Area between circular curves

Question

I'm trying to calculate the surface between two circular curves (yellow surface in this picture as simplification) but I'm somehow stuck since I don't have datapoints at the same angular values of the two curves. Any ideas?

Thanks for your help!

Picture:

Answer 1

function area = area_between_curves(initial,corrected)

   interval = 0.1;
   x = -80:interval:80;
   y = -80:interval:80;
   [X,Y] = meshgrid(x,y);

   in_initial = inpolygon(X,Y,initial(:,1),initial(:,2));
   in_corrected = inpolygon(X,Y,corrected(:,1),corrected(:,2));
   in_area = xor(in_initial,in_corrected);

   area = interval^2*nnz(in_area);

   % visualization
   figure
   hold on
   plot(X(in_area),Y(in_area),'r.')
   plot(X(~in_area),Y(~in_area),'b.')

end

If I use the lines of the question, this is the result:

area = 1.989710000000001e+03