You will design a game interface in a MATLAB program named HDTask1.m . In this g

Question

You will design a game interface in a MATLAB program named HDTask1.m. In this game, an animation should be created to display the flying trajectories of the ball shot from a fixed initial height and fixed initial velocity at release. The game player will attempt to adjust the release angle (shooting angle) of the ball to hit a board placed at the ground. Once the ball hits the board, the player will score one point. Then, the board will be randomly re-located to another position for the player to attempt another round. The specific design requirements are given below:

Initial height of ball at release is fixed at 1.5 m.

Initial velocity of ball at release is fixed at 4 m/s.

Board length is of 0.5 m and located at height 0 horizontally.

Diameter of ball is approximately one-third of the board length.

The ball should be at rest on the board for at least 0.5 second once hit.

The board should be randomly re-located within a range reachable by the ball for

each new round.

Scores should be displayed.

The player could adjust the shooting angle in command window and command the

action of shooting.

The program should have a command for player to exit the program.

The program should handle exceptions such as when player enters an invalid

shooting angle, etc.

The program should not crash MATLAB during running (i.e., good reliability).

You may add additional functions to your program to make it funny.

Show the screenshot of your game interface and the animation snapshots. You should add comments in your program to describe the codes allowing others to understand your code easily.

Screenshots of the game may look this:

Any help would be greatly appreciated, I am struggling a bit with it

Thank you

Game starting: Figure Ele Edit View Insert Tools Desktop Window Help - Ball Shooter Game 2.5 2 Score: 0 0.5 -0.5 -1 0 0.5 1.5 22.53 3.5 4 Player enters the shooting angle: Command Window New to MATLAB? See resources for Getting Started. To exit the game, enter x. To play the game, enter a shooting angle between -90 and 90 degree: 60 Scoring:

Explanation / Answer

% Simulation models of a TENNIS ball in VACUUM and AIR with and without
% spin using Symbolic MATH, MuPAD, ODEx solvers and SIMULINK
% This script executes all Simulink models and M-files except for MuPAD
% commands.
% NB: place all scripts and SIMULINK models in the same directory, and then
% execute this script RUN_all.m
% NB: Plot figures require from a user to indicate graphically where to
% display final computed data in the plot area.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
clearvars
close all
%% MATLAB 2010 or earlier versions
%{
In VACUUM
x_z_vac=dsolve('D2x=0', 'D2z=-g','x(0)=0',...
'Dx(0)=v0*sin(eta*pi/180)','z(0)=h', ...
'Dz(0)=v0*cos(eta*pi/180)', 't');
x=x_z_vac.x %#ok
z=x_z_vac.z %#ok
%}

%% MATLAB 2012 or later versions
%{
In VACUUM
syms x(t) z(t)
syms g h eta v0
Dx=diff(x); Dz=diff(z);
D2x=diff(x,2); D2z=diff(z,2);

x_z_vac=dsolve(D2x==0, D2z==-g,...
x(0)==0,Dx(0)==v0*sin(eta*pi/180),...
z(0)==h,Dz(0)==v0*cos(eta*pi/180));
x(t)=x_z_vac.x %#ok
z(t)=x_z_vac.z %#ok
%}
%% Analytical solution of the ball trajectory in vacuum
% Case #1
%% In MuPAD
%{
#ICs:

V0:=25; h:=1;eta:=15;g:=9.8;
ODE_eqn1:=ode({x''(t)=0, x(0)=0, x'(0)=V0*float(cos(eta*PI/180))}, x(t));
ODE_eqn2:=ode({z''(t)=-g, z(0)=h, z'(0)=V0*float(sin(eta*PI/180))},
z(t));
Sols1:=ode::solve(ODE_eqn1);
Sols2:=ode::solve(ODE_eqn2);
Sol_CURVE:=plot::Curve2d([24.14814566*t, 1.0 - t*(4.9*t - 6.470476128)],
t=0..2, ViewingBox = [0..35.5, 0..3.35]);
plot(Sol_CURVE, #G);
%}
%% In Symbolic MATH
% syms x(t) z(t)
% syms g h eta v0
% Dx=diff(x); Dz=diff(z);
% D2x=diff(x,2); D2z=diff(z,2);
%
x_z_vac=dsolve('D2x=0', 'D2z=-g','x(0)=0',...
'Dx(0)=v0*cos(eta*pi/180)','z(0)=h', ...
'Dz(0)=v0*sin(eta*pi/180)', 't');
xt=x_z_vac.x %#ok
zt=x_z_vac.z %#ok
g=9.8; % gravitational accl
h=1; % ball hit 1 m above ground
eta=15; % ball hit under 15 degrees
v0=25; % initial velocity of ball
xt=vectorize(xt);
zt=vectorize(zt);
t=linspace(0,3.5, 200);
xt=eval(xt);
zt=eval(zt);
z_i=find(zt==min(abs(zt)));
touch_gr=xt(z_i);
t_touch = t(z_i);
figure
plot(xt, zt,'ko', 'markersize', 4,'MarkerFaceColor','y'), grid on
xlim([0, touch_gr]);
text0=('Ball is hit h=1[m] above ground & under eta=15^0');
gtext(text0, 'fontsize', 10);

text1=['Ball hits the ground in distance (of x) ' num2str(touch_gr) '[m]'];
gtext(text1);
text2=['Ball hits the ground after : ' num2str(t_touch) ' [sec]'];
gtext(text2);

title('Trajectory of TENNIS ball hit in VACUUM, v_0=25 [m/s] ')
xlabel('x, (horizontal) [m]'), ylabel('z, [m]')
%
%% Solved by ODEx
% Trajectory of a Tennis Ball
% Given: x" = -Cd*alfa*v*x'+eta*Cm*alfa*v*z'
% y" = -g-Cd*alfa*v*z'-eta*Cm*alfa*v*x'
%{
x(0)=0; z(0)=0; x'(0)=v0*cos(eta);
z'(0)=v0*sin(eta); eta=1; v0=25 [m/*sec^-1];
eta=15 [deg]; ro=1.29 [kg*m^-3]; g=9.81 [kg*m];
v=sqrt(x'^2+z'^2); d=.063 [m]; m=.05 [kg];
%}
clearvars
h =1; % [m];
v0=25; % [m*sec^-1];
theta=15; % [deg];
ro=1.29; % [kg*m^-3];
g=9.81; % [kg*m]
d=.063; % [m];
m=.05; % [kg];
w=20; % [m*sec^-1]; angular velocity of a spinning ball
eta=1; % describes direction(+-) of rotation;
% eta=1 is for topspin.
alfa=ro*pi*d^2/(8*m);
time=0:.01:1.5;
ICs=[0, 1, v0*cos(theta*pi/180), v0*sin(theta*pi/180)];

u = @(t,x)sqrt(x(3).^2+x(4).^2);
CD = @(t,x)(0.508+(1./(22.053+4.196*(u(t,x)./w).^(5/2))).^(2/5));
CM = @(t,x)(1/(2.022+.981*(u(t,x)./w)));
vacuum = @(t,x)([x(3); x(4); 0; -g]);
nospin = @(t,x)([x(3); x(4);
(-1)*CD(t,x)*alfa*u(t,x)*x(3);
(-1)*g-CD(t,x)*alfa*u(t,x)*x(4)]);
topspin= @(t,x)([x(3); x(4);
(-1)*CD(t,x)*alfa*u(t,x)*x(3)+eta*CM(t,x)*alfa*u(t,x)*x(4);
(-1)*g-CD(t,x)*alfa*u(t,x)*x(4)-eta*CM(t,x)*alfa*u(t,x)*x(3)]);

[tvac, XZvac]= ode23(vacuum, time, ICs, []);
[tns, XZns] = ode45(nospin, time, ICs, []);
[tts, XZts] = ode113(topspin, time, ICs, []);

% It is also important to find when the ball hits the ground
% (x-axis) and after how many seconds.
% For three cases: Vacuum, nospin and top-spin

% Case #1. Vacuum
z_i=find(abs(XZvac(:,2))<=min(abs(XZvac(:,2))));
t_gr=XZvac(z_i,1);
t_t = time(z_i);

% Case #2. No-spin
z1_i =find(abs(XZns(:,2))<=min(abs(XZns(:,2))));
t_gr1=XZns(z1_i,1);
t_t1 = time(z1_i);

% Case #3. Top-spin
z2_i =find(abs(XZts(:,2))<=min(abs(XZts(:,2))));
t_gr2=XZts(z2_i,1);
t_t2 = time(z2_i);
figure
plot(XZvac(:,1), XZvac(:,2), 'bo', 'linewidth', 1), grid
hold on
plot(XZns(:,1), XZns(:,2), 'm', 'linewidth', 2)
plot(XZts(:,1), XZts(:,2), 'ko-', 'linewidth', 1.0)
legend('In Vacuum','No-Spin in Air','Top-Spin in Air',0)
ylim([0, 3.35])
title 'Trajectory of a Tennis Ball hit under eta=15^0, h=1 m'
xlabel 'Distance, [m]', ylabel 'Height, [m]'

tt1=['VACUUM: Ball hits the ground (x-axis):' num2str(t_gr) '[m]'];
gtext(tt1);
tt1a=['VACUUM: Ball hits the ground after: ' num2str(t_t) '[sec]'];
gtext(tt1a);
tt2=['Nospin: Ball hits the ground: ' num2str(t_gr1) '[m]'];
gtext(tt2);
tt2a=['Nospin: Ball hits the ground: ' num2str(t_t1) ' [sec]'];
gtext(tt2a);
tt3=['Topspin: Ball hits the ground: ' num2str(t_gr2) '[m]'];
gtext(tt3);
tt3a=['Topspin: Ball hits the ground: ' num2str(t_t2) '[sec]'];
gtext(tt3a);
hold off
%
%% Simulink model
eta=1;
open('TENNIS_Ball.mdl')
set_param('TENNIS_Ball','Solver','ode3','StopTime','1.5');
[tout, SIMout]=sim('TENNIS_Ball.mdl');
% plot(tout, SIMout(:,1), 'gd-', tout, SIMout(:,3),'ko', tout, SIMout(:,5),'rh');
% title('Simulation of the Simulink model')
% xlabel('time, [sec]'), ylabel('Height, [m]')
% ylim([0, 3.35])
% legend('Vacuum','NO-spin','TOP-spin',0)
figure
plot(SIMout(:,2), SIMout(:,1),'gd-',SIMout(:,4),SIMout(:,3),'ko',SIMout(:,6), SIMout(:,5),'rh')
ylim([0, 3.35])
title('Simulation of the Simulink model')
xlabel('ground, [m]'), ylabel('Height, [m]')
legend('Vacuum','TOP-spin','NO-spin',0)
shg
%% Spin value influence on distance covered by the ball
%{
clear all
open('TENNIS_Ball.mdl')
set_param('TENNIS_Ball','Solver','ode4','StopTime','1.5');
ETA=0:.2:1;
% Plot label settings;
Labelit = {};
Colorit = 'brgckmygrckmbgrygr';
Lineit = '--:-:--:-:--:----:----:--';
Markit = 'oxd+s*h+^v<p>.xsh+od+*^v';
figure
for ii=1:length(ETA)
eta=ETA(ii);
[tout{ii},SIMout{ii}]=sim('TENNIS_Ball.mdl');
Stylo = [Colorit(ii) Lineit(ii) Markit(ii)];
plot(SIMout{:,ii}(:,4), SIMout{:,ii}(:,3), Stylo)
Labelit{ii} = ['eta = ' num2str(eta)];
legend(Labelit{:},3)
hold on
end
title(['Trajectory of a Ball with different spin values. ',...
'eta=1 (highest spin), eta=0 (no spin)'])
ylim([0, 3.0])
xlabel('ground, [m]'), ylabel('Height, [m]')
hold off
shg
%}
%% Alternative version and more compact version.
clear all
open('TENNIS_Ball.mdl')
set_param('TENNIS_Ball','Solver','ode4','StopTime','1.5');
ETA=0:.2:1;
% Plot label settings;
Labelit = {};
Colorit = 'brgckmygrckmbgrygr';
Lineit = '--:-:--:-:--:----:----:--';
Markit = 'oxd+s*h+^v<p>.xsh+od+*^v';
figure
for ii=1:length(ETA)
eta=ETA(ii);
[tout,SIMout]=sim('TENNIS_Ball.mdl');
Stylo = [Colorit(ii) Lineit(ii) Markit(ii)];
plot(SIMout(:,4), SIMout(:,3), Stylo)
Labelit{ii} = ['eta = ' num2str(eta)];
legend(Labelit{:},3)
hold on
end
title(['Trajectory of a Ball with different spin values. ',...
'eta=1 (highest spin), eta=0 (no spin)'])
ylim([0, 3.0])
xlabel('ground, [m]'), ylabel('Height, [m]')
hold off
shg

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