For Intersecting Circles, how to remove overlapping arcs for 3 or more circles?

In the attached image if you project the red lined plane to z=0 (2D) is there a way to plot the circles with chords shown, and arcs removed in MATLAB (as well as an extension to N circles)?

Circle Interactions

I have a solution posted from a previous question (2 circles) which will be shown here (with some minor changes):

clear all
clc

m       = 100;    % Number of points on circle
x_max   = 50;     % Uppermost x location of circle center
y_max   = 50;     % Uppermost y location of circle center
theta   = 0:2*pi/m:2*pi;     % Evaluated angles for circle

i       = 1;                           
k       = 2; %%%%%%%%%%%

rad(i)      = 15*rand;                  % Save circle radii to array
x_pos(i)    = x_max*rand;               % Save circle xi-positions to array
y_pos(i)    = y_max*rand;               % Save circle yi-positions to array
rad(k)      = 15*rand;                  % Save circle radii to array
x_pos(k)    = x_max*rand;               % Save circle xk-positions to array
y_pos(k)    = y_max*rand;               % Save circle yk-positions to array

Xk=x_pos(k)+rad(k)*cos(theta);
Yk=y_pos(k)+rad(k)*sin(theta);
Xi=x_pos(i)+rad(i)*cos(theta);
Yi=y_pos(i)+rad(i)*sin(theta);
dC1 = sqrt((Xi-x_pos(k)).^2+(Yi-y_pos(k)).^2)>=rad(k);
dC2 = sqrt((Xk-x_pos(i)).^2+(Yk-y_pos(i)).^2)>=rad(i);
plot(Xk(dC2.'),Yk(dC2.'),'m',Xi(dC1.'),Yi(dC1.'),'c');
axis([0 100 0 100]);
hold on
axis equal

Or maybe there is a way to have N circles fit the requirements above with a carefully restricted Voronoi/Delaunay plot?

Answer 1

[Joseph Cheng]

Well... feels like i'm answering this again but what you can do is a for loop

clear all
clc

m       = 1000;    % Number of points on circle
x_max   = 50;     % Uppermost x location of circle center
y_max   = 50;     % Uppermost y location of circle center
theta   = 0:2*pi/m:2*pi;     % Evaluated angles for circle

k=3
%generate circles and store their points.
for i =1:k
    rad(i)      = 15*rand;                  % Save circle radii to array
    x_pos(i)    = x_max*rand;               % Save circle xi-positions to array
    y_pos(i)    = y_max*rand;               % Save circle yi-positions to array

      X{i}=x_pos(i)+rad(i)*cos(theta);
      Y{i}=y_pos(i)+rad(i)*sin(theta);

end

figure,
hold on
for j=1:3
plot(X{j},Y{j})

    end

%perform loops for comparison.
  for i=1:k-1
      for j=i+1:k
          dC1 = sqrt((X{i}-x_pos(j)).^2+(Y{i}-y_pos(j)).^2)>=rad(j);
          X{i}(~dC1)=NaN;
          Y{i}(~dC1)=NaN;
          dC2 = sqrt((X{j}-x_pos(i)).^2+(Y{j}-y_pos(i)).^2)>=rad(i);    
          X{j}(~dC2)=NaN;
          Y{j}(~dC2)=NaN;
      end
  end
  figure,
  hold on
  for j=1:3
      X{j}(isnan(X{j})) = [];
      Y{j}(isnan(Y{j})) = [];
  plot(X{j},Y{j})
  end

[Sean]

Yeah, I just couldn't figure out how to expand to n circles. I appreciate your help Joseph.