Need some suggestions about transforming a projected image


Hi all, I need some suggestions about getting back the original object from the projected object. In the attached figure, AB is the projected object onto the XY plane. I need to get back the original object A’B’ from the projected object. I have the corresponding rotation matrix as the object rotates from its ideal position A’C’. The ideal position makes the objected aligned with the XYZ coordinates.

I only have the projected object AB (marked with red line) and the rotation matrix. I have no other information. How can get the corresponding 3D coordinates (A’B’) from the projected object.

Please provide me some suggestion.

In the figure, it is shown that rotation takes place around the end point A. Will it be any different if rotation takes place w.r.t. the origin?