hello
seems to me there is a simple solution to your problem - simply combine x,y data of both curves and use unique to remove duplicate points
the final result (black curve) I added a magnifcation factor of 1.02 (to be removed) just to make the curve easier to see
here we have 6 points in common between C1 & C2
% generate some dummy C and C2 coordinates
theta = linspace(0,pi/2,20);
n = 7;
t1 = theta(1:end-n);
t2 = theta(n+1:end);
x1 = cos(t1);
y1 = sin(t1);
x2 = cos(t2);
y2 = sin(t2);
% combine both curves
x = [x1(:);x2(:)];
y = [y1(:);y2(:)];
[x,ia,ic] = unique(x);
y = y(ia);
plot(x1,y1,'bd-',x2,y2,'r*-',x*1.02,y*1.02,'k*--'); % factor *1.02 on black curve just to make vizualisation easier
axis square
