Overlapping area of two circles

[the_jackass]

Hi all, I have a very simple question.

Given the coordinates of centres and radii of two circles on the plane, I need to calculate the area of the overlapping region.

I have made a formula but it seems to be giving wrong answers. Can I get an hint what is wrong with my formula?

The derivation:



The distance between the centres d is computed with the coordinates of centres. So we know all sides of the triangle (r1, r2 and d). alpha and beta are calculated with arccos and the cosine formula of triangle. Area of a segment is given by 1/2*r^2[theta - sin(theta)]. So I compute the segment areas of both circles and add them up...with theta = 2*alpha and 2*beta in each case.

But this seems to be giving wrong results. For example with the following data:

C1(-0.5,0), r1 = 1.0
C2( 0.5,0), r2 = 1.0

the answer is supposed to be approx. 5.0548 but my technique is giving 1.2284.

Where am I making a mistake?

[GReaper]

Computing the circular segments and adding them up should work. Maybe you implemented the algorithm wrong.

[the_jackass]

Oh okay.

I got it.

The problem asked to compute the area of the whole figure, whereas I'm just computing the area of the overlapping part.
How did I not notice the area of overlap between two unit circles can never be more than pi? xD

When I do area of circle 1 + area of circle 2 - overlapping area I get the correct answer.