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From: davis@bedlam.asd.sgi.com (Tom Davis)
Newsgroups: comp.graphics
Subject: Re: Wanted: algorithm to compute intersection of square and circle
Message-ID: <1991Apr26.011221.3305@odin.corp.sgi.com>
Date: 26 Apr 91 01:12:21 GMT
References: <1991Apr25.192400.8438@cfa203.harvard.edu>
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Reply-To: davis@bedlam.asd.sgi.com (Tom Davis)
Organization: Silicon Graphics, Inc., Mountain View, CA.
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If you just need a numerical approximation, why not approximate the
circle with an n-sided regular polygon, and use standard clipping
procedures to clip that polygon against the square.  Then if the (clipped)
vertices are (x[0], y[0]), (x[1], y[1]), ... (x[m-1], y[m-1]), the area is
given by:

1/2 * sum { x[i](y[i+1] - y[i]) - y[i](x[i+1] - x[i])}

The sum goes from i = 0 to i = m-1, and assume x[m] = x[0] and y[m] = y[0].
Pick a big enough n, and you ought to do OK.