%
% Linear transformations of the plane
% 
disp('Create two random matrices A and B')
pause
%
A=floor(5*rand(2,2)-2)
B=floor(5*rand(2,2)-2)
%
pause
format rational
disp('Calculate the products C=A*B and D=B*A and the inverses Ainv and Binv')
pause
C=A*B
D=B*A
pause
Ainv=eye(2)/A
Binv=eye(2)/B
pause
disp('Check that these are indeed inverses:')
pause
disp('A*Ainv=')
A*Ainv
disp('Ainv*A=')
Ainv*A
disp('B*Binv=')
B*Binv
disp('Binv*B=')
Binv*B
pause
disp('Next create a polygonal figure in the plane')
cla reset
xx=[0 1 1 0 0]
yy=[0 0 1 1 0]
disp('and plot the polygon.')
disp('Rather than using the predefined colors, we play with RGB-values!')
pause
fill(xx,yy,[.3 .2 .9])
axis([-4,4,-4,4])
drawnow
disp('Arrange the windows so that you can see both the figure and the command window.')
hold on
pause
disp('Next calculate how A and B transform the points')
pause
pts=[xx;yy]
Apts=A*pts
Bpts=B*pts
pause
disp('and overlay the transformed polygons')
plot(Apts(1,:),Apts(2,:),'c-')
drawnow
plot(Bpts(1,:),Bpts(2,:),'m-')
drawnow
disp('click on the figure window to see the overlaid polygons')
pause
disp('Verify that (A*B)*pts and A*(B*pts) are the same etc.')
pause
A*Bpts
C*pts
disp('Here the message is: Matrix multiplication corresponds to')
disp('COMPOSITION of linear maps (transformations)')
pause
disp('To have some more fun, redo the above with your own polygon!')
disp('For inspiration, look at the following ten distorted cats.')
disp('You need to toggle between the command window and the figure')
disp('window, most easily using the ALT-TAB key combination.')
pause
cla reset
for i=1:10
    catt
    drawnow
    pause
    end
disp('Now it is your turn.')