Answer Happy

Consider a camera with internal matrix: 5 00 5 0 00 1 K = 0 and position it point (50, 0, 0) in the world frame and aim it to the origin (i.e. the camera Z-axis should be pointing to the origin of the world frame. 1. Determine the external matrix numerically. 2. Make a 2D plot of the projections of the 8 vertices of the cube. 3. It is going to look a lot better in case you make a wire frame plot of the cube, i.e. connect the vertices with a line (except for all diagonals). 4. What happens when you move the camera towards the cube? And what when you move it away from the cube? Both movements along the X axis. 5. (extra points) Make a movie while you move the camera from its position at (50, 0, 0) along a circle around the origin while keeping it pointed to the origin (hint: keep the Z axis of the camera pointing upwards and calculate the frame transform parameterized with being the angle between the X axis of the world frame and the Z axis of the camera frame).