For objective 1, the function for bank shot and swish has been deduced. By changing the subject relationship of and v required for scoring is deduced, the range of β and v is represented by the area between two functions. The larger the area, the higher the possibility of scoring.
For the objective 2, in the bank shot condition, the position of the player is defined as (x, Θ). x increases, namely the player is further from the basket, the range of β and v decreases, the wiggle room increases, the shift angle variation (γ) decreases. When α increases, the wiggle room(s) increases, the range for and v increases, the shift angle variation (γ) decreases. The range forand v, the shift angle variation (γ) and the wiggle room(s) were used to show the possibility of scoring in 3-D condition. These variables increases, the possibility of scoring increases. Individual variables vary differently according to the change of position and height of the player. A combination of all these variables is needed.
For objective 3, h increases, release height increases, the range for and v increases.
Therefore the player should release the basketball from a point as high as possible.
For the objective 2, in the bank shot condition, the position of the player is defined as (x, Θ). x increases, namely the player is further from the basket, the range of β and v decreases, the wiggle room increases, the shift angle variation (γ) decreases. When α increases, the wiggle room(s) increases, the range for and v increases, the shift angle variation (γ) decreases. The range forand v, the shift angle variation (γ) and the wiggle room(s) were used to show the possibility of scoring in 3-D condition. These variables increases, the possibility of scoring increases. Individual variables vary differently according to the change of position and height of the player. A combination of all these variables is needed.
For objective 3, h increases, release height increases, the range for and v increases.
Therefore the player should release the basketball from a point as high as possible.