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Use binary subdivision rather than Newton-Raphson iteration when the slope is very near 0 to avoid failing to converge correctly. (Bug 501569) r=dbaron
This commit is contained in:
Brian Birtles
parent
38bd4e6447
commit
2572fb5ff8
@ -245,6 +245,10 @@ nsSMILAnimationFunction::ComposeResult(const nsISMILAttr& aSMILAttr,
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if (NS_FAILED(rv))
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return;
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// GetValues may update the error state
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if (mErrorFlags != 0)
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return;
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// If this interval is active, we must have a non-negative
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// mSampleTime and a resolved or indefinite mSimpleDuration.
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// (Otherwise, we're probably just frozen.)
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@ -36,9 +36,13 @@
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* ***** END LICENSE BLOCK ***** */
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#include "nsSMILKeySpline.h"
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#include "prtypes.h"
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#include <math.h>
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#define NEWTON_ITERATIONS 4
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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 double nsSMILKeySpline::kSampleStepSize =
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1.0 / double(kSplineTableSize - 1);
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@ -68,7 +72,7 @@ nsSMILKeySpline::GetSplineValue(double aX) const
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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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for (PRUint32 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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@ -87,35 +91,78 @@ 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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return 3.0 * A(aA1, aA2)*aT*aT + 2.0 * B(aA1, aA2) * aT + C(aA1);
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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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// Find interval where t lies
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double intervalStart = 0.0;
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const double* currentSample = &mSampleValues[1];
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const double* 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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// 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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// Interpolate to provide an initial guess for t
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double dist = (aX - *currentSample) /
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(*(currentSample+1) - *currentSample);
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double guessForT = intervalStart + dist * 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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// 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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double 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, intervalStart + kSampleStepSize);
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}
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}
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double
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nsSMILKeySpline::NewtonRaphsonIterate(double aX, double aGuessT) const
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{
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// Refine guess with Newton-Raphson iteration
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for (PRUint32 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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double currentX = CalcBezier(aGuessT, mX1, mX2) - aX;
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double currentSlope = GetSlope(aGuessT, mX1, mX2);
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if (currentSlope == 0.0)
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return currentT;
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return aGuessT;
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currentT -= (currentX - aX) * currentSlope;
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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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double
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nsSMILKeySpline::BinarySubdivide(double aX, double aA, double aB) const
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{
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double currentX;
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double currentT;
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PRUint32 i = 0;
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do
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{
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currentT = aA + (aB - aA) / 2.0;
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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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@ -38,16 +38,14 @@
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#ifndef NS_SMILKEYSPLINE_H_
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#define NS_SMILKEYSPLINE_H_
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#include "prtypes.h"
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/**
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* Utility class to provide scaling defined in a keySplines element.
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*/
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class nsSMILKeySpline
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{
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public:
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/*
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* Create a new key spline control point description.
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/**
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* Creates a new key spline control point description.
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*
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* aX1, etc. are the x1, y1, x2, y2 cubic Bezier control points as defined by
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* SMILANIM 3.2.3. They must each be in the range 0.0 <= x <= 1.0
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@ -55,10 +53,11 @@ public:
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nsSMILKeySpline(double aX1, double aY1,
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double aX2, double aY2);
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/*
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* Get the output (y) value for an input (x).
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/**
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* Gets the output (y) value for an input (x).
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*
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* x should be a floating-point number between 0 and 1 (inclusive).
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* @param aX The input x value. A floating-point number between 0 and
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* 1 (inclusive).
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*/
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double GetSplineValue(double aX) const;
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@ -66,15 +65,27 @@ private:
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void
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CalcSampleValues();
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/**
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* Returns x(t) given t, x1, and x2, or y(t) given t, y1, and y2.
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*/
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static double
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CalcBezier(double aT, double aA1, double aA2);
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/**
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* Returns dx/dt given t, x1, and x2, or dy/dt given t, y1, and y2.
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*/
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static double
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GetSlope(double aT, double aA1, double aA2);
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double
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GetTForX(double aX) const;
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double
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NewtonRaphsonIterate(double aX, double aGuessT) const;
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double
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BinarySubdivide(double aX, double aA, double aB) const;
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static double
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A(double aA1, double aA2)
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{
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@ -47,6 +47,7 @@ include $(topsrcdir)/config/rules.mk
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_TEST_FILES = test_smilRestart.xhtml \
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test_smilGetStartTime.xhtml \
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test_smilGetSimpleDuration.xhtml \
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test_smilKeySplines.xhtml \
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test_smilSetCurrentTime.xhtml \
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test_smilSync.xhtml \
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test_smilSyncTransform.xhtml \
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297
content/smil/test/test_smilKeySplines.xhtml
Normal file
297
content/smil/test/test_smilKeySplines.xhtml
Normal file
@ -0,0 +1,297 @@
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<html xmlns="http://www.w3.org/1999/xhtml">
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<head>
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<title>Test for SMIL keySplines</title>
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<script type="text/javascript" src="/MochiKit/packed.js"></script>
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<script type="text/javascript" src="/tests/SimpleTest/SimpleTest.js"></script>
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<link rel="stylesheet" type="text/css" href="/tests/SimpleTest/test.css" />
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</head>
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<body>
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<p id="display"></p>
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<div id="content" style="display: none">
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<svg id="svg" xmlns="http://www.w3.org/2000/svg" width="120px" height="120px">
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<circle cx="-100" cy="20" r="15" fill="blue" id="circle"/>
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</svg>
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</div>
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<pre id="test">
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<script class="testbody" type="text/javascript">
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<![CDATA[
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/** Test for SMIL keySplines **/
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/* Global Variables */
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const svgns="http://www.w3.org/2000/svg";
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var svg = document.getElementById("svg");
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var circle = document.getElementById('circle');
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SimpleTest.waitForExplicitFinish();
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function createAnim() {
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var anim = document.createElementNS(svgns,'animate');
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anim.setAttribute('attributeName','cx');
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anim.setAttribute('dur','10s');
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anim.setAttribute('begin','0s');
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anim.setAttribute('fill', 'freeze');
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return circle.appendChild(anim);
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}
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function main() {
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svg.pauseAnimations();
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var tests =
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[ testSimpleA, // these first four are from SVG 1.1
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testSimpleB,
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testSimpleC,
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testSimpleD,
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testSimpleE, // bug 501569
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testMultipleIntervalsA,
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testMultipleIntervalsB,
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testMultipleIntervalsC,
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testOneValue,
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testFromTo,
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testWrongNumSplines,
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testToAnimation,
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testOkSyntax,
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testBadSyntaxA,
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testBadSyntaxB
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];
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for (var i = 0; i < tests.length; i++) {
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var anim = createAnim();
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svg.setCurrentTime(0);
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tests[i](anim);
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removeElement(anim);
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}
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SimpleTest.finish();
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}
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function checkSample(time, expectedValue) {
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svg.setCurrentTime(time);
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is(circle.cx.animVal.value, expectedValue);
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}
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function checkSampleRough(time, expectedValue, precision) {
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const defaultPrecision = 0.00001;
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if (typeof precision == "undefined") {
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precision = defaultPrecision;
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}
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svg.setCurrentTime(time);
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var diff = Math.abs(expectedValue - circle.cx.animVal.value);
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ok(diff <= precision,
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"Unexpected sample value got " + circle.cx.animVal.value
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+ ", expected " + expectedValue + " [error: " + diff
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+ " > tolerance: " + precision + "]");
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}
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/*
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* These first four tests are the examples given in SVG 1.1, section 19.2.7
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*/
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function testSimpleA(anim) {
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anim.setAttribute('dur','4s');
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anim.setAttribute('values', '10; 20');
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anim.setAttribute('keyTimes', '0; 1');
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anim.setAttribute('calcMode', 'spline');
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anim.setAttribute('keySplines', '0 0 1 1');
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checkSample(0, 10);
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checkSample(1, 12.5);
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checkSample(2, 15);
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checkSample(3, 17.5);
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checkSample(4, 20);
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}
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function testSimpleB(anim) {
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anim.setAttribute('dur','4s');
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anim.setAttribute('values', '10; 20');
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anim.setAttribute('keyTimes', '0; 1');
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anim.setAttribute('calcMode', 'spline');
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anim.setAttribute('keySplines', '.5 0 .5 1');
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checkSample(0, 10);
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checkSampleRough(1, 11.058925);
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checkSample(2, 15);
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checkSampleRough(3, 18.941075);
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checkSample(4, 20);
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}
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function testSimpleC(anim) {
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anim.setAttribute('dur','4s');
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anim.setAttribute('values', '10; 20');
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anim.setAttribute('keyTimes', '0; 1');
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anim.setAttribute('calcMode', 'spline');
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anim.setAttribute('keySplines', '0 .75 .25 1');
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checkSample(0, 10);
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checkSampleRough(1, 18.101832);
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checkSampleRough(2, 19.413430);
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checkSampleRough(3, 19.886504);
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checkSample(4, 20);
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}
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function testSimpleD(anim) {
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anim.setAttribute('dur','4s');
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anim.setAttribute('values', '10; 20');
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anim.setAttribute('keyTimes', '0; 1');
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anim.setAttribute('calcMode', 'spline');
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anim.setAttribute('keySplines', '1 0 .25 .25');
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checkSample(0, 10);
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checkSampleRough(1, 10.076925);
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checkSampleRough(2, 10.644369);
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checkSampleRough(3, 16.908699);
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checkSample(4, 20);
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}
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// Bug 501569 -- nsSMILKeySpline(1, 0, 0, 1) miscalculates values just under 0.5
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function testSimpleE(anim) {
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anim.setAttribute('dur','10s');
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anim.setAttribute('values', '0; 10');
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anim.setAttribute('keyTimes', '0; 1');
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anim.setAttribute('calcMode', 'spline');
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anim.setAttribute('keySplines', '1 0 0 1');
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checkSample(0, 0);
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checkSampleRough(0.001, 0);
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checkSampleRough(4.95, 3.409174);
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checkSampleRough(4.98, 3.819443);
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checkSampleRough(4.99, 4.060174);
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checkSampleRough(4.999, 4.562510);
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checkSample(5, 5);
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checkSampleRough(5.001, 5.437490);
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checkSampleRough(5.01, 5.939826);
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checkSampleRough(5.015, 6.075002);
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checkSampleRough(5.02, 6.180557);
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checkSampleRough(9.9999, 10);
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checkSample(10, 10);
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}
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function testMultipleIntervalsA(anim) {
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anim.setAttribute('dur','4s');
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anim.setAttribute('values', '10; 20; 30');
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anim.setAttribute('keyTimes', '0; 0.25; 1');
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anim.setAttribute('calcMode', 'spline');
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anim.setAttribute('keySplines', '0 0 1 1; .5 0 .5 1;');
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checkSample(0.5, 15);
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checkSampleRough(0.999, 20, 0.02);
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checkSample(1, 20);
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checkSampleRough(1.001, 20, 0.05);
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checkSample(2.5, 25);
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checkSampleRough(3.25, 29, 0.1);
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}
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function testMultipleIntervalsB(anim) {
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// as above but without keyTimes
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anim.setAttribute('dur','4s');
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anim.setAttribute('values', '10; 20; 30');
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anim.setAttribute('calcMode', 'spline');
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anim.setAttribute('keySplines', '0 0 1 1; .5 0 .5 1;');
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checkSample(1, 15);
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checkSampleRough(1.999, 20, 0.01);
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checkSample(2, 20);
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checkSampleRough(2.001, 20, 0.01);
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checkSample(3, 25);
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checkSampleRough(3.5, 29, 0.1);
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}
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function testMultipleIntervalsC(anim) {
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// test some unusual (but valid) syntax
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anim.setAttribute('dur','4s');
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anim.setAttribute('values', '10; 20; 30');
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anim.setAttribute('calcMode', 'spline');
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anim.setAttribute('keySplines', ' 0 .75 0.25 1 ; 1, 0 ,.25 .25 \t');
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checkSampleRough(3.5, 26.9, 0.2);
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}
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function testOneValue(anim) {
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anim.setAttribute('dur','4s');
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anim.setAttribute('values', '5');
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anim.setAttribute('calcMode', 'spline');
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anim.setAttribute('keySplines', '0 0 1 1');
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checkSample(0, 5);
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checkSample(1.5, 5);
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}
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function testFromTo(anim) {
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anim.setAttribute('dur','4s');
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anim.setAttribute('from', '10');
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anim.setAttribute('to', '20');
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anim.setAttribute('calcMode', 'spline');
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anim.setAttribute('keySplines', '.5 0 .5 1');
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checkSample(0, 10);
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checkSampleRough(1, 11, 0.1);
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}
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function testWrongNumSplines(anim) {
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anim.setAttribute('dur','4s');
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anim.setAttribute('from', '10');
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anim.setAttribute('to', '20');
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anim.setAttribute('calcMode', 'spline');
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anim.setAttribute('keySplines', '.5 0 .5 1; 0 0 1 1');
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// animation is in error, should do nothing
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checkSample(1.5, -100);
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}
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function testToAnimation(anim) {
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anim.setAttribute('dur','4s');
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anim.setAttribute('to', '20');
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anim.setAttribute('calcMode', 'spline');
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anim.setAttribute('keySplines', '.5 0 .5 1');
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checkSample(0, -100);
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checkSampleRough(1, -87.3, 0.1);
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}
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function testOkSyntax(anim) {
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var okStrs = ['0,0,0,0', // all commas
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' 0 0 , 0 ,0 ', // mix of separators
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'0 0 0 0;', // trailing semi-colon
|
||||
'0 0 0 0 ;']; // " "
|
||||
|
||||
for (var i = 0; i < okStrs.length; i++) {
|
||||
testAnim = createAnim();
|
||||
testAnim.setAttribute('dur','4s');
|
||||
testAnim.setAttribute('from', '0');
|
||||
testAnim.setAttribute('to', '20');
|
||||
testAnim.setAttribute('calcMode', 'spline');
|
||||
testAnim.setAttribute('keySplines', okStrs[i]);
|
||||
checkSample(4, 20);
|
||||
}
|
||||
}
|
||||
|
||||
function testBadSyntaxA(anim) {
|
||||
anim.setAttribute('dur','4s');
|
||||
anim.setAttribute('from', '0');
|
||||
anim.setAttribute('to', '20');
|
||||
anim.setAttribute('calcMode', 'spline');
|
||||
|
||||
var badStrs = ['', // empty
|
||||
' ', // whitespace only
|
||||
'0,1.1,0,0', // bad range
|
||||
'0,0,0,-0.1', // " "
|
||||
' 0 0 , 0 0 ,', // stray comma
|
||||
'1-1 0 0', // path-style separators
|
||||
'0 0 0', // wrong number of values
|
||||
'0 0 0 0 0', // " "
|
||||
'0 0 0 0 0 0 0 0', // " "
|
||||
'0 0 0; 0 0 0 0', // " "
|
||||
'0 0 0; 0', // mis-placed semi-colon
|
||||
';0 0 0 0']; // " "
|
||||
|
||||
for (var i = 0; i < badStrs.length; i++) {
|
||||
testAnim = createAnim();
|
||||
testAnim.setAttribute('dur','4s');
|
||||
testAnim.setAttribute('from', '0');
|
||||
testAnim.setAttribute('to', '20');
|
||||
testAnim.setAttribute('calcMode', 'spline');
|
||||
testAnim.setAttribute('keySplines', badStrs[i]);
|
||||
checkSample(4, -100);
|
||||
}
|
||||
}
|
||||
|
||||
function testBadSyntaxB(anim) {
|
||||
// test some illegal syntax
|
||||
anim.setAttribute('dur','4s');
|
||||
anim.setAttribute('values', '10; 20; 30');
|
||||
anim.setAttribute('calcMode', 'spline');
|
||||
anim.setAttribute('keySplines', ' 0 .75 0.25 1 ; 1, A0 ,.25 .25 \t');
|
||||
// animation is in error, should do nothing
|
||||
checkSample(3.5, -100);
|
||||
}
|
||||
|
||||
window.addEventListener("load", main, false);
|
||||
]]>
|
||||
</script>
|
||||
</pre>
|
||||
</body>
|
||||
</html>
|
||||
Loading…
Reference in New Issue
Block a user