Support system for pocket billiards - Estimation of 3D cue direction

A support system for beginners of pocket billiards has been developed. The system exhibits all the guiding lines, which mean the directions to shoot the cue ball in order to sink any of the balls into a pocket, and helps the player to know the easiest shot to sink a ball. The player, however, can not know if the direction is correct or not when shooting the cue ball because the player can not watch the display monitor. This problem can be solved by a function to inform the player the error of the cue direction in real time. However, the error between the cue direction in a captured image and the guiding line is not appropriate to use because the cue direction in the image (2D cue direction) changes depending on the position and the tilt angle of the cue stick. We therefore realized a function to estimate the 3D direction of a cue stick (3D cue direction). The 3D cue direction was parallel projected on the billiard table, and can be compared with the guiding line to know if the cue direction is correct or not. Experimental results show the average error of the parallel projected directions was 0.77 deg, which, we think, is effective for beginners.