105 lines
3.3 KiB
JavaScript
105 lines
3.3 KiB
JavaScript
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/**
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* https://github.com/gre/bezier-easing
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* BezierEasing - use bezier curve for transition easing function
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* by Gaëtan Renaudeau 2014 - 2015 – MIT License
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*/
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// These values are established by empiricism with tests (tradeoff: performance VS precision)
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var NEWTON_ITERATIONS = 4;
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var NEWTON_MIN_SLOPE = 0.001;
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var SUBDIVISION_PRECISION = 0.0000001;
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var SUBDIVISION_MAX_ITERATIONS = 10;
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var kSplineTableSize = 11;
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var kSampleStepSize = 1.0 / (kSplineTableSize - 1.0);
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var float32ArraySupported = typeof Float32Array === 'function';
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function A(aA1, aA2) { return 1.0 - 3.0 * aA2 + 3.0 * aA1; }
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function B(aA1, aA2) { return 3.0 * aA2 - 6.0 * aA1; }
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function C(aA1) { return 3.0 * aA1; }
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// Returns x(t) given t, x1, and x2, or y(t) given t, y1, and y2.
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function calcBezier(aT, aA1, aA2) { return ((A(aA1, aA2) * aT + B(aA1, aA2)) * aT + C(aA1)) * aT; }
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// Returns dx/dt given t, x1, and x2, or dy/dt given t, y1, and y2.
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function getSlope(aT, aA1, aA2) { return 3.0 * A(aA1, aA2) * aT * aT + 2.0 * B(aA1, aA2) * aT + C(aA1); }
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function binarySubdivide(aX, aA, aB, mX1, mX2) {
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var currentX, currentT, i = 0;
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do {
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currentT = aA + (aB - aA) / 2.0;
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currentX = calcBezier(currentT, mX1, mX2) - aX;
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if (currentX > 0.0) {
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aB = currentT;
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} else {
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aA = currentT;
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}
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} while (Math.abs(currentX) > SUBDIVISION_PRECISION && ++i < SUBDIVISION_MAX_ITERATIONS);
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return currentT;
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}
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function newtonRaphsonIterate(aX, aGuessT, mX1, mX2) {
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for (var i = 0; i < NEWTON_ITERATIONS; ++i) {
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var currentSlope = getSlope(aGuessT, mX1, mX2);
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if (currentSlope === 0.0) {
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return aGuessT;
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}
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var currentX = calcBezier(aGuessT, mX1, mX2) - aX;
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aGuessT -= currentX / currentSlope;
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}
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return aGuessT;
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}
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function LinearEasing(x) {
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return x;
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}
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export const Bezier = function (mX1, mY1, mX2, mY2) {
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if (!(0 <= mX1 && mX1 <= 1 && 0 <= mX2 && mX2 <= 1)) {
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throw new Error('bezier x values must be in [0, 1] range');
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}
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if (mX1 === mY1 && mX2 === mY2) {
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return LinearEasing;
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}
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// Precompute samples table
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var sampleValues = float32ArraySupported ? new Float32Array(kSplineTableSize) : new Array(kSplineTableSize);
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for (var i = 0; i < kSplineTableSize; ++i) {
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sampleValues[i] = calcBezier(i * kSampleStepSize, mX1, mX2);
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}
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function getTForX(aX) {
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var intervalStart = 0.0;
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var currentSample = 1;
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var lastSample = kSplineTableSize - 1;
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for (; currentSample !== lastSample && sampleValues[currentSample] <= aX; ++currentSample) {
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intervalStart += kSampleStepSize;
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}
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--currentSample;
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// Interpolate to provide an initial guess for t
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var dist = (aX - sampleValues[currentSample]) / (sampleValues[currentSample + 1] - sampleValues[currentSample]);
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var guessForT = intervalStart + dist * kSampleStepSize;
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var initialSlope = getSlope(guessForT, mX1, mX2);
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if (initialSlope >= NEWTON_MIN_SLOPE) {
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return newtonRaphsonIterate(aX, guessForT, mX1, mX2);
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} else if (initialSlope === 0.0) {
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return guessForT;
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} else {
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return binarySubdivide(aX, intervalStart, intervalStart + kSampleStepSize, mX1, mX2);
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}
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}
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return function BezierEasing(x) {
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// Because JavaScript number are imprecise, we should guarantee the extremes are right.
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if (x === 0 || x === 1) {
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return x;
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}
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return calcBezier(getTForX(x), mY1, mY2);
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};
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};
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