@immutabl3/anime/src/bezier.js

JavaScript animation engine

// BezierEasing https://github.com/gre/bezier-easing

const kSplineTableSize = 11;
const kSampleStepSize = 1.0 / (kSplineTableSize - 1.0);

const A = (aA1, aA2) => 1.0 - 3.0 * aA2 + 3.0 * aA1;
const B = (aA1, aA2) => 3.0 * aA2 - 6.0 * aA1;
const C = aA1 => 3.0 * aA1;

const calcBezier = (aT, aA1, aA2) => ((A(aA1, aA2) * aT + B(aA1, aA2)) * aT + C(aA1)) * aT;
const getSlope = (aT, aA1, aA2) => 3.0 * A(aA1, aA2) * aT * aT + 2.0 * B(aA1, aA2) * aT + C(aA1);

const binarySubdivide = (aX, aA, aB, mX1, mX2) => {
  let currentX;
  let currentT;
  let i = 0;
  // eslint-disable-next-line no-restricted-syntax
  do {
    currentT = aA + (aB - aA) / 2.0;
    currentX = calcBezier(currentT, mX1, mX2) - aX;
    if (currentX > 0.0) {
      // eslint-disable-next-line no-param-reassign
      aB = currentT;
    } else {
      // eslint-disable-next-line no-param-reassign
      aA = currentT;
    };
  } while (Math.abs(currentX) > 0.0000001 && ++i < 10);
  return currentT;
};

const newtonRaphsonIterate = (aX, aGuessT, mX1, mX2) => {
  for (let i = 0; i < 4; ++i) {
    const currentSlope = getSlope(aGuessT, mX1, mX2);
    if (currentSlope === 0.0) return aGuessT;
    const currentX = calcBezier(aGuessT, mX1, mX2) - aX;
    // eslint-disable-next-line no-param-reassign
    aGuessT -= currentX / currentSlope;
  }
  return aGuessT;
};

const bezier = (mX1, mY1, mX2, mY2) => {
  if (!(0 <= mX1 && mX1 <= 1 && 0 <= mX2 && mX2 <= 1)) return;
  const sampleValues = new Float32Array(kSplineTableSize);

  if (mX1 !== mY1 || mX2 !== mY2) {
    for (let i = 0; i < kSplineTableSize; ++i) {
      sampleValues[i] = calcBezier(i * kSampleStepSize, mX1, mX2);
    }
  }

  const getTForX = aX => {
    let intervalStart = 0;
    let currentSample = 1;
    const lastSample = kSplineTableSize - 1;

    for (; currentSample !== lastSample && sampleValues[currentSample] <= aX; ++currentSample) {
      intervalStart += kSampleStepSize;
    }

    --currentSample;

    const dist = (aX - sampleValues[currentSample]) / (sampleValues[currentSample + 1] - sampleValues[currentSample]);
    const guessForT = intervalStart + dist * kSampleStepSize;
    const initialSlope = getSlope(guessForT, mX1, mX2);

    if (initialSlope >= 0.001) return newtonRaphsonIterate(aX, guessForT, mX1, mX2);
    
    if (initialSlope === 0.0) return guessForT;
    
    return binarySubdivide(aX, intervalStart, intervalStart + kSampleStepSize, mX1, mX2);
  };

  return x => {
    if (mX1 === mY1 && mX2 === mY2) return x;
    if (x === 0 || x === 1) return x;
    return calcBezier(getTForX(x), mY1, mY2);
  };
};

export default bezier;