We can click and drag Graphics3D objects. Suppose you click and drag on such an object in the center of it and move your pointer of mouse in a circle of radius r.

If I wanted to do the same by code instead of mouse what would be the equivalent geometric transformation?

I tried using code with parameter fi, but it is behaving strangely, not as expected.

GeometricTransformation[graphics,RotationTransform[{{1, 0, 0}, 
   RotationMatrix[fi, {1, 1, 1}] . {1, 0, 0}}, (0,0,0}]]
  • $\begingroup$ "Strangely" - what is happening exactly? If you describe the problem, it's easier to propose a solution. Also please include complete executable code, for instance including a sample graphics object to work on, values of fi, and how you used your code for visualization. $\endgroup$
    – MarcoB
    Sep 11, 2022 at 14:17
  • $\begingroup$ I mean I can not figure out the required transformation. Just evaluate Graphics3D[Cuboid[], SphericalRegion -> True] then click somewhere in the middle of the object and drag by mouse in a circle. Then do the same with code using Manipulate or Animate. $\endgroup$ Sep 11, 2022 at 14:22
  • $\begingroup$ It is clearly some rotation. But you should define more clearly what rotation you want. About a fixed axes or about a moving axis. $\endgroup$ Sep 11, 2022 at 15:26
  • 2
    $\begingroup$ The default option for "RotationControl" in Graphics3D is "ArcBall". Therefore, you should look online for the equations of the arcball camera (example). $\endgroup$
    – Domen
    Sep 11, 2022 at 15:38
  • $\begingroup$ @Daniel Huber: What is not clear? Exact same transformation that dragging by mouse is doing on 3D objects + mouse is doing circle on the screen. It is perfectly stated. mathematica.stackexchange.com/questions/273253/… $\endgroup$ Sep 11, 2022 at 16:12

1 Answer 1


Likely not the simpler approach or the smoother movement. I want the ViewPoint to move in a circle around the current ViewPoint. This is a circle on a sphere. I get a bunch of points on this circle, order them and use them to adjust the ViewPoint in animate.

g = Graphics3D[Cuboid[]]
vp = Options[g, ViewPoint][[1]][[2]];
d = EuclideanDistance[{0, 0, 0}, vp];
fi = Values[
    EuclideanDistance[{0, 0, 0}, {x, y, z}] == d && 
     EuclideanDistance[vp, {x, y, z}] == 0.4, {x, y, z}, Reals, 300]];
nr = NestList[Flatten[Nearest[fi = DeleteCases[fi, #], #], 1] &, 
   fi[[1]], 299];
Show[g, ViewPoint -> n],
 {n, nr}]

enter image description here

The following shows the initial camera position (ViewPoint) in red and the circular ViewPoints generated by 300 points for the animation.

Show[g, Graphics3D[{Point[nr], Red, Point[vp]}]]

enter image description here


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