79 lines
1.9 KiB
JavaScript
79 lines
1.9 KiB
JavaScript
'use strict';
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module.exports = UnitBezier;
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function UnitBezier(p1x, p1y, p2x, p2y) {
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// Calculate the polynomial coefficients, implicit first and last control points are (0,0) and (1,1).
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this.cx = 3.0 * p1x;
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this.bx = 3.0 * (p2x - p1x) - this.cx;
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this.ax = 1.0 - this.cx - this.bx;
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this.cy = 3.0 * p1y;
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this.by = 3.0 * (p2y - p1y) - this.cy;
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this.ay = 1.0 - this.cy - this.by;
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this.p1x = p1x;
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this.p1y = p1y;
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this.p2x = p2x;
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this.p2y = p2y;
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}
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UnitBezier.prototype = {
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sampleCurveX: function (t) {
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// `ax t^3 + bx t^2 + cx t' expanded using Horner's rule.
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return ((this.ax * t + this.bx) * t + this.cx) * t;
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},
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sampleCurveY: function (t) {
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return ((this.ay * t + this.by) * t + this.cy) * t;
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},
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sampleCurveDerivativeX: function (t) {
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return (3.0 * this.ax * t + 2.0 * this.bx) * t + this.cx;
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},
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solveCurveX: function (x, epsilon) {
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if (epsilon === undefined) epsilon = 1e-6;
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if (x < 0.0) return 0.0;
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if (x > 1.0) return 1.0;
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var t = x;
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// First try a few iterations of Newton's method - normally very fast.
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for (var i = 0; i < 8; i++) {
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var x2 = this.sampleCurveX(t) - x;
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if (Math.abs(x2) < epsilon) return t;
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var d2 = this.sampleCurveDerivativeX(t);
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if (Math.abs(d2) < 1e-6) break;
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t = t - x2 / d2;
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}
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// Fall back to the bisection method for reliability.
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var t0 = 0.0;
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var t1 = 1.0;
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t = x;
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for (i = 0; i < 20; i++) {
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x2 = this.sampleCurveX(t);
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if (Math.abs(x2 - x) < epsilon) break;
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if (x > x2) {
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t0 = t;
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} else {
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t1 = t;
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}
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t = (t1 - t0) * 0.5 + t0;
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}
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return t;
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},
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solve: function (x, epsilon) {
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return this.sampleCurveY(this.solveCurveX(x, epsilon));
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}
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};
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