"use strict";

( function ( NS ) {

var cubicBezier = function ( p1x, p1y, p2x, p2y ) {
 // Calculate constants in parametric bezier formular
 // http://www.moshplant.com/direct-or/bezier/math.html
 var cX = 3 * p1x,
   bX = 3 * ( p2x - p1x ) - cX,
   aX = 1 - cX - bX,

   cY = 3 * p1y,
   bY = 3 * ( p2y - p1y ) - cY,
   aY = 1 - cY - bY;

 // Functions for calculating x, x', y for t
 var bezierX = function ( t ) {
   return t * ( cX + t * ( bX + t * aX ) );
 };
 var bezierXDerivative = function ( t ) {
   return cX + t * ( 2 * bX + 3 * aX * t );
 };

 // Use Newton-Raphson method to find t for a given x.
 // Since x = a*t^3 + b*t^2 + c*t, we find the root for
 // a*t^3 + b*t^2 + c*t - x = 0, and thus t.
 var newtonRaphson = function ( x ) {
   var prev,
     // Initial estimation is linear
     t = x;
   do {
     prev = t;
     t = t - ( ( bezierX( t ) - x ) / bezierXDerivative( t ) );
   } while ( Math.abs( t - prev ) > 1e-4 );

   return t;
 };

 return function ( x ) {
   var t = newtonRaphson( x );
   // This is y given t on the bezier curve.
   return t * ( cY + t * ( bY + t * aY ) );
 }.extend({
   cssName: 'cubic-bezier(' + p1x + ',' + p1y + ',' + p2x + ',' + p2y + ')'
 });
};