Re: Dynamic tangential plane - how?

*To*: mathgroup at smc.vnet.net*Subject*: [mg92916] Re: Dynamic tangential plane - how?*From*: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>*Date*: Sun, 19 Oct 2008 05:40:44 -0400 (EDT)*References*: <gdcdh5$fkf$1@smc.vnet.net>

Hi, f[x_, y_] := (1 - x^2) (2 x - y^3) DynamicModule[{plt, plane, z, t1, t2}, plt = Plot3D[f[x, y], {x, -2, 2}, {y, -2, 2}]; t1 = {1, 0, D[f[x, y], x]}; t2 = {0, 1, D[f[x, y], y]}; Manipulate[ z = Append[p, (f @@ p) + 0.1]; plane = ParametricPlot3D[(z + t1*u + t2*v /. Thread[{x, y} -> p]), {u, -0.5, 0.5}, {v, -0.5, 0.5}, Evaluated -> True, Mesh -> False]; Graphics3D[{plt[[1]], {Opacity[1], plane[[1]]}, {RGBColor[1, 0, 0], Sphere[z, 0.1]}}, BoxRatios -> {1, 1, 1}], {{p, {0, 0}}, {-2, -2}, {2, 2}, Slider2D}] ] ?? Regards Jens m.g. 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 >