%Orthographic.m

%This program paints copies of a photo on three sides 
%of a cube using an orthographic projection. 
%It is important to know that this program has been 
%designed to emphasize the mathematics we have
%been discussing and it does not use MATLAB's built-in 
%tools for rendering three dimensional
%objects. Readers who are knowledgable about MATLAB 
%or another programming language may
%wish to design a more efficient program.
%Although a z-buffer is not needed for this 
%particular object, one is included in order to make the
%program more easily adaptable.
%In the first line the photo is read into memory. 
%The word 'infile' should be replaced by the 
%filename of your image file which must be stored in 
%the current directory. Next, we find the 
%dimensions of the input photo. We also find the 
%edge size to make a square.

inpic=imread('infile');

row = size(inpic,1);

col = size(inpic,2);

s=min(row,col);

%In the following lines we fix the parameters 
%that determine the direction to the viewer's eye.

theta=pi/3;			%theta is called the azimuth angle.

phi=pi/2-pi/9;			%phi is the complement of the angle of elevation.

a=cos(theta)*sin(phi);

b=sin(theta)*sin(phi);

c=cos(phi);			%(a,b,c) gives the direction from the origin to the eye.

%We enter estimated bounds on the computed coordinates, 
%initialize the output file by assigning 
%the color (255,255,255) to each pixel 
%(rescales to (1,1,1) -- white), 
%and initialize the z-buffer 
%array by entering -Inf for negative infinity.

c1min=-2*s;

c1max=3*s;				%Chosen so c1min < coef1 < c1max.

c2min=-2*s;

c2max=3*s;				%Chosen so c2min < coef2 < c2max.

outpic(1:round(1+c2max-c2min),1:round(1+c1max-c1min),1:3) = 255;

zbuffer(1:round(1+c2max-c2min),1:round(1+c1max-c1min)) = -Inf;

for i=1:s

 for j=1:s

%Front face:

x0=s;		y0=j;		z0=s-i+1;

%Orthographic projection routine starts here. 

coef1=-sin(theta)*x0+cos(theta)*y0;

coef2=-cos(theta)*cos(phi)*x0-sin(theta)*cos(phi)*y0+sin(phi)*z0;

distance= x0*a+y0*b+z0*c;		%This scalar projection plays the role of a distance.

    if (c1min<=coef1 & coef1<=c1max    & c2min<=coef2 & coef2<=c2max)

 	if distance > zbuffer(round(1+c2max-coef2),round(1+coef1-c1min))

 			outpic(round(1+c2max-coef2),round(1+coef1-c1min),:)=inpic(i,j,:);

 		zbuffer(round(1+c2max-coef2),round(1+coef1-c1min))=distance;

	end

	end

%Orthographic projection routine ends here.

%Right face:

x0=s-j+1;	y0=s;		z0=s-i+1;

%Orthographic projection routine starts here. 

coef1=-sin(theta)*x0+cos(theta)*y0;

coef2=-cos(theta)*cos(phi)*x0-sin(theta)*cos(phi)*y0+sin(phi)*z0;

distance= x0*a+y0*b+z0*c;		%This scalar projection plays the role of a distance.

    if (c1min<=coef1 & coef1<=c1max &    c2min<=coef2 & coef2<=c2max)

 	if distance > zbuffer(round(1+c2max-coef2),round(1+coef1-c1min))

 			outpic(round(1+c2max-coef2),round(1+coef1-c1min),:)=inpic(i,j,:);

 		zbuffer(round(1+c2max-coef2),round(1+coef1-c1min))=distance;

	end

	end

%Orthographic projection routine ends here.

%Top face:   

x0=i;		y0=j;		z0=s;

%Orthographic projection routine starts here. 

coef1=-sin(theta)*x0+cos(theta)*y0;

coef2=-cos(theta)*cos(phi)*x0-sin(theta)*cos(phi)*y0+sin(phi)*z0;

distance= x0*a+y0*b+z0*c;		%This scalar projection plays the role of a distance.

    if (c1min<=coef1 & coef1<=c1max &    c2min<=coef2 & coef2<=c2max)

 	if distance > zbuffer(round(1+c2max-coef2),round(1+coef1-c1min))

 			outpic(round(1+c2max-coef2),round(1+coef1-c1min),:)=inpic(i,j,:);

 		zbuffer(round(1+c2max-coef2),round(1+coef1-c1min))=distance;

	end

	end

%Orthographic projection routine ends here.

end

 end

%Finally, the output image is sent to the screen and 
%also saved to a file. Runtime is shorter if you
%do not send the image to the screen. Just put a "%" 
%in front of that line to disable it. On the other
%hand, you may want to view the image on the screen 
%but not save it to a file. In that case disable
%the imwrite line.

image(outpic/255); axis equal

imwrite(outpic/255,'outfile.jpg','jpg')