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graphics3d - How to make a 3D plot auto-rotate?


When doing presentation with Mathematica, I often want a 3D plot to rotate automatically, so the 3D feeling is stronger. I don't want to drag the mouse every time.


So, I want a general function like


autoRotate["3D graphics here"]

The out put is a rotating version, and I can stop/start the rotation by click a control.



Question: How can I implement this function efficiently so the rotation is as smooth as possible?


Here is my first try: Get viewpoint and compute the rotation matrix;


g = Plot3D[Sin[x y], {x, 0, 3}, {y, 0, 3}];
vc = AbsoluteOptions[g, ViewCenter][[1, 2]];
vp = AbsoluteOptions[g, ViewPoint][[1, 2]];
m = RotationMatrix[3 Degree, {0., 0., 1.}];
newvp = m.(vp - vc);

then manipulate:


Manipulate[If[start, newvp = m.newvp]; 

 Show[g, ViewPoint -> Dynamic[newvp + vc], 
  SphericalRegion -> True ], {start, {False, True }}]

This seems slow and I lose the ability to zoom/rotate the plot manually.


Second try:


DynamicModule[{}, 
   Show[g, ViewPoint -> 
   Dynamic[newvp = m.newvp; newvp + vc, UpdateInterval -> 1.], 
  SphericalRegion -> True ]]


This seems faster, but I can't control the refreshrate. UpdateInterval ->1 seems to lose effect and I also can't zoom/rotate the plot manually.


Update: Based on Rojo's idea and Silvia's comment, here is what I currently use:


autoRotate[gr_Graphics3D, rate_: 7] := 
 DynamicModule[{vp, va, vv, vc }, {vp, va, vv, vc} = 
   gr~AbsoluteOptions~#~OptionValue~# &@{ViewPoint, ViewAngle, 
     ViewVertical, ViewCenter};
  Overlay[{Show[Graphics3D[], ViewPoint -> Dynamic[vp],
     ViewAngle -> Dynamic[va], SphericalRegion -> True], 
    Show[gr, SphericalRegion -> True, 
     ViewPoint -> Dynamic[RotationMatrix[Clock[2 \[Pi], rate], vv].vp],

     ViewAngle -> Dynamic[va], Boxed -> False , Axes -> False]}, All, 
   1]]


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