This is the TimingFunction class like CAMediaTimingFunction available in AnyWhere also SpriteKit. All the cool animation curves from `CAMediaTimingFunction` but it is limited to use with CoreAnimation. See what you can do with cubic Bezier curves here: http://cubic-bezier.com

SKTimingFunction.swift

//
//  SKTimingFunction.swift
//  Pods
//
//  Created by Takuya Okamoto on 2015/10/06.
//
//

// inspired by https://gist.github.com/raphaelschaad/6739676


import UIKit

/**
# CAMediaTimingFunction in Anywhere.
All the cool animation curves from `CAMediaTimingFunction` but it is only available to use with CoreAnimation.
This is the TimingFunction class like CAMediaTimingFunction available in AnyWhere.

This is translated by [JavaScript](http://greweb.me/2012/02/bezier-curve-based-easing-functions-from-concept-to-implementation/).

# Usage
``` swift
let move = SKAction.moveTo(point, duration:2.0)
let timingFunc = SKTimingFunction(controlPoints: 0.6, 0.0, 0.1, 0.6)
move.timingFunction = {timingFunc.get($0)}
```
*/
class SKTimingFunction {
    
    let mX1: CGFloat
    let mY1: CGFloat
    let mX2: CGFloat
    let mY2: CGFloat
    
    init(controlPoints c1x: CGFloat, _ c1y: CGFloat, _ c2x: CGFloat, _ c2y: CGFloat) {
        self.mX1 = c1x
        self.mY1 = c1y
        self.mX2 = c2x
        self.mY2 = c2y
    }
    
    func get(aX: CGFloat) -> CGFloat {
        if (mX1 == mY1 && mX2 == mY2) { return aX }// linear
        return calcBezier(getTForX(aX), mY1, mY2)
    }
    
    func get(t: Float) -> Float {
        return Float(self.get(CGFloat(t)))
    }
    
    func A(aA1: CGFloat, _ aA2: CGFloat) -> CGFloat { return 1.0 - 3.0 * aA2 + 3.0 * aA1 }
    func B(aA1: CGFloat, _ aA2: CGFloat) -> CGFloat { return 3.0 * aA2 - 6.0 * aA1 }
    func C(aA1: CGFloat)               -> CGFloat { return 3.0 * aA1 }
    
    // Returns x(t) given t, x1, and x2, or y(t) given t, y1, and y2.
    func calcBezier(aT: CGFloat, _ aA1: CGFloat, _ aA2: CGFloat) -> CGFloat {
        return ((A(aA1, aA2)*aT + B(aA1, aA2))*aT + C(aA1))*aT
    }
    
    // Returns dx/dt given t, x1, and x2, or dy/dt given t, y1, and y2.
    func getSlope(aT: CGFloat, _ aA1: CGFloat, _ aA2: CGFloat) -> CGFloat {
        return 3.0 * A(aA1, aA2)*aT*aT + 2.0 * B(aA1, aA2) * aT + C(aA1)
    }
    
    func getTForX(aX: CGFloat) -> CGFloat {
        // Newton raphson iteration
        var aGuessT = aX
        for (var i = 0; i < 4; ++i) {
            let currentSlope = getSlope(aGuessT, mX1, mX2)
            if (currentSlope == 0.0) {return aGuessT}
            let currentX = calcBezier(aGuessT, mX1, mX2) - aX
            aGuessT -= currentX / currentSlope
        }
        return aGuessT
    }
}

Nice! Thanks for the shout out to the Objective-C version https://gist.github.com/raphaelschaad/6739676

Note to future explorers: When a timing function returns a value outside 0...1 the action stops executing right away. If you want to achieve any effects that require timing outside of this range (eg easeInBack) then you will need to wrap your method in a SKAction.customAction(withDuration:actionBlock:) with linear timing, and then call these functions to calculate your custom timing curves

Thank you @dataxpress! Very useful information.