After Effects Expressions

scrolling.js

// MOMENTUM SCROLLING
// 
// Nice easings without the hassle. Doesn't work well for very long distances.
//
// 1. Separate dimensions on layer to scroll (right click _> separate dimensions)
// 2. Apply the expression to the layers Y Position
// 3. Add keyframes. Easing will adapt to mimic momentum scrolling.

const c = thisLayer("Transform")("Y Position")

var NEWTON_ITERATIONS = 4;
var NEWTON_MIN_SLOPE = 0.001;
var SUBDIVISION_PRECISION = 0.0000001;
var SUBDIVISION_MAX_ITERATIONS = 10;
var kSplineTableSize = 11;
var kSampleStepSize = 1.0 / (kSplineTableSize - 1.0);
var float32ArraySupported = typeof Float32Array === 'function';

function A (aA1, aA2) { return 1.0 - 3.0 * aA2 + 3.0 * aA1; }
function B (aA1, aA2) { return 3.0 * aA2 - 6.0 * aA1; }
function C (aA1)      { return 3.0 * aA1; }
function calcBezier (aT, aA1, aA2) { return ((A(aA1, aA2) * aT + B(aA1, aA2)) * aT + C(aA1)) * aT; }
function getSlope (aT, aA1, aA2) { return 3.0 * A(aA1, aA2) * aT * aT + 2.0 * B(aA1, aA2) * aT + C(aA1); }

function binarySubdivide (aX, aA, aB, mX1, mX2) {

  var currentX, currentT, i = 0

  do {
    currentT = aA + (aB - aA) / 2.0
    currentX = calcBezier(currentT, mX1, mX2) - aX
    if (currentX > 0.0) {
      aB = currentT
    } else {
      aA = currentT
    }
  } while (Math.abs(currentX) > SUBDIVISION_PRECISION && ++i < SUBDIVISION_MAX_ITERATIONS);

  return currentT;

}

function newtonRaphsonIterate (aX, aGuessT, mX1, mX2) {

 for (var i = 0; i < NEWTON_ITERATIONS; ++i) {

   var currentSlope = getSlope(aGuessT, mX1, mX2)

   if (currentSlope === 0.0) {
     return aGuessT
   }

   var currentX = calcBezier(aGuessT, mX1, mX2) - aX

   aGuessT -= currentX / currentSlope

 }
 
 return aGuessT
 
}

function LinearEasing (x) {
  return x
}

function bezier(mX1, mY1, mX2, mY2) {

  if (!(0 <= mX1 && mX1 <= 1 && 0 <= mX2 && mX2 <= 1)) {
    throw new Error('bezier x values must be in [0, 1] range')
  }
 
  if (mX1 === mY1 && mX2 === mY2) {
    return LinearEasing
  }
 
  var sampleValues = float32ArraySupported ? new Float32Array(kSplineTableSize) : new Array(kSplineTableSize)
  
  for (var i = 0; i < kSplineTableSize; ++i) {
    sampleValues[i] = calcBezier(i * kSampleStepSize, mX1, mX2)
  }
 
  function getTForX (aX) {
    var intervalStart = 0.0
    var currentSample = 1
    var lastSample = kSplineTableSize - 1
    for (; currentSample !== lastSample && sampleValues[currentSample] <= aX; ++currentSample) {
      intervalStart += kSampleStepSize
    }
    --currentSample
    // Interpolate to provide an initial guess for t
    var dist = (aX - sampleValues[currentSample]) / (sampleValues[currentSample + 1] - sampleValues[currentSample])
    var guessForT = intervalStart + dist * kSampleStepSize
    var initialSlope = getSlope(guessForT, mX1, mX2)
    if (initialSlope >= NEWTON_MIN_SLOPE) {
      return newtonRaphsonIterate(aX, guessForT, mX1, mX2)
    } else if (initialSlope === 0.0) {
      return guessForT;
    } else {
      return binarySubdivide(aX, intervalStart, intervalStart + kSampleStepSize, mX1, mX2);
    }
  }

  return function BezierEasing (x) {

    if (x === 0 || x === 1) {
      return x
    }

    return calcBezier(getTForX(x), mY1, mY2)

  }
 
}

try {
    
    let index = c.numKeys

    while (c.key(index).time > time) {
        index--
    }
    
    const transform = (value, range1, range2) => {
        return ( (value - range1[0]) / (range1[1] - range1[0]) ) * (range2[1] - range2[0]) + range2[0]
    }
    
    const k1 = c.key(index)
    const k2 = c.key(index + 1)
    const progress = (time - k1.time) / (k2.time - k1.time)
    const duration = k2.time - k1.time
    const distance = Math.abs(k2.value - k1.value)
    const pxFactor = 1800
    const magnitude = duration * pxFactor / distance 
    const attack = 0.11 * magnitude
    const ease = 1 - attack
    
    const easing = bezier(attack, 0, attack / 1.5, 1)

    transform(easing(progress), [0, 1], [k1.value, k2.value])

} catch (e) {
    
    value
    
}