Suppose we have two Cartesian coordinate systems: (X,Y,Z) and (X,Y,Z). Between these two coordinate systems, the rotation matrix is R and the translation vector is T. (a) Write the rigid transformation between these two coordinate systems. (b) Suppose (X,Y,Z) is the world coordinate system, and (X,Y,Z) is the camera coordinate system. The camera has a focal length f and pixel size s. Write the transformation that relates the a point (X,Y,Z) and its projection (u,v) on the camera image plane. (c) If the camera is rotated counter-clockwise by some degree along Z direction; derive the transformation between the original (u,v) and the new one