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122 lines
3.9 KiB
C++
122 lines
3.9 KiB
C++
/* -*- Mode: C++; tab-width: 2; indent-tabs-mode: nil; c-basic-offset: 2 -*- */
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/* ***** BEGIN LICENSE BLOCK *****
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* Version: MPL 1.1/GPL 2.0/LGPL 2.1
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*
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* The contents of this file are subject to the Mozilla Public License Version
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* 1.1 (the "License"); you may not use this file except in compliance with
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* the License. You may obtain a copy of the License at
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* http://www.mozilla.org/MPL/
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*
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* Software distributed under the License is distributed on an "AS IS" basis,
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* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License
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* for the specific language governing rights and limitations under the
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* License.
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*
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* The Original Code is the Mozilla SMIL module.
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*
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* The Initial Developer of the Original Code is Brian Birtles.
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* Portions created by the Initial Developer are Copyright (C) 2005
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* the Initial Developer. All Rights Reserved.
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*
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* Contributor(s):
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* Brian Birtles <birtles@gmail.com>
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*
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* Alternatively, the contents of this file may be used under the terms of
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* either of the GNU General Public License Version 2 or later (the "GPL"),
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* or the GNU Lesser General Public License Version 2.1 or later (the "LGPL"),
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* in which case the provisions of the GPL or the LGPL are applicable instead
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* of those above. If you wish to allow use of your version of this file only
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* under the terms of either the GPL or the LGPL, and not to allow others to
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* use your version of this file under the terms of the MPL, indicate your
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* decision by deleting the provisions above and replace them with the notice
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* and other provisions required by the GPL or the LGPL. If you do not delete
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* the provisions above, a recipient may use your version of this file under
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* the terms of any one of the MPL, the GPL or the LGPL.
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*
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* ***** END LICENSE BLOCK ***** */
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#include "nsSMILKeySpline.h"
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#include <math.h>
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#define NEWTON_ITERATIONS 4
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const double nsSMILKeySpline::kSampleStepSize =
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1.0 / double(kSplineTableSize - 1);
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nsSMILKeySpline::nsSMILKeySpline(double aX1,
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double aY1,
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double aX2,
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double aY2)
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: mX1(aX1),
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mY1(aY1),
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mX2(aX2),
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mY2(aY2)
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{
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if (mX1 != mY1 || mX2 != mY2)
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CalcSampleValues();
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}
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double
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nsSMILKeySpline::GetSplineValue(double aX) const
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{
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if (mX1 == mY1 && mX2 == mY2)
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return aX;
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return CalcBezier(GetTForX(aX), mY1, mY2);
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}
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void
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nsSMILKeySpline::CalcSampleValues()
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{
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for (int i = 0; i < kSplineTableSize; ++i) {
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mSampleValues[i] = CalcBezier(double(i) * kSampleStepSize, mX1, mX2);
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}
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}
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/*static*/ double
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nsSMILKeySpline::CalcBezier(double aT,
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double aA1,
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double aA2)
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{
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// use Horner's scheme to evaluate the Bezier polynomial
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return ((A(aA1, aA2)*aT + B(aA1, aA2))*aT + C(aA1))*aT;
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}
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/*static*/ double
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nsSMILKeySpline::GetSlope(double aT,
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double aA1,
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double aA2)
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{
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double denom = (3.0 * A(aA1, aA2)*aT*aT + 2.0 * B(aA1, aA2) * aT + C(aA1));
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return (denom == 0.0) ? 0.0 : 1.0 / denom;
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}
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double
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nsSMILKeySpline::GetTForX(double aX) const
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{
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int i;
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// Get an initial guess.
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//
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// Note: This is better than just taking x as our initial guess as cases such
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// as where the control points are (1, 1), (0, 0) will take some 20 iterations
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// to converge to a good accuracy. By taking an initial guess in this way we
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// only need 3~4 iterations depending on the size of the table.
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for (i = 0; i < kSplineTableSize - 2 && mSampleValues[i] < aX; ++i);
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double currentT =
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double(i) * kSampleStepSize + (aX - mSampleValues[i]) * kSampleStepSize;
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// Refine with Newton-Raphson iteration
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for (i = 0; i < NEWTON_ITERATIONS; ++i) {
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double currentX = CalcBezier(currentT, mX1, mX2);
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double currentSlope = GetSlope(currentT, mX1, mX2);
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if (currentSlope == 0.0)
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return currentT;
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currentT -= (currentX - aX) * currentSlope;
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}
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return currentT;
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}
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