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Animation: Fix case where QEasingCurve::valueForProgress returns nan

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Previously, we would divide by zero in BezierEase::findTForX if factorT3
was zero when solving the cubic equation.

This change fixes the problem by adding solutions for the special cases
where the cubic equation can be reduced to a quadratic or linear
equation.

This change also adds tests that cover cases where the equation becomes
quadratic, linear or invalid.

Task-number: QTBUG-67061
Change-Id: I2b59f7e0392eb807663c3c8927509fd8b226ebc7
Reviewed-by: Christian Stromme <christian.stromme@qt.io>
This commit is contained in:
Svenn-Arne Dragly 2018-03-14 16:36:09 +01:00
parent 411a4cb67c
commit 50cfbd6112
2 changed files with 120 additions and 17 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

67
src/corelib/tools/qeasingcurve.cpp
View File

@ -797,27 +797,60 @@ struct BezierEase : public QEasingCurveFunction
return t3;
}
qreal static inline findTForX(const SingleCubicBezier &singleCubicBezier, qreal x)
{
const qreal p0 = singleCubicBezier.p0x;
const qreal p1 = singleCubicBezier.p1x;
const qreal p2 = singleCubicBezier.p2x;
const qreal p3 = singleCubicBezier.p3x;
bool static inline almostZero(qreal value)
{
// 1e-3 might seem excessively fuzzy, but any smaller value will make the
// factors a, b, and c large enough to knock out the cubic solver.
return value > -1e-3 && value < 1e-3;
}
const qreal factorT3 = p3 - p0 + 3 * p1 - 3 * p2;
const qreal factorT2 = 3 * p0 - 6 * p1 + 3 * p2;
const qreal factorT1 = -3 * p0 + 3 * p1;
const qreal factorT0 = p0 - x;
qreal static inline findTForX(const SingleCubicBezier &singleCubicBezier, qreal x)
{
const qreal p0 = singleCubicBezier.p0x;
const qreal p1 = singleCubicBezier.p1x;
const qreal p2 = singleCubicBezier.p2x;
const qreal p3 = singleCubicBezier.p3x;
const qreal a = factorT2 / factorT3;
const qreal b = factorT1 / factorT3;
const qreal c = factorT0 / factorT3;
const qreal factorT3 = p3 - p0 + 3 * p1 - 3 * p2;
const qreal factorT2 = 3 * p0 - 6 * p1 + 3 * p2;
const qreal factorT1 = -3 * p0 + 3 * p1;
const qreal factorT0 = p0 - x;
return singleRealSolutionForCubic(a, b, c);
// Cases for quadratic, linear and invalid equations
if (almostZero(factorT3)) {
if (almostZero(factorT2)) {
if (almostZero(factorT1))
return 0.0;
//one new iteration to increase numeric stability
//return newtonIteration(singleCubicBezier, t, x);
}
return -factorT0 / factorT1;
}
const qreal discriminant = factorT1 * factorT1 - 4.0 * factorT2 * factorT0;
if (discriminant < 0.0)
return 0.0;
if (discriminant == 0.0)
return -factorT1 / (2.0 * factorT2);
const qreal solution1 = (-factorT1 + std::sqrt(discriminant)) / (2.0 * factorT2);
if (solution1 >= 0.0 && solution1 <= 1.0)
return solution1;
const qreal solution2 = (-factorT1 - std::sqrt(discriminant)) / (2.0 * factorT2);
if (solution2 >= 0.0 && solution2 <= 1.0)
return solution2;
return 0.0;
}
const qreal a = factorT2 / factorT3;
const qreal b = factorT1 / factorT3;
const qreal c = factorT0 / factorT3;
return singleRealSolutionForCubic(a, b, c);
//one new iteration to increase numeric stability
//return newtonIteration(singleCubicBezier, t, x);
}
};
struct TCBEase : public BezierEase

70
tests/auto/corelib/tools/qeasingcurve/tst_qeasingcurve.cpp
View File

@ -54,6 +54,7 @@ private slots:
void testCbrtDouble();
void testCbrtFloat();
void cpp11();
void quadraticEquation();
};
void tst_QEasingCurve::type()
@ -804,5 +805,74 @@ void tst_QEasingCurve::cpp11()
#endif
}
void tst_QEasingCurve::quadraticEquation() {
// We find the value for a given time by solving a cubic equation.
// ax^3 + bx^2 + cx + d = 0
// However, the solver also needs to take care of cases where a = 0,
// b = 0 or c = 0, and the equation becomes quadratic, linear or invalid.
// A naive cubic solver might divide by zero and return nan, even
// when the solution is a real number.
// This test should triggers those cases.
{
// If the control points are spaced 1/3 apart of the distance of the
// start- and endpoint, the equation becomes linear.
QEasingCurve test(QEasingCurve::BezierSpline);
const qreal p1 = 1.0 / 3.0;
const qreal p2 = 1.0 - 1.0 / 3.0;
const qreal p3 = 1.0;
test.addCubicBezierSegment(QPointF(p1, 0.0), QPointF(p2, 1.0), QPointF(p3, 1.0));
QVERIFY(qAbs(test.valueForProgress(0.25) - 0.15625) < 1e-6);
QVERIFY(qAbs(test.valueForProgress(0.5) - 0.5) < 1e-6);
QVERIFY(qAbs(test.valueForProgress(0.75) - 0.84375) < 1e-6);
}
{
// If both the start point and the first control point
// are placed a 0.0, and the second control point is
// placed at 1/3, we get a case where a = 0 and b != 0
// i.e. a quadratic equation.
QEasingCurve test(QEasingCurve::BezierSpline);
const qreal p1 = 0.0;
const qreal p2 = 1.0 / 3.0;
const qreal p3 = 1.0;
test.addCubicBezierSegment(QPointF(p1, 0.0), QPointF(p2, 1.0), QPointF(p3, 1.0));
QVERIFY(qAbs(test.valueForProgress(0.25) - 0.5) < 1e-6);
QVERIFY(qAbs(test.valueForProgress(0.5) - 0.792893) < 1e-6);
QVERIFY(qAbs(test.valueForProgress(0.75) - 0.950962) < 1e-6);
}
{
// If both the start point and the first control point
// are placed a 0.0, and the second control point is
// placed close to 1/3, we get a case where a = ~0 and b != 0.
// It's not truly a quadratic equation, but should be treated
// as one, because it causes some cubic solvers to fail.
QEasingCurve test(QEasingCurve::BezierSpline);
const qreal p1 = 0.0;
const qreal p2 = 1.0 / 3.0 + 1e-6;
const qreal p3 = 1.0;
test.addCubicBezierSegment(QPointF(p1, 0.0), QPointF(p2, 1.0), QPointF(p3, 1.0));
QVERIFY(qAbs(test.valueForProgress(0.25) - 0.499999) < 1e-6);
QVERIFY(qAbs(test.valueForProgress(0.5) - 0.792892) < 1e-6);
QVERIFY(qAbs(test.valueForProgress(0.75) - 0.950961) < 1e-6);
}
{
// A bad case, where the segment is of zero length.
// However, it might still happen in user code,
// and we should return a sensible answer.
QEasingCurve test(QEasingCurve::BezierSpline);
const qreal p0 = 0.0;
const qreal p1 = p0;
const qreal p2 = p0;
const qreal p3 = p0;
test.addCubicBezierSegment(QPointF(p1, 0.0), QPointF(p2, 1.0), QPointF(p3, 1.0));
test.addCubicBezierSegment(QPointF(p3, 1.0), QPointF(1.0, 1.0), QPointF(1.0, 1.0));
QCOMPARE(test.valueForProgress(0.0), 0.0);
}
}
QTEST_MAIN(tst_QEasingCurve)
#include "tst_qeasingcurve.moc"