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Bezier function generator
Gaëtan Renaudeau's BezierEasing
https://github.com/gre/bezier-easing/blob/master/src/index.js
https://github.com/gre/bezier-easing/blob/master/LICENSE
You're a hero
Use
const easeOut = cubicBezier(.17,.67,.83,.67);
const x = easeOut(0.5); // returns 0.627...
*/
import { linear } from "."
const a = (a1: number, a2: number) => 1.0 - 3.0 * a2 + 3.0 * a1
const b = (a1: number, a2: number) => 3.0 * a2 - 6.0 * a1
const c = (a1: number) => 3.0 * a1
// Returns x(t) given t, x1, and x2, or y(t) given t, y1, and y2.
const calcBezier = (t: number, a1: number, a2: number) =>
((a(a1, a2) * t + b(a1, a2)) * t + c(a1)) * t
// Returns dx/dt given t, x1, and x2, or dy/dt given t, y1, and y2.
const getSlope = (t: number, a1: number, a2: number) =>
3.0 * a(a1, a2) * t * t + 2.0 * b(a1, a2) * t + c(a1)
const subdivisionPrecision = 0.0000001
const subdivisionMaxIterations = 10
function binarySubdivide(
aX: number,
aA: number,
aB: number,
mX1: number,
mX2: number
) {
let currentX: number
let currentT: number
let i: number = 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) > subdivisionPrecision &&
++i < subdivisionMaxIterations
)
return currentT
}
const newtonIterations = 8
const newtonMinSlope = 0.001
function newtonRaphsonIterate(
aX: number,
aGuessT: number,
mX1: number,
mX2: number
) {
for (let i = 0; i < newtonIterations; ++i) {
const currentSlope = getSlope(aGuessT, mX1, mX2)
Iif (currentSlope === 0.0) {
return aGuessT
}
const currentX = calcBezier(aGuessT, mX1, mX2) - aX
aGuessT -= currentX / currentSlope
}
return aGuessT
}
const kSplineTableSize = 11
const kSampleStepSize = 1.0 / (kSplineTableSize - 1.0)
export function cubicBezier(
mX1: number,
mY1: number,
mX2: number,
mY2: number
) {
// If this is a linear gradient, return linear easing
if (mX1 === mY1 && mX2 === mY2) return linear
// Precompute samples table
const sampleValues = new Float32Array(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)
Eif (initialSlope >= newtonMinSlope) {
return newtonRaphsonIterate(aX, guessForT, mX1, mX2)
} else if (initialSlope === 0.0) {
return guessForT
} else {
return binarySubdivide(
aX,
intervalStart,
intervalStart + kSampleStepSize,
mX1,
mX2
)
}
}
// If animation is at start/end, return t without easing
return (t: number) =>
t === 0 || t === 1 ? t : calcBezier(getTForX(t), mY1, mY2)
}
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