Calculating the percentage area overlap between circles in PHP. Built for Jon Hazan @ Bam UK

circle_overlap.php

<?php

/** 
 * Returns the percentage area overlap between two circles
 * NB. Doesn't validate input.
 *
 * Built for Jon Hazan of Bam UK student marketing
 *
 * @author JP Hastings-Spital
 * @param float distance between the two circles' origins
 * @param array The two radii (floats)
 * @return float percentage_overlap
 **/
function circle_overlap($d,$rs){	
	// Make sure the larger circle is left-most (for convenience)
	$r1 = max($rs);
	$r2 = min($rs);
	
	// Are the circles non-overlapping?
	if ($d >= $r1 + $r2) {
		return 0; // 0% coverage
	}
	
	// Is one circle entirely within the other?
	elseif (max($rs) >= $d + min($rs)) {
		return 1; // 100% Coverage
	}
	
	// Partial overlap
	else {
		// Distance of cross-point from origin of left circle
		$x1 = ($d*$d - $r2*$r2 + $r1*$r1 )/(2*$d); 
		// Distance of cross-point from origin of right circle
		// (symmetry means we can shortcut with absolute value)
		$x2 = abs($d - $x1);
		
		$y = sqrt($r1*$r1 - ($x1*$x1));
		
		// Area of left lens
		$a1 = ($r1*$r1) * acos($x1 / $r1) - $x1 * $y;
		// Area of right lens
		$a2 = ($r2*$r2) * acos($x2 / $r2) - $x2 * $y;
				
		// Special case, if the cross-point is further away from the origin of
		// the first circle than the second circle is, then a2 needs to be the
		// large side of the circle, not the small one:
		if ($x1 > $d)
			$a2 = (pi() * $r2*$r2) - $a2;
		
		$overlap_area = $a1 + $a2;
		
		// The total area of the union is:
		// area of circle 1 + area of circle 2 - overlap_area
		// (as the overlap area only needs to be counted once)
		$total_area = pi() * ($r1*$r1 + $r2*$r2) - $overlap_area;
		return $overlap_area / $total_area;
	}
}