% nonlinear.m contrasts the image of the unit square under linear and nonlinear transformations

clf;

x=ones(101,11)*diag(0:0.1:1);     % x coordinates for grid
y=diag(0:0.01:1)*ones(101,11);    % y coordinates for grid

s=y;
t=x;

subplot(2,2,1)

plot(x,y,'k-'); hold on
plot(s,t,'k:')
grid on
axis([0 1.5 0 1.5])
title('Grid on the unit square')

subplot(2,2,2)

a = (2*x + y)/3; 
b = (x + 3*y)/3; 
plot(a,b,'k-'); 
hold on
c = (2*s + t)/3; 
d = (s+3*t)/3; 
plot(c,d,'k:');
grid on
axis([0 1.5 0 1.5])
title('Image under a linear transformation')

subplot(2,2,3)

plot(x,y,'k-'); hold on
plot(s,t,'k:')
axis([0 1.5 0 1.5])
grid on
title('Grid on the unit square')

subplot(2,2,4)

p = pi/2;
a = x .* cos(p*y); 
b = x .* sin(p*y); 
plot(a,b,'k-'); 
hold on
c = s .* cos(p*t); 
d = s .* sin(p*t); 
plot(c,d,'k:');

axis([0 1.5 0 1.5])
grid on
title('Image under a nonlinear transformation')