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.
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