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authorMatt A. Tobin <mattatobin@localhost.localdomain>2018-02-02 04:16:08 -0500
committerMatt A. Tobin <mattatobin@localhost.localdomain>2018-02-02 04:16:08 -0500
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Add m-esr52 at 52.6.0
Diffstat (limited to 'dom/smil/nsSMILKeySpline.cpp')
-rw-r--r--dom/smil/nsSMILKeySpline.cpp151
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diff --git a/dom/smil/nsSMILKeySpline.cpp b/dom/smil/nsSMILKeySpline.cpp
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+/* -*- Mode: C++; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 2 -*- */
+/* vim: set ts=8 sts=2 et sw=2 tw=80: */
+/* This Source Code Form is subject to the terms of the Mozilla Public
+ * License, v. 2.0. If a copy of the MPL was not distributed with this
+ * file, You can obtain one at http://mozilla.org/MPL/2.0/. */
+
+#include "nsSMILKeySpline.h"
+#include <stdint.h>
+#include <math.h>
+
+#define NEWTON_ITERATIONS 4
+#define NEWTON_MIN_SLOPE 0.02
+#define SUBDIVISION_PRECISION 0.0000001
+#define SUBDIVISION_MAX_ITERATIONS 10
+
+const double nsSMILKeySpline::kSampleStepSize =
+ 1.0 / double(kSplineTableSize - 1);
+
+void
+nsSMILKeySpline::Init(double aX1,
+ double aY1,
+ double aX2,
+ double aY2)
+{
+ mX1 = aX1;
+ mY1 = aY1;
+ mX2 = aX2;
+ mY2 = aY2;
+
+ if (mX1 != mY1 || mX2 != mY2)
+ CalcSampleValues();
+}
+
+double
+nsSMILKeySpline::GetSplineValue(double aX) const
+{
+ if (mX1 == mY1 && mX2 == mY2)
+ return aX;
+
+ return CalcBezier(GetTForX(aX), mY1, mY2);
+}
+
+void
+nsSMILKeySpline::GetSplineDerivativeValues(double aX, double& aDX, double& aDY) const
+{
+ double t = GetTForX(aX);
+ aDX = GetSlope(t, mX1, mX2);
+ aDY = GetSlope(t, mY1, mY2);
+}
+
+void
+nsSMILKeySpline::CalcSampleValues()
+{
+ for (uint32_t i = 0; i < kSplineTableSize; ++i) {
+ mSampleValues[i] = CalcBezier(double(i) * kSampleStepSize, mX1, mX2);
+ }
+}
+
+/*static*/ double
+nsSMILKeySpline::CalcBezier(double aT,
+ double aA1,
+ double aA2)
+{
+ // use Horner's scheme to evaluate the Bezier polynomial
+ return ((A(aA1, aA2)*aT + B(aA1, aA2))*aT + C(aA1))*aT;
+}
+
+/*static*/ double
+nsSMILKeySpline::GetSlope(double aT,
+ double aA1,
+ double aA2)
+{
+ return 3.0 * A(aA1, aA2)*aT*aT + 2.0 * B(aA1, aA2) * aT + C(aA1);
+}
+
+double
+nsSMILKeySpline::GetTForX(double aX) const
+{
+ // Early return when aX == 1.0 to avoid floating-point inaccuracies.
+ if (aX == 1.0) {
+ return 1.0;
+ }
+ // Find interval where t lies
+ double intervalStart = 0.0;
+ const double* currentSample = &mSampleValues[1];
+ const double* const lastSample = &mSampleValues[kSplineTableSize - 1];
+ for (; currentSample != lastSample && *currentSample <= aX;
+ ++currentSample) {
+ intervalStart += kSampleStepSize;
+ }
+ --currentSample; // t now lies between *currentSample and *currentSample+1
+
+ // Interpolate to provide an initial guess for t
+ double dist = (aX - *currentSample) /
+ (*(currentSample+1) - *currentSample);
+ double guessForT = intervalStart + dist * kSampleStepSize;
+
+ // Check the slope to see what strategy to use. If the slope is too small
+ // Newton-Raphson iteration won't converge on a root so we use bisection
+ // instead.
+ double initialSlope = GetSlope(guessForT, mX1, mX2);
+ if (initialSlope >= NEWTON_MIN_SLOPE) {
+ return NewtonRaphsonIterate(aX, guessForT);
+ } else if (initialSlope == 0.0) {
+ return guessForT;
+ } else {
+ return BinarySubdivide(aX, intervalStart, intervalStart + kSampleStepSize);
+ }
+}
+
+double
+nsSMILKeySpline::NewtonRaphsonIterate(double aX, double aGuessT) const
+{
+ // Refine guess with Newton-Raphson iteration
+ for (uint32_t i = 0; i < NEWTON_ITERATIONS; ++i) {
+ // We're trying to find where f(t) = aX,
+ // so we're actually looking for a root for: CalcBezier(t) - aX
+ double currentX = CalcBezier(aGuessT, mX1, mX2) - aX;
+ double currentSlope = GetSlope(aGuessT, mX1, mX2);
+
+ if (currentSlope == 0.0)
+ return aGuessT;
+
+ aGuessT -= currentX / currentSlope;
+ }
+
+ return aGuessT;
+}
+
+double
+nsSMILKeySpline::BinarySubdivide(double aX, double aA, double aB) const
+{
+ double currentX;
+ double currentT;
+ uint32_t i = 0;
+
+ do
+ {
+ currentT = aA + (aB - aA) / 2.0;
+ currentX = CalcBezier(currentT, mX1, mX2) - aX;
+
+ if (currentX > 0.0) {
+ aB = currentT;
+ } else {
+ aA = currentT;
+ }
+ } while (fabs(currentX) > SUBDIVISION_PRECISION
+ && ++i < SUBDIVISION_MAX_ITERATIONS);
+
+ return currentT;
+}