Given a 4x4 homogeneous matrix, how can I get 3D world coords?

The matrix is a 4x4 matrix, but as you've just got a single dimensional matrix it appears that the elements are arranged as follows.

euclideanspace.com/maths/geometry/affine... - here is the explanation how the 4x4 matrices work. The first minor 3x3 - is a rotation matrix. The last column except last element is a translation vector.

And element4, 4 is a scale factor. Read more about this at the link.

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