@antv/g/es/utils/bezier-easing.js

/**
 * 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)
export var NEWTON_ITERATIONS = 4;
export var NEWTON_MIN_SLOPE = 0.001;
export var SUBDIVISION_PRECISION = 0.0000001;
export var SUBDIVISION_MAX_ITERATIONS = 10;
export var kSplineTableSize = 11;
export var kSampleStepSize = 1.0 / (kSplineTableSize - 1.0);
export var float32ArraySupported = typeof Float32Array === 'function';
export var A = function A(aA1, aA2) {
  return 1.0 - 3.0 * aA2 + 3.0 * aA1;
};
export var B = function B(aA1, aA2) {
  return 3.0 * aA2 - 6.0 * aA1;
};
export var C = function C(aA1) {
  return 3.0 * aA1;
}; // Returns x(t) given t, x1, and x2, or y(t) given t, y1, and y2.

export var calcBezier = 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.

export var getSlope = function getSlope(aT, aA1, aA2) {
  return 3.0 * A(aA1, aA2) * aT * aT + 2.0 * B(aA1, aA2) * aT + C(aA1);
};
export var binarySubdivide = 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;
};
export var newtonRaphsonIterate = 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;
};
export var bezier = 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 function (t) {
    return t;
  }; // Precompute samples table

  var sampleValues = float32ArraySupported ? new Float32Array(kSplineTableSize) : new Array(kSplineTableSize);

  for (var i = 0; i < kSplineTableSize; ++i) {
    sampleValues[i] = calcBezier(i * kSampleStepSize, mX1, mX2);
  }

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