function fitcircle($X, $Y)
{
$points = sizeof($X);
if ($points < 3) {
return array("cx" => 0, "cy" => 0, "r" => 0, "err" => 100);
}
// Mean of points
$meanX = 0;
$meanY = 0;
for ($i = 0; $i < sizeof($X); $i++) {
$meanX += $X[$i];
$meanY += $Y[$i];
}
$meanX /= $points;
$meanY /= $points;
// Auxiliary means
$mXx = 0;
$mXy = 0;
$mYy = 0;
$mRx = 0;
$mRy = 0;
for ($i = 0; $i < sizeof($X); $i++) {
$x = $X[$i];
$y = $Y[$i];
$r = $x * $x + $y * $y;
$mXx += $x * ($x - $meanX);
$mXy += $x * ($y - $meanY);
$mYy += $y * ($y - $meanY);
$mRx += $r * ($x - $meanX);
$mRy += $r * ($y - $meanY);
}
$mXx /= $points;
$mXy /= $points;
$mYy /= $points;
$mRx /= $points;
$mRy /= $points;
// Assemble matrix
$A[0][0] = $mXx;
$A[0][1] = 2.0 * $mXy;
$A[1][0] = 0.0;
$A[1][1] = $mYy;
$matrixA = new Matrix($A);
// A=A+transpose(A)
$matrixA = $matrixA->plus($matrixA->transpose());
// Assemble B vector
$b[0][0] = $mRx;
$b[1][0] = $mRy;
$matrixB = new Matrix($b);
// Calculate center Solve A*x=b for x,then center=x
$LU = new LUDecomposition($matrixA);
if ($LU->isNonsingular()) {
$C = $matrixA->solve($matrixB);
$cx = $C->get(0, 0);
$cy = $C->get(1, 0);
// Calculate radius
$meanR2 = 0;
$maxR2 = 0;
$minR2 = 10000;
for ($i = 0; $i < sizeof($X); $i++) {
$x = $X[$i];
$y = $Y[$i];
$r2 = ($x - $cx) * ($x - $cx) + ($y - $cy) * ($y - $cy);
if ($r2 > $maxR2) {
$maxR2 = $r2;
}
if ($r2 < $minR2) {
$minR2 = $r2;
}
$meanR2 += $r2;
}
$meanR2 /= $points;
$radius = sqrt($meanR2);
// Calculate error
$err = sqrt($maxR2) / sqrt($minR2);
// Return
return array("cx" => $cx, "cy" => $cy, "r" => $radius, "err" => $err);
} else {
return array("cx" => 0, "cy" => 0, "r" => 0, "err" => 100);
}
}
