在VR中進行籃球戰術訓練有研究證明是有效的。而在VR籃球訓練系統中，雖然可以讓教練在電子戰術板上草擬進攻軌跡，但是若能提供即時的生成防守軌跡，將會提高訓練系統的實用性。因此為了能夠提供更好的虛擬訓練體驗，我們提出基於自迴歸特性的方法來模擬更逼真的防守軌跡。在我們所提出的方法中，我們藉由先前防守軌跡以及當前進攻者和球的位置作為輸入，並且設計出一種基於可微分位置採樣算法和因果卷積機制的生成模型，來學習玩家位置之間的關係。我們以客觀和主觀的方式評估生成防守軌跡與真實防守軌跡之間的相似性。為了進行客觀評估，我們以球員的防守位置、運動速度和加速度，以及基於沃羅諾伊算法計算球員在球場上的可進攻空間和防守壓力來比較生成軌跡和真實軌跡之間的差異。而為了進行主觀評估，我們邀請70名受試者進行問卷調查，讓他們判斷影片中顯示的防守軌跡是否為真實。根據問卷調查結果，受試者很難分辨真實的籃球防守軌跡和生成的防守軌跡區的差異。這表示我們所提出的自回歸模型可以生成真實的防守軌跡。

Tactics learning in VR has been proved to be effective for basketball training. In VR training system, the coach can input offensive trajectories by drawing via an electronic tactic board, but defensive trajectories should be generated automatically to improve the efficiency and usability. To provide a better virtual training process, we aim to simulate more realistic defensive trajectories based on an autoregressive method. In the proposed method, the previous defensive trajectories, the current offender positions, and the current ball position are taken as the input. Then, a generative model based on a differential position sampling algorithm and a causal convolution mechanism is designed to learn the relation between player positions. The similarity between the generated defensive trajectory and the real defensive trajectory is evaluated in both objective and subjective manners. For objective evaluation, we compare the defensive position, movement speed, and acceleration difference between the generated trajectories and the real ones. In addition, we calculate the empty space for the offender and the defensive pressure based on the Voronoi algorithm to compare defensive trajectories. For subjective evaluation, we recruited 70 experimenters to conduct questionnaires for judging whether the defensive trajectories shown in the video is realistic. According to the questionnaire result, the experimenters are difficult to distinguish the real basketball defensive trajectories from the generated ones. This implies that the proposed autoregressive model can generate realistic defensive trajectories.

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