本撞球軌跡系統結合了視覺導引介面，用來指示使用者做出可靠的擊球。整合的系統平台是以個人電腦(PC)運行。本視覺系統可用在母球、子球和球桿的軌跡偵測。使用最小平方差法將現實世界跟虛擬世界的撞球座標做校正，以計算出精確的導引線。使用者能夠根據個人電腦螢幕上所顯示的視覺導引線，在撞球桌上調整擊球桿的位置。根據碰撞移動分析來計算出母球理想的視覺導引線，除了要計算出理想的視覺導引，在不同的子球跟袋口中選擇最佳擊球點，也是一個須要探究的影響因素。由子球與袋口的理想導引線，其可容忍進袋的角度大小就代表一個成功擊球的難度，而難度是依序地根據袋口與子球的距離、子球與母球的距離、和這兩個向量的角度大小，此三者來決定。將這些功能條件來模擬容忍角度的測試。選定一子球廣泛的使用不同的幾何參數做測試，包括使用及不使用本整合系統所得到的結果。並選擇不同熟練程度的球員來做實驗。結果顯示所有的球員在技巧的加強方面，都因為我們提出的視覺導引系統而得到了改善，而技術較差的球員更因為本系統的幫助而改善了最多的技巧。包括最大和平均擊球率，所有得到的結果都獲得了改善。擊球率的實驗結果範例跟我們的分析是一致的。擊球率和分析出的子球入袋的容忍角度有著緊密的關聯。種種結果證明了本系統良好的效能，並且此分析結果可以用於有效的遊戲競賽策略。 A billiard ball tracking system is designed to combine with a visual guide interface to instruct users for a reliable strike. The system makes use of a vision system for cue ball, object ball and cue stick tracking. Users are able to adjust the cue stick on the pool table according to a visual guidance line instruction displayed on a PC monitor. In addition to calculating the ideal visual guide, the factors influencing selection of the best shot among different object balls and pockets are explored. It is found that a tolerance angle around the ideal line for the object ball to roll into a pocket determines the difficulty of a strike. This angle depends in turn on the distance from the pocket to the object, the distance from the object to the cue ball, and the angle between these two vectors. Simulation results for tolerance angles as a function of these quantities are given. A selected object ball was tested extensively with respect to various geometrical parameters with and without using our integrated system. Players with different proficiency levels were selected for the experiment. The results indicate that all players benefit from our proposed visual guidance system in enhancing their skills, while low-skill players show the maximum enhancement in skill with the help of our system. All exhibit enhanced maximum and average hit-in rates. Experimental results on hit-in rates have shown a pattern consistent with that of the analysis. The hit-in rate is thus tightly connected with the analyzed tolerance angles for sinking object balls into a target pocket. These results prove the efficiency of our system, and the analysis results can be used to attain an efficient game-playing strategy.
