Fig. 1.

Demonstration of geometrical relationships with a bunny model. The mouth point is the control point o. In algorithm, all virtual points rotate and scale around the control point p_o = q_o = x_o. We use the tail point to exemplify p_i and its projection q_i. Plane A is parallel to the imaging plane and passes the camera optical center. Without loss of generality and for clearer demonstration, in this figure we use focal length f = 1 and all depthes are distances between points and plane A.