Cubic Bezier Easing Curve

CBezierEase.js

/*
  Quick hacked together function to use a 4 point bezier curve as an easing function.
  Some limitations :
    - Curve CAN NOT intersect, each X value must be unqiue.
    - First point must have an X = 0, y can be anything you want.
    - Last point must have an X = 1, y can be anything you  want.
    
  t value for a bezier curve isn't really time, its more like the normalized length of the curve.
  But we can use the x value as long as it exists between 0 and 1 as time. To do that, I'm performing
  a simple binary searching looking for the target time (x). When x is found within ome margin of error, the t 
  value can then be used to get the corrisponding y value.
*/

function CBezierEase(target, x0,y0, x1,y1, x2,y2, x3,y3 ){
	const TRIES		= 30;     // Max tries to find the best Y value
	const MARGIN	= 0.001;  // How far from target to accept as correct value.

	//TODO, Avoid doing binary search if near the beginning or the end.
	//if(target <= 0.00001) // Target is Zero
	//else if(target > 0.99999 ) //target is One

	let	a 	= 0,        //  Start  of Range
		b	= 1,        //  End  of Range
		loop	= 0,
		t,tt, i, ii, x;

	//Limit search by a few attempts.
	while( loop++ < TRIES ){
		t	= (b - a) * 0.5  + a; // Get the Mid value between A  and B
		i	= 1 - t;              // Get the inverse of t
		tt	= t * t;            // Save some time since t^2 is used more the once
		ii	= i * i;            // Save for i
		x 	= i*ii*x0 + 3*t*ii*x1 + 3*tt*i*x2 + t*tt*x3;  // x value in the range's mid point

		//If X is found by some margin of precision, good enough.
		if( Math.abs(target - x) < MARGIN ) break; //console.log("found target at", t);

		if(target > x)		  a = t;  // Target is over, shift the start  of the range to t
		else if(target < x)	b = t;  // Target is under, shift the end of the range to t
	}

	return i*ii*y0 + 3*t*ii*y1 + 3*tt*i*y2 + t*tt*y3; //Return the best possible Y value found
}