A robot knows the gravity vector with respect to the camera coordinate system. Assume that the Z-axis of the world coordinate system is the same as the gravity direction. There is one unknown orientation (we call it the yaw angle) in the unknown orientation matrix between camera and world coordinates. Assume further that we know the projections of two points (x1,y1) and (x2,y2) in calibrated coordinates (no need to multiply with K1) and the corresponding 3D world coordinates (X1,Y1,Z1) and (X2,Y2,Z2). We have four projection equations with four unknowns (,tx,ty ,tz ). 1. Find the unknowns (,tx,ty ,tz ). Hint: Eliminate the translation parameters. Then express cos and sin as a function of one unknown, so that you get a polynomial equation on that unknown. 2. Argue qualitatively why gravity and two points are sufficient to recover the pose of the camera. Which would be a singular case when this cannot happen