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+/*
+ * Copyright (C) 2008 Apple Inc. All Rights Reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ * 1. Redistributions of source code must retain the above copyright
+ * notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ * notice, this list of conditions and the following disclaimer in the
+ * documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY APPLE INC. ``AS IS'' AND ANY
+ * EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
+ * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL APPLE INC. OR
+ * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+ * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+ * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+ * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
+ * OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+ * OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ */
+
+#ifndef MBGL_UTIL_UNITBEZIER
+#define MBGL_UTIL_UNITBEZIER
+
+#include <cmath>
+
+namespace mbgl {
+namespace util {
+
+struct UnitBezier {
+ UnitBezier(double p1x, double p1y, double p2x, double p2y) {
+ // Calculate the polynomial coefficients, implicit first and last control points are (0,0) and (1,1).
+ cx = 3.0 * p1x;
+ bx = 3.0 * (p2x - p1x) - cx;
+ ax = 1.0 - cx - bx;
+
+ cy = 3.0 * p1y;
+ by = 3.0 * (p2y - p1y) - cy;
+ ay = 1.0 - cy - by;
+ }
+
+ double sampleCurveX(double t) {
+ // `ax t^3 + bx t^2 + cx t' expanded using Horner's rule.
+ return ((ax * t + bx) * t + cx) * t;
+ }
+
+ double sampleCurveY(double t) {
+ return ((ay * t + by) * t + cy) * t;
+ }
+
+ double sampleCurveDerivativeX(double t) {
+ return (3.0 * ax * t + 2.0 * bx) * t + cx;
+ }
+
+ // Given an x value, find a parametric value it came from.
+ double solveCurveX(double x, double epsilon) {
+ double t0;
+ double t1;
+ double t2;
+ double x2;
+ double d2;
+ int i;
+
+ // First try a few iterations of Newton's method -- normally very fast.
+ for (t2 = x, i = 0; i < 8; ++i) {
+ x2 = sampleCurveX(t2) - x;
+ if (fabs (x2) < epsilon)
+ return t2;
+ d2 = sampleCurveDerivativeX(t2);
+ if (fabs(d2) < 1e-6)
+ break;
+ t2 = t2 - x2 / d2;
+ }
+
+ // Fall back to the bisection method for reliability.
+ t0 = 0.0;
+ t1 = 1.0;
+ t2 = x;
+
+ if (t2 < t0)
+ return t0;
+ if (t2 > t1)
+ return t1;
+
+ while (t0 < t1) {
+ x2 = sampleCurveX(t2);
+ if (fabs(x2 - x) < epsilon)
+ return t2;
+ if (x > x2)
+ t0 = t2;
+ else
+ t1 = t2;
+ t2 = (t1 - t0) * .5 + t0;
+ }
+
+ // Failure.
+ return t2;
+ }
+
+ double solve(double x, double epsilon) {
+ return sampleCurveY(solveCurveX(x, epsilon));
+ }
+
+private:
+ double ax;
+ double bx;
+ double cx;
+
+ double ay;
+ double by;
+ double cy;
+};
+
+}
+}
+
+#endif