How to calculate the area of the overlapping lens between 2 circles [using -code- used to fill this overlapping lens]??

Hi all, I had found the following code which is used to fill the overlapping lens between 2 circles. https://www.mathworks.com/matlabcentral/answers/267866-how-we-can-generate-a-union-area-of-overlapping-2-circles-3-circles-multiple-n-circles?s_tid=answers_rc1-1_p1_MLT

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

My question is: how to use this code to calculate the area of this overlapping lens that had been filled by green color ?? as shown in the following photo

[Image Analyst]

Original question (in case he deletes it like the others):

How to calculate the area of the overlapping lens between 2 circles [using -code- used to fill this overlapping lens]??

Hi all, I had found the following code which is used to fill the overlapping lens between 2 circles. https://www.mathworks.com/matlabcentral/answers/267866-how-we-can-generate-a-union-area-of-overlapping-2-circles-3-circles-multiple-n-circles?s_tid=answers_rc1-1_p1_MLT

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

My question is: how to use this code to calculate the area of this overlapping lens that had been filled by green color ?? as shown in the following photo

Answer 1

[KSSV]

You have that region points in your hand......get the points arrange them in anticlockwise order and use polyarea.

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,:))
% get coordinates 
x = [fillx fliplr(fillx)] ;
y = [filly fliplr(filly)] ;
P = [x; y]; % coordinates / points 
c = mean(P,2); % mean/ central point 
d = P-c ; % vectors connecting the central point and the given points 
th = atan2(d(2,:),d(1,:)); % angle above x axis
[th, idx] = sort(th);   % sorting the angles 
P = P(:,idx); % sorting the given points
P = [P P(:,1)]; % add the first at the end to close the polygon 
plot( P(1,:), P(2,:), '.-r');
fill(P(1,:),P(2,:), 'g', 'EdgeColor','none')
hold off
axis square
area = polyarea(P(1,:),P(2,:))

[Eman S]

Thanks for your reply. But, running the code gave the following error as shown in the following picture:

[KSSV]

That code is working fine for me...did you make any changes? Show us the full code.

[Eman S]

No. I didn't make any changes. I just copy your code. Then, I paste it in Matlab and run it.Then,the previous error appears. My Matlab version is 2015a.

[KSSV]

Try:

d = P-repmat(c,size(P,1),1) ;

[Eman S]

Unfortunately, it gave the same error.