Question

If given a rotation axis normalized, such as {1/Sqrt[3],1/Sqrt[3],1/Sqrt[3]}, and a 3d plot, for example,

z[x_, y_] := Exp[-(Sqrt[x^2 + y^2]/Power[4, (3)^-1]) +
Power[4, (3)^-1]*Sqrt[1/2*(Sqrt[x^2 + y^2] + x)]];

Plot3D[2*z[x, y], {x, -5, 5}, {y, -5, 5}]

I want to create an animation for this plot about the axis {1/Sqrt[3],1/Sqrt[3],1/Sqrt[3]} (could be any other arbitary one), and then export it as an animated gif. Would anyone please help? Many thanks.

Edit

I also left out one degree of freedom in specifying the rotation. Could any one please help, if also given the coordinate of a point which the rotational axis must pass, how to do the visualization/animation?
Thanks again.

Answer 1

Could do as below.

axis = {1, 1, 1};

Animate[
  Plot3D[2*z[x, y], {x, -5, 5}, {y, -5, 5}] /. 
    gg : GraphicsComplex[___] :> Rotate[gg, theta, axis],
  {theta, 0., 2.*Pi}]

Daniel Lichtblau
Wolfram Research