/* -*- 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; }