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 {
    static let linear = SKTimingFunction(controlPoints: 0, 0, 1, 1)
    static let easeIn = SKTimingFunction(controlPoints: 0.42, 0, 1, 1)
    static let easeOut = SKTimingFunction(controlPoints: 0, 0, 0.58, 1)
    static let easeInOut = SKTimingFunction(controlPoints: 0.42, 0, 0.58, 1)
    static let defaultCurve = SKTimingFunction(controlPoints: 0.25, 0.1, 0.25, 1)
    
    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 _ in 0..<4 {
            let currentSlope = getSlope(aGuessT, mX1, mX2)
            if (currentSlope == 0.0) {return aGuessT}
            let currentX = calcBezier(aGuessT, mX1, mX2) - aX
            aGuessT -= currentX / currentSlope
        }
        return aGuessT
    }
}