125 lines
3.6 KiB
C++
125 lines
3.6 KiB
C++
/* -*- Mode: C++; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 2 -*- */
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/* vim: set ts=8 sts=2 et sw=2 tw=80: */
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/* This Source Code Form is subject to the terms of the Mozilla Public
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* License, v. 2.0. If a copy of the MPL was not distributed with this
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* file, You can obtain one at http://mozilla.org/MPL/2.0/. */
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#include "vinterpolator.h"
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#include <cmath>
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V_BEGIN_NAMESPACE
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#define NEWTON_ITERATIONS 4
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#define NEWTON_MIN_SLOPE 0.02
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#define SUBDIVISION_PRECISION 0.0000001
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#define SUBDIVISION_MAX_ITERATIONS 10
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const float VInterpolator::kSampleStepSize =
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1.0f / float(VInterpolator::kSplineTableSize - 1);
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void VInterpolator::init(float aX1, float aY1, float aX2, float aY2)
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{
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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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if (mX1 != mY1 || mX2 != mY2) CalcSampleValues();
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}
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/*static*/ float VInterpolator::CalcBezier(float aT, float aA1, float 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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void VInterpolator::CalcSampleValues()
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{
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for (int i = 0; i < kSplineTableSize; ++i) {
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mSampleValues[i] = CalcBezier(float(i) * kSampleStepSize, mX1, mX2);
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}
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}
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float VInterpolator::GetSlope(float aT, float aA1, float aA2)
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{
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return 3.0f * A(aA1, aA2) * aT * aT + 2.0f * B(aA1, aA2) * aT + C(aA1);
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}
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float VInterpolator::value(float aX) const
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{
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if (mX1 == mY1 && mX2 == mY2) return aX;
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return CalcBezier(GetTForX(aX), mY1, mY2);
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}
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float VInterpolator::GetTForX(float aX) const
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{
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// Find interval where t lies
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float intervalStart = 0.0;
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const float* currentSample = &mSampleValues[1];
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const float* const lastSample = &mSampleValues[kSplineTableSize - 1];
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for (; currentSample != lastSample && *currentSample <= aX;
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++currentSample) {
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intervalStart += kSampleStepSize;
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}
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--currentSample; // t now lies between *currentSample and *currentSample+1
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// Interpolate to provide an initial guess for t
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float dist =
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(aX - *currentSample) / (*(currentSample + 1) - *currentSample);
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float guessForT = intervalStart + dist * kSampleStepSize;
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// Check the slope to see what strategy to use. If the slope is too small
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// Newton-Raphson iteration won't converge on a root so we use bisection
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// instead.
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float initialSlope = GetSlope(guessForT, mX1, mX2);
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if (initialSlope >= NEWTON_MIN_SLOPE) {
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return NewtonRaphsonIterate(aX, guessForT);
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} else if (initialSlope == 0.0) {
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return guessForT;
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} else {
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return BinarySubdivide(aX, intervalStart,
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intervalStart + kSampleStepSize);
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}
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}
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float VInterpolator::NewtonRaphsonIterate(float aX, float aGuessT) const
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{
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// Refine guess with Newton-Raphson iteration
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for (int i = 0; i < NEWTON_ITERATIONS; ++i) {
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// We're trying to find where f(t) = aX,
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// so we're actually looking for a root for: CalcBezier(t) - aX
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float currentX = CalcBezier(aGuessT, mX1, mX2) - aX;
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float currentSlope = GetSlope(aGuessT, mX1, mX2);
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if (currentSlope == 0.0) return aGuessT;
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aGuessT -= currentX / currentSlope;
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}
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return aGuessT;
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}
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float VInterpolator::BinarySubdivide(float aX, float aA, float aB) const
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{
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float currentX;
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float currentT;
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int i = 0;
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do {
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currentT = aA + (aB - aA) / 2.0f;
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currentX = CalcBezier(currentT, mX1, mX2) - aX;
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if (currentX > 0.0) {
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aB = currentT;
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} else {
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aA = currentT;
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}
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} while (fabs(currentX) > SUBDIVISION_PRECISION &&
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++i < SUBDIVISION_MAX_ITERATIONS);
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return currentT;
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}
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V_END_NAMESPACE
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