/* -*- 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;

}