  q = Dynamic @ Plot3D[{f[x, y], f[a, b] + grad[a, b].{x - a, y - b}},
{x, -2, 2}, {y, -2, 2}]
  }
 ]

Changes f[x,y] (!!!), but only a and b are dynamically changing. How
could this happen??

Any hints appreciated.

Greeting from Germany

Mike


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