How to rotate an image actor in libgdx by the middle point?

You have to properly set the "origin" of you actor. You can read from the Actor API that the origin is relative to the position and is used for scale and rotation.

So, calculate your middle point, and set origin to middle point.

Actor a;....a.setOrigin(a.getWidth()/2, a.getHeight()/2);

The easiest and shortest way I found for setting the origin is to call:

Actor a;...a.setOrigin(Align.center);

The easiest way is to translate the object so the 0,0 point is the centre, rotate it, then translate it back into position. I'm not familiar with libGDX, but there should be a method for aggregating the three transforms, meaning you apply only the one aggregated transform to your object. Keep in mind the order you aggregate the transforms, makes a difference.

A much more complicated way that gives exactly the same result involves calculating the amount of offset created by the rotate and translating the image back to its origin. Don't do it this way. Combining three simple transforms is the way to go and one of the best reasons for using transforms.

** EditLooking at the API the Actor object has a translate() method. Use this to shift your image so the 0,0 point is in the centre. In psuedocode;

x = this.getX();y = this.getY();cx = this.getWidth() * .5;cy = this.getHeight() * .5;this.translate(-(x+cx), -(y+cy)); // move so 0,0 is the centre of the Actor objectthis.rotate(thisMuch);  // rotate the Actorthis.translate((x+cx), (y+cy)); // move it back to its original location

This will result in your object rotating on its centre point, on the spot. It looks convoluted, but its pretty efficient in practise, more so if you are able to work direct with the matrices (transforms) that will be driving these methods.