%% E5 MatLab - 2nd class demo
%%
% This file (both .html and .m script) are available on E5 web site.  From
% the schedule, click on the link for "Lab 6 files" located on the schedule
% (in the week 6 spot, not surprisingly).  Last week's files are also here.

%% some special matrices
%% 
% The identity matrix - note variable name at the left
I=eye(3)

%%
% A matrix of zeros  (by default, square)
Z=zeros(3)

%%
% A non-square matrix of zeros
Z=zeros(2,5)

%%
% Can also create a matrix of ones...
O=ones(3)

%%
% We can make the matrix the same size as another array
O=ones(size(Z))

%% 
% Define a matrix of random numbers
R=rand(2,5)


%% Working with arrays and subsets of arrays
A=[1 -2 3 -4; -2 3 -4 5; -2 -4 -6 -8]

%%
% find size
size(A)

%%
% find number of rows (the first dimension of the A matrix)
size(A,1)

%% 
% what is the 2nd row?
A(2,:)

%% 
% what is the 3rd column?
A(:,3)

%%
% Define an array of zeros same size as a row of A  (1 row, same number of columns)
z=zeros(1, size(A,2))

%%
% now change the last row
A(3,:)=z


%% Higher dimensional arrays
X=rand(2,4,3)

%%
% Take "top" array
X(:,:,1)

%%
% Take 3rd column of "middle" array
X(:,3,2)

%%
% Take first two elements of 2nd row of "bottom" array
X(2,1:2,3)

%% Using a function
%
p=3  % Define a variable "p" for no real reason.

%%
% Define x and y values of a complicated shape (a smile)
x1Smile=linspace(-0.5,0.5);            x2Smile=linspace(0.5,-0.5);
y1Smile=0.8*x1Smile.^2+0.1;            y2Smile=01.2*x2Smile.^2;
xSmile=[x1Smile x2Smile];              ySmile=[y1Smile y2Smile];
smile=patch(xSmile,ySmile,[1 0 0]);    axis([-2 2 -2 2],'square')

%%
% Find the perimeter
smilePerimeter=perim(xSmile,ySmile)

%%
% Note that the variable p is unchanged
p


%% Graphical transformations
%% Rotation
% Define a point in 2-d space as a column vector (x,y)=(1,-2)
x=1; y=-2;

%%
% Draw line from the origin with a blue dotted line.
plot([0 x],[0 y],'b:');  

%%
% add a blue circle at end, without erasing.
hold on;
plot(x, y, 'bo');

%% 
% Now add labels, scale axes and add grid.
xlabel('x'); ylabel('y'); 
title('The point (x,y) = (1,-2)');
axis([-3 3 -3 3], 'square'); grid on


%%
% Define transformation matrix for a -90 degree rotation
theta = -90 * pi/180;
T=[cos(theta) sin(-theta) 0; 
   sin(theta) cos(theta) 0;
   0 0 1]

%%
% Perform rotation and plot
% Note, for the transformations we add a third row that is always 1
xy=[x; y; 1]

%%
xyp=T*xy

%%
xp=xyp(1)
yp=xyp(2)

%%
% Plot
plot([0 xp],[0 yp],'b-','Linewidth',2);
plot(xp,yp,'bo','MarkerFaceColor','b');
title('The point (1,-2) rotated by -90^\circ')

hold off;  %Next plot will clear the screen

%% Translation
% Now for a translation, tx=1, ty=4
tx=1;  ty=4;
T=[1 0 tx; 0 1 ty; 0 0 1]

%%
% do transformation
xyp=T*xy
xp=xyp(1);  yp=xyp(2);

%%
% Plot both points
plot([0 x],[0 y],'b:');  hold on;  plot(x, y, 'bo');
xlabel('x'); ylabel('y'); 
plot([0 xp],[0 yp],'b-','Linewidth',2);
plot(xp,yp,'bo','MarkerFaceColor','b');
title('The point (1,-2) translated by t_x=1.0, t_y=4');
axis([-3 3 -3 3],'square');  grid on


hold off;  %Next plot will clear the screen

%% Combined rotation and translation
theta=-90*pi/180;  tx=1;  ty=4;
T=[cos(theta) sin(-theta) tx; 
   sin(theta) cos(theta) ty;
   0 0 1]

%%
% do transformation
xyp=T*xy
xp=xyp(1);  yp=xyp(2);

%% 
% Plot both points
plot([0 x],[0 y],'b:');  hold on;  plot(x, y, 'bo');
xlabel('x'); ylabel('y'); 
plot([0 xp],[0 yp],'b-','Linewidth',2);
plot(xp,yp,'bo','MarkerFaceColor','b');
title('(1,-2) Rotation: -90^\circ, Translation: t_x=1, t_y=4');
axis([-3 3 -3 3], 'square');  grid on;

hold off;  %Next plot will clear the screen

%% Manipulating graphical objects (patches)
%% 
% Clear the figure, set axis limits, grid
clf;  axis([-3 3 -3 3], 'square'); grid on;

%%
% Define a patch by its vertices
x=[0 2 2];  y=[0 1 0];
myTriangle=patch(x,y,'r');


%% 
% Rotate by 45 degrees and translate by 1, -2
xy=[x; y; ones(size(x))]

%%
theta=45*pi/180;  tx=1;  ty=-2;
T=[cos(theta) sin(-theta) tx; 
   sin(theta) cos(theta) ty;
   0 0 1]

%%
% do transformation
xyp=T*xy

%%
% Pull out new x and y values
xp=xyp(1,:)
yp=xyp(2,:)

%%
% Update shape
set(myTriangle,'Xdata',xp,'Ydata',yp);