react-native/Libraries/Animated/src/bezier.js

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

 // These values are established by empiricism with tests (tradeoff: performance VS precision)
 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; }

 // Returns x(t) given t, x1, and x2, or y(t) given t, y1, and y2.
 function calcBezier (aT, aA1, aA2) { 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, 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;
 }

 module.exports = function bezier (mX1, mY1, mX2, mY2) {
   if (!(0 <= mX1 && mX1 <= 1 && 0 <= mX2 && mX2 <= 1)) { // eslint-disable-line yoda
     throw new Error('bezier x values must be in [0, 1] range');
   }

   // Precompute samples table
   var sampleValues = float32ArraySupported ? new Float32Array(kSplineTableSize) : new Array(kSplineTableSize);
   if (mX1 !== mY1 || mX2 !== mY2) {
     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 (mX1 === mY1 && mX2 === mY2) {
       return x; // linear
     }
     // Because JavaScript number are imprecise, we should guarantee the extremes are right.
     if (x === 0) {
       return 0;
     }
     if (x === 1) {
       return 1;
     }
     return calcBezier(getTForX(x), mY1, mY2);
   };
 };