I have a given rectangle that I need to transform into a given quadrilateral shape that resulted from a rotation and translation in 3D space, and subsequent projection.
*---------* *---------* | | --> \ / | | \ / *---------* *------*
I only have the coordinates of the projected rectangle (i.e. the four coordinates of the quadrilateral's corners). I need to get back to the 3D rotation and translation that resulted in that projected shape.
Is there a simple mathematical formula that would enable me to compute the values of the rotation vector, rotation angle and translation vector?