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