/**************************************************************************** ** ** Copyright (C) 2016 The Qt Company Ltd. ** Contact: https://www.qt.io/licensing/ ** ** This file is part of the QtCore module of the Qt Toolkit. ** ** $QT_BEGIN_LICENSE:LGPL$ ** Commercial License Usage ** Licensees holding valid commercial Qt licenses may use this file in ** accordance with the commercial license agreement provided with the ** Software or, alternatively, in accordance with the terms contained in ** a written agreement between you and The Qt Company. For licensing terms ** and conditions see https://www.qt.io/terms-conditions. For further ** information use the contact form at https://www.qt.io/contact-us. ** ** GNU Lesser General Public License Usage ** Alternatively, this file may be used under the terms of the GNU Lesser ** General Public License version 3 as published by the Free Software ** Foundation and appearing in the file LICENSE.LGPL3 included in the ** packaging of this file. Please review the following information to ** ensure the GNU Lesser General Public License version 3 requirements ** will be met: https://www.gnu.org/licenses/lgpl-3.0.html. ** ** GNU General Public License Usage ** Alternatively, this file may be used under the terms of the GNU ** General Public License version 2.0 or (at your option) the GNU General ** Public license version 3 or any later version approved by the KDE Free ** Qt Foundation. The licenses are as published by the Free Software ** Foundation and appearing in the file LICENSE.GPL2 and LICENSE.GPL3 ** included in the packaging of this file. Please review the following ** information to ensure the GNU General Public License requirements will ** be met: https://www.gnu.org/licenses/gpl-2.0.html and ** https://www.gnu.org/licenses/gpl-3.0.html. ** ** $QT_END_LICENSE$ ** ****************************************************************************/ /* | *property* | *Used for type* | | period | QEasingCurve::{In,Out,InOut,OutIn}Elastic | | amplitude | QEasingCurve::{In,Out,InOut,OutIn}Bounce, QEasingCurve::{In,Out,InOut,OutIn}Elastic | | overshoot | QEasingCurve::{In,Out,InOut,OutIn}Back | */ /*! \class QEasingCurve \inmodule QtCore \since 4.6 \ingroup animation \brief The QEasingCurve class provides easing curves for controlling animation. Easing curves describe a function that controls how the speed of the interpolation between 0 and 1 should be. Easing curves allow transitions from one value to another to appear more natural than a simple constant speed would allow. The QEasingCurve class is usually used in conjunction with the QVariantAnimation and QPropertyAnimation classes but can be used on its own. It is usually used to accelerate the interpolation from zero velocity (ease in) or decelerate to zero velocity (ease out). Ease in and ease out can also be combined in the same easing curve. To calculate the speed of the interpolation, the easing curve provides the function valueForProgress(), where the \a progress argument specifies the progress of the interpolation: 0 is the start value of the interpolation, 1 is the end value of the interpolation. The returned value is the effective progress of the interpolation. If the returned value is the same as the input value for all input values the easing curve is a linear curve. This is the default behaviour. For example, \code QEasingCurve easing(QEasingCurve::InOutQuad); for(qreal t = 0.0; t < 1.0; t+=0.1) qWarning() << "Effective progress" << t << " is << easing.valueForProgress(t); \endcode will print the effective progress of the interpolation between 0 and 1. When using a QPropertyAnimation, the associated easing curve will be used to control the progress of the interpolation between startValue and endValue: \code QPropertyAnimation animation; animation.setStartValue(0); animation.setEndValue(1000); animation.setDuration(1000); animation.setEasingCurve(QEasingCurve::InOutQuad); \endcode The ability to set an amplitude, overshoot, or period depends on the QEasingCurve type. Amplitude access is available to curves that behave as springs such as elastic and bounce curves. Changing the amplitude changes the height of the curve. Period access is only available to elastic curves and setting a higher period slows the rate of bounce. Only curves that have "boomerang" behaviors such as the InBack, OutBack, InOutBack, and OutInBack have overshoot settings. These curves will interpolate beyond the end points and return to the end point, acting similar to a boomerang. The \l{Easing Curves Example} contains samples of QEasingCurve types and lets you change the curve settings. */ /*! \enum QEasingCurve::Type The type of easing curve. \value Linear \image qeasingcurve-linear.png \caption Easing curve for a linear (t) function: velocity is constant. \value InQuad \image qeasingcurve-inquad.png \caption Easing curve for a quadratic (t^2) function: accelerating from zero velocity. \value OutQuad \image qeasingcurve-outquad.png \caption Easing curve for a quadratic (t^2) function: decelerating to zero velocity. \value InOutQuad \image qeasingcurve-inoutquad.png \caption Easing curve for a quadratic (t^2) function: acceleration until halfway, then deceleration. \value OutInQuad \image qeasingcurve-outinquad.png \caption Easing curve for a quadratic (t^2) function: deceleration until halfway, then acceleration. \value InCubic \image qeasingcurve-incubic.png \caption Easing curve for a cubic (t^3) function: accelerating from zero velocity. \value OutCubic \image qeasingcurve-outcubic.png \caption Easing curve for a cubic (t^3) function: decelerating to zero velocity. \value InOutCubic \image qeasingcurve-inoutcubic.png \caption Easing curve for a cubic (t^3) function: acceleration until halfway, then deceleration. \value OutInCubic \image qeasingcurve-outincubic.png \caption Easing curve for a cubic (t^3) function: deceleration until halfway, then acceleration. \value InQuart \image qeasingcurve-inquart.png \caption Easing curve for a quartic (t^4) function: accelerating from zero velocity. \value OutQuart \image qeasingcurve-outquart.png \caption Easing curve for a quartic (t^4) function: decelerating to zero velocity. \value InOutQuart \image qeasingcurve-inoutquart.png \caption Easing curve for a quartic (t^4) function: acceleration until halfway, then deceleration. \value OutInQuart \image qeasingcurve-outinquart.png \caption Easing curve for a quartic (t^4) function: deceleration until halfway, then acceleration. \value InQuint \image qeasingcurve-inquint.png \caption Easing curve for a quintic (t^5) easing in: accelerating from zero velocity. \value OutQuint \image qeasingcurve-outquint.png \caption Easing curve for a quintic (t^5) function: decelerating to zero velocity. \value InOutQuint \image qeasingcurve-inoutquint.png \caption Easing curve for a quintic (t^5) function: acceleration until halfway, then deceleration. \value OutInQuint \image qeasingcurve-outinquint.png \caption Easing curve for a quintic (t^5) function: deceleration until halfway, then acceleration. \value InSine \image qeasingcurve-insine.png \caption Easing curve for a sinusoidal (sin(t)) function: accelerating from zero velocity. \value OutSine \image qeasingcurve-outsine.png \caption Easing curve for a sinusoidal (sin(t)) function: decelerating to zero velocity. \value InOutSine \image qeasingcurve-inoutsine.png \caption Easing curve for a sinusoidal (sin(t)) function: acceleration until halfway, then deceleration. \value OutInSine \image qeasingcurve-outinsine.png \caption Easing curve for a sinusoidal (sin(t)) function: deceleration until halfway, then acceleration. \value InExpo \image qeasingcurve-inexpo.png \caption Easing curve for an exponential (2^t) function: accelerating from zero velocity. \value OutExpo \image qeasingcurve-outexpo.png \caption Easing curve for an exponential (2^t) function: decelerating to zero velocity. \value InOutExpo \image qeasingcurve-inoutexpo.png \caption Easing curve for an exponential (2^t) function: acceleration until halfway, then deceleration. \value OutInExpo \image qeasingcurve-outinexpo.png \caption Easing curve for an exponential (2^t) function: deceleration until halfway, then acceleration. \value InCirc \image qeasingcurve-incirc.png \caption Easing curve for a circular (sqrt(1-t^2)) function: accelerating from zero velocity. \value OutCirc \image qeasingcurve-outcirc.png \caption Easing curve for a circular (sqrt(1-t^2)) function: decelerating to zero velocity. \value InOutCirc \image qeasingcurve-inoutcirc.png \caption Easing curve for a circular (sqrt(1-t^2)) function: acceleration until halfway, then deceleration. \value OutInCirc \image qeasingcurve-outincirc.png \caption Easing curve for a circular (sqrt(1-t^2)) function: deceleration until halfway, then acceleration. \value InElastic \image qeasingcurve-inelastic.png \caption Easing curve for an elastic (exponentially decaying sine wave) function: accelerating from zero velocity. The peak amplitude can be set with the \e amplitude parameter, and the period of decay by the \e period parameter. \value OutElastic \image qeasingcurve-outelastic.png \caption Easing curve for an elastic (exponentially decaying sine wave) function: decelerating to zero velocity. The peak amplitude can be set with the \e amplitude parameter, and the period of decay by the \e period parameter. \value InOutElastic \image qeasingcurve-inoutelastic.png \caption Easing curve for an elastic (exponentially decaying sine wave) function: acceleration until halfway, then deceleration. \value OutInElastic \image qeasingcurve-outinelastic.png \caption Easing curve for an elastic (exponentially decaying sine wave) function: deceleration until halfway, then acceleration. \value InBack \image qeasingcurve-inback.png \caption Easing curve for a back (overshooting cubic function: (s+1)*t^3 - s*t^2) easing in: accelerating from zero velocity. \value OutBack \image qeasingcurve-outback.png \caption Easing curve for a back (overshooting cubic function: (s+1)*t^3 - s*t^2) easing out: decelerating to zero velocity. \value InOutBack \image qeasingcurve-inoutback.png \caption Easing curve for a back (overshooting cubic function: (s+1)*t^3 - s*t^2) easing in/out: acceleration until halfway, then deceleration. \value OutInBack \image qeasingcurve-outinback.png \caption Easing curve for a back (overshooting cubic easing: (s+1)*t^3 - s*t^2) easing out/in: deceleration until halfway, then acceleration. \value InBounce \image qeasingcurve-inbounce.png \caption Easing curve for a bounce (exponentially decaying parabolic bounce) function: accelerating from zero velocity. \value OutBounce \image qeasingcurve-outbounce.png \caption Easing curve for a bounce (exponentially decaying parabolic bounce) function: decelerating from zero velocity. \value InOutBounce \image qeasingcurve-inoutbounce.png \caption Easing curve for a bounce (exponentially decaying parabolic bounce) function easing in/out: acceleration until halfway, then deceleration. \value OutInBounce \image qeasingcurve-outinbounce.png \caption Easing curve for a bounce (exponentially decaying parabolic bounce) function easing out/in: deceleration until halfway, then acceleration. \omitvalue InCurve \omitvalue OutCurve \omitvalue SineCurve \omitvalue CosineCurve \value BezierSpline Allows defining a custom easing curve using a cubic bezier spline \sa addCubicBezierSegment() \value TCBSpline Allows defining a custom easing curve using a TCB spline \sa addTCBSegment() \value Custom This is returned if the user specified a custom curve type with setCustomType(). Note that you cannot call setType() with this value, but type() can return it. \omitvalue NCurveTypes */ /*! \typedef QEasingCurve::EasingFunction This is a typedef for a pointer to a function with the following signature: \snippet code/src_corelib_tools_qeasingcurve.cpp 0 */ #include "qeasingcurve.h" #include #ifndef QT_NO_DEBUG_STREAM #include #include #endif #ifndef QT_NO_DATASTREAM #include #endif #include #include QT_BEGIN_NAMESPACE static bool isConfigFunction(QEasingCurve::Type type) { return (type >= QEasingCurve::InElastic && type <= QEasingCurve::OutInBounce) || type == QEasingCurve::BezierSpline || type == QEasingCurve::TCBSpline; } struct TCBPoint { QPointF _point; qreal _t; qreal _c; qreal _b; TCBPoint() {} TCBPoint(QPointF point, qreal t, qreal c, qreal b) : _point(point), _t(t), _c(c), _b(b) {} bool operator==(const TCBPoint &other) const { return _point == other._point && qFuzzyCompare(_t, other._t) && qFuzzyCompare(_c, other._c) && qFuzzyCompare(_b, other._b); } }; Q_DECLARE_TYPEINFO(TCBPoint, Q_PRIMITIVE_TYPE); typedef QVector TCBPoints; class QEasingCurveFunction { public: QEasingCurveFunction(QEasingCurve::Type type, qreal period = 0.3, qreal amplitude = 1.0, qreal overshoot = 1.70158) : _t(type), _p(period), _a(amplitude), _o(overshoot) { } virtual ~QEasingCurveFunction() {} virtual qreal value(qreal t); virtual QEasingCurveFunction *copy() const; bool operator==(const QEasingCurveFunction &other) const; QEasingCurve::Type _t; qreal _p; qreal _a; qreal _o; QVector _bezierCurves; TCBPoints _tcbPoints; }; static QEasingCurve::EasingFunction curveToFunc(QEasingCurve::Type curve); qreal QEasingCurveFunction::value(qreal t) { QEasingCurve::EasingFunction func = curveToFunc(_t); return func(t); } QEasingCurveFunction *QEasingCurveFunction::copy() const { QEasingCurveFunction *rv = new QEasingCurveFunction(_t, _p, _a, _o); rv->_bezierCurves = _bezierCurves; rv->_tcbPoints = _tcbPoints; return rv; } bool QEasingCurveFunction::operator==(const QEasingCurveFunction &other) const { return _t == other._t && qFuzzyCompare(_p, other._p) && qFuzzyCompare(_a, other._a) && qFuzzyCompare(_o, other._o) && _bezierCurves == other._bezierCurves && _tcbPoints == other._tcbPoints; } QT_BEGIN_INCLUDE_NAMESPACE #include "../../3rdparty/easing/easing.cpp" QT_END_INCLUDE_NAMESPACE class QEasingCurvePrivate { public: QEasingCurvePrivate() : type(QEasingCurve::Linear), config(0), func(&easeNone) { } QEasingCurvePrivate(const QEasingCurvePrivate &other) : type(other.type), config(other.config ? other.config->copy() : 0), func(other.func) { } ~QEasingCurvePrivate() { delete config; } void setType_helper(QEasingCurve::Type); QEasingCurve::Type type; QEasingCurveFunction *config; QEasingCurve::EasingFunction func; }; struct BezierEase : public QEasingCurveFunction { struct SingleCubicBezier { qreal p0x, p0y; qreal p1x, p1y; qreal p2x, p2y; qreal p3x, p3y; }; QVector _curves; QVector _intervals; int _curveCount; bool _init; bool _valid; BezierEase(QEasingCurve::Type type = QEasingCurve::BezierSpline) : QEasingCurveFunction(type), _curves(10), _intervals(10), _init(false), _valid(false) { } void init() { if (_bezierCurves.constLast() == QPointF(1.0, 1.0)) { _init = true; _curveCount = _bezierCurves.count() / 3; for (int i=0; i < _curveCount; i++) { _intervals[i] = _bezierCurves.at(i * 3 + 2).x(); if (i == 0) { _curves[0].p0x = 0.0; _curves[0].p0y = 0.0; _curves[0].p1x = _bezierCurves.at(0).x(); _curves[0].p1y = _bezierCurves.at(0).y(); _curves[0].p2x = _bezierCurves.at(1).x(); _curves[0].p2y = _bezierCurves.at(1).y(); _curves[0].p3x = _bezierCurves.at(2).x(); _curves[0].p3y = _bezierCurves.at(2).y(); } else if (i == (_curveCount - 1)) { _curves[i].p0x = _bezierCurves.at(_bezierCurves.count() - 4).x(); _curves[i].p0y = _bezierCurves.at(_bezierCurves.count() - 4).y(); _curves[i].p1x = _bezierCurves.at(_bezierCurves.count() - 3).x(); _curves[i].p1y = _bezierCurves.at(_bezierCurves.count() - 3).y(); _curves[i].p2x = _bezierCurves.at(_bezierCurves.count() - 2).x(); _curves[i].p2y = _bezierCurves.at(_bezierCurves.count() - 2).y(); _curves[i].p3x = _bezierCurves.at(_bezierCurves.count() - 1).x(); _curves[i].p3y = _bezierCurves.at(_bezierCurves.count() - 1).y(); } else { _curves[i].p0x = _bezierCurves.at(i * 3 - 1).x(); _curves[i].p0y = _bezierCurves.at(i * 3 - 1).y(); _curves[i].p1x = _bezierCurves.at(i * 3).x(); _curves[i].p1y = _bezierCurves.at(i * 3).y(); _curves[i].p2x = _bezierCurves.at(i * 3 + 1).x(); _curves[i].p2y = _bezierCurves.at(i * 3 + 1).y(); _curves[i].p3x = _bezierCurves.at(i * 3 + 2).x(); _curves[i].p3y = _bezierCurves.at(i * 3 + 2).y(); } } _valid = true; } else { _valid = false; } } QEasingCurveFunction *copy() const Q_DECL_OVERRIDE { BezierEase *rv = new BezierEase(); rv->_t = _t; rv->_p = _p; rv->_a = _a; rv->_o = _o; rv->_bezierCurves = _bezierCurves; rv->_tcbPoints = _tcbPoints; return rv; } void getBezierSegment(SingleCubicBezier * &singleCubicBezier, qreal x) { int currentSegment = 0; while (currentSegment < _curveCount) { if (x <= _intervals.data()[currentSegment]) break; currentSegment++; } singleCubicBezier = &_curves.data()[currentSegment]; } qreal static inline newtonIteration(const SingleCubicBezier &singleCubicBezier, qreal t, qreal x) { qreal currentXValue = evaluateForX(singleCubicBezier, t); const qreal newT = t - (currentXValue - x) / evaluateDerivateForX(singleCubicBezier, t); return newT; } qreal value(qreal x) Q_DECL_OVERRIDE { Q_ASSERT(_bezierCurves.count() % 3 == 0); if (_bezierCurves.isEmpty()) { return x; } if (!_init) init(); if (!_valid) { qWarning("QEasingCurve: Invalid bezier curve"); return x; } SingleCubicBezier *singleCubicBezier = 0; getBezierSegment(singleCubicBezier, x); return evaluateSegmentForY(*singleCubicBezier, findTForX(*singleCubicBezier, x)); } qreal static inline evaluateSegmentForY(const SingleCubicBezier &singleCubicBezier, qreal t) { const qreal p0 = singleCubicBezier.p0y; const qreal p1 = singleCubicBezier.p1y; const qreal p2 = singleCubicBezier.p2y; const qreal p3 = singleCubicBezier.p3y; const qreal s = 1 - t; const qreal s_squared = s*s; const qreal t_squared = t*t; const qreal s_cubic = s_squared * s; const qreal t_cubic = t_squared * t; return s_cubic * p0 + 3 * s_squared * t * p1 + 3 * s * t_squared * p2 + t_cubic * p3; } qreal static inline evaluateForX(const SingleCubicBezier &singleCubicBezier, qreal t) { const qreal p0 = singleCubicBezier.p0x; const qreal p1 = singleCubicBezier.p1x; const qreal p2 = singleCubicBezier.p2x; const qreal p3 = singleCubicBezier.p3x; const qreal s = 1 - t; const qreal s_squared = s*s; const qreal t_squared = t*t; const qreal s_cubic = s_squared * s; const qreal t_cubic = t_squared * t; return s_cubic * p0 + 3 * s_squared * t * p1 + 3 * s * t_squared * p2 + t_cubic * p3; } qreal static inline evaluateDerivateForX(const SingleCubicBezier &singleCubicBezier, qreal t) { const qreal p0 = singleCubicBezier.p0x; const qreal p1 = singleCubicBezier.p1x; const qreal p2 = singleCubicBezier.p2x; const qreal p3 = singleCubicBezier.p3x; const qreal t_squared = t*t; return -3*p0 + 3*p1 + 6*p0*t - 12*p1*t + 6*p2*t + 3*p3*t_squared - 3*p0*t_squared + 9*p1*t_squared - 9*p2*t_squared; } qreal static inline _cbrt(qreal d) { qreal sign = 1; if (d < 0) sign = -1; d = d * sign; qreal t = _fast_cbrt(d); //one step of Halley's Method to get a better approximation const qreal t_cubic = t * t * t; const qreal f = t_cubic + t_cubic + d; if (f != qreal(0.0)) t = t * (t_cubic + d + d) / f; //another step /*qreal t_i = t; t_i_cubic = pow(t_i, 3); t = t_i * (t_i_cubic + d + d) / (t_i_cubic + t_i_cubic + d);*/ return t * sign; } float static inline _fast_cbrt(float x) { union { float f; quint32 i; } ux; const unsigned int B1 = 709921077; ux.f = x; ux.i = (ux.i / 3 + B1); return ux.f; } double static inline _fast_cbrt(double d) { union { double d; quint32 pt[2]; } ut, ux; const unsigned int B1 = 715094163; #if Q_BYTE_ORDER == Q_LITTLE_ENDIAN const int h0 = 1; #else const int h0 = 0; #endif ut.d = 0.0; ux.d = d; quint32 hx = ux.pt[h0]; //high word of d ut.pt[h0] = hx / 3 + B1; return ut.d; } qreal static inline _acos(qreal x) { return std::sqrt(1-x)*(1.5707963267948966192313216916398f + x*(-0.213300989f + x*(0.077980478f + x*-0.02164095f))); } qreal static inline _cos(qreal x) //super fast _cos { const qreal pi_times2 = 2 * M_PI; const qreal pi_neg = -1 * M_PI; const qreal pi_by2 = M_PI / 2.0; x += pi_by2; //the polynom is for sin if (x < pi_neg) x += pi_times2; else if (x > M_PI) x -= pi_times2; const qreal a = 0.405284735; const qreal b = 1.27323954; const qreal x_squared = x * x; if (x < 0) { qreal cos = b * x + a * x_squared; if (cos < 0) return 0.225 * (cos * -1 * cos - cos) + cos; return 0.225 * (cos * cos - cos) + cos; } //else qreal cos = b * x - a * x_squared; if (cos < 0) return 0.225 * (cos * 1 *-cos - cos) + cos; return 0.225 * (cos * cos - cos) + cos; } bool static inline inRange(qreal f) { return (f >= -0.01 && f <= 1.01); } void static inline cosacos(qreal x, qreal &s1, qreal &s2, qreal &s3 ) { //This function has no proper algebraic representation in real numbers. //We use approximations instead const qreal x_squared = x * x; const qreal x_plus_one_sqrt = qSqrt(1.0 + x); const qreal one_minus_x_sqrt = qSqrt(1.0 - x); //cos(acos(x) / 3) //s1 = _cos(_acos(x) / 3); s1 = 0.463614 - 0.0347815 * x + 0.00218245 * x_squared + 0.402421 * x_plus_one_sqrt; //cos(acos((x) - M_PI) / 3) //s3 = _cos((_acos(x) - M_PI) / 3); s3 = 0.463614 + 0.402421 * one_minus_x_sqrt + 0.0347815 * x + 0.00218245 * x_squared; //cos((acos(x) + M_PI) / 3) //s2 = _cos((_acos(x) + M_PI) / 3); s2 = -0.401644 * one_minus_x_sqrt - 0.0686804 * x + 0.401644 * x_plus_one_sqrt; } qreal static inline singleRealSolutionForCubic(qreal a, qreal b, qreal c) { //returns the real solutiuon in [0..1] //We use the Cardano formula //substituiton: x = z - a/3 // z^3+pz+q=0 if (c < 0.000001 && c > -0.000001) return 0; const qreal a_by3 = a / 3.0; const qreal a_cubic = a * a * a; const qreal p = b - a * a_by3; const qreal q = 2.0 * a_cubic / 27.0 - a * b / 3.0 + c; const qreal q_squared = q * q; const qreal p_cubic = p * p * p; const qreal D = 0.25 * q_squared + p_cubic / 27.0; if (D >= 0) { const qreal D_sqrt = qSqrt(D); qreal u = _cbrt( -q * 0.5 + D_sqrt); qreal v = _cbrt( -q * 0.5 - D_sqrt); qreal z1 = u + v; qreal t1 = z1 - a_by3; if (inRange(t1)) return t1; qreal z2 = -1 *u; qreal t2 = z2 - a_by3; return t2; } //casus irreducibilis const qreal p_minus_sqrt = qSqrt(-p); //const qreal f = sqrt(4.0 / 3.0 * -p); const qreal f = qSqrt(4.0 / 3.0) * p_minus_sqrt; //const qreal sqrtP = sqrt(27.0 / -p_cubic); const qreal sqrtP = -3.0*qSqrt(3.0) / (p_minus_sqrt * p); const qreal g = -q * 0.5 * sqrtP; qreal s1; qreal s2; qreal s3; cosacos(g, s1, s2, s3); qreal z1 = -1* f * s2; qreal t1 = z1 - a_by3; if (inRange(t1)) return t1; qreal z2 = f * s1; qreal t2 = z2 - a_by3; if (inRange(t2)) return t2; qreal z3 = -1 * f * s3; qreal t3 = z3 - a_by3; 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); } }; struct TCBEase : public BezierEase { TCBEase() : BezierEase(QEasingCurve::TCBSpline) { } qreal value(qreal x) Q_DECL_OVERRIDE { Q_ASSERT(_bezierCurves.count() % 3 == 0); if (_bezierCurves.isEmpty()) { qWarning("QEasingCurve: Invalid tcb curve"); return x; } return BezierEase::value(x); } }; struct ElasticEase : public QEasingCurveFunction { ElasticEase(QEasingCurve::Type type) : QEasingCurveFunction(type, qreal(0.3), qreal(1.0)) { } QEasingCurveFunction *copy() const Q_DECL_OVERRIDE { ElasticEase *rv = new ElasticEase(_t); rv->_p = _p; rv->_a = _a; rv->_bezierCurves = _bezierCurves; rv->_tcbPoints = _tcbPoints; return rv; } qreal value(qreal t) Q_DECL_OVERRIDE { qreal p = (_p < 0) ? qreal(0.3) : _p; qreal a = (_a < 0) ? qreal(1.0) : _a; switch(_t) { case QEasingCurve::InElastic: return easeInElastic(t, a, p); case QEasingCurve::OutElastic: return easeOutElastic(t, a, p); case QEasingCurve::InOutElastic: return easeInOutElastic(t, a, p); case QEasingCurve::OutInElastic: return easeOutInElastic(t, a, p); default: return t; } } }; struct BounceEase : public QEasingCurveFunction { BounceEase(QEasingCurve::Type type) : QEasingCurveFunction(type, qreal(0.3), qreal(1.0)) { } QEasingCurveFunction *copy() const Q_DECL_OVERRIDE { BounceEase *rv = new BounceEase(_t); rv->_a = _a; rv->_bezierCurves = _bezierCurves; rv->_tcbPoints = _tcbPoints; return rv; } qreal value(qreal t) Q_DECL_OVERRIDE { qreal a = (_a < 0) ? qreal(1.0) : _a; switch(_t) { case QEasingCurve::InBounce: return easeInBounce(t, a); case QEasingCurve::OutBounce: return easeOutBounce(t, a); case QEasingCurve::InOutBounce: return easeInOutBounce(t, a); case QEasingCurve::OutInBounce: return easeOutInBounce(t, a); default: return t; } } }; struct BackEase : public QEasingCurveFunction { BackEase(QEasingCurve::Type type) : QEasingCurveFunction(type, qreal(0.3), qreal(1.0), qreal(1.70158)) { } QEasingCurveFunction *copy() const Q_DECL_OVERRIDE { BackEase *rv = new BackEase(_t); rv->_o = _o; rv->_bezierCurves = _bezierCurves; rv->_tcbPoints = _tcbPoints; return rv; } qreal value(qreal t) Q_DECL_OVERRIDE { qreal o = (_o < 0) ? qreal(1.70158) : _o; switch(_t) { case QEasingCurve::InBack: return easeInBack(t, o); case QEasingCurve::OutBack: return easeOutBack(t, o); case QEasingCurve::InOutBack: return easeInOutBack(t, o); case QEasingCurve::OutInBack: return easeOutInBack(t, o); default: return t; } } }; static QEasingCurve::EasingFunction curveToFunc(QEasingCurve::Type curve) { switch(curve) { case QEasingCurve::Linear: return &easeNone; case QEasingCurve::InQuad: return &easeInQuad; case QEasingCurve::OutQuad: return &easeOutQuad; case QEasingCurve::InOutQuad: return &easeInOutQuad; case QEasingCurve::OutInQuad: return &easeOutInQuad; case QEasingCurve::InCubic: return &easeInCubic; case QEasingCurve::OutCubic: return &easeOutCubic; case QEasingCurve::InOutCubic: return &easeInOutCubic; case QEasingCurve::OutInCubic: return &easeOutInCubic; case QEasingCurve::InQuart: return &easeInQuart; case QEasingCurve::OutQuart: return &easeOutQuart; case QEasingCurve::InOutQuart: return &easeInOutQuart; case QEasingCurve::OutInQuart: return &easeOutInQuart; case QEasingCurve::InQuint: return &easeInQuint; case QEasingCurve::OutQuint: return &easeOutQuint; case QEasingCurve::InOutQuint: return &easeInOutQuint; case QEasingCurve::OutInQuint: return &easeOutInQuint; case QEasingCurve::InSine: return &easeInSine; case QEasingCurve::OutSine: return &easeOutSine; case QEasingCurve::InOutSine: return &easeInOutSine; case QEasingCurve::OutInSine: return &easeOutInSine; case QEasingCurve::InExpo: return &easeInExpo; case QEasingCurve::OutExpo: return &easeOutExpo; case QEasingCurve::InOutExpo: return &easeInOutExpo; case QEasingCurve::OutInExpo: return &easeOutInExpo; case QEasingCurve::InCirc: return &easeInCirc; case QEasingCurve::OutCirc: return &easeOutCirc; case QEasingCurve::InOutCirc: return &easeInOutCirc; case QEasingCurve::OutInCirc: return &easeOutInCirc; // Internal for, compatibility with QTimeLine only ?? case QEasingCurve::InCurve: return &easeInCurve; case QEasingCurve::OutCurve: return &easeOutCurve; case QEasingCurve::SineCurve: return &easeSineCurve; case QEasingCurve::CosineCurve: return &easeCosineCurve; default: return 0; }; } static QEasingCurveFunction *curveToFunctionObject(QEasingCurve::Type type) { switch(type) { case QEasingCurve::InElastic: case QEasingCurve::OutElastic: case QEasingCurve::InOutElastic: case QEasingCurve::OutInElastic: return new ElasticEase(type); case QEasingCurve::OutBounce: case QEasingCurve::InBounce: case QEasingCurve::OutInBounce: case QEasingCurve::InOutBounce: return new BounceEase(type); case QEasingCurve::InBack: case QEasingCurve::OutBack: case QEasingCurve::InOutBack: case QEasingCurve::OutInBack: return new BackEase(type); case QEasingCurve::BezierSpline: return new BezierEase; case QEasingCurve::TCBSpline: return new TCBEase; default: return new QEasingCurveFunction(type, qreal(0.3), qreal(1.0), qreal(1.70158)); } return 0; } /*! \fn QEasingCurve::QEasingCurve(QEasingCurve &&other) Move-constructs a QEasingCurve instance, making it point at the same object that \a other was pointing to. \since 5.2 */ /*! Constructs an easing curve of the given \a type. */ QEasingCurve::QEasingCurve(Type type) : d_ptr(new QEasingCurvePrivate) { setType(type); } /*! Construct a copy of \a other. */ QEasingCurve::QEasingCurve(const QEasingCurve &other) : d_ptr(new QEasingCurvePrivate(*other.d_ptr)) { // ### non-atomic, requires malloc on shallow copy } /*! Destructor. */ QEasingCurve::~QEasingCurve() { delete d_ptr; } /*! \fn QEasingCurve &QEasingCurve::operator=(const QEasingCurve &other) Copy \a other. */ /*! \fn QEasingCurve &QEasingCurve::operator=(QEasingCurve &&other) Move-assigns \a other to this QEasingCurve instance. \since 5.2 */ /*! \fn void QEasingCurve::swap(QEasingCurve &other) \since 5.0 Swaps curve \a other with this curve. This operation is very fast and never fails. */ /*! Compare this easing curve with \a other and returns \c true if they are equal. It will also compare the properties of a curve. */ bool QEasingCurve::operator==(const QEasingCurve &other) const { bool res = d_ptr->func == other.d_ptr->func && d_ptr->type == other.d_ptr->type; if (res) { if (d_ptr->config && other.d_ptr->config) { // catch the config content res = d_ptr->config->operator==(*(other.d_ptr->config)); } else if (d_ptr->config || other.d_ptr->config) { // one one has a config object, which could contain default values res = qFuzzyCompare(amplitude(), other.amplitude()) && qFuzzyCompare(period(), other.period()) && qFuzzyCompare(overshoot(), other.overshoot()); } } return res; } /*! \fn bool QEasingCurve::operator!=(const QEasingCurve &other) const Compare this easing curve with \a other and returns \c true if they are not equal. It will also compare the properties of a curve. \sa operator==() */ /*! Returns the amplitude. This is not applicable for all curve types. It is only applicable for bounce and elastic curves (curves of type() QEasingCurve::InBounce, QEasingCurve::OutBounce, QEasingCurve::InOutBounce, QEasingCurve::OutInBounce, QEasingCurve::InElastic, QEasingCurve::OutElastic, QEasingCurve::InOutElastic or QEasingCurve::OutInElastic). */ qreal QEasingCurve::amplitude() const { return d_ptr->config ? d_ptr->config->_a : qreal(1.0); } /*! Sets the amplitude to \a amplitude. This will set the amplitude of the bounce or the amplitude of the elastic "spring" effect. The higher the number, the higher the amplitude. \sa amplitude() */ void QEasingCurve::setAmplitude(qreal amplitude) { if (!d_ptr->config) d_ptr->config = curveToFunctionObject(d_ptr->type); d_ptr->config->_a = amplitude; } /*! Returns the period. This is not applicable for all curve types. It is only applicable if type() is QEasingCurve::InElastic, QEasingCurve::OutElastic, QEasingCurve::InOutElastic or QEasingCurve::OutInElastic. */ qreal QEasingCurve::period() const { return d_ptr->config ? d_ptr->config->_p : qreal(0.3); } /*! Sets the period to \a period. Setting a small period value will give a high frequency of the curve. A large period will give it a small frequency. \sa period() */ void QEasingCurve::setPeriod(qreal period) { if (!d_ptr->config) d_ptr->config = curveToFunctionObject(d_ptr->type); d_ptr->config->_p = period; } /*! Returns the overshoot. This is not applicable for all curve types. It is only applicable if type() is QEasingCurve::InBack, QEasingCurve::OutBack, QEasingCurve::InOutBack or QEasingCurve::OutInBack. */ qreal QEasingCurve::overshoot() const { return d_ptr->config ? d_ptr->config->_o : qreal(1.70158) ; } /*! Sets the overshoot to \a overshoot. 0 produces no overshoot, and the default value of 1.70158 produces an overshoot of 10 percent. \sa overshoot() */ void QEasingCurve::setOvershoot(qreal overshoot) { if (!d_ptr->config) d_ptr->config = curveToFunctionObject(d_ptr->type); d_ptr->config->_o = overshoot; } /*! Adds a segment of a cubic bezier spline to define a custom easing curve. It is only applicable if type() is QEasingCurve::BezierSpline. Note that the spline implicitly starts at (0.0, 0.0) and has to end at (1.0, 1.0) to be a valid easing curve. \a c1 and \a c2 are the control points used for drawing the curve. \a endPoint is the endpoint of the curve. */ void QEasingCurve::addCubicBezierSegment(const QPointF & c1, const QPointF & c2, const QPointF & endPoint) { if (!d_ptr->config) d_ptr->config = curveToFunctionObject(d_ptr->type); d_ptr->config->_bezierCurves << c1 << c2 << endPoint; } QVector static inline tcbToBezier(const TCBPoints &tcbPoints) { const int count = tcbPoints.count(); QVector bezierPoints; bezierPoints.reserve(3 * (count - 1)); for (int i = 1; i < count; i++) { const qreal t_0 = tcbPoints.at(i - 1)._t; const qreal c_0 = tcbPoints.at(i - 1)._c; qreal b_0 = -1; qreal const t_1 = tcbPoints.at(i)._t; qreal const c_1 = tcbPoints.at(i)._c; qreal b_1 = 1; QPointF c_minusOne; //P1 last segment - not available for the first point const QPointF c0(tcbPoints.at(i - 1)._point); //P0 Hermite/TBC const QPointF c3(tcbPoints.at(i)._point); //P1 Hermite/TBC QPointF c4; //P0 next segment - not available for the last point if (i > 1) { //first point no left tangent c_minusOne = tcbPoints.at(i - 2)._point; b_0 = tcbPoints.at(i - 1)._b; } if (i < (count - 1)) { //last point no right tangent c4 = tcbPoints.at(i + 1)._point; b_1 = tcbPoints.at(i)._b; } const qreal dx_0 = 0.5 * (1-t_0) * ((1 + b_0) * (1 + c_0) * (c0.x() - c_minusOne.x()) + (1- b_0) * (1 - c_0) * (c3.x() - c0.x())); const qreal dy_0 = 0.5 * (1-t_0) * ((1 + b_0) * (1 + c_0) * (c0.y() - c_minusOne.y()) + (1- b_0) * (1 - c_0) * (c3.y() - c0.y())); const qreal dx_1 = 0.5 * (1-t_1) * ((1 + b_1) * (1 - c_1) * (c3.x() - c0.x()) + (1 - b_1) * (1 + c_1) * (c4.x() - c3.x())); const qreal dy_1 = 0.5 * (1-t_1) * ((1 + b_1) * (1 - c_1) * (c3.y() - c0.y()) + (1 - b_1) * (1 + c_1) * (c4.y() - c3.y())); const QPointF d_0 = QPointF(dx_0, dy_0); const QPointF d_1 = QPointF(dx_1, dy_1); QPointF c1 = (3 * c0 + d_0) / 3; QPointF c2 = (3 * c3 - d_1) / 3; bezierPoints << c1 << c2 << c3; } return bezierPoints; } /*! Adds a segment of a TCB bezier spline to define a custom easing curve. It is only applicable if type() is QEasingCurve::TCBSpline. The spline has to start explitly at (0.0, 0.0) and has to end at (1.0, 1.0) to be a valid easing curve. The tension \a t changes the length of the tangent vector. The continuity \a c changes the sharpness in change between the tangents. The bias \a b changes the direction of the tangent vector. \a nextPoint is the sample position. All three parameters are valid between -1 and 1 and define the tangent of the control point. If all three parameters are 0 the resulting spline is a Catmull-Rom spline. The begin and endpoint always have a bias of -1 and 1, since the outer tangent is not defined. */ void QEasingCurve::addTCBSegment(const QPointF &nextPoint, qreal t, qreal c, qreal b) { if (!d_ptr->config) d_ptr->config = curveToFunctionObject(d_ptr->type); d_ptr->config->_tcbPoints.append(TCBPoint(nextPoint, t, c ,b)); if (nextPoint == QPointF(1.0, 1.0)) { d_ptr->config->_bezierCurves = tcbToBezier(d_ptr->config->_tcbPoints); d_ptr->config->_tcbPoints.clear(); } } /*! \fn QList QEasingCurve::cubicBezierSpline() const \obsolete Use toCubicSpline() instead. */ /*! \since 5.0 Returns the cubicBezierSpline that defines a custom easing curve. If the easing curve does not have a custom bezier easing curve the list is empty. */ QVector QEasingCurve::toCubicSpline() const { return d_ptr->config ? d_ptr->config->_bezierCurves : QVector(); } /*! Returns the type of the easing curve. */ QEasingCurve::Type QEasingCurve::type() const { return d_ptr->type; } void QEasingCurvePrivate::setType_helper(QEasingCurve::Type newType) { qreal amp = -1.0; qreal period = -1.0; qreal overshoot = -1.0; QVector bezierCurves; QVector tcbPoints; if (config) { amp = config->_a; period = config->_p; overshoot = config->_o; bezierCurves = std::move(config->_bezierCurves); tcbPoints = std::move(config->_tcbPoints); delete config; config = 0; } if (isConfigFunction(newType) || (amp != -1.0) || (period != -1.0) || (overshoot != -1.0) || !bezierCurves.isEmpty()) { config = curveToFunctionObject(newType); if (amp != -1.0) config->_a = amp; if (period != -1.0) config->_p = period; if (overshoot != -1.0) config->_o = overshoot; config->_bezierCurves = std::move(bezierCurves); config->_tcbPoints = std::move(tcbPoints); func = 0; } else if (newType != QEasingCurve::Custom) { func = curveToFunc(newType); } Q_ASSERT((func == 0) == (config != 0)); type = newType; } /*! Sets the type of the easing curve to \a type. */ void QEasingCurve::setType(Type type) { if (d_ptr->type == type) return; if (type < Linear || type >= NCurveTypes - 1) { qWarning("QEasingCurve: Invalid curve type %d", type); return; } d_ptr->setType_helper(type); } /*! Sets a custom easing curve that is defined by the user in the function \a func. The signature of the function is qreal myEasingFunction(qreal progress), where \e progress and the return value are considered to be normalized between 0 and 1. (In some cases the return value can be outside that range) After calling this function type() will return QEasingCurve::Custom. \a func cannot be zero. \sa customType() \sa valueForProgress() */ void QEasingCurve::setCustomType(EasingFunction func) { if (!func) { qWarning("Function pointer must not be null"); return; } d_ptr->func = func; d_ptr->setType_helper(Custom); } /*! Returns the function pointer to the custom easing curve. If type() does not return QEasingCurve::Custom, this function will return 0. */ QEasingCurve::EasingFunction QEasingCurve::customType() const { return d_ptr->type == Custom ? d_ptr->func : 0; } /*! Return the effective progress for the easing curve at \a progress. Whereas \a progress must be between 0 and 1, the returned effective progress can be outside those bounds. For example, QEasingCurve::InBack will return negative values in the beginning of the function. */ qreal QEasingCurve::valueForProgress(qreal progress) const { progress = qBound(0, progress, 1); if (d_ptr->func) return d_ptr->func(progress); else if (d_ptr->config) return d_ptr->config->value(progress); else return progress; } #ifndef QT_NO_DEBUG_STREAM QDebug operator<<(QDebug debug, const QEasingCurve &item) { QDebugStateSaver saver(debug); debug << "type:" << item.d_ptr->type << "func:" << item.d_ptr->func; if (item.d_ptr->config) { debug << QString::fromLatin1("period:%1").arg(item.d_ptr->config->_p, 0, 'f', 20) << QString::fromLatin1("amp:%1").arg(item.d_ptr->config->_a, 0, 'f', 20) << QString::fromLatin1("overshoot:%1").arg(item.d_ptr->config->_o, 0, 'f', 20); } return debug; } #endif // QT_NO_DEBUG_STREAM #ifndef QT_NO_DATASTREAM /*! \fn QDataStream &operator<<(QDataStream &stream, const QEasingCurve &easing) \relates QEasingCurve Writes the given \a easing curve to the given \a stream and returns a reference to the stream. \sa {Serializing Qt Data Types} */ QDataStream &operator<<(QDataStream &stream, const QEasingCurve &easing) { stream << quint8(easing.d_ptr->type); stream << quint64(quintptr(easing.d_ptr->func)); bool hasConfig = easing.d_ptr->config; stream << hasConfig; if (hasConfig) { stream << easing.d_ptr->config->_p; stream << easing.d_ptr->config->_a; stream << easing.d_ptr->config->_o; } return stream; } /*! \fn QDataStream &operator>>(QDataStream &stream, QEasingCurve &easing) \relates QEasingCurve Reads an easing curve from the given \a stream into the given \a easing curve and returns a reference to the stream. \sa {Serializing Qt Data Types} */ QDataStream &operator>>(QDataStream &stream, QEasingCurve &easing) { QEasingCurve::Type type; quint8 int_type; stream >> int_type; type = static_cast(int_type); easing.setType(type); quint64 ptr_func; stream >> ptr_func; easing.d_ptr->func = QEasingCurve::EasingFunction(quintptr(ptr_func)); bool hasConfig; stream >> hasConfig; delete easing.d_ptr->config; easing.d_ptr->config = Q_NULLPTR; if (hasConfig) { QEasingCurveFunction *config = curveToFunctionObject(type); stream >> config->_p; stream >> config->_a; stream >> config->_o; easing.d_ptr->config = config; } return stream; } #endif // QT_NO_DATASTREAM QT_END_NAMESPACE #include "moc_qeasingcurve.cpp"