% letters.m displays and alters letters

clf;

letterF;
unitsquare;

subplot(3,3,1)
plot(US(1,:), US(2,:),'r');
hold on
plot(F(1,:), F(2,:));
axis([0 2.5 0 3]);
title('The letter F');

subplot(3,3,2)
A = [[2 0]; [0 2]];
G = A*F;
H = A*US;
plot(H(1,:), H(2,:),'r');
hold on
plot(G(1,:), G(2,:));
axis([0 2.5 0 3]);
title('Dilated');

subplot(3,3,3)
A = [[2 0]; [0 1]];
G = A*F;
H = A*US;
plot(H(1,:), H(2,:),'r');
hold on
plot(G(1,:), G(2,:));
axis([0 2.5 0 3]);
title('Stretched in the x direction');

subplot(3,3,4)
A = [[2 1]; [0 2]];
G = A*F;
H = A*US;
plot(H(1,:), H(2,:),'r');
hold on
plot(G(1,:), G(2,:));
axis([0 3 0 3]);
title('Italic F, sheared forward');

subplot(3,3,5)
A = [[2 -1]; [0 2]];
G = A*F;
H = A*US;
plot(H(1,:), H(2,:),'r');
hold on
plot(G(1,:), G(2,:));
axis([-1 2 0 3]);
title('Sheared back');

subplot(3,3,6)
A = [[0 1]; [1 0]];
G = A*F;
H = A*US;
plot(H(1,:), H(2,:),'r');
hold on
plot(G(1,:), G(2,:));
axis([0 2.5 0 3]);
title('Reflected across y=x');

subplot(3,3,7)
A = [[0.85 0.15]; [0.15 0.85]];
G = A*F;
H = A*US;
plot(H(1,:), H(2,:),'r');
hold on
plot(G(1,:), G(2,:));
axis([0 2.5 0 3]);
title('Going ... ');
text(0.88,0.15, '(1,0) goes to (0.85, 0.15)');

subplot(3,3,8)
A = [[0.7 0.3]; [0.3 0.7]];
G = A*F;
H = A*US;
plot(H(1,:), H(2,:),'r');
hold on
plot(G(1,:), G(2,:));
axis([0 2.5 0 3]);
title('... going ...');
text(0.75,0.3, '(1,0) goes to (0.7, 0.3)');

subplot(3,3,9)
A = [[0.5 0.5]; [0.5 0.5]];
G = A*F;
H = A*US;
plot(H(1,:), H(2,:),'r');
hold on
plot(G(1,:), G(2,:));
axis([0 2.5 0 3]);
title('... gone!');
text(0.55,0.5, '(1,0) goes to (0.5, 0.5)');