[Basketball- MATLAB]

clear all; clc; close all;

format long;

num_shots = 7;

% preallocate results structure

results(num_shots) = struct('Zo', [], 'phi', [], 'status', [], 'X', [], 'Y', [], 'Z', [], 'U', [], 'V', [], 'W', [], 'T', []);

% loop over shots

for shot_num = 1:num_shots

   [Xo, Yo, Zo, Umag0, theta, phi, omgX, omgY, omgZ] = read_input('test_study_parameter.txt', shot_num);

   [T, X, Y, Z, U, V, W, status] = basketball(Xo, Yo, Zo, Umag0, theta, phi, omgX, omgY, omgZ);

   results(shot_num).Zo = Zo;

   results(shot_num).phi = phi;

   results(shot_num).status = status;

   results(shot_num).X = X;

   results(shot_num).Y = Y;

   results(shot_num).Z = Z;

   results(shot_num).U = U;

   results(shot_num).V = V;

   results(shot_num).W = W;

   T = T(end);

   results(shot_num).T = T;

end

figure(1);

hold on;

load('court_geometry.mat');

figure(1); hold on;

plot3(Xcourt,Ycourt,Zcourt,'.','color',[0.5 0.2 0.3]);

plot3(Xrim,Yrim,Zrim,'-','color',[.8 0 0.8]);

plot3(Xboard,Yboard,Zboard,'.','color',[1 0.9 1]);

box on; grid on; axis tight; axis equal;

xlabel('x (m)'); ylabel('y (m)'); zlabel('z (m)');

title('Basketball Court');

view(3);

set(gca,'FontSize',16);

colors = lines(num_shots); % generate a set of distinct colors for each shot

for shot_num = 1:num_shots

   plot3(results(shot_num).X, results(shot_num).Y, results(shot_num).Z, 'color', colors(shot_num,:), 'LineWidth', 1.5, 'DisplayName', ['Shot ', num2str(shot_num)]);

   plot3(results(shot_num).X(1), results(shot_num).Y(1), results(shot_num).Z(1), 'o');

   plot3(results(shot_num).X(end), results(shot_num).Y(end), results(shot_num).Z(end), '*');

end

title('Optimal Shooting Angles Study');

xlabel('X Position (m)');

ylabel('Y Position (m)');

zlabel('Z Position (m)');

grid on;

hold off;

%make the data strucutre

ball_stat = struct('shot_number', cell(1, num_shots), 'time', cell(1, num_shots), 'max_height_position', cell(1, num_shots), 'landing_position', cell(1, num_shots), 'landing_speed', cell(1, num_shots), 'travel_distance', cell(1, num_shots));

for shot_num = 1:num_shots

   ball_stat(shot_num).shot_number = shot_num;

   ball_stat(shot_num).time = results(shot_num).T;

   [~, idx_max_height] = max(results(shot_num).Z);

   ball_stat(shot_num).max_height_position = [results(shot_num).X(idx_max_height), results(shot_num).Y(idx_max_height), results(shot_num).Z(idx_max_height)];

   ball_stat(shot_num).landing_position = [results(shot_num).X(end), results(shot_num).Y(end), results(shot_num).Z(end)];

   landing_velocity = [results(shot_num).U(end), results(shot_num).V(end), results(shot_num).W(end)] ; % [Ux, Vy, Wz]

   ball_stat(shot_num).landing_speed = sqrt(landing_velocity(1)^2 + landing_velocity(2)^2 + landing_velocity(3)^2);

   travel_distance = 0;

   for i = 2:length(results(shot_num).X)

       dx = results(shot_num).X(i) - results(shot_num).X(i-1);

       dy = results(shot_num).Y(i) - results(shot_num).Y(i-1);

       dz = results(shot_num).Z(i) - results(shot_num).Z(i-1);

       travel_distance = travel_distance + sqrt(dx^2 + dy^2 + dz^2);

   end

   ball_stat(shot_num).travel_distance = travel_distance;

end

%study on optimal shooting angles

num_simulations = 1200;

results5(num_simulations) = struct('Zo', [], 'phi', [], 'status', [], 'X', [], 'Y', [], 'Z', [], 'U', [], 'V', [], 'W', [], 'T', []);

for shot_num = 1:num_simulations

   [Xo, Yo, Zo, Umag0, theta, phi, omgX, omgY, omgZ] = read_input('best_angle_study_parameter.txt', shot_num);

   [T2, X2, Y2, Z2, U2, V2, W2, status] = basketball(Xo, Yo, Zo, Umag0, theta, phi, omgX, omgY, omgZ);

   results5(shot_num).Zo = Zo;

   results5(shot_num).phi = phi;

   results5(shot_num).status = status;

   results5(shot_num).X = X2;

   results5(shot_num).Y = Y2;

   results5(shot_num).Z = Z2;

   results5(shot_num).U = U2;

   results5(shot_num).V = V2;

   results5(shot_num).W = W2;

   T = T2(end);

   results5(shot_num).T = T2;

end

figure(2); hold on;

for shot_num = 1:num_simulations

   if results5(shot_num).status == 1

   plot(results5(shot_num).Zo, results5(shot_num).phi, 'o', 'MarkerSize', 5, 'MarkerFaceColor', 'r', 'MarkerEdgeColor', 'r');

   end

   if results5(shot_num).status == 0

   plot(results5(shot_num).Zo, results5(shot_num).phi, 'o', 'MarkerSize', 5, 'MarkerFaceColor', 'k', 'MarkerEdgeColor', 'k');

   end

end

xlabel('Initial Vertical Position Z0 (m)');

ylabel('Shooting Angle \phi (degrees)');

title('Optimal Shooting Angles Study');

legend({'Successful Shot', 'Missed Shot'}, 'Location', 'best');

hold off;

good = 0;

for i = 1:1200

   if results5(i).status == 1

       good = good + 1;

   end

end

disp(good)

function [T, X, Y, Z, U, V, W, status] = basketball(Xo, Yo, Zo, Umag0, theta, phi, omgX, omgY, omgZ)

%basketball returns a vector for time, x-positions, y-positions, z-positions,

% x-velocities, y-velocities, z-velocities, and status of shot throughout

% the ball's time in the air.

%Call format: [T, X, Y, Z, U, V, W, status] = basketball(Xo, Yo, Zo, Umag0,

%theta, phi, omgX, omgY, omgZ);

m = 0.625;

r = 0.12;

A = pi * r^2;

drim = 0.46;

rrim = drim/2;

rho = 1.2;

g = 9.81;

Cd = 0.3;

Cm = 0.13;

dt = 0.01;

load('court_geometry.mat', 'Xboard', 'Yboard', 'Zboard', 'Xrim', 'Yrim', 'Zrim');

Xrim_center = mean(Xrim);  % Calculate the center

Yrim_center = mean(Yrim);

Zrim_center = mean(Zrim);

U0 = Umag0 * cosd(phi) * cosd(theta);

V0 = Umag0 * cosd(phi) * sind(theta);

W0 = Umag0 * sind(phi);

num_steps = 100000;

T = zeros(1, num_steps);

X = zeros(1, num_steps);

Y = zeros(1, num_steps);

Z = zeros(1, num_steps);

U = zeros(1, num_steps);

V = zeros(1, num_steps);

W = zeros(1, num_steps);

n = 1;

T(1) = 0;

X(1) = Xo;

Y(1) = Yo;

Z(1) = Zo;

U(1) = U0;

V(1) = V0;

W(1) = W0;

status = 0;

passed_hoop = 0;

while Z(n) >= r && X(n) >= -14.4 + r && X(n) <= -r && Y(n) >= -7.5 + r && Y(n) <= 7.5 - r

   U_mag = sqrt(U(n)^2 + V(n)^2 + W(n)^2);

   U(n+1) = U(n) - ( (Cd * rho * A / (2 * m) * U(n) * U_mag - Cm * rho * A * r / (2 * m) * (omgY * W(n) - omgZ * V(n))) * dt );

   V(n+1) = V(n) - ( (Cd * rho * A / (2 * m) * V(n) * U_mag - Cm * rho * A * r / (2 * m) * (omgZ * U(n) - omgX * W(n))) * dt );

   W(n+1) = W(n) - ( (Cd * rho * A / (2 * m) * W(n) * U_mag - Cm * rho * A * r / (2 * m) * (omgX * V(n) - omgY * U(n))) * dt + g * dt );

   X(n+1) = X(n) + U(n+1) * dt;

   Y(n+1) = Y(n) + V(n+1) * dt;

   Z(n+1) = Z(n) + W(n+1) * dt;

   T(n+1) = T(n) + dt;

dist_to_rim = sqrt((X(n) - Xrim).^2 + (Y(n) - Yrim).^2 + (Z(n) - Zrim).^2);

   %passed hoop check

   if abs(Z(n) - Zrim) <= 0.019

       if abs(X(n)- max(Xrim)) <= drim

           if abs(Y(n)- max(Yrim)) <= drim

               if any(((drim/2) - dist_to_rim) > 0)

                   passed_hoop = 1;

               end

           end

       end

   end

   %hit rim check

   if any(dist_to_rim < r)

       status = 0;

       if passed_hoop

           status = 1;

           break;

       end

       break;

   end

   %hit backboard check

   dist_to_backboard = sqrt((X(n+1) - Xboard).^2 + (Y(n+1) - Yboard).^2 + (Z(n+1) - Zboard).^2);

   if any(dist_to_backboard <= r)

       break;

   end

   if passed_hoop

       status = 1;

   end

   n = n + 1;

end

T = T(1:n);

X = X(1:n);

Y = Y(1:n);

Z = Z(1:n);

U = U(1:n);

V = V(1:n);

W = W(1:n);

end