Initial commit

node_modules/@mapbox/unitbezier/index.js

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