global proc fit2dParabolaFromThreePoints(
		float $in_x1, float $in_x2, float $in_x3, 
		float $in_y1, float $in_y2, float $in_y3,
		float $o_result[]
){
	float $denom = ($in_x1 - $in_x2)*($in_x1 - $in_x3)*($in_x2 - $in_x3);
	$o_result[0] = ($in_x3 * ($in_y2 - $in_y1) + $in_x2 * ($in_y1 - $in_y3) + $in_x1 * ($in_y3 - $in_y2)) / $denom;
	$o_result[1] = ($in_x3*$in_x3 * ($in_y1 - $in_y2) + $in_x2*$in_x2 * ($in_y3 - $in_y1) + $in_x1*$in_x1 * ($in_y2 - $in_y3)) / $denom;
	$o_result[2] = ($in_x2 * $in_x3 * ($in_x2 - $in_x3) * $in_y1 + $in_x3 * $in_x1 * ($in_x3 - $in_x1) * $in_y2 + $in_x1 * $in_x2 * ($in_x1 - $in_x2) * $in_y3) / $denom;
};

// Example
// createXYParabolaAnimExpression("pSphere1", 1, 1, 0, 0.1, -30);
global proc createXYParabolaAnimExpression(
	string $target_transform, 
	float $a, float $b, float $c, 
	float $speed, 
	float $frame_offset
){
	string $tx = $target_transform + ".tx";
	string $ty = $target_transform + ".ty";
	string $exp_str = 
		"float $a="+$a+";\n"+
		"float $b="+$b+";\n"+
		"float $c="+$c+";\n"+
		"float $speed="+$speed+";\n"+
		$tx+" = (frame+"+$frame_offset+")*$speed;\n"+
		$ty+" = $a*"+$tx+"*"+$tx+" + $b*"+$tx+"+$c;";
	expression -s $exp_str;
};

// Example
// createXYParabolaAnimExpression_SelectedThreePoints("pSphere1", 0.1, -30);
global proc createXYParabolaAnimExpression_SelectedThreePoints(
	string $target_transform, 
	float $speed, 
	float $frame_offset
){
	string $point_list[] = `ls -sl`;
	if(size($point_list)<3){
		print "error: Number of selected point is not enough, must be more than 3."; return;
	}
	float $coefs[3];
	fit2dParabolaFromThreePoints(
		`getAttr ($point_list[0]+".tx")`,
		`getAttr ($point_list[1]+".tx")`,
		`getAttr ($point_list[2]+".tx")`,
		`getAttr ($point_list[0]+".ty")`,
		`getAttr ($point_list[1]+".ty")`,
		`getAttr ($point_list[2]+".ty")`,
		$coefs
	);
	createXYParabolaAnimExpression($target_transform, $coefs[0], $coefs[1], $coefs[2], $speed, $frame_offset);
}