From 50cfbd6112a2682228cdf34cd72b5abae967cdb2 Mon Sep 17 00:00:00 2001 From: Svenn-Arne Dragly Date: Wed, 14 Mar 2018 16:36:09 +0100 Subject: Animation: Fix case where QEasingCurve::valueForProgress returns nan 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 --- .../tools/qeasingcurve/tst_qeasingcurve.cpp | 70 ++++++++++++++++++++++ 1 file changed, 70 insertions(+) (limited to 'tests/auto/corelib/tools/qeasingcurve') diff --git a/tests/auto/corelib/tools/qeasingcurve/tst_qeasingcurve.cpp b/tests/auto/corelib/tools/qeasingcurve/tst_qeasingcurve.cpp index 0714883855..79309f960d 100644 --- a/tests/auto/corelib/tools/qeasingcurve/tst_qeasingcurve.cpp +++ b/tests/auto/corelib/tools/qeasingcurve/tst_qeasingcurve.cpp @@ -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" -- cgit v1.2.3