Overlay a surface and gradient feild

[Adam_Caudell]

I am trying to produce a single graphic that has the surface

Code: Select all

f[x_,y_]:=3x^2y+4xy^2-6xy^3+4x^2y^2

and below it its associated gradient field. I can generate the surface and the gradient field, but I cannot combine them into a single graphic. I have tried naming each plot and using the Show[ ] function, but it does not work.

Essentially, I trying to get this: http://upload.wikimedia.org/wikipedia/e ... ient99.png

Albeit this is a different function, this is what I am trying to accomplish.

Any suggestions?

Thanks,

Adam

[Jose_Luis_Gomez]

f[x_, y_] := 3 x^2 y + 4 x*y^2 - 6 x*y^3 + 4 (x^2)*(y^2);
mygrad[x_, y_, z_] := Evaluate[D[f[x, y], {{x, y, z}}]];
vp3d = VectorPlot3D[ mygrad[x, y, z], {x, -1, 1}, {y, -1, 1}, {z, -16, -14}, VectorStyle -> "Dart"];
shiftedvp3d = vp3d /. {x_?NumberQ, y_?NumberQ, z_?NumberQ} :> {x, y, -20};
Show[Plot3D[f[x, y], {x, -1, 1}, {y, -1, 1}, PlotRange -> All, PlotStyle -> Opacity[0]], shiftedvp3d]

[Adam_Caudell]

Wow...would have never figured that out on my own. Thanks!