Question

I have three intersecting circles with inaccurate radii. How can I determine three out of six intersection points which form the intersection area? I was initially thinking of simply getting the cluster points – points which have smallest distances between them. But since the radii are not always correct, there might be cases where the cluster points are not the points forming the intersection area. Any ideas?

Answer 1

For each pair of circles, find the two intersections (if they exist) on their boundary. Then test to see if one of these points is inside the third circle (distance to the center less than the radius of that circle).

This will identify the three “corner” points of the region of triple intersection, at least when such an intersection exists.

By the way, the intersection of two circles is really more of a linear problem than a quadratic one, properly approached.