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overlapping area between two circles

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m. muner
m. muner 2016-3-12
回答： Roger Stafford 2016-3-14
hello i have 25 circles each with center coordinates and all of the same radius how to calculate the overlapping area between any two or more circles
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Ahmet Cecen
Ahmet Cecen 2016-3-12
I feel like this is better solved in MAPLE or Mathematica if you are looking for an exact answer in continuous space.

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Star Strider
Star Strider 2016-3-12
I was filling in the area of the overlap of two circles in How we can generate a union area of overlapping 2 circles, 3 circles, multiple n circles, not calculating the area. However you could adapt that idea to calculate the area of the overlap between any two of them using trapz.

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Roger Stafford
Roger Stafford 2016-3-14
Let the distance between the centers of two circles be d and their two radii be r1 and r2. Then the area, A, of the overlap region of the two circles can be calculated as follows using Matlab's 'atan2' function:
t = sqrt((d+r1+r2)*(d+r1-r2)*(d-r1+r2)*(-d+r1+r2));
A = r1^2*atan2(t,d^2+r1^2-r2^2)+r2^2*atan2(t,d^2-r1^2+r2^2)-t/2;
Note that if 't' is imaginary, then either the circles don't intersect at all in which case the overlap area is zero, or one circle lies entirely within the other in which case the overlap area is just that of this inner circle.
Ahmet Cecen
Ahmet Cecen 2016-3-12
If the formula is correct, here is a function that will calculate the area:
a = @(d,r,R) (1/d).*sqrt(4*(d.^2)*(R.^2) - ((d.^2)-(r.^2)+(R.^2)).^2)
Now all you do to get the area is:
d = distance between two centers
area = a(d,radius1,radius2)
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m. muner
m. muner 2016-3-13
thank you very much you have two radius i guess since there is R and r if they are the same its ok for the function

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