% Hess.m

clear all;
close all;

phi = linspace(-45,45,300);
for theta = 50:5:130,
    x = tand(phi);
    y = 1/tand(theta)./cosd(phi);
    if mod(theta,15) == 0,
        plot(x,y,'r-');
    else
        plot(x,y,'r:');
    end
    hold on;
end

beta = linspace(-45,45,300);
for alpha = 50:5:130,
    x = 1/tand(alpha)./cosd(beta);
    y = tand(beta);
    if mod(alpha,15) == 0,
        plot(x,y,'b-');
    else
        plot(x,y,'b:');
    end
    hold on;
end

axis([-1 1 -1 1]);
axis square;

xs = -5;
ys = -6;
alpha = 90-xs*5;
theta = 90-ys*5;
phi = atand(cosd(alpha)/sqrt(sind(theta)^2-cosd(alpha)^2));
x = tand(phi);
y = 1/(tand(theta)* cosd(phi));
plot(x,y,'kx');
text(x+0.05,y,['(' num2str(xs) ',' num2str(ys) ')']);
title('Projection Onto Screen');
xlabel('x');
ylabel('y');