%                    The University of Queensland
%     School of Information Technology & Electrical Engineering
%     ENGG7302 Advanced Computational Techniques in Engineering

% Plot some p-norms in 2D

% 1 norm

figure;
fill([1, 0, -1, 0], [0, 1, 0, -1], [0.5, 0.5, 1]);
axis equal;
axis off;
box off;

% 2 norm

figure;
theta = 2*pi*(0:0.01:1);
fill(cos(theta), sin(theta), [0.5, 0.5, 1]);
axis equal;
axis off;
box off;

% infinity norm

figure;
fill([1, 1, -1, -1], [1, -1, -1, 1], [0.5, 0.5, 1]);
axis equal;
axis off;
box off;

% p norm

figure;
p4 = (cos(theta).^4 + sin(theta).^4).^(1/4);
fill(cos(theta)./p4, sin(theta)./p4, [0.5, 0.5, 1]);
axis equal;
axis off;
box off;