calculate the area of three circles overlapping

I have 3 circles. We know the center coordinates of each circle and also their radii.

For example:

circle 1: radius=r1 , center coordinate=(x1,y1)

circle 2: radius=r2 , center coordinate=(x2,y2)

circle 3: radius=r3 , center coordinate=(x3,y3)

I want to calculate the overlapping area of these three circles. I mean just the area which all these three circles have in common

thanks

Answer 1

[Image Analyst]

I suggest you start with this answer by Roger: http://www.mathworks.com/matlabcentral/answers/86975#answer_96518

[Sunita Saha]

The example referred is showing only the pair wise overlapped area between two circles. i want to calculate the area if three circles have common area overlapped. can you please help me with that. i have multiple number of circles where overlapping is obvious. I could solved the overlapped area between each pair of circles but not the case when three circles have same common area overlapped.

[Image Analyst]

If you have digital images, then yes, I could help. If you have analytical formulas/equations, then no, I can't help.

[Sunita Saha]

this is my problem. I need the total overlapped area considering just once.

[Image Analyst]

Create a digital image with the faq http://matlab.wikia.com/wiki/FAQ#How_do_I_create_a_circle.3F. Then sum the circle binary image into a cumulative one as you draw each circle.

sumImage = zeros(rows, columns);
for k = 1 : numCircles
    thisOneCircle = .... use FAQ to create image of one circle.
    sumImage = sumImage + thisOneCircle;
end

Then use sum to count the number of pixels where the count is more than 2

overlappedPixels = sumImage >= 2;
numOverlapPixels = sum(overlappedPixels (:));

[Sunita Saha]

Thank you for the solution suggestion.