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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
#include "SMILKeySpline.h"
#include <stdint.h>
#include <math.h>
namespace mozilla {
#define NEWTON_ITERATIONS 4
#define NEWTON_MIN_SLOPE 0.02
#define SUBDIVISION_PRECISION 0.0000001
#define SUBDIVISION_MAX_ITERATIONS 10
const double SMILKeySpline::kSampleStepSize =
1.0 / double(kSplineTableSize - 1);
void SMILKeySpline::Init(double aX1, double aY1, double aX2, double aY2) {
mX1 = aX1;
mY1 = aY1;
mX2 = aX2;
mY2 = aY2;
if (mX1 != mY1 || mX2 != mY2) CalcSampleValues();
}
double SMILKeySpline::GetSplineValue(double aX) const {
if (mX1 == mY1 && mX2 == mY2) return aX;
return CalcBezier(GetTForX(aX), mY1, mY2);
}
void SMILKeySpline::GetSplineDerivativeValues(double aX, double& aDX,
double& aDY) const {
double t = GetTForX(aX);
aDX = GetSlope(t, mX1, mX2);
aDY = GetSlope(t, mY1, mY2);
}
void SMILKeySpline::CalcSampleValues() {
for (uint32_t i = 0; i < kSplineTableSize; ++i) {
mSampleValues[i] = CalcBezier(double(i) * kSampleStepSize, mX1, mX2);
}
}
/*static*/
double SMILKeySpline::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 SMILKeySpline::GetSlope(double aT, double aA1, double aA2) {
return 3.0 * A(aA1, aA2) * aT * aT + 2.0 * B(aA1, aA2) * aT + C(aA1);
}
double SMILKeySpline::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);
}
if (initialSlope == 0.0) {
return guessForT;
}
return BinarySubdivide(aX, intervalStart, intervalStart + kSampleStepSize);
}
double SMILKeySpline::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 SMILKeySpline::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;
}
} // namespace mozilla