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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