General Bezier Curve http://en.wikipedia.org/wiki/B%C3%A9zier_curve#Explicit_definition

GeneralBezierCurve.php

<?php

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

// calculate C(n,k) aka binomial coefficient
// http://php.net/manual/en/ref.math.php#57895
function C($n, $k)
{
	$j = $res = 1;

	if($k < 0 || $k > $n)
		return 0;

	if(($n - $k) < $k)
		$k = $n - $k;

	while($j <= $k)
	{
		$res *= $n--;
		$res /= $j++;
	}

	return $res;
}

// t : [0, 1]
// P0, P1, ..., Pn : n-dimensional point
// B(t) = sum i=0...n C(n,i) * (1-t)^(n-i) * t^i * Pi
function GeneralBezierCurve($t /* , P0, P1, ..., Pn */)
{
	$n = func_num_args() - 2;

	$u = 1 - $t;

	$p = array_fill(0, count(func_get_arg(1)) - 1, 0);

	for($i = 0; $i <= $n; $i++)
	{
		$P_i = func_get_arg($i + 1);

		$C_i = C($n, $i);
		$u_i = pow($u, $n - $i);
		$t_i = pow($t, $i);

		// $T_i = C($n, $i) * pow($u, $n - $i) * pow($t, $i) * $P_i;
		$function = function($i) use ($C_i, $u_i, $t_i) {
			return $C_i * $u_i * $t_i * $i;
		};
		$T_i = array_map($function, $P_i);

		// sum of terms
		// $p += $T_i;
		$function = function($a, $b) {
			return $a + $b;
		};
		$p = array_map($function, $p, $T_i);
	}

	return $p;
}

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

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

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

	// second term
	// $t2 = 2 * $u * $t * $p1;
	$function = function($i) use ($u, $t) {
		return 2 * $u * $t * $i;
	};
	$t2 = array_map($function, $p1);

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

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

	return $p;
}

// 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);

for($t = 0.0; $t < 1.0; $t += 0.1)
{
	$p_quadratic = QuadraticBezierCurve($t, $p0, $p1, $p2);
	echo $t . "\t" . implode(",", $p_quadratic) . "\n";

	$p_general = GeneralBezierCurve($t, $p0, $p1, $p2);
	echo $t . "\t" . implode(",", $p_general) . "\n";
}

$p0 = array(0, 50, 150);
$p1 = array(50, 100, 0);
$p2 = array(200, 200, 150);
$p3 = array(100, 200, 50);

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

	$p_general = GeneralBezierCurve($t, $p0, $p1, $p2, $p3);
	echo $t . "\t" . implode(",", $p_general) . "\n";
}

$p0 = array(0, 50);
$p1 = array(50, 100);
$p2 = array(200, 200);
$p3 = array(100, 200);
$p4 = array(100, 50);

for($t = 0.0; $t < 1.0; $t += 0.1)
{
	$p_general = GeneralBezierCurve($t, $p0, $p1, $p2, $p3, $p4);
	echo $t . "\t" . implode(",", $p_general) . "\n";
}

?>