% 
% Homework #4 - Sample Solutions
% 3-D "Sombrero" Plotting & Working with Polar Coordinates
%

% 
% PART 1 - 3D Plotting and Manipulations
%

% Sombrero Set-up Equations
dim1 = [ -8 : 0.5 : 8 ];
dim2 = dim1;
[x,y] = meshgrid(dim1, dim2);
r = sqrt(x.^2 + y.^2);
r(find(r==0))=eps;			% Lose the divide by 0 error
hat = sin(r)./r;

% Mesh plot of sombrero
mesh(hat);
title('Sombrero');
pause

% Interesting views - Lots of acceptable combinations
view(0, 0);				% Straight on
title('Sombrero view - Straight on');
pause
view(-37.5, -30);			% From the bottom
title('Sombrero view - From below');
pause
view(0, 60);				% From above
title('Sombrero view - From above');
pause
view(-37.5, 30)				% Restore default

% Sombrero with a contour
meshc(hat);
title('Sombrero with contour');
pause

% Sombrero with a reference plane
meshz(hat);
title('Sombrero with a reference plane (on a pedastal)');
pause

% Cap the Sombrero peak(s) to 70% of their value
hat(find(hat>=0.7))=0.7;
mesh(hat);
title('Sombrero - Capped at 70% of it''s peak');
pause

%
% PART 2 - Plotting with Coordinates
%

clear all;

theta = [0:pi/180:2*pi];		% Full circle. Theta in RADIANS!!!

% Equations
rho1 = 1 + cos(theta);
rho2 = theta / (2*pi);

% Display the plots
polar(theta, rho1); hold on;
polar(theta, rho2); hold off;

% What position are the curves the closest?  (Ans: 130 degrees)
theta(find(abs(rho1-rho2) == min(abs(rho1-rho2)))) * 360 / (2*pi)

% Note: The two curves never truely intersect (in continuous time
%       they do, but not using discretized increments of pi/180
%	radians in Matlab). Although the polar plot makes it look 
%       like there are two points of intersection, there is no
%	intersection in the actual data.

% The theta(...) * 360 / (2*pi) just converts a theta value to degrees.