bouncing ball simulation

hello i have a functioning bouncing ball simulation but i would like to make it appear as though it is being squished when it hits the ground using a scale factor can someone please point me in the right direction in order to accomplish this

%ee150_bball.m
function ee150_bball
%----------------------------------
% Constants
%----------------------------------
radius = 0.7;     % radius of the ball
x0 = 0;           % position of the center of the ball
y0 = 10 + radius;
w = 3*pi;        % angular velocity (radians/sec.)
g = 9.81;         % gravitational acceleration constant in m/s

%----------------------------------
% Duration of the movie, frames per second, and other values
%----------------------------------
duration = 15;
framerate = 30;
maxframes = duration * framerate + 1;
dt = 1/framerate; % delta time between each frame

%----------------------------------
% Draw the initial ball, ground, and target
%----------------------------------
% to draw the ball we'll have 512 points around the circumference
n = 512;

% Creates a vector of 512 angles from [0 2*PI] radians to be used
% to calculate the points on the circumference of the ball
% rotate/spin the ball
arg = [0 : 2*pi/n : 2*pi];

% Initial ball circumference X,Y coordinates matrix 
%    We will never change this representation of the ball and just 
%    rotate it for each frame
%    8 Rows (1 for each sector) x 512/8 + 1 cols
%    Extra col => starting point of each sector is 0,0
xi = zeros(8,1+n/8);
yi = zeros(8,1+n/8);

%=== For LAB completion====
% We'll cut the ball into 8 sectors filling each sector w/ a unique color
% To do this, modify the xi, yi matrices such that the 1st point of each
% row vector is 0,0 and the rest of the points are the circumference 
% points of the circle (i.e. use the 'arg' vector when calculating your
% circumference points along with the 'radius' value). 
for i=1:8
    j=(i-1)*n/8;
    k=(i*n/8) - 1;
    xi(i,:)=[0 radius*cos(arg(j+1:k+1))];
     yi(i,:)=[0 radius*sin(arg(j+1:k+1))];
end

% Draw the 8 sectors filling them with color
draw_ball(xi,yi);
hold on;
line([-1 20],[0 0], 'Color', 'b' );  % Draw the ground
axis([-1 20 -1 20]);
hold off;

% Now let the user pick the initial velocity and angle of the ball
initV = input('Enter the initial velocity in m/s: ');
angle = input('Enter the angle in degrees of the ball: ');
rad = pi*angle/180;
%=== For PRELAB completion====
vy = initV*sin(rad);     % change these assignments appropriately for the ball's velocity
vx = initV*cos(rad);

%----------------------------------
% Ball Path/Trajectory Calculation
%----------------------------------  
% xc and yc are coordinates of the center of the ball at each time
xc = zeros(1,maxframes);
yc = zeros(1,maxframes);

% theta = angle of rotation of the ball at each time frame
theta = zeros(1,maxframes);

% sx, sy are the scaling factors of the ball in the x and y direction
%  at each time frame
sx = ones(1,maxframes);
sy = ones(1,maxframes);

% set the time = 0
t = 0;

%set initial position of the ball and its angle
yc(1) = y0;
xc(1) = x0;
sx(1) = 1;
sy(1) = 1;
theta(1) = 0;
% Calculate the velocity of the ball and change in angle at each timestep i
%   You will need to calculate theta, sx, sy, vx, vy, xc, yc, w, & status
%   You will also need to update i and t in each iteration
% Continue calculation until the LAST position of the ball is past the edge  
%   of the screen (i.e. 20 meters) or the current time has reached the 
%   end of the movie (i.e. time less than (duration - dt) )
% Change the while loop below to perform these operations
i=2;
%=== For PRELAB completion==== 
while xc(i-1)<20+radius && t<=duration - dt
   [vx, vy, w, xc(i), yc(i), theta(i)] = physics_update(vx, vy, w, xc(i-1), yc(i-1), theta(i-1), dt, radius);
   i = i+1;
   t = t+dt;
end
% set the number of frames based on how many times the loop iterated
numframes = i-1;

%plot the path of the center of the ball
figure;
plot(xc(1:numframes),yc(1:numframes)); hold on;
line([-1 20], [0 0], 'Color', 'b');  % Draw the ground
axis([-1 20 -1 20]);

%open a new figure;
figure;

%----------------------------------
% Animation (Ball Rotation/Translation along trajectory path)
%----------------------------------

% Rotated, translated ball circumference X,Y coordinates matrix at each
%     frame (we will rotate and traslate xi and yi at each frame to produce 
%     these matrices)
%     8 Rows (1 for each sector) x 512/8 + 1 cols
x = zeros(8,1+n/8);
y = zeros(8,1+n/8);

% Create the movie object
mymovie = moviein(numframes);

% Draw the ball for EACH frame using trajectory/physics calculations 
%      performed above
%  T = Translation matrix - move the ball to the (xc,yc) position
%  S = Scaling matrix - Scaling values for this frame 
%  R = Rotation matrix - Rotation values for this frame
for h = 1:numframes
  %=== For LAB completion====   
  % Calculate the geometric modification matrices T, S, R

    % For each sector perform the affine transformation and place the
    % result in the x,y vectors

    T=[1 0 xc(h); 0 1 yc(h); 0 0 1];
    R=[cos(theta(h)) -sin(theta(h)) 0; sin(theta(h)) cos(theta(h)) 0;  0 0 1;  ];
    S=[sx(h),0,0;0,sy(h),0;0,0,1 ];
    M=T*S*R;

    for i=1:8
        for j=1:1+n/8
        p=[xi(i,j); yi(i,j); 1 ];
        p=M*p;
        x(i,j)=p(1);
        y(i,j)=p(2);
        end
    end 
    % Draw the 8 sectors filling them with color
    draw_ball(x,y);
    hold on;
    line([-1 20], [0 0], 'Color', 'b');  % Draw the ground
    axis([-1 20 -1 20]);
    hold off;
    a=[19.5 19.5]
  b=[15 20]
  line(a,b)

a=[19.5 19.5]
b=[0 10]
line(a,b)

    % write the frame to the movie
    mymovie(:,h)=getframe;

end

% Playback the movie
movie(mymovie,1,framerate*2);

end

function [vx, vy, w, xc_o, yc_o, theta_o] = physics_update(vx, vy, w, xc_i, yc_i, theta_i, dt, radius)
    g = 9.81;
    %=== For PRELAB completion==== 
    % Remember to check if the ball is hitting the ground and update your
    %  velocities appropriately
    sx_o=1;
    sy_o=1;
    yc_o =yc_i+vy*dt; 
    xc_o = xc_i+vx*dt;
    vy = vy-g*dt;

      if yc_o> 10 && yc_o<15
  a=[19.5 19.5]
  b=[0 10]
  line(a,b,'Color','g')

a=[19.5 19.5]
b=[15 20]
line(a,b,'Color','g')

else
   a=[19.5 19.5]
b=[0 10]
line(a,b,'Color','r')

a=[19.5 19.5]
b=[15 20]
line(a,b,'Color','r') 
    end

    %  vx = 0;
      theta_o = theta_i-w*dt;

      if yc_o <= radius 
          vy=-.85*vy
          yc_o=radius
          vx=.9*vx
          w=.8*w
      end
      % w=o;

end

% Expects 8xN x and y point matrices
function draw_ball(x,y)

fill(x(1,:),y(1,:),'r'); hold on
fill(x(2,:),y(2,:),'b'); hold on
fill(x(3,:),y(3,:),'y'); hold on
fill(x(4,:),y(4,:),'c'); hold on
fill(x(5,:),y(5,:),'g') ; hold on
fill(x(6,:),y(6,:),'w') ; hold on
fill(x(7,:),y(7,:),'k') ; hold on
fill(x(8,:),y(8,:),'m') ; hold off

%=== For LAB completion====
  % Draw the 8 sectors filling them with color (turn hold on after the
  % first sector and turn hold off after the last sector

end

[Sven]

Do we need to turn up to your lab to fill in the bits marked "For LAB completion"?

If you have a specific question go ahead and ask it. Entire homework assignments are a little too broad.

[Walter Roberson]

You posted what looks like the same question, about an hour earlier. Perhaps you have updated the code between the two postings. One of the two questions would seem to be unneeded. Please delete one of the two.

The other copy of the question is at http://www.mathworks.com/matlabcentral/answers/22275-bouncing-ball-simulation

[Elizabeth Crist]

Hi, I am trying to export the xy data from the code. The ball successfully bounces and everything, however, there are no variables saved to the workspace. Is there a way to export that data?

Thank you!

[Walter Roberson]

function [saved_x, saved_y]= ee150_bball

and

saved_x(:,:,h) = x;
saved_y(:,:,h) = y;

[Elizabeth Crist]

Where do I place that code? Within the function ee150_bball ?

[Walter Roberson]

You need to change the very first line to the function line I show. The other two lines can go just after

       mymovie(:,h)=getframe;

[Elizabeth Crist]

I ran it with those adjustments and now have this as my workspace. It looks like x and y are a part of the variable ans. Are x and y within ans?

[Walter Roberson]

Run with something like

[record_of_x, record_of_y] = ee150_bball();

and then record_of_x will be the saved x and record_of_y will be the saved y. The third dimension of the variables will be the frame number. The first dimension will be the 8 sectors. At the moment I am not sure what the 65 represents.

Answer 1

[Walter Roberson]

You cannot make a ball look squished by using a scale factor.

Notice that the ball does not simply go to an ellipsoid shape.

You need a Finite Element Mesh calculation of Elastic Deformation in order to make a bouncing ball look squished properly.

See also http://www.tcm.phy.cam.ac.uk/~dek12/tales/Tale-00.pdf