How can I remove the lines that are not in the cross section of the annulus?

    % Declare experimental variables
R1=75;                   % inner radius
R2=150;                  % outer radius of pipe cross-section
N=4;                     % number of devices

    % Create arrays and internal variables
r=linspace(R1,R2,200);   % array of radial points for temp data
theta=0:360;             % array of angles for temp data
alpha=360/N;             % spacing for devices 
alpha_ar=round([0:alpha:359]);        % array of angles for outter devices in R2
alpha_ar2=round([alpha/2:alpha:359]); % array of angles for inner devices in R1


   % Mark devices
for d=1:length(alpha_ar)
    for f=1:length(alpha_ar2)
    x1=R1*cosd(alpha_ar2(d));
    y1=R1*sind(alpha_ar2(d));
    plot(x1,y1,'rd','MarkerSize',1,'LineWidth',4);
    
    x2=R2*cosd(alpha_ar(f));
    y2=R2*sind(alpha_ar(f));
    plot(x2,y2,'rd','MarkerSize',1,'LineWidth',4);
    
    end
end

for i=1:length(alpha_ar)
    for k=1:length(alpha_ar2)
    alpha1=alpha_ar(i);     % i = index for alpha1 (device angle)
    alpha3=alpha_ar2(k);
    j=1;                    % initialize j, the index for alpha2
    while j<=length(alpha_ar)  
        if j==i             % i and j reference different devices...
            j=j+1;          % if i=j then increment j again
        end

        if j<=length(alpha_ar)  
            alpha2=alpha_ar(j); % j = index for alpha2 (device angle)
        end
        
        
        x=[R2*cosd(alpha_ar(i)),R2*cosd(alpha_ar(j)),R1*cosd(alpha_ar2(k)),R1*cosd(alpha_ar2(k))]; % x values of US devices
        y=[R2*sind(alpha_ar(i)),R2*sind(alpha_ar(j)),R1*sind(alpha_ar2(k)),R1*sind(alpha_ar2(k))]; % y values of US devices
               
       
        figure(1);
        
        % add lj line to temperature profile
        hold on;
        line(x,y,'color','red');
                
        j=j+1;  % increment to next transducer
        if j==length(alpha_ar) && j==i  % increment j again after last  
            j=j+1;                      % tao to break out of loop
        end

    end

end  
end

[KSSV]

The code given plots the annulus?

[Cnell]

No, I had excluded that to make the code more readable.

[Rik]

Question body recovered from Google cache:

  % Declare experimental variables
R1=75;                   % inner radius
R2=150;                  % outer radius of pipe cross-section
N=4;                     % number of devices
    % Create arrays and internal variables
r=linspace(R1,R2,200);   % array of radial points for temp data
theta=0:360;             % array of angles for temp data
alpha=360/N;             % spacing for devices 
alpha_ar=round([0:alpha:359]);        % array of angles for outter devices in R2
alpha_ar2=round([alpha/2:alpha:359]); % array of angles for inner devices in R1
   % Mark devices
for d=1:length(alpha_ar)
    for f=1:length(alpha_ar2)
    x1=R1*cosd(alpha_ar2(d));
    y1=R1*sind(alpha_ar2(d));
    plot(x1,y1,'rd','MarkerSize',1,'LineWidth',4);
    
    x2=R2*cosd(alpha_ar(f));
    y2=R2*sind(alpha_ar(f));
    plot(x2,y2,'rd','MarkerSize',1,'LineWidth',4);
    
    end
end
for i=1:length(alpha_ar)
    for k=1:length(alpha_ar2)
    alpha1=alpha_ar(i);     % i = index for alpha1 (device angle)
    alpha3=alpha_ar2(k);
    j=1;                    % initialize j, the index for alpha2
    while j<=length(alpha_ar)  
        if j==i             % i and j reference different devices...
            j=j+1;          % if i=j then increment j again
        end
        if j<=length(alpha_ar)  
            alpha2=alpha_ar(j); % j = index for alpha2 (device angle)
        end
        
        
        x=[R2*cosd(alpha_ar(i)),R2*cosd(alpha_ar(j)),R1*cosd(alpha_ar2(k)),R1*cosd(alpha_ar2(k))]; % x values of US devices
        y=[R2*sind(alpha_ar(i)),R2*sind(alpha_ar(j)),R1*sind(alpha_ar2(k)),R1*sind(alpha_ar2(k))]; % y values of US devices
               
       
        figure(1);
        
        % add lj line to temperature profile
        hold on;
        line(x,y,'color','red');
                
        j=j+1;  % increment to next transducer
        if j==length(alpha_ar) && j==i  % increment j again after last  
            j=j+1;                      % tao to break out of loop
        end
    end
end
end

[Rena Berman]

(Answers Dev) Restored edit

Answer 1

[Matt J]

        figure(1);
        
        
        % add lj line to temperature profile
        hold on;
        
        for ii=0:1
        [P1,P2]=deal([x(1+ii);y(1+ii)], [x(2+ii);y(2+ii)]);
         
         fun=@(t) norm(t*P1+(1-t)*P2);
         [~,R]=fminbnd(fun,0,1);
        
         if R<R1; continue; end
         line([P1(1),P2(1)],[P1(2),P2(2)],'color','red');
        end

[Cnell]

Thank you, you're amazing!

[Cnell]

If you have time, could you explain how this works?

[Matt J]

These lines

         fun=@(t) norm(t*P1+(1-t)*P2);
         [~,R]=fminbnd(fun,0,1);

find the distance R of the line segment [P1,P2] to the origin. Based on that, you can test whether the line segment remains within the annulus.