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 --- src/corelib/tools/qeasingcurve.cpp | 75 +++++++++++++++++++++++++++----------- 1 file changed, 54 insertions(+), 21 deletions(-) (limited to 'src/corelib/tools/qeasingcurve.cpp') diff --git a/src/corelib/tools/qeasingcurve.cpp b/src/corelib/tools/qeasingcurve.cpp index 0b8fa4ca74..e66db58ed7 100644 --- a/src/corelib/tools/qeasingcurve.cpp +++ b/src/corelib/tools/qeasingcurve.cpp @@ -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; - - 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; - - 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); - } + 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; + } + + 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 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; + + // Cases for quadratic, linear and invalid equations + if (almostZero(factorT3)) { + if (almostZero(factorT2)) { + if (almostZero(factorT1)) + return 0.0; + + 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 -- cgit v1.2.3