qeasingcurve.cpp

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// Copyright (C) 2016 The Qt Company Ltd.
// SPDX-License-Identifier: LicenseRef-Qt-Commercial OR LGPL-3.0-only OR GPL-2.0-only OR GPL-3.0-only
 
/*
 
| *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   |
 
*/
 
 
 
 
#include "qeasingcurve.h"
#include <cmath>
 
#ifndef QT_NO_DEBUG_STREAM
#include <QtCore/qdebug.h>
#include <QtCore/qstring.h>
#endif
 
#ifndef QT_NO_DATASTREAM
#include <QtCore/qdatastream.h>
#endif
 
#include <QtCore/qpoint.h>
#include <QtCore/qlist.h>
 
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);
 
QDataStream &operator<<(QDataStream &stream, const TCBPoint &point)
{
    stream << point._point
           << point._t
           << point._c
           << point._b;
    return stream;
}
 
QDataStream &operator>>(QDataStream &stream, TCBPoint &point)
{
    stream >> point._point
           >> point._t
           >> point._c
           >> point._b;
    return stream;
}
 
typedef QList<TCBPoint> 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;
    QList<QPointF> _bezierCurves;
    TCBPoints _tcbPoints;
 
};
 
QDataStream &operator<<(QDataStream &stream, QEasingCurveFunction *func)
{
    if (func) {
        stream << func->_p;
        stream << func->_a;
        stream << func->_o;
        if (stream.version() > QDataStream::Qt_5_12) {
            stream << func->_bezierCurves;
            stream << func->_tcbPoints;
        }
    }
    return stream;
}
 
QDataStream &operator>>(QDataStream &stream, QEasingCurveFunction *func)
{
    if (func) {
        stream >> func->_p;
        stream >> func->_a;
        stream >> func->_o;
        if (stream.version() > QDataStream::Qt_5_12) {
            stream >> func->_bezierCurves;
            stream >> func->_tcbPoints;
        }
    }
    return stream;
}
 
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(nullptr),
          func(&easeNone)
    { }
    QEasingCurvePrivate(const QEasingCurvePrivate &other)
        : type(other.type),
          config(other.config ? other.config->copy() : nullptr),
          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;
    };
 
    QList<SingleCubicBezier> _curves;
    QList<qreal> _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.size() / 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.size() - 4).x();
                    _curves[i].p0y = _bezierCurves.at(_bezierCurves.size() - 4).y();
 
                    _curves[i].p1x = _bezierCurves.at(_bezierCurves.size() - 3).x();
                    _curves[i].p1y = _bezierCurves.at(_bezierCurves.size() - 3).y();
 
                    _curves[i].p2x = _bezierCurves.at(_bezierCurves.size() - 2).x();
                    _curves[i].p2y = _bezierCurves.at(_bezierCurves.size() - 2).y();
 
                    _curves[i].p3x = _bezierCurves.at(_bezierCurves.size() - 1).x();
                    _curves[i].p3y = _bezierCurves.at(_bezierCurves.size() - 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 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) override
    {
        Q_ASSERT(_bezierCurves.size() % 3 == 0);
 
        if (_bezierCurves.isEmpty()) {
            return x;
        }
 
        if (!_init)
            init();
 
        if (!_valid) {
            qWarning("QEasingCurve: Invalid bezier curve");
            return x;
        }
 
        // The bezier computation is not always precise on the endpoints, so handle explicitly
        if (!(x > 0))
            return 0;
        if (!(x < 1))
            return 1;
 
        SingleCubicBezier *singleCubicBezier = nullptr;
        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;
    }
 
    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
{
    TCBEase()
        : BezierEase(QEasingCurve::TCBSpline)
    { }
 
    qreal value(qreal x) override
    {
        Q_ASSERT(_bezierCurves.size() % 3 == 0);
 
        if (_bezierCurves.isEmpty()) {
            qWarning("QEasingCurve: Invalid tcb curve");
            return x;
        }
 
        return BezierEase::value(x);
    }
 
    QEasingCurveFunction *copy() const override
    {
        return new TCBEase{*this};
    }
};
 
struct ElasticEase : public QEasingCurveFunction
{
    ElasticEase(QEasingCurve::Type type)
        : QEasingCurveFunction(type, qreal(0.3), qreal(1.0))
    { }
 
    QEasingCurveFunction *copy() const override
    {
        ElasticEase *rv = new ElasticEase(_t);
        rv->_p = _p;
        rv->_a = _a;
        rv->_bezierCurves = _bezierCurves;
        rv->_tcbPoints = _tcbPoints;
        return rv;
    }
 
    qreal value(qreal t) 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 override
    {
        BounceEase *rv = new BounceEase(_t);
        rv->_a = _a;
        rv->_bezierCurves = _bezierCurves;
        rv->_tcbPoints = _tcbPoints;
        return rv;
    }
 
    qreal value(qreal t) 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 override
    {
        BackEase *rv = new BackEase(_t);
        rv->_o = _o;
        rv->_bezierCurves = _bezierCurves;
        rv->_tcbPoints = _tcbPoints;
        return rv;
    }
 
    qreal value(qreal t) override
    {
        // The *Back() functions are not always precise on the endpoints, so handle explicitly
        if (!(t > 0))
            return 0;
        if (!(t < 1))
            return 1;
        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 - needed for QTimeLine backward-compatibility:
    case QEasingCurve::InCurve:
        return &easeInCurve;
    case QEasingCurve::OutCurve:
        return &easeOutCurve;
    case QEasingCurve::SineCurve:
        return &easeSineCurve;
    case QEasingCurve::CosineCurve:
        return &easeCosineCurve;
    default:
        return nullptr;
    };
}
 
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 nullptr;
}
 
QEasingCurve::QEasingCurve(Type type)
    : d_ptr(new QEasingCurvePrivate)
{
    setType(type);
}
 
QEasingCurve::QEasingCurve(const QEasingCurve &other)
    : d_ptr(new QEasingCurvePrivate(*other.d_ptr))
{
    // ### non-atomic, requires malloc on shallow copy
}
 
QEasingCurve::~QEasingCurve()
{
    delete d_ptr;
}
 
bool comparesEqual(const QEasingCurve &lhs, const QEasingCurve &rhs) noexcept
{
    bool res = lhs.d_ptr->func == rhs.d_ptr->func
            && lhs.d_ptr->type == rhs.d_ptr->type;
    if (res) {
        if (lhs.d_ptr->config && rhs.d_ptr->config) {
            // catch the config content
            res = lhs.d_ptr->config->operator==(*(rhs.d_ptr->config));
 
        } else if (lhs.d_ptr->config || rhs.d_ptr->config) {
            // one one has a config object, which could contain default values
            res = qFuzzyCompare(lhs.amplitude(), rhs.amplitude())
               && qFuzzyCompare(lhs.period(), rhs.period())
               && qFuzzyCompare(lhs.overshoot(), rhs.overshoot());
        }
    }
    return res;
}
 
qreal QEasingCurve::amplitude() const
{
    return d_ptr->config ? d_ptr->config->_a : qreal(1.0);
}
 
void QEasingCurve::setAmplitude(qreal amplitude)
{
    if (!d_ptr->config)
        d_ptr->config = curveToFunctionObject(d_ptr->type);
    d_ptr->config->_a = amplitude;
}
 
qreal QEasingCurve::period() const
{
    return d_ptr->config ? d_ptr->config->_p : qreal(0.3);
}
 
void QEasingCurve::setPeriod(qreal period)
{
    if (!d_ptr->config)
        d_ptr->config = curveToFunctionObject(d_ptr->type);
    d_ptr->config->_p = period;
}
 
qreal QEasingCurve::overshoot() const
{
    return d_ptr->config ? d_ptr->config->_o : qreal(1.70158);
}
 
void QEasingCurve::setOvershoot(qreal overshoot)
{
    if (!d_ptr->config)
        d_ptr->config = curveToFunctionObject(d_ptr->type);
    d_ptr->config->_o = overshoot;
}
 
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;
}
 
QList<QPointF> static inline tcbToBezier(const TCBPoints &tcbPoints)
{
    const int count = tcbPoints.size();
    QList<QPointF> 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;
}
 
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();
    }
 
}
 
QList<QPointF> QEasingCurve::toCubicSpline() const
{
    return d_ptr->config ? d_ptr->config->_bezierCurves : QList<QPointF>();
}
 
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;
    QList<QPointF> bezierCurves;
    QList<TCBPoint> 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 = nullptr;
    }
 
    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 = nullptr;
    } else if (newType != QEasingCurve::Custom) {
        func = curveToFunc(newType);
    }
    Q_ASSERT((func == nullptr) == (config != nullptr));
    type = newType;
}
 
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);
}
 
void QEasingCurve::setCustomType(EasingFunction func)
{
    if (!func) {
        qWarning("Function pointer must not be null");
        return;
    }
    d_ptr->func = func;
    d_ptr->setType_helper(Custom);
}
 
QEasingCurve::EasingFunction QEasingCurve::customType() const
{
    return d_ptr->type == Custom ? d_ptr->func : nullptr;
}
 
qreal QEasingCurve::valueForProgress(qreal progress) const
{
    progress = qBound<qreal>(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:" << reinterpret_cast<const void *>(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
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;
    }
    return stream;
}
 
QDataStream &operator>>(QDataStream &stream, QEasingCurve &easing)
{
    QEasingCurve::Type type;
    quint8 int_type;
    stream >> int_type;
    type = static_cast<QEasingCurve::Type>(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 = nullptr;
    if (hasConfig) {
        QEasingCurveFunction *config = curveToFunctionObject(type);
        stream >> config;
        easing.d_ptr->config = config;
    }
    return stream;
}
#endif // QT_NO_DATASTREAM
 
QT_END_NAMESPACE
 
#include "moc_qeasingcurve.cpp"