[b]Note[/b][br]Given complexity of the simulation it's [i][b]highly advisable[/b][/i] to download the .ggb file and run it through the [i]Geogebra classic[/i] desktop program. The web/smarphone Geogebra apps [b]can’t run it in a proper way[/b].[br][br][size=85]The worksheet Basketball 3D (v. 3.4.4) is a refinement of the previous material [url=https://www.geogebra.org/m/tMrZheXb]Basketball3D[/url] with the [b]addition of rebounds[/b] against the backboard and the rim together with the ball bounces when hitting the floor. It also uses exact parabolic trajectories instead of some sort of numerical integration.[br]Adding rebounds was not an easy task but greatly enhances the realism of the simulation.[br]It also enrich the shooting practice with the possibility of [url=https://en.wikipedia.org/wiki/Glossary_of_basketball_terms#R]rimshots[/url] and [url=https://en.wikipedia.org/wiki/Glossary_of_basketball_terms#B]bankshots[/url].[br]The guide to the use of the worksheet and the meaning of the controls are at the end of this page, together with a demo video.[/size][br][br]Author's website: [url=https://www.lucamoroni.it]www.lucamoroni.it[/url]

[b]Trajectories in the Graphics3D window[/b][br]When the file is opened the first two parabolic trajectories are shown, calculated from the shot parameters. These will later become, in case of rebounds, the [i]current[/i] and the [i]next[/i] trajectories.[br][br][b]Basic operations[/b][br][list][*]Click “[b][i]New Trial[/i][/b]” to position the shooter (the shooter will be placed randomly on the half-field). The position of the player can also be changed by manually moving the [b][i]A[/i][/b] point.[br][/*][*]Through the sliders adjust the parameters “[math]\alpha[/math]” (horizontal direction), “[math]\phi[/math]” (vertical inclination) and “‍v[sub]0[/sub]‍” to direct the shot to the basket.[br][/*][*]The checkbox “[math]\alpha[/math] fine tuning”, if checked will change the maximum and minimum values of the [math]\alpha[/math] slider will be closer to the correct horizontal direction, making it easier to fine tuning its value.[br]After a new placement of the player the shot parameters are automatically set in a semi-random manner: they are not the correct parameters to guarantee a successful shot but they are neither very far from the correct values. [br]Alternatively you can use the small buttons placed to the left of the sliders to automatically set the parameters:[br][list][*]set [math]\alpha[/math]: will set the right horizontal direction [br][/*][*]set [math]\phi[/math]: will set the right vertical slope of the shoot (given the actual value of v[sub]0[/sub])[br][/*][*]set v[sub]0[/sub]: will set the right speed of the shot (given the actual value of [math]\phi[/math]).[/*][/list][/*][/list][*]Click “[b][i]Shoot![/i][/b]” to start the animation[/*]See the result and repeat the operation[br][br][b]The “[i]Shoot![/i]”[/b][br]With the same “[i]Shoot![/i]” button it’s possible not only to start the animation, but also to pause/resume it.[br]The animation speed can be controlled by the “Speed” slider. The reference value for this parameter is 1, that correspond, more or less, to a physically based real-time speed.[br]However, a smaller speed will increase the accuracy of the simulation, the correct detection of the rebounds and the correct recording of the result.[br]After the rebounds (when the ball ends up below the horizontal plane passing by the center of the ring) the shot result will be shown in the Graphics view 3D, with the following[br]possible outcomes: “[b]Fail[/b]”, “[b]OK – 3pts[/b]”, “[b]OK – 2pts[/b]”.[br]The points scored in the single shot are also used to update the statistics of the session in the “[i]Stats[/i]” table.[br][br][b]Other parameters and buttons[/b][br]“[b][i]dmpflo[/i][/b]”: the amount of dumping or speed reduction of the ball after it hits the floor.[br]A value in the range 0.7-0.8 works fine.[br]“[b][i]dmpbb[/i][/b]” : the amount of dumping or speed reduction of the ball after it hits the floor.[br]A value in the range 0.7-0.8 works fine.[br]“[b][i]dmprim[/i][/b]”: the amount of dumping or speed reduction of the ball after it hits the rim.[br]Values in the range 0.5-0.6 are suggested.[br]“[b][i]IC[/i][/b]” (drop-down list): in case an interesting initial condition is found (i.e, one with nice rebounds) it’s possible to save its relevant parameters (position of the player, direction and speed of the shot) in one of three lists, to be retrieved later. This drop-down list allows to select the initial condition (IC1, IC2, IC3) on which to operate for saving in it the current configuration or for retrieving form it the parameters to substitute the ones of the current configuration.[br]“[b][i]SaveIC[/i][/b]” button: saves the current configuration in the list selected through the [i]IC[/i] drop-down list.[br]“[b][i]RestoreIC[/i][/b]” button: load in the current configuration the configuration previously saved in the list selected through the IC drop-down list.[br][br][b]Visual aids[/b][br][list][*]The “h[sub]max[/sub]” (point) is the vertex of the initial parabola.[/*][*]A blue point on the backboard marks the point of impact of the ball with the backboard. In case of no impact with the backboard this point is smaller and lighter and take the meaning of the point of intersection between the ball initial trajectory and the plane of the backboard.[/*][*]There is a moving gray disk representing the ball projection (shadow) on the floor.[/*][*]In the 3D window there are buttons to quickly change the point of view.[/*][/list][b]Possible issues[/b][br][list][*]Many mistakes have been detected in the previous versions of this worksheet. Even if the actual version has been tested thoroughly, it can’t be excluded that some other (more elusive) error is still present in the calculation of the rebounds or in the setting of the score.[/*][*]In some circumstances the “[i]t[/i]” slider , controlling the whole animation, may start being jerky and irregular. If this should happen, to restore a more smoother behavior of the animation it’s necessary to close the Geogebra program and re-open it. [/*][*]If the speed of the animation is too high rebounds and the result of the shot may not be properly calculated or visualized. It’s advisable to keep the speed value less than 0.8 or even less in case of shots from a great distance.[/*][/list][b]Note[/b][br]Given complexity of the simulation it's [i][b]highly advisable[/b][/i] to download the .ggb file and run it through the [i]Geogebra classic[/i] desktop program. The web/smarphone apps can’t run it in a proper way.[br][br]