Re: Dynamic tangential plane - how?

*To*: mathgroup at smc.vnet.net*Subject*: [mg92914] Re: Dynamic tangential plane - how?*From*: magma <maderri2 at gmail.com>*Date*: Sun, 19 Oct 2008 05:40:22 -0400 (EDT)*References*: <gdcdh5$fkf$1@smc.vnet.net>

On Oct 18, 12:24 pm, "m.g." <m... at michaelgamer.de> wrote: > 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 David Park shows you a general method he uses, in another post. Here I just wanted to show you the little changes necessary to make your example work DynamicModule[{x, y, a, b}, x = Dynamic[aufpunkt[[1]]]; Dynamic[aufpunkt[[2]]^2]] HTH