Normalize a rotation around the Z-axis (issue with GLM)

I’m trying to undo some transformations coming from an external tool*. I’m getting different results depending on subtle differences in the input and wondering how to convert to a rotation about the Z-axis only.

The transformations are expressed as a matrix = translation * rotation * -translation. I want to decompose the resulting matrix into a single translation and rotation around Z — I know this is possible given the source material (2D plane).

My problem is coming from GLM decompose. Given a matrix that looks like this:

[         -0.5 |     0.866025 |            0 |            0 ] [    -0.866025 |         -0.5 |            0 |            0 ] [            0 |            0 |            1 |            0 ] [            0 |            0 |            0 |            1 ] 

If I call decompose, then take the eulerAngles of the Rotation I end up with either:

  • ( 0, -0, 2.09439 ) from quat( 0.5, 0, 0.866025, 0 )
  • ( 3.14159, 1.0472, 3.14159 ) from quat( 0.5, 0, 0, 0.866025 )

The difference depends on how the matrix was generated, whether the rotation was 120degrees or -240degrees. The display must be clipping the floating point, introducing a subtle change.

I’m assuming both these rotations are actually the same.

How do I force/convert the result to be a rotation about the Z axis only.


*The external tool is Inkscape which uses the CSS/SVG function rotate(r, cx, cy) instead of a rotation and transform. That function results in the matrix: translate(cx,cy,0) * rotate(r, (0,0,1)) * translate(-cx,cy,0)