Cubic Bezier Curve http://en.wikipedia.org/wiki/B%C3%A9zier_curve#Cubic_B.C3.A9zier_curves

CubicBezierCurve.php

<?php

// http://en.wikipedia.org/wiki/B%C3%A9zier_curve#Cubic_B.C3.A9zier_curves

// t : [0, 1]
// p0, p1, p2, p3 : n-dimensional point
// B(t) = (1-t)^3 * p0 + 3*(1-t)^2*t * p1 + 3*(1-t)*t^2 * p2 + t^3 * p3
function CubicBezierCurve($t, $p0, $p1, $p2, $p3)
{
	$u = 1 - $t;
	$uu = $u * $u;
	$uuu = $uu * $u;
	$tt = $t * $t;
	$ttt = $tt * $t;

	// first term
	// $t1 = $uuu * $p0;
	$function = function($i) use ($uuu) {
		return $uuu * $i;
	};
	$t1 = array_map($function, $p0);

	// second term
	// $t2 = 3 * $uu * $t * $p1;
	$function = function($i) use ($uu, $t) {
		return 3 * $uu * $t * $i;
	};
	$t2 = array_map($function, $p1);

	// third term
	// $t3 = 3 * $u * $tt * $p2;
	$function = function($i) use ($u, $tt) {
		return 3 * $u * $tt * $i;
	};
	$t3 = array_map($function, $p2);

	// fourth term
	// $t4 = $ttt * $p3;
	$function = function($i) use ($ttt) {
		return $ttt * $i;
	};
	$t4 = array_map($function, $p3);

	// sum of terms
	// $p = $t1 + $t2 + $t3 + $t4;
	$function = function($a, $b, $c, $d) {
		return $a + $b + $c + $d;
	};
	$p = array_map($function, $t1, $t2, $t3, $t4);

	return $p;
}

$p0 = array(0, 50);
$p1 = array(50, 100);
$p2 = array(200, 200);
$p3 = array(100, 200);

for($t = 0.0; $t < 1.0; $t += 0.1)
{
	$p = CubicBezierCurve($t, $p0, $p1, $p2, $p3);
	echo $t . "\t" . implode(",", $p) . "\n";
}

$p0 = array(0, 0, 0);
$p1 = array(64, 32, 255);
$p2 = array(128, 255, 16);
$p3 = array(255, 16, 16);

for($t = 0.0; $t < 1.0; $t += 0.1)
{
	$p = CubicBezierCurve($t, $p0, $p1, $p2, $p3);
	$p = array_map("round", $p);
	echo $t . "\t" . implode(",", $p) . "\n";
}

?>