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Using GIMP, I have split an image into multiple layers, each holding a similar part of the image (object). I want to perform a z-axis rotation on each of these objects/layers, to give the impression that the object is not flat, but rather extending into the image (as in How to z-rotate a rectangle in perspective using inskcape?).

I am currently trying to achieve this using the Perspective Tool. This works well for one object/layer, but I can't find a way to apply the same transformation automatically to multiple objects/layers. It is difficult to manually achieve the exact same transformation matrix every time, and it would be great if there was a way to do this automatically by selecting multiple layers at once, or at least save the transformation matrix and apply it to each layer without having to manually adjust it each time. Is this possible in GIMP or am I better pasting my bitmaps into Inkscape and trying it there?

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You just "chain" them all together using the chain link icon in the Layers list (see here).

When things are chained (and this also includes channels and paths), transforms applied to one of them are applied to the others.

Another method is to put them all in the same layer group and to apply the transform to the group.

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