% Use 
%
%     help plot3
%
% to get some documentation on plotting.
%
% The command
%
%     plot3(x,y,z)
%
% draws a polygon through the points 
%	(x(1),y(1),z(1)) ,..., (x(n),y(n),z(n)),
% where x,y,z are column vectors of length n.
%
% To get a cube, imagine tracing the edges in sequence
% and then put the vertex coordinates into x,y, and z
% in the order they are encountered. It is OK to retrace edges.
%
% The following solution with n=16 retraces 3 edges:

% Vertices (as row vectors) in the order they are encountered:
u0 = [ 0 0 0; 1 0 0; 1 0 1; 1 1 1; 1 1 0; 0 1 0; 0 1 1; 0 0 1;
	0 0 0; 0 1 0; 0 1 1; 1 1 1; 1 1 0; 1 0 0; 1 0 1; 0 0 1; 0 0 0]
% NOTE: Since the vertices are row vectors in this formulation,
%       we must transpose u before applying a rotation matrix
%	on the left, then transpose back before plotting the vertices.

% Clear the current figure
clf

% Copy columns into x,y,z and plot the original cube with black lines:
x=u0(:,1); y=u0(:,2); z=u0(:,3); plot3(x,y,z,'Color', 'black')

% Set the axes big enough to see the cube in context:
lims = [-2 2]; axis([lims lims lims]); axis manual;

% Hold multiple plots in the same figure
hold on

% Identify the X, Y, and Z axes with labels:
xlabel("X"); ylabel("Y"); zlabel("Z");

% Make the rotation matrices
alpha = pi/3; c=cos(alpha); s=sin(alpha); Rx=[1 0 0; 0 c -s; 0 s c];
beta = -pi/4; c=cos(beta); s=sin(beta); Ry=[c 0 s; 0 1 0; -s 0 c];
gamma = 0.5; c=cos(gamma); s=sin(gamma); Rz=[c -s 0; s c 0; 0 0 1];

% Apply the rotation matrices to the original cube's vertices and plot
%       the results using three different colors:
% NOTE: here we use the lemma: (R*u')' = u*R'
u = u0*Rx'; x=u(:,1); y=u(:,2); z=u(:,3); plot3(x,y,z,'Color', 'red')
u = u0*Ry'; x=u(:,1); y=u(:,2); z=u(:,3); plot3(x,y,z,'Color', 'green')
u = u0*Rz'; x=u(:,1); y=u(:,2); z=u(:,3); plot3(x,y,z,'Color', 'blue')