export function cubicBezier(p1x : number, p1y : number, p2x : number, p2y : number):(x: number)=> number {
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const ZERO_LIMIT = 1e-6;
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// Calculate the polynomial coefficients,
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// implicit first and last control points are (0,0) and (1,1).
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const ax = 3 * p1x - 3 * p2x + 1;
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const bx = 3 * p2x - 6 * p1x;
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const cx = 3 * p1x;
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const ay = 3 * p1y - 3 * p2y + 1;
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const by = 3 * p2y - 6 * p1y;
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const cy = 3 * p1y;
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function sampleCurveDerivativeX(t : number) : number {
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// `ax t^3 + bx t^2 + cx t` expanded using Horner's rule
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return (3 * ax * t + 2 * bx) * t + cx;
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}
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function sampleCurveX(t : number) : number {
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return ((ax * t + bx) * t + cx) * t;
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}
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function sampleCurveY(t : number) : number {
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return ((ay * t + by) * t + cy) * t;
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}
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// Given an x value, find a parametric value it came from.
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function solveCurveX(x : number) : number {
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let t2 = x;
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let derivative : number;
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let x2 : number;
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// https://trac.webkit.org/browser/trunk/Source/WebCore/platform/animation
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// first try a few iterations of Newton's method -- normally very fast.
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// http://en.wikipedia.org/wikiNewton's_method
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for (let i = 0; i < 8; i++) {
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// f(t) - x = 0
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x2 = sampleCurveX(t2) - x;
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if (Math.abs(x2) < ZERO_LIMIT) {
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return t2;
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}
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derivative = sampleCurveDerivativeX(t2);
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// == 0, failure
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/* istanbul ignore if */
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if (Math.abs(derivative) < ZERO_LIMIT) {
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break;
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}
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t2 -= x2 / derivative;
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}
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// Fall back to the bisection method for reliability.
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// bisection
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// http://en.wikipedia.org/wiki/Bisection_method
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let t1 = 1;
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/* istanbul ignore next */
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let t0 = 0;
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/* istanbul ignore next */
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t2 = x;
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/* istanbul ignore next */
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while (t1 > t0) {
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x2 = sampleCurveX(t2) - x;
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if (Math.abs(x2) < ZERO_LIMIT) {
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return t2;
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}
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if (x2 > 0) {
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t1 = t2;
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} else {
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t0 = t2;
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}
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t2 = (t1 + t0) / 2;
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}
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// Failure
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return t2;
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}
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return function (x : number) : number {
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return sampleCurveY(solveCurveX(x));
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}
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// return solve;
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}
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