本研究皆在建立一套數學模式，模擬單打比賽平擊球之發球與接發球的攻防關係。 研究方法：第一步驟，使用攝影方法分析一位網球選手接發球的反應時間及回擊時間，再運用Splines曲線函數模擬選手三度空間的接發球防守空間。第二步驟，建立網球平擊球之飛行數學方程。第三步驟，以C++電腦程式語言將步驟一、二建立之數學模式，編寫成應用程式進行模擬分析。結論：經由實驗及電腦模擬得知，本研究所建立之數學模式，確實可以模擬發球與接發球之間的攻防關係，且可以發展成為應用軟體，提供給受測選手在賽前進行模擬分析。

The purpose of this study was to simulate the relationship between a serve and a service return in tennis singles by formulating a mathematic model. The methodology was as follows. First, photography was used to analyze the tennis player's time of reaction and service return. Then the Splines curve was used to simulate the defense space of service return in three dimension. Second, the mathematic equation of the flat ball's flight was built. Third, C++ was adopted to edit the above-mentioned mathematic model into the software program for simulation and analysis. Through experiments, it was found that the mathematic model established in this study was really able to simulate the relationship between serve and service return, and that a model could be developed into practical software which provided players with the pre-game analysis from simulation.