% Variables
d = 0.05; % Offset for labels

% Calculate the parabolas
x = [-1:0.001:1];
y = [-1:0.001:1];
y_t = (1 - x.^2) / 2;   % top parabola
y_b = (x.^2 - 1) / 2;   % bottom parabola
x_l = (y.^2 - 1) / 2;   % left parabola
x_r = (1 - y.^2) / 2;   % right parabola

% Plot the axes
plot([0, 0], [1, -1], 'k-', [1, -1], [0, 0], 'k-');
hold on;

% Plot the centre
plot(0, 0, 'o');
text(0 + d, 0 + d, 'C (0, 0)');

% Plot the parabolas
plot(x, y_t, 'b.', x, y_b, 'b.', x_l, y, 'b.', x_r, y, 'b.');
text(0 - d, 0.5 - d, 'x^2 = 1 - 2y');  % label for top parabola
text(0 - d, -0.5 + d, 'x^2 = 1 + 2y'); % label for bottom parabola
text(-0.5 + d, 0 + d, 'y^2 = 1 + 2x'); % label for left parabola
text(0.5 + d, 0 + d, 'y^2 = 1 - 2x');  % label for right parabola

% Plot the intersection points
r = sqrt(2) - 1;
rlabel = strcat(';r = ', num2str(r), ';');

plot(r, r, strcat('ro', rlabel));   % 1st quadrant
text(r + d, r + d, 'B (r, r)');

plot(-r, r, 'ro');                  % 2nd quadrant
text(-r + d, r - d, 'A (-r, r)');

plot(-r, -r, 'ro');                 % 3rd quadrant
text(-r + d, -r + d, 'D (-r, -r)');

plot(r, -r, 'ro');                  % 4th quadrant
text(r + d, -r + d, 'C (r, -r)');

grid('on');
xlabel('x');
ylabel('y');
title(strcat('All points within the closed region, ABCD, is closer ',
             'to the centre than the edges.'));
hold off;
replot;
print('graph.png');