I have two 4x4 transformation matrices (rigid transformation) that are applied to the same cylindrical surface-object. Now, what I would like to do is to measure the difference of the objects along the direction of the cylinder (let's call it z'-axis) and also in the xy'-plane. Because the coordination system changes, I find it difficult to figure out how to calculate the difference in the correct direction (i.e. along the axis of the cylinder and xy'-plane).

Help would be appreciated!