From: <HIDDEN>
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Subject: Re: circle intersection help
Date: Thu, 26 Feb 2009 21:54:01 +0000 (UTC)
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"John D'Errico" <> wrote in message <go6uuh$qbj$>...
> Roger, you too must realize that there is very
> possibly no common intersection of all 4 circles.
> Computation of the centroid will be more difficult
> then.
> John

  John, if my understanding of Bala's statement is correct, he isn't looking for a common intersection of the four circles, but rather the intersection of four disks, which is a different matter.  This intersection set will be convex and bounded by a series of presumably no more than six circular arcs with varying radii and centers.  From among the possible intersections of each pair of circles, those which are not on or inside both other circles can be eliminated, thereby arriving at the endpoints of the arc segments which form the region's boundary.  The challenge is then to use these to compute the area contained within the region and the location of its centroid.

  I am certain that this area can be successfully computed in terms of the locations of the arc endpoints and centers of the arcs by a simple process involving signed areas of projections from the arcs to some common point (though admittedly I haven't written these out yet,) but a few hen-scratchings have also convinced me that the centroid computations of these projected areas should follow along rather similar lines. 

Roger Stafford