MATLAB: How we can generate a union area of overlapping 2 circles, 3 circles, multiple n circles

extremely not urgentset mathematics

How we can generate a union area of overlapping 2 circles, 3 circles, multiple n circles

Best Answer

Here it is for two circles:
t = linspace(0, 2*pi, 100);
cir = @(r,ctr) [r*cos(t)+ctr(1); r*sin(t)+ctr(2)];                      % Circle Function
c1 = cir(1.0, [0; 0]);
c2 = cir(1.5, [1; 1]);
in1 = find(inpolygon(c1(1,:), c1(2,:), c2(1,:), c2(2,:)));              % Circle #1 Points Inside Circle #2
in2 = find(inpolygon(c2(1,:), c2(2,:), c1(1,:), c1(2,:)));              % Circle #2 Points Inside Circle #1
[fillx,ix] = sort([c1(1,in1) c2(1,in2)]);                               % Sort Points
filly = [c1(2,in1) (c2(2,in2))];
filly = filly(ix);
figure(1)
plot(c1(1,:), c1(2,:))
hold on
plot(c2(1,:), c2(2,:))
fill([fillx fliplr(fillx)], [filly fliplr(filly)], 'g', 'EdgeColor','none')
hold off
axis square
I will let you adapt it for more circles. That will require doing the find(inpolygon( ...)), sort, plot, and fill calls for each two-circle intersection. This would become complicated for more than two intersecting circles in the same area, but is probably possible.
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