pjs/content/smil/nsSMILKeySpline.cpp

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 * Version: MPL 1.1/GPL 2.0/LGPL 2.1
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 * The contents of this file are subject to the Mozilla Public License Version
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 *
 * The Original Code is the Mozilla SMIL module.
 *
 * The Initial Developer of the Original Code is Brian Birtles.
 * Portions created by the Initial Developer are Copyright (C) 2005
 * the Initial Developer. All Rights Reserved.
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 * Contributor(s):
 *   Brian Birtles <birtles@gmail.com>
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#include "nsSMILKeySpline.h"
#include <math.h>

#define NEWTON_ITERATIONS   4

const double nsSMILKeySpline::kSampleStepSize = 
                                        1.0 / double(kSplineTableSize - 1);

nsSMILKeySpline::nsSMILKeySpline(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::CalcSampleValues()
{
  for (int 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)
{
  double denom = (3.0 * A(aA1, aA2)*aT*aT + 2.0 * B(aA1, aA2) * aT + C(aA1)); 
  return (denom == 0.0) ? 0.0 : 1.0 / denom;
}

double
nsSMILKeySpline::GetTForX(double aX) const
{
  int i;

  // Get an initial guess.
  //
  // Note: This is better than just taking x as our initial guess as cases such
  // as where the control points are (1, 1), (0, 0) will take some 20 iterations
  // to converge to a good accuracy. By taking an initial guess in this way we
  // only need 3~4 iterations depending on the size of the table.
  for (i = 0; i < kSplineTableSize - 2 && mSampleValues[i] < aX; ++i);
  double currentT = 
    double(i) * kSampleStepSize + (aX - mSampleValues[i]) * kSampleStepSize;

  // Refine with Newton-Raphson iteration
  for (i = 0; i < NEWTON_ITERATIONS; ++i) {
    double currentX = CalcBezier(currentT, mX1, mX2);
    double currentSlope = GetSlope(currentT, mX1, mX2);

    if (currentSlope == 0.0)
      return currentT;

    currentT -= (currentX - aX) * currentSlope;
  }

  return currentT;
}