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Use bezier-easing 3.2 closed-form solver in Easing.bezier #58941

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Use bezier-easing 3.2 closed-form solver in Easing.bezier #58941

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50 changes: 49 additions & 1 deletion packages/react-native/Libraries/Animated/__tests__/bezier-itest.js
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Original file line number Diff line number Diff line change
Expand Up @@ -11,7 +11,7 @@
/**
* BezierEasing - use bezier curve for transition easing function
* https://github.com/gre/bezier-easing
* @copyright 2014-2015 Gaetan Renaudeau. MIT License.
* @copyright 2014-2026 Gaetan Renaudeau. MIT License.
*/

import '@react-native/fantom/src/setUpDefaultReactNativeEnvironment';
Expand Down Expand Up @@ -110,6 +110,54 @@ describe('bezier', function () {
});
});
});
describe('precision', function () {
it('should match points of the curve', function () {
repeat(10)(function () {
const a = Math.random(),
b = 2 * Math.random() - 0.5,
c = Math.random(),
d = 2 * Math.random() - 0.5;
const easing = bezier(a, b, c, d);
for (let i = 1; i < 100; ++i) {
const t = i / 100;
const x =
3 * a * t * (1 - t) * (1 - t) + 3 * c * t * t * (1 - t) + t * t * t;
const y =
3 * b * t * (1 - t) * (1 - t) + 3 * d * t * t * (1 - t) + t * t * t;
assertClose(easing(x), y, 8);
}
});
});
it('should be precise near the extremes', function () {
// x(t) = t³, y(t) = t² (3 - 2t)
const easing = bezier(0, 0, 0, 1);
for (const t of [1e-6, 1e-3, 0.999]) {
// relative precision
assertClose(easing(t * t * t) / (t * t * (3 - 2 * t)), 1, 10);
}
expect(easing(Number.MIN_VALUE)).toBeGreaterThan(0);
});
it('should be monotonic on steep curves', function () {
const easing = bezier(1, 0, 0, 1);
let previous = 0;
for (let i = 1; i <= 10000; ++i) {
const y = easing(0.49 + (0.02 * i) / 10000);
expect(y).toBeGreaterThanOrEqual(previous);
previous = y;
}
});
});
describe('outside of [0, 1]', function () {
it('should saturate to 0 / 1', function () {
const easing = bezier(0.25, 0.1, 0.25, 1);
expect(easing(-0.5)).toBe(0);
expect(easing(1.5)).toBe(1);
expect(Number.isNaN(easing(NaN))).toBe(true);
});
it('should keep linear curves as the identity', function () {
expect(bezier(0.3, 0.3, 0.6, 0.6)(-0.5)).toBe(-0.5);
});
});
describe('two same instances', function () {
it('should be strictly equals', function () {
repeat(10)(function () {
Expand Down
163 changes: 39 additions & 124 deletions packages/react-native/Libraries/Animated/bezier.js
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Original file line number Diff line number Diff line change
Expand Up @@ -11,85 +11,34 @@
/**
* BezierEasing - use bezier curve for transition easing function
* https://github.com/gre/bezier-easing
* @copyright 2014-2015 Gaëtan Renaudeau. MIT License.
* @copyright 2014-2026 Gaëtan Renaudeau. MIT License.
*/

'use strict';

// 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,
aA = _aA,
aB = _aB;
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,
) {
let aGuessT = _aGuessT;
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;
// Solves x(t) = ((2a * t + 3b) * t + 3c) * t = x for t, with x in (0, 1):
// u = 1/t is the largest real root of x·u³ − 3c·u² − 3b·u − 2a = 0
function solveTForX(x: number, a: number, b: number, c: number): number {
const j = 1 / Math.max(c, Math.sqrt(x));
const k = x * j;
const l = k * j;
const s = c * j;
const q = b * l;
const m = s * s + q;
const h = -s * (s * s + 1.5 * q) - a * k * l;
const D = h * h - m * m * m;
let v: number;
if (m === 0 || D > 1e-12 * h * h) {
// one real root (Cardano)
const U = -Math.cbrt(h < 0 ? h - Math.sqrt(D) : h + Math.sqrt(D));
v = U + m / U || 0;
} else {
// three real roots, take the largest
const r = Math.sqrt(m);
v =
2 * r * Math.cos(Math.acos(Math.max(-1, Math.min(1, -h / (m * r)))) / 3);
}
return aGuessT;
return Math.min(1, k / (v + s));
}

export default function bezier(
Expand All @@ -102,63 +51,29 @@ export default function bezier(
throw new Error('bezier x values must be in [0, 1] range');
}

// Precompute samples table
const sampleValues = float32ArraySupported
? new Float32Array(kSplineTableSize)
: new Array<number>(kSplineTableSize);
if (mX1 !== mY1 || mX2 !== mY2) {
for (let i = 0; i < kSplineTableSize; ++i) {
sampleValues[i] = calcBezier(i * kSampleStepSize, mX1, mX2);
}
if (mX1 === mY1 && mX2 === mY2) {
return function LinearEasing(x: number): number {
return x;
};
}

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,
);
}
}
// x(t) = ((2a * t + 3b) * t + 3c) * t, y(t) = ((ay * t + by) * t + cy) * t
const a = (3 * mX1 - 3 * mX2 + 1) / 2;
const b = mX2 - 2 * mX1;
const c = mX1;
const ay = 3 * mY1 - 3 * mY2 + 1;
const by = 3 * (mY2 - 2 * mY1);
const cy = 3 * mY1;

return function BezierEasing(x: number): number {
if (mX1 === mY1 && mX2 === mY2) {
return x; // linear
}
// Because JavaScript number are imprecise, we should guarantee the extremes are right.
if (x === 0) {
// x outside (0, 1) saturates to 0 / 1
if (x <= 0) {
return 0;
}
if (x === 1) {
if (x >= 1) {
return 1;
}
return calcBezier(getTForX(x), mY1, mY2);
const t = solveTForX(x, a, b, c);
return ((ay * t + by) * t + cy) * t;
};
}
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