Selecting the best sequence of shots for a given cue position is not an easy task in a game of billiards. The repositioning of the cue after its collision with an object ball determines its success on successive shots. A previous paper by the author was able to assist users in order to perfect a shot based on a selection criterion of maximum angle tolerance. This paper further extends the aiming capability to include a calculation of the ideal speed for the repositioning of the cue ball. The system makes use of a vision system for cue and object balls, and cue stick tracking. Users are able to adjust the cue stick in terms of both the aiming direction and hitting velocity according to the guidance information analyzed by a gaming strategy of this work. A new strategy is proposed to apply the maximum tolerance angle search sequentially twice. One on the pre-collision shot and the second on the post collision path. Additional to the maximum tolerance angle criterion, this paper also proposes a new visible object ball count criterion to assist cue ball repositioning strategy for both direct and indirect shots. This criterion was developed based on an analysis of the zero tolerance zone angle. It has been specifically tested to verify its relation with the successive sink rate using proposed guidance system. The experimental results of the maximum tolerance angle repositioning strategy of our training facility as tested by users with different skill levels all out performed the results without the advice for the same set of users. In addition, the distribution pattern of maximum tolerance test showed the highest degree of similarity with that of accessibility count as user skill level increases. This not only proves the reliability of our training system, but also proves the effectiveness of our algorithm for optimal repositioning. ? 2011 Elsevier B.V. All rights reserved.
