Overlap between N circles

Hello everyone I have an excel file with 2 columns (x and y) and 2111 rows. What my program does as far now is to : call the file from matlab, place all the couples (xi,yi) on the graph and construct one circle for each point of the excel matrix

clc

close all

clear all

DataSelect='celapossofare';

[v,X,vX]=xlsread('celapossofare.xlsx');

x=v(:,1);y=v(:,2); 

plot(x,y,'.');                    

r  = x*0 + 1000;

CIP=circles_new(x,y,r);

Now I would like to calculate the overlapping of this circles (that has as centre xi, yi).

Can someone help me?

[EDIT] CHIARA'S "ANSWER" MOVED HERE:

what I did is the following code

d2 = (x2-x1)^2+(y2-y1)^2;               
 d = sqrt(d2);                       
 t = ((2*r)^2-d2)*(d2);                  
 if r <= d <= 2*r                            
   A = 2*r^2*acos(d2/(2*d*r))-1/2*sqrt(t);
 elseif d > 2*r                       
   A = 0;
 else  % d < r                         
   A = pi*r^2;
 end

My problem Is very stupid but I just started to prgram in matlab.

I don't know How to take x,y from a matrix that I have in excel

[Sara]

Do you need the points where the circles intersect or the area of the overlap?

[chiara]

I would like to calculate the area where the circles overlap Thank you for your comment

[Roger Wohlwend]

Do you want to know just the size of the area or do you want to know exactly where it is so that you could highlight it in a diagram for example?

[chiara]

I prefer to know exactly where it is if possible

Answer 1

[Roger Wohlwend]

Construct a grid. Calculate for each point the distances to the circle centers. All points whose distances to the circle centers are smaller than the radiuses belong to the overlapping area.

[John D'Errico]

Of course, this will be highly inexact, being equivalent to a very simple integration, essentially rectangle rule. Note that an exact answer was asked for (not that that will be possible.)

[Roger Wohlwend]

Yes, I admit it is not very exact. Perhaps a better solution is taking paper and a pencil and calculate a formula.

[Image Analyst]

With a fine enough grid, it can be made as close as is needed. Perhaps it's just an exercise in numerical analysis. She could decrease the grid spacing until the answer "levels out" and becomes relatively stable.

Answer 2

[Sara]

If you have the mapping toolbox, you can use polybool.

Answer 3

[chiara]

What I did is this but I have a silly problem I don't know how to take x1,x2 y1,y2 from a matrix that I have in excel

d2 = (x2-x1)^2+(y2-y1)^2;              
 d = sqrt(d2);                         
   t = ((2*r)^2-d2)*(d2);                  
   if r <= d <= 2*r                            
     A = 2*r^2*acos(d2/(2*d*r))-1/2*sqrt(t);
   elseif d > 2*r                      
     A = 0;
   else  % d < r                         
     A = pi*r^2;
 end