%{
This is a program to generate the Moire effect of 2 or more patterns, pattern rotation angle and pitch can be changed
12/17/18 by AO for Agira Photonics

Adapted from:
https://www.mathworks.com/matlabcentral/answers/306128-how-do-i-represent-an-image-and-add-a-moire-pattern
https://www.mathworks.com/matlabcentral/answers/155213-i-wish-to-generate-moire-pattern-for-straight-radial-and-circular-patterns-how-to-write-code
and used the lcms function from https://www.mathworks.com/matlabcentral/fileexchange/24670-least-common-multiple-set
%}

clc
clear
%% GET INPUTS FROM USER
num=input('How many patterns are there? Enter an integer from 2 to 4: ');  %set up for 2, 3, or 4 overlaid patterns

if num > 4                                                                 %checking for incorrect entry
    input('Oops, can''t do that');
end
if num < 1
    input('Oops, can''t do that');                                         %checking for incorrect entry
end 
if num==2
        pitch1=input('Enter pattern 1 pitch: ');
        pitch2=input('Keeping your units consistent, enter pattern 2 pitch: ');
        angle1=input('Enter angle of rotation between patterns: ');
        m=lcms([pitch1,pitch2]);                                           %m is the least common multiple, to be used later
        pitch3=0;                                                          %defining variables but setting equal to zero for setup for rest of program
        pitch4=0;
        angle2=0;
        angle3=0;
        if m < 200                                                         %image comes out pixelated and small if the lcm is less than approx 200
            while m < 200                                                  %multiply m by 2 until greater than 200
            m=2*m;
            end
        end
end
if num==3                                                                  %if user input "3" as number of patterns 
    pitch1=input('Enter pattern 1 pitch: ');
    pitch2=input('Keeping your units consistent, enter pattern 2 pitch: ');
    angle1=input('Enter angle of rotation between patterns 1 and 2: ');
    pitch3=input('Keeping your units consistent, enter pattern 3 pitch: ');
    angle2=input('Enter angle of rotation between patterns 1 and 3: ');    %note that pattern 1 is reference of zero degrees
    m=lcms([pitch1,pitch2,pitch3]);                                        %m is the least common multiple of three patterns
    pitch4=0;                                                              %defining variables but setting equal to zero for setup for rest of program
    angle3=0;
    if m < 200                                                         %image comes out pixelated and small if the lcm is less than approx 200
            while m < 200                                                  %multiply m by 2 until greater than 200
            m=2*m;
            end
    end
end
if num==4
   pitch1=input('Enter pattern 1 pitch: ');
   pitch2=input('Keeping your units consistent, enter pattern 2 pitch: ');
   angle1=input('Enter angle of rotation between patterns 1 and 2: ');
   pitch3=input('Keeping your units consistent, enter pattern 3 pitch: ');
   angle2=input('Enter angle of rotation between patterns 1 and 3: '); 
   pitch4=input('Keeping your units consistent, enter pattern 4 pitch: ');
   angle3=input('Enter angle of rotation between patterns 1 and 4: ');
   m=lcms([pitch1,pitch2,pitch3,pitch4]);                                  %m is the least common multiple of the four patterns
   if m < 200                                                              %image comes out pixelated and small if the lcm is less than approx 200
            while m < 200                                                  %multiply m by 2 until greater than 200
            m=2*m;
            end
        end
end
  
%% SET UP VECTOR SPACE
 rowVector1= (1:m);                                                        %single row of m columns
 period1 = pitch1;                                                         %setting up cosine function with same period as pitch 1 
 cosVector1=(1+cos(2*pi*rowVector1/period1)); 
 Pattern1 = repmat(cosVector1,m, 1);                                       %repmat is repeating pattern of the cosine function values for a total matrix of size m x m
 
 rowVector2= (1:m);                                                        
 period2 = pitch2;                                                         %setting up cosine function with same period as pitch 2
 cosVector2=(1+cos(2*pi*rowVector2/period2)); 
 Pattern2 = repmat(cosVector2, m, 1);                                      

 rowVector3= (1:m);                                                        
 period3 = pitch3;                                                         %setting up cosine function with same period as pitch 3
 cosVector3=(1+cos(2*pi*rowVector3/period3)); 
 Pattern3 = repmat(cosVector3, m, 1);                                      
 
 rowVector4= (1:m);                                                        
 period4 = pitch4;                                                         %setting up cosine function with same period as pitch 4
 cosVector4=(1+cos(2*pi*rowVector4/period4)); 
 Pattern4 = repmat(cosVector4, m, 1);                                      
 
 %% CONVERT VALUES INTO GRAYSCALE IMAGE
 subplot(2,2,1);                                                           %puts image in top left corner of window
 imshow(Pattern1, [])
 title('PATTERN 1');
 
 Rotate2=imrotate(Pattern2,angle1,'crop');                                 %rotate pattern 2 by angle between patterns 1 and 2, crop to fit display
 subplot(2,2,2);                                                           %puts image in top right of window
 imshow(Rotate2, [])
 title('PATTERN 2');
 
 if num==3                                                                 %if there are three patterns, third one goes in bottom left corner of window
     Rotate3=imrotate(Pattern3,angle2,'crop');                             %rotate pattern 3 by angle between patterns 1 and 3, crop to fit display
     subplot(2,2,3);
     imshow(Rotate3,[])
     title('PATTERN 3');   
 end
 
 if num==4                                                                 %if there are four patterns
     Rotate3=imrotate(Pattern3,angle2,'crop');                             %rotate pattern 3 by angle between patterns 1 and 3, crop to fit display
     subplot(2,2,3);                                                       %third one goes in bottom left corner of window
     imshow(Rotate3,[])
     title('PATTERN 3');
     
     subplot(2,2,4);                                                       %fourth one goes in bottom right corner of window
     Rotate4=imrotate(Pattern4,angle3,'crop');                             %rotate pattern 4 by angle between patterns 1 and 4, crop to fit display
     imshow(Rotate4,[])
     title('PATTERN 4');
     end
 %% MULTIPLY FOR MOIRE IMAGE
 figure('Name','Moire Pattern');                                           %creating and titling new figure
 if num==2                                                                 %for two patterns, only need to multiply pattern 1 and pattern 2 
     moire= Pattern1 .* double(Rotate2);
     imshow(moire,[]);                                                           
 end
 
 if num==3
     moire1=Pattern1.*double(Rotate2);  
     moire2=moire1.*double(Rotate3);
     imshow(moire2,[]);                                                    %multiply the three patterns together and show as single image
 end
 
 if num==4
     moire1=Pattern1.*double(Rotate2);
     moire2=moire1.*double(Rotate3);
     moire3=moire2.*double(Rotate4);
     imshow(moire3,[]);                                                    %multiply the four patterns together and show as single image
 end