Current Issue

A parabolic motion refers to the motion when an object receives force in a direction not the same as the motion direction. As shown in Figure 2, the concept of parabolic motion has an initial velocity (v_ox, v_oy), and the components of the horizontal and vertical directions when the object is launched from the surface can be obtained as Equation 1.

Fig. 2. 
Concept of the parabolic motion formula

Since there is only acceleration in the vertical direction, the velocity in the horizontal direction is constant, being equal to v₀ cosθ [7]. The vertical velocity follows the free fall motion and the acceleration is constant. Therefore, the acceleration at the coordinate P(x, y) in Figure 2 has the values of 0 and –g, respectively. Here, the g, which is he value of 9.81m/s² near the surface of the earth, is the acceleration due to gravity.

The velocity at the coordinate P(x, y) does not change in the horizontal direction, and the vertical direction increases constantly by the gravity g, so it is expressed as Equation 2.

Also, the displacement in the horizontal and vertical directions according to time t is as shown in Equation 3 [7].

In general, the free fall motion refers to a motion in which an object falls near the surface with the gravity g. This section describes the method of obtaining the velocity and displacement values during free fall of a parabolic [8]-[10].

First, the velocity of an object with mass can be obtained by integrating the acceleration over time, and is shown in Equation 4.

Here, the initial velocity v₀ is a value of 0. Second, if the initial displacement is S₀, the displacement of the object can be obtained by integrating the velocity, and is shown in Equation 5.

The composition and flow of the proposed basketball game content system are shown in Figure 3. The transition or flow between activities in the proposed content is similar to the flow of various mobile-based basketball game contents, but it aims to give a realism like enjoying a real basketball by applying the parabolic motion and free fall motion suggested in Section 2.

Fig. 3. 
Flowchart of proposed basketball game content

As shown in Figure 4, the proposed basketball game contents consisted of competition, arcade and last ball game modes. First, the competition mode is a game mode in which a player competes in PVE or PVP for 45 seconds, and wins if the player scores higher than the opponent. Second, the arcade mode has the following features and scenarios as a way to get a score higher than the suggested mission score with three balls.

Fig. 4. 
Three game modes for basketball game content

․ Whenever the ball is not inserted, the ball decreases by one.
․ The game is over when you run out of balls.
․ If you get a score higher than the mission score, you win.
․ Mission scores increase as users keep winning streak.

Lastly, the last ball mode is a game mode in which a free throw is played with one ball, and if the free throw is successful, the game can continue. In particular, the competition and arcade games applied the winning streak system, and the level or mission score increased as the streak continued.

Figure 5 is the main screen corresponding to the overall flow of the basketball game content presented in Figure 3, and shows the results in the arcade mode. Shooting is carried out by dragging from the start position of the screen to a randomly generated position within the ball control time as shown in Figure 5(e). In addition, an item shop function, which can select or upgrade items such as players, uniforms, courts and balls, is implemented as shown in Figure 6 in order to increase the enjoyment and satisfaction of users. The item shop has 6 players, 15 uniforms, 2 basketball courts, and 30 balls. For each item, the ball control time, goal-in area accuracy, pivot time and experience value were applied differently.

Fig. 5. 
Screens for each stage of the proposed basketball game content

Fig. 6. 
Designs implemented in the item shop

The overall flow and designs of the proposed basketball game contents described in this section were implemented within the environment presented in Table 1. In this paper, 3ds Max 2015 and Photoshop CS6 were used for the design of characters, game backgrounds, and various items as shown in Figure 6, and the game engine Unity 2019 was used for overall content design and implementation.

Due to the nature of the proposed basketball game, in order to throw a basketball naturally, the parabolic formula described in Section 2.1 is basically required. First, in order to create the natural trajectory of the ball, the highest position of the parabolic line must be obtained, and the point of arrival (goal-in) must be selected higher than the position of the player throwing the ball. In fact, if the shooting angle is more than 45 degrees, it does not matter to apply that height. However, if the maximum height of the parabola is fixed and the distance between the shooting point and the goal-in is gradually increasing, the firing angle will be 45 degrees or less. This can lead to an unnatural trajectory due to the abnormal ball firing speed. Therefore, when the distance is over a certain distance, the trajectory of the basketball must be naturally produced by setting the height so that the shooting angle is 45 degrees. The code for calculating the distance between the shooting point and the goal-in point on the plane is presented in Table 2.

Second, the free fall time can be calculated as the time to reach the goal-in point using Equation 5, and can be derived as Equation 6.

Finally, as shown in Figure 2, the velocity in the vertical direction at the shooting point must be calculated. The velocity in the vertical direction is the same as the constant acceleration motion because only gravity acts when the resistance of air is ignored. Therefore, the free fall speed v_y is the same as the speed when it reaches the ground as shown in Equation 7.

In addition, codes for calculating the time and the velocity during free fall described in Equations 6 and 7 are presented in Tables 3 and 4, respectively. Figure 7 shows the result screens applied with the contents described in this section.

Fig. 7. 
Result screens based on physical forces