Hi Dominic,

We do support interaction of 3D graphics in the Wolfram Cloud based on webgl. That means you can rotate, pan, and zoom your 3D object with just a web browser. The initial rendering is an image, when you interact with the graphic it will switch to webgl, and then transition back to an image when interaction is finished.

However, we do not fully support all primitives or options in Graphics3D that the desktop does and in those cases you will only get a static image.

There will be delay in your Manipulate case, because it makes a round trip back to the server when you move the slider.

Are you still having problems deploying 3D content and getting errors with red boxes?

Just an update. As a start, I can set up a Manipulate to rotate the graphics in the cloud but there is a lot of delay between moving the slider and rendering the graphics, and the quality of the graphics in the cloud is not as good as in the notebook. Is there a way to improve this?

CloudDeploy[
 Animate[With[{v = RotationTransform[\[Theta], {0, 0, 1}][{3, 0, 3}]},
   Show[Plot3D[Sin[x y], {x, -5, 5}, {y, -5, 5}, PlotRange -> 4, 
     ViewPoint -> v]]], {\[Theta], 0, 2 Pi}, 
  AnimationRunning -> False]]

which gives me the link:

link to cloud