title: how to animate 3d plot given a rotation axis in mathematics
body: <p>If given a rotation axis normalized, such as {1/Sqrt[3],1/Sqrt[3],1/Sqrt[3]}, and a 3d plot, for example, </p>
  
  <p><code>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)]];</code></p>
  
  <p><code>Plot3D[2*z[x, y], {x, -5, 5}, {y, -5, 5}]</code></p>
  
  <p>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.</p>
  
  <p><strong>Edit</strong></p>
  
  <p>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.</p>