SolalDR/animate

/**
 * https://github.com/gre/bezier-easing
 * BezierEasing - use bezier curve for transition easing function
 * by Gaëtan Renaudeau 2014 - 2015 – MIT License
 */

// These values are established by empiricism with tests (tradeoff: performance VS precision)
const NEWTON_ITERATIONS = 4;
const NEWTON_MIN_SLOPE = 0.001;
const SUBDIVISION_PRECISION = 0.0000001;
const SUBDIVISION_MAX_ITERATIONS = 10;

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

const float32ArraySupported = typeof Float32Array === 'function';

function A (aA1: number, aA2: number) { return 1.0 - 3.0 * aA2 + 3.0 * aA1; }
function B (aA1: number, aA2: number) { return 3.0 * aA2 - 6.0 * aA1; }
function C (aA1: number)      { return 3.0 * aA1; }

// Returns x(t) given t, x1, and x2, or y(t) given t, y1, and y2.
function calcBezier (aT: number, aA1: number, aA2: number) {
  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.
function getSlope (aT: number, aA1: number, aA2: number) {
  return 3.0 * A(aA1, aA2) * aT * aT + 2.0 * B(aA1, aA2) * aT + C(aA1);
}

function binarySubdivide (aX: number, aA: number, aB: number, mX1: number, mX2: number) {
  let 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: number, aGuessT: number, mX1: number, mX2: number) {
 for (let i = 0; i < NEWTON_ITERATIONS; ++i) {
   const currentSlope = getSlope(aGuessT, mX1, mX2);
   if (currentSlope === 0.0) {
     return aGuessT;
   }
   const currentX = calcBezier(aGuessT, mX1, mX2) - aX;
   aGuessT -= currentX / currentSlope;
 }
 return aGuessT;
}

function LinearEasing (x: number) {
  return x;
}

export function bezier (mX1: number, mY1: number, mX2: number, mY2: number): (...args: number[]) => number {
  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;
  }

  // Precompute samples table
  const sampleValues = float32ArraySupported ? new Float32Array(kSplineTableSize) : new Array(kSplineTableSize);
  for (let i = 0; i < kSplineTableSize; ++i) {
    sampleValues[i] = calcBezier(i * kSampleStepSize, mX1, mX2);
  }

  function getTForX (aX: number) {
    let intervalStart = 0.0;
    let currentSample = 1;
    const lastSample = kSplineTableSize - 1;

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

    // Interpolate to provide an initial guess for t
    const dist = (aX - sampleValues[currentSample]) / (sampleValues[currentSample + 1] - sampleValues[currentSample]);
    const guessForT = intervalStart + dist * kSampleStepSize;

    const 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) {
    // Because JavaScript number are imprecise, we should guarantee the extremes are right.
    if (x === 0 || x === 1) {
      return x;
    }
    return calcBezier(getTForX(x), mY1, mY2);
  };
}