The purpose of the study is to formulate the offense and defense model in a tennis match by adopting mathemetical methods to locate tennis placements and the defense space.A four-phase study was designed. First, the flying algorithm was established with the application of physics theory. Next, with the use of Spline function, the algorithm for 3D defense space of the receiver was formualted. Then two male students in a college tennis team (Age: 21±1.9years; Height: 175.5±3.5cm ;weight: 70.0±1.4Kg)were asked to move from the preparatory position to hit each of the 100 balls evenly distributed in the space. The data on each returning time were collected through the high-speed video camera (200Hz). In the fourth phase, based on the established algorithm, a computer program was editted to simulate serving and service returning in an attempt to locate the optimal tennis placement and the best defense space. The result showed that:(1) Whether in singles or doubles, a better placement by the striker would be achieved if the service was farther away from the two sides of the receiver (V effect), (2) In singles, if the initial position of the receiver and the contact position of the striker form a disgonal line or a bisecting line, it would lead to the optimal defense space (area bisecting effect), (3) In doubles, if the contact position of the striker and the preparatory positions of two receivers formed an isosceles triangle, it would be the best defense space for the receivers (isosceles triangle effect). When the above three effects are further verified through real-life tennis matches, the designed algorithm can be used to establish an offense and defense model of multiballs; moreover, the simulation model can assist tennis players in effective training
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