% This file may be used freely for any non-commercial, educational purpose.
% Copyright (c) 2003, Eamonn Keogh, Jessica Lin. All rights reserved.
%
% This function demonstrates the danger of dimensionality reduction by showing how a cloud of
% points appear to have different shapes when projected onto different planes. 

function demo_shape


speed = 0.01; % This varible controls the speed of the animation. WARNING Use low value, less than 0.05

data= rand(3000,3);     % Create an initial cloud of points in the unit cube



% Prune off any points outside a circle in the X,Y plane
for i = 1 : size(data,1)
    
    x = data(i,1) - 0.5;
    y = data(i,2) - 0.5;
   
    if (x^2 + y^2) > 0.25        
        data(i,1) =[nan ];
        data(i,2) =[nan ];
        data(i,3) =[nan ];
    end       
end


% Prune off any points outside a triangle in the X,Z plane
for i = 1 : size(data,1)
   if~isnan(data(i,1))
        
    x = data(i,1) ;
    z = data(i,3) ;
   
    if  x < .5  & (x < (0.5*z))       
        data(i,1) =[nan ];
        data(i,2) =[nan ];
        data(i,3) =[nan ];        
    elseif ((1-x) < 0.5*z)  
        data(i,1) =[nan ];
        data(i,2) =[nan ];
        data(i,3) =[nan ];        
    end  
  end
end



hold on;
grid on;
view(135,35);
h = plot3(data(:,1) , data(:,2)  , data(:,3), 'r.' );                           % Plot 3-D cloud of points

set(0,'units','pixels');
screenwidth=get(0,'screensize');
set(gcf,'position',screenwidth*0.9);

set(gca,'xlim',[-1 2] );
set(gca,'ylim',[-1 2] );
set(gca,'zlim',[-1 2] );



title('Assume that you have this cloud of points in 3 dimensions... Click anywhere to continue')
[X,Y] = ginput(1);


title('What will happen if you reduce the dimensionality to just 2 dimensions?  Click anywhere to continue')
[X,Y] = ginput(1);


plot3(data(:,1) , data(:,2)  , (data(:,3)*0)-1, 'b.' )
title('If you use the X and Y values you get a circle... Click anywhere to continue');
[X,Y] = ginput(1);

plot3(data(:,1) , (data(:,2)*0)-1  , data(:,3), 'g.' )
title('If you use the X and Z values you get a triangle... Click anywhere to continue');
[X,Y] = ginput(1);


plot3((data(:,1)*0)-1 , data(:,2)  , data(:,3), 'm.' )
title('If you use the Y and Z values you get a rectangle... Click anywhere to continue');
[X,Y] = ginput(1);

title(' ');

pause(1) 







% Begin a simple animation that rotates the axis to the XY view, the XZ view and the YZ view, pausing briefly at each.
pause(1) 
for i = 135 : 5 : 180  
    view(i,35 - (abs(i-135)*35/45) )
    pause(speed)    
end
pause(1) 
for i = 180 :-5: 135  
    view(i,35 - (abs(i-135)*35/45) )
    pause(speed)    
end

for i = 135 :-5: 90  
    view(i,35 - (abs(i-135)*35/45) )
    pause(speed)    
end
pause(1) 
for i = 90 : 5 : 135  
    view(i,35 - (abs(i-135)*35/45) )
    pause(speed)    
end

for i = 35 : 5 : 90  
    view(135,i)
    pause(speed)    
end
pause(1) 

for i = 90 :-5 : 35
    view(135,i)
    pause(speed)    
end

title('(c) Eamonn Keogh, Jessica Lin, used with permission')