@okikio/animate/src/bezier-easing.ts

An animation library for the modern web which utilizes the Web Animation API (WAAPI) to create butter smooth animation.

/**
 * 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 const NEWTON_ITERATIONS = 4;
export const NEWTON_MIN_SLOPE = 0.001;
export const SUBDIVISION_PRECISION = 0.0000001;
export const SUBDIVISION_MAX_ITERATIONS = 10;

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

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

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

// Returns x(t) given t, x1, and x2, or y(t) given t, y1, and y2.
export const calcBezier = (aT: number, aA1: number, aA2: number) => ((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 const getSlope = (aT: number, aA1: number, aA2: number) => 3.0 * A(aA1, aA2) * aT * aT + 2.0 * B(aA1, aA2) * aT + C(aA1);
export const binarySubdivide = (aX: number, aA: number, aB: number, mX1: number, mX2: number) => {
    let currentX: number, currentT: number, 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 const newtonRaphsonIterate = (aX: number, aGuessT: number, mX1: number, mX2: number) => {
    for (var i = 0; i < NEWTON_ITERATIONS; ++i) {
        let currentSlope = getSlope(aGuessT, mX1, mX2);
        if (currentSlope === 0.0) return aGuessT;

        let currentX = calcBezier(aGuessT, mX1, mX2) - aX;
        aGuessT -= currentX / currentSlope;
    }

    return aGuessT;
}

export const bezier = (mX1: number, mY1: number, mX2: number, mY2: 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 (t: number) => 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);
    }

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

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

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

        let 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 (t: number) => {
        // 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);
    };
};

export default bezier;