qquickpath.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
// Qt-Security score:significant reason:default
 
#include "qquickpath_p.h"
#include "qquickpath_p_p.h"
#include "qquicksvgparser_p.h"
 
#include <QSet>
#include <QTime>
 
#include <private/qbezier_p.h>
#include <QtCore/qmath.h>
#include <QtCore/private/qnumeric_p.h>
 
QT_BEGIN_NAMESPACE
 
Q_STATIC_LOGGING_CATEGORY(lcPath, "qt.quick.shapes.path")
 
void QQuickPathPrivate::enablePathElement(QQuickPathElement *pathElement)
{
    Q_Q(QQuickPath);
 
    if (QQuickCurve *curve = qobject_cast<QQuickCurve *>(pathElement)) {
        _pathCurves.append(curve);
    } else if (QQuickPathText *text = qobject_cast<QQuickPathText *>(pathElement)) {
        _pathTexts.append(text);
    } else {
        QQuickPathAttribute *attribute = qobject_cast<QQuickPathAttribute *>(pathElement);
        if (attribute && !_attributes.contains(attribute->name()))
            _attributes.append(attribute->name());
    }
 
    // There may be multiple entries of the same value
    if (!_pathElements.contains(pathElement))
        q->connect(pathElement, SIGNAL(changed()), q, SLOT(processPath()));
}
 
void QQuickPathPrivate::disablePathElement(QQuickPathElement *pathElement)
{
    Q_Q(QQuickPath);
 
    if (QQuickCurve *curve = qobject_cast<QQuickCurve *>(pathElement)) {
        _pathCurves.removeOne(curve);
    } else if (QQuickPathText *text = qobject_cast<QQuickPathText *>(pathElement)) {
        _pathTexts.removeOne(text);
    } else if (QQuickPathAttribute *attribute = qobject_cast<QQuickPathAttribute *>(pathElement)) {
        const QString name = attribute->name();
        bool found = false;
 
        // TODO: This is rather expensive. Why do the attributes have to be unique?
        for (QQuickPathElement *other : std::as_const(_pathElements)) {
            QQuickPathAttribute *otherAttribute = qobject_cast<QQuickPathAttribute *>(other);
            if (otherAttribute && otherAttribute->name() == name) {
                found = true;
                break;
            }
        }
 
        if (!found)
            _attributes.removeOne(name);
    }
 
    // There may be multiple entries of the same value
    if (!_pathElements.contains(pathElement))
        q->disconnect(pathElement, SIGNAL(changed()), q, SLOT(processPath()));
}
 
/*!
    \qmltype PathElement
    \nativetype QQuickPathElement
    \inqmlmodule QtQuick
    \ingroup qtquick-animation-paths
    \brief PathElement is the base path type.
 
    This type is the base for all path types.  It cannot
    be instantiated.
 
    \sa Path, PathAttribute, PathPercent, PathLine, PathPolyline, PathQuad, PathCubic, PathArc,
        PathAngleArc, PathCurve, PathSvg, PathRectangle
*/
 
/*!
    \qmltype Path
    \nativetype QQuickPath
    \inqmlmodule QtQuick
    \ingroup qtquick-animation-paths
    \brief Defines a path for use by \l PathView and \l Shape.
 
    A Path is composed of one or more path segments - PathLine, PathPolyline, PathQuad,
    PathCubic, PathArc, PathAngleArc, PathCurve, PathSvg.
 
    The spacing of the items along the Path can be adjusted via a
    PathPercent object.
 
    PathAttribute allows named attributes with values to be defined
    along the path.
 
    Path and the other types for specifying path elements are shared between
    \l PathView and \l Shape. The following table provides an overview of the
    applicability of the various path elements:
 
    \table
    \header
        \li Element
        \li PathView
        \li Shape
        \li Shape, software
    \row
        \li PathMove
        \li N/A
        \li Yes
        \li Yes
    \row
        \li PathLine
        \li Yes
        \li Yes
        \li Yes
    \row
        \li PathPolyline
        \li Yes
        \li Yes
        \li Yes
    \row
    \li PathMultiline
        \li Yes
        \li Yes
        \li Yes
    \row
        \li PathQuad
        \li Yes
        \li Yes
        \li Yes
    \row
        \li PathCubic
        \li Yes
        \li Yes
        \li Yes
    \row
        \li PathArc
        \li Yes
        \li Yes
        \li Yes
    \row
        \li PathAngleArc
        \li Yes
        \li Yes
        \li Yes
    \row
        \li PathSvg
        \li Yes
        \li Yes
        \li Yes
    \row
        \li PathRectangle
        \li Yes
        \li Yes
        \li Yes
    \row
        \li PathAttribute
        \li Yes
        \li N/A
        \li N/A
    \row
        \li PathPercent
        \li Yes
        \li N/A
        \li N/A
    \row
        \li PathCurve
        \li Yes
        \li No
        \li No
    \endtable
 
    \note Path is a non-visual type; it does not display anything on its own.
    To draw a path, use \l Shape.
 
    \sa PathView, Shape, PathAttribute, PathPercent, PathLine, PathPolyline, PathMove, PathQuad, PathCubic, PathArc, PathAngleArc, PathCurve, PathSvg, PathRectangle
*/
QQuickPath::QQuickPath(QObject *parent)
 : QObject(*(new QQuickPathPrivate), parent)
{
}
 
QQuickPath::QQuickPath(QQuickPathPrivate &dd, QObject *parent)
    : QObject(dd, parent)
{
}
 
QQuickPath::~QQuickPath()
{
}
 
/*!
    \qmlproperty real QtQuick::Path::startX
    \qmlproperty real QtQuick::Path::startY
    These properties hold the starting position of the path.
*/
qreal QQuickPath::startX() const
{
    Q_D(const QQuickPath);
    return d->startX.isValid() ? d->startX.value() : 0;
}
 
void QQuickPath::setStartX(qreal x)
{
    Q_D(QQuickPath);
    if (d->startX.isValid() && qFuzzyCompare(x, d->startX))
        return;
    d->startX = x;
    emit startXChanged();
    processPath();
}
 
bool QQuickPath::hasStartX() const
{
    Q_D(const QQuickPath);
    return d->startX.isValid();
}
 
qreal QQuickPath::startY() const
{
    Q_D(const QQuickPath);
    return d->startY.isValid() ? d->startY.value() : 0;
}
 
void QQuickPath::setStartY(qreal y)
{
    Q_D(QQuickPath);
    if (d->startY.isValid() && qFuzzyCompare(y, d->startY))
        return;
    d->startY = y;
    emit startYChanged();
    processPath();
}
 
bool QQuickPath::hasStartY() const
{
    Q_D(const QQuickPath);
    return d->startY.isValid();
}
 
/*!
    \qmlproperty bool QtQuick::Path::closed
    This property holds whether the start and end of the path are identical.
*/
bool QQuickPath::isClosed() const
{
    Q_D(const QQuickPath);
    if (d->_pathElements.isEmpty())
        return false;
    return d->closed;
}
 
/*!
    \qmlproperty list<PathElement> QtQuick::Path::pathElements
    This property holds the objects composing the path.
 
    \qmldefault
 
    A path can contain the following path objects:
    \list
        \li \l PathLine - a straight line to a given position.
        \li \l PathPolyline - a polyline specified as a list of coordinates.
        \li \l PathMultiline - a list of polylines specified as a list of lists of coordinates.
        \li \l PathQuad - a quadratic Bezier curve to a given position with a control point.
        \li \l PathCubic - a cubic Bezier curve to a given position with two control points.
        \li \l PathArc - an arc to a given position with a radius.
        \li \l PathAngleArc - an arc specified by center point, radii, and angles.
        \li \l PathSvg - a path specified as an SVG path data string.
        \li \l PathRectangle - a rectangle with a given position and size
        \li \l PathCurve - a point on a Catmull-Rom curve.
        \li \l PathAttribute - an attribute at a given position in the path.
        \li \l PathPercent - a way to spread out items along various segments of the path.
    \endlist
 
    \snippet qml/pathview/pathattributes.qml 2
*/
 
QQmlListProperty<QQuickPathElement> QQuickPath::pathElements()
{
    return QQmlListProperty<QQuickPathElement>(this,
                                               nullptr,
                                               pathElements_append,
                                               pathElements_count,
                                               pathElements_at,
                                               pathElements_clear,
                                               pathElements_replace,
                                               pathElements_removeLast);
}
 
static QQuickPathPrivate *privatePath(QObject *object)
{
    QQuickPath *path = static_cast<QQuickPath*>(object);
 
    return QQuickPathPrivate::get(path);
}
 
QQuickPathElement *QQuickPath::pathElements_at(QQmlListProperty<QQuickPathElement> *property, qsizetype index)
{
    QQuickPathPrivate *d = privatePath(property->object);
 
    return d->_pathElements.at(index);
}
 
void QQuickPath::pathElements_append(QQmlListProperty<QQuickPathElement> *property, QQuickPathElement *pathElement)
{
    QQuickPathPrivate *d = privatePath(property->object);
    d->appendPathElement(pathElement);
}
 
qsizetype QQuickPath::pathElements_count(QQmlListProperty<QQuickPathElement> *property)
{
    QQuickPathPrivate *d = privatePath(property->object);
 
    return d->_pathElements.size();
}
 
void QQuickPath::pathElements_clear(QQmlListProperty<QQuickPathElement> *property)
{
    QQuickPathPrivate *d = privatePath(property->object);
    d->clearPathElements();
}
 
void QQuickPath::pathElements_replace(
        QQmlListProperty<QQuickPathElement> *property, qsizetype position,
        QQuickPathElement *pathElement)
{
    privatePath(property->object)->replacePathElement(position, pathElement);
}
 
void QQuickPath::pathElements_removeLast(QQmlListProperty<QQuickPathElement> *property)
{
    privatePath(property->object)->removeLastPathElement();
}
 
void QQuickPath::interpolate(int idx, const QString &name, qreal value)
{
    Q_D(QQuickPath);
    interpolate(d->_attributePoints, idx, name, value);
}
 
void QQuickPath::interpolate(QList<AttributePoint> &attributePoints, int idx, const QString &name, qreal value)
{
    if (!idx)
        return;
 
    qreal lastValue = 0;
    qreal lastPercent = 0;
    int search = idx - 1;
    while(search >= 0) {
        const AttributePoint &point = attributePoints.at(search);
        if (point.values.contains(name)) {
            lastValue = point.values.value(name);
            lastPercent = point.origpercent;
            break;
        }
        --search;
    }
 
    ++search;
 
    const AttributePoint &curPoint = attributePoints.at(idx);
 
    for (int ii = search; ii < idx; ++ii) {
        AttributePoint &point = attributePoints[ii];
 
        qreal val = lastValue + (value - lastValue) * (point.origpercent - lastPercent) / (curPoint.origpercent - lastPercent);
        point.values.insert(name, val);
    }
}
 
void QQuickPath::endpoint(const QString &name)
{
    Q_D(QQuickPath);
    const AttributePoint &first = d->_attributePoints.first();
    qreal val = first.values.value(name);
    for (int ii = d->_attributePoints.size() - 1; ii >= 0; ii--) {
        const AttributePoint &point = d->_attributePoints.at(ii);
        if (point.values.contains(name)) {
            for (int jj = ii + 1; jj < d->_attributePoints.size(); ++jj) {
                AttributePoint &setPoint = d->_attributePoints[jj];
                setPoint.values.insert(name, val);
            }
            return;
        }
    }
}
 
void QQuickPath::endpoint(QList<AttributePoint> &attributePoints, const QString &name)
{
    const AttributePoint &first = attributePoints.first();
    qreal val = first.values.value(name);
    for (int ii = attributePoints.size() - 1; ii >= 0; ii--) {
        const AttributePoint &point = attributePoints.at(ii);
        if (point.values.contains(name)) {
            for (int jj = ii + 1; jj < attributePoints.size(); ++jj) {
                AttributePoint &setPoint = attributePoints[jj];
                setPoint.values.insert(name, val);
            }
            return;
        }
    }
}
 
void QQuickPath::processPath()
{
    Q_D(QQuickPath);
 
    if (!d->componentComplete)
        return;
 
    if (!d->asynchronous) {
        doProcessPath();
    } else if (!d->processPending) {
        d->processPending = true;
        QMetaObject::invokeMethod(this, &QQuickPath::doProcessPath, Qt::QueuedConnection);
    }
}
 
void QQuickPath::doProcessPath()
{
    Q_D(QQuickPath);
 
    d->processPending = false;
 
    if (!d->componentComplete)
        return;
 
    if (d->useCustomPath)
        return;
 
    d->_pointCache.clear();
    d->prevBez.isValid = false;
 
    if (d->isShapePath) {
        // This path is a ShapePath, so avoid extra overhead
        d->_path = createShapePath(QPointF(), QPointF(), d->pathLength, &d->closed);
    } else {
        d->_path = createPath(QPointF(), QPointF(), d->_attributes, d->pathLength, d->_attributePoints, &d->closed);
    }
 
    if (d->simplify)
        d->_path = d->_path.simplified();
 
    emit changed();
}
 
inline static void scalePath(QPainterPath &path, const QSizeF &scale)
{
    const qreal xscale = scale.width();
    const qreal yscale = scale.height();
    if (xscale == 1 && yscale ==  1)
        return;
 
    for (int i = 0; i < path.elementCount(); ++i) {
        const QPainterPath::Element &element = path.elementAt(i);
        path.setElementPositionAt(i, element.x * xscale, element.y * yscale);
    }
}
 
QPainterPath QQuickPath::createPath(const QPointF &startPoint, const QPointF &endPoint, const QStringList &attributes, qreal &pathLength, QList<AttributePoint> &attributePoints, bool *closed)
{
    Q_D(QQuickPath);
 
    pathLength = 0;
    attributePoints.clear();
 
    if (!d->componentComplete)
        return QPainterPath();
 
    QPainterPath path;
 
    AttributePoint first;
    for (int ii = 0; ii < attributes.size(); ++ii)
        first.values[attributes.at(ii)] = 0;
    attributePoints << first;
 
    qreal startX = d->startX.isValid() ? d->startX.value() : startPoint.x();
    qreal startY = d->startY.isValid() ? d->startY.value() : startPoint.y();
    path.moveTo(startX, startY);
 
    const QString percentString = QStringLiteral("_qfx_percent");
 
    bool usesPercent = false;
    int index = 0;
    qCDebug(lcPath).nospace() << this << " is creating path starting at " << startPoint
        << " and ending at " << endPoint << " with " << pathLength << " element(s):";
    for (QQuickPathElement *pathElement : std::as_const(d->_pathElements)) {
        if (QQuickCurve *curve = qobject_cast<QQuickCurve *>(pathElement)) {
            QQuickPathData data;
            data.index = index;
            data.endPoint = endPoint;
            data.curves = d->_pathCurves;
            curve->addToPath(path, data);
            AttributePoint p;
            p.origpercent = path.length();
            attributePoints << p;
            ++index;
            qCDebug(lcPath) << "- index" << index << "curve:" << data.curves.at(data.index);
        } else if (QQuickPathAttribute *attribute = qobject_cast<QQuickPathAttribute *>(pathElement)) {
            AttributePoint &point = attributePoints.last();
            point.values[attribute->name()] = attribute->value();
            interpolate(attributePoints, attributePoints.size() - 1, attribute->name(), attribute->value());
            qCDebug(lcPath) << "- index" << index << "attribute:" << attribute->value();
        } else if (QQuickPathPercent *percent = qobject_cast<QQuickPathPercent *>(pathElement)) {
            AttributePoint &point = attributePoints.last();
            point.values[percentString] = percent->value();
            interpolate(attributePoints, attributePoints.size() - 1, percentString, percent->value());
            qCDebug(lcPath) << "- index" << index << "percent:" << percent->value();
            usesPercent = true;
        } else if (QQuickPathText *text = qobject_cast<QQuickPathText *>(pathElement)) {
            text->addToPath(path);
            qCDebug(lcPath) << "- index" << index << "text:" << text->text();
        }
    }
 
    // Fixup end points
    const AttributePoint &last = attributePoints.constLast();
    for (int ii = 0; ii < attributes.size(); ++ii) {
        if (!last.values.contains(attributes.at(ii)))
            endpoint(attributePoints, attributes.at(ii));
    }
    if (usesPercent && !last.values.contains(percentString)) {
        d->_attributePoints.last().values[percentString] = 1;
        interpolate(d->_attributePoints.size() - 1, percentString, 1);
    }
    scalePath(path, d->scale);
 
    // Adjust percent
    qreal length = path.length();
    qreal prevpercent = 0;
    qreal prevorigpercent = 0;
    for (int ii = 0; ii < attributePoints.size(); ++ii) {
        const AttributePoint &point = attributePoints.at(ii);
        if (point.values.contains(percentString)) { //special string for QQuickPathPercent
            if ( ii > 0) {
                qreal scale = (attributePoints[ii].origpercent/length - prevorigpercent) /
                            (point.values.value(percentString)-prevpercent);
                attributePoints[ii].scale = scale;
            }
            attributePoints[ii].origpercent /= length;
            attributePoints[ii].percent = point.values.value(percentString);
            prevorigpercent = attributePoints.at(ii).origpercent;
            prevpercent = attributePoints.at(ii).percent;
        } else {
            attributePoints[ii].origpercent /= length;
            attributePoints[ii].percent = attributePoints.at(ii).origpercent;
        }
    }
 
    if (closed) {
        QPointF end = path.currentPosition();
        *closed = length > 0 && startX * d->scale.width() == end.x() && startY * d->scale.height() == end.y();
    }
    pathLength = length;
 
    return path;
}
 
QPainterPath QQuickPath::createShapePath(const QPointF &startPoint, const QPointF &endPoint, qreal &pathLength, bool *closed)
{
    Q_D(QQuickPath);
 
    if (!d->componentComplete)
        return QPainterPath();
 
    QPainterPath path;
 
    qreal startX = d->startX.isValid() ? d->startX.value() : startPoint.x();
    qreal startY = d->startY.isValid() ? d->startY.value() : startPoint.y();
    path.moveTo(startX, startY);
 
    int index = 0;
    qCDebug(lcPath).nospace() << this << " is creating shape path from " << d->_pathCurves.size()
        << " curve(s) with endPoint " << endPoint << ":";
    for (QQuickCurve *curve : std::as_const(d->_pathCurves)) {
        QQuickPathData data;
        data.index = index;
        data.endPoint = endPoint;
        data.curves = d->_pathCurves;
        curve->addToPath(path, data);
        qCDebug(lcPath) << "- index" << data.index << data.curves.at(data.index);
        ++index;
    }
 
    for (QQuickPathText *text : std::as_const(d->_pathTexts))
        text->addToPath(path);
 
    if (closed) {
        QPointF end = path.currentPosition();
        *closed = startX == end.x() && startY == end.y();
    }
    scalePath(path, d->scale);
 
    // Note: ShapePaths do not employ the QQuickPathPrivate caching (pathLength and _pointCache),
    // but may utilize the QPainterPath caching in case of trimming
    pathLength = 0;
    path.setCachingEnabled(true);
 
    return path;
}
 
void QQuickPath::classBegin()
{
    Q_D(QQuickPath);
    d->componentComplete = false;
}
 
void QQuickPath::disconnectPathElements()
{
    Q_D(const QQuickPath);
 
    for (QQuickPathElement *pathElement : d->_pathElements) {
        if (pathElement)
            disconnect(pathElement, SIGNAL(changed()), this, SLOT(processPath()));
    }
}
 
void QQuickPath::connectPathElements()
{
    Q_D(const QQuickPath);
 
    for (QQuickPathElement *pathElement : d->_pathElements) {
        if (pathElement)
            connect(pathElement, SIGNAL(changed()), this, SLOT(processPath()));
    }
}
 
void QQuickPath::gatherAttributes()
{
    Q_D(QQuickPath);
 
    QSet<QString> attributes;
 
    Q_ASSERT(d->_pathCurves.isEmpty());
 
    // First gather up all the attributes
    for (QQuickPathElement *pathElement : std::as_const(d->_pathElements)) {
        if (QQuickCurve *curve = qobject_cast<QQuickCurve *>(pathElement))
            d->_pathCurves.append(curve);
        else if (QQuickPathText *text = qobject_cast<QQuickPathText *>(pathElement))
            d->_pathTexts.append(text);
        else if (QQuickPathAttribute *attribute = qobject_cast<QQuickPathAttribute *>(pathElement))
            attributes.insert(attribute->name());
    }
 
    d->_attributes = attributes.values();
}
 
void QQuickPath::componentComplete()
{
    Q_D(QQuickPath);
    d->componentComplete = true;
 
    // These functions do what pathElements_append does, except for all elements at once.
    gatherAttributes();
 
    doProcessPath();
 
    connectPathElements();
}
 
QPainterPath QQuickPath::path() const
{
    Q_D(const QQuickPath);
    return d->_path;
}
 
void QQuickPath::setPath(const QPainterPath &path)
{
    Q_D(QQuickPath);
    d->useCustomPath = !path.isEmpty();
    d->_pointCache.clear();
    d->prevBez.isValid = false;
    d->_path = path;
    emit changed();
}
 
QStringList QQuickPath::attributes() const
{
    Q_D(const QQuickPath);
    if (!d->componentComplete) {
        QSet<QString> attrs;
 
        // First gather up all the attributes
        for (QQuickPathElement *pathElement : d->_pathElements) {
            if (QQuickPathAttribute *attribute =
                qobject_cast<QQuickPathAttribute *>(pathElement))
                attrs.insert(attribute->name());
        }
        return attrs.values();
    }
    return d->_attributes;
}
 
static inline QBezier nextBezier(const QPainterPath &path, int *current, qreal *bezLength, bool reverse = false)
{
    const int lastElement = reverse ? 0 : path.elementCount() - 1;
    const int start = reverse ? *current - 1 : *current + 1;
    for (int i=start; reverse ? i >= lastElement : i <= lastElement; reverse ? --i : ++i) {
        const QPainterPath::Element &e = path.elementAt(i);
 
        switch (e.type) {
        case QPainterPath::MoveToElement:
            break;
        case QPainterPath::LineToElement:
        {
            QLineF line(path.elementAt(i-1), e);
            *bezLength = line.length();
            QPointF a = path.elementAt(i-1);
            QPointF delta = e - a;
            *current = i;
            return QBezier::fromPoints(a, a + delta / 3, a + 2 * delta / 3, e);
        }
        case QPainterPath::CurveToElement:
        {
            QBezier b = QBezier::fromPoints(path.elementAt(i-1),
                                            e,
                                            path.elementAt(i+1),
                                            path.elementAt(i+2));
            *bezLength = b.length();
            *current = i;
            return b;
        }
        default:
            break;
        }
    }
    *current = lastElement;
    *bezLength = 0;
    return QBezier();
}
 
static inline int segmentCount(const QPainterPath &path, qreal pathLength)
{
    // In the really simple case of a single straight line we can interpolate without jitter
    // between just two points.
    if (path.elementCount() == 2
            && path.elementAt(0).type == QPainterPath::MoveToElement
            && path.elementAt(1).type == QPainterPath::LineToElement) {
        return 1;
    }
    // more points means less jitter between items as they move along the
    // path, but takes longer to generate
    return qCeil(pathLength*5);
}
 
//derivative of the equation
static inline qreal slopeAt(qreal t, qreal a, qreal b, qreal c, qreal d)
{
    return 3*t*t*(d - 3*c + 3*b - a) + 6*t*(c - 2*b + a) + 3*(b - a);
}
 
void QQuickPath::createPointCache() const
{
    Q_D(const QQuickPath);
    qreal pathLength = d->pathLength;
    if (pathLength <= 0 || qt_is_nan(pathLength))
        return;
 
    const int segments = segmentCount(d->_path, pathLength);
    const int lastElement = d->_path.elementCount() - 1;
    d->_pointCache.resize(segments+1);
 
    int currElement = -1;
    qreal bezLength = 0;
    QBezier currBez = nextBezier(d->_path, &currElement, &bezLength);
    qreal currLength = bezLength;
    qreal epc = currLength / pathLength;
 
    for (int i = 0; i < d->_pointCache.size(); i++) {
        //find which set we are in
        qreal prevPercent = 0;
        qreal prevOrigPercent = 0;
        for (int ii = 0; ii < d->_attributePoints.size(); ++ii) {
            qreal percent = qreal(i)/segments;
            const AttributePoint &point = d->_attributePoints.at(ii);
            if (percent < point.percent || ii == d->_attributePoints.size() - 1) { //### || is special case for very last item
                qreal elementPercent = (percent - prevPercent);
 
                qreal spc = prevOrigPercent + elementPercent * point.scale;
 
                while (spc > epc) {
                    if (currElement > lastElement)
                        break;
                    currBez = nextBezier(d->_path, &currElement, &bezLength);
                    if (bezLength == 0.0) {
                        currLength = pathLength;
                        epc = 1.0;
                        break;
                    }
                    currLength += bezLength;
                    epc = currLength / pathLength;
                }
                qreal realT = (pathLength * spc - (currLength - bezLength)) / bezLength;
                d->_pointCache[i] = currBez.pointAt(qBound(qreal(0), realT, qreal(1)));
                break;
            }
            prevOrigPercent = point.origpercent;
            prevPercent = point.percent;
        }
    }
}
 
void QQuickPath::invalidateSequentialHistory() const
{
    Q_D(const QQuickPath);
    d->prevBez.isValid = false;
}
 
/*! \qmlproperty bool QtQuick::Path::simplify
    \since 6.6
 
    When set to true, the path will be simplified. This implies merging all subpaths that intersect,
    creating a path where there are no self-intersections. Consecutive parallel lines will also be
    merged. The simplified path is intended to be used with ShapePath.OddEvenFill. Bezier curves may
    be flattened to line segments due to numerical instability of doing bezier curve intersections.
*/
void QQuickPath::setSimplify(bool s)
{
    Q_D(QQuickPath);
    if (d->simplify == s)
        return;
 
    d->simplify = s;
    processPath();
 
    emit simplifyChanged();
}
 
bool QQuickPath::simplify() const
{
    Q_D(const QQuickPath);
    return d->simplify;
}
 
/*! \qmlproperty bool QtQuick::Path::asynchronous
    \since 6.9
 
    When set to true, the path will be processed asynchronously. This is an optimization
    to process the path only once, after all the methods that possibly affect the path.
    This means that when set to \c true, the updated path is not available immediately
    after e.g. adjusting \l startX, \l scale or appending an element, only after the Qt
    event loop has been processed. The default value is \c false.
*/
bool QQuickPath::isAsynchronous() const
{
    Q_D(const QQuickPath);
    return d->asynchronous;
}
 
void QQuickPath::setAsynchronous(bool a)
{
    Q_D(QQuickPath);
    if (d->asynchronous == a)
        return;
 
    d->asynchronous = a;
    emit asynchronousChanged();
}
 
/*!
    \qmlproperty size QtQuick::Path::scale
 
    This property holds the scale factor for the path.
    The width and height of \a scale can be different, to
    achieve anisotropic scaling.
 
    \note Setting this property will not affect the border width.
 
    \since QtQuick 2.14
*/
QSizeF QQuickPath::scale() const
{
    Q_D(const QQuickPath);
    return d->scale;
}
 
void QQuickPath::setScale(const QSizeF &scale)
{
    Q_D(QQuickPath);
    if (scale == d->scale)
        return;
    d->scale = scale;
    emit scaleChanged();
    processPath();
}
 
QPointF QQuickPath::sequentialPointAt(qreal p, qreal *angle) const
{
    Q_D(const QQuickPath);
    return sequentialPointAt(d->_path, d->pathLength, d->_attributePoints, d->prevBez, p, angle);
}
 
QPointF QQuickPath::sequentialPointAt(const QPainterPath &path, const qreal &pathLength, const QList<AttributePoint> &attributePoints, QQuickCachedBezier &prevBez, qreal p, qreal *angle)
{
    Q_ASSERT(p >= 0.0 && p <= 1.0);
 
    if (!prevBez.isValid)
        return p > .5 ? backwardsPointAt(path, pathLength, attributePoints, prevBez, p, angle) :
                        forwardsPointAt(path, pathLength, attributePoints, prevBez, p, angle);
 
    return p < prevBez.p ? backwardsPointAt(path, pathLength, attributePoints, prevBez, p, angle) :
                           forwardsPointAt(path, pathLength, attributePoints, prevBez, p, angle);
}
 
QPointF QQuickPath::forwardsPointAt(const QPainterPath &path, const qreal &pathLength, const QList<AttributePoint> &attributePoints, QQuickCachedBezier &prevBez, qreal p, qreal *angle)
{
    if (pathLength <= 0 || qt_is_nan(pathLength))
        return path.pointAtPercent(0);  //expensive?
 
    const int lastElement = path.elementCount() - 1;
    bool haveCachedBez = prevBez.isValid;
    int currElement = haveCachedBez ? prevBez.element : -1;
    qreal bezLength = haveCachedBez ? prevBez.bezLength : 0;
    QBezier currBez = haveCachedBez ? prevBez.bezier : nextBezier(path, &currElement, &bezLength);
    qreal currLength = haveCachedBez ? prevBez.currLength : bezLength;
    qreal epc = currLength / pathLength;
 
    //find which set we are in
    qreal prevPercent = 0;
    qreal prevOrigPercent = 0;
    for (int ii = 0; ii < attributePoints.size(); ++ii) {
        qreal percent = p;
        const AttributePoint &point = attributePoints.at(ii);
        if (percent < point.percent || ii == attributePoints.size() - 1) {
            qreal elementPercent = (percent - prevPercent);
 
            qreal spc = prevOrigPercent + elementPercent * point.scale;
 
            while (spc > epc) {
                Q_ASSERT(!(currElement > lastElement));
                Q_UNUSED(lastElement);
                currBez = nextBezier(path, &currElement, &bezLength);
                currLength += bezLength;
                epc = currLength / pathLength;
            }
            prevBez.element = currElement;
            prevBez.bezLength = bezLength;
            prevBez.currLength = currLength;
            prevBez.bezier = currBez;
            prevBez.p = p;
            prevBez.isValid = true;
 
            qreal realT = (pathLength * spc - (currLength - bezLength)) / bezLength;
 
            if (angle) {
                qreal m1 = slopeAt(realT, currBez.x1, currBez.x2, currBez.x3, currBez.x4);
                qreal m2 = slopeAt(realT, currBez.y1, currBez.y2, currBez.y3, currBez.y4);
                *angle = QLineF(0, 0, m1, m2).angle();
            }
 
            return currBez.pointAt(qBound(qreal(0), realT, qreal(1)));
        }
        prevOrigPercent = point.origpercent;
        prevPercent = point.percent;
    }
 
    return QPointF(0,0);
}
 
//ideally this should be merged with forwardsPointAt
QPointF QQuickPath::backwardsPointAt(const QPainterPath &path, const qreal &pathLength, const QList<AttributePoint> &attributePoints, QQuickCachedBezier &prevBez, qreal p, qreal *angle)
{
    if (pathLength <= 0 || qt_is_nan(pathLength))
        return path.pointAtPercent(0);
 
    const int firstElement = 1; //element 0 is always a MoveTo, which we ignore
    bool haveCachedBez = prevBez.isValid;
    int currElement = haveCachedBez ? prevBez.element : path.elementCount();
    qreal bezLength = haveCachedBez ? prevBez.bezLength : 0;
    QBezier currBez = haveCachedBez ? prevBez.bezier : nextBezier(path, &currElement, &bezLength, true /*reverse*/);
    qreal currLength = haveCachedBez ? prevBez.currLength : pathLength;
    qreal prevLength = currLength - bezLength;
    qreal epc = prevLength / pathLength;
 
    for (int ii = attributePoints.size() - 1; ii > 0; --ii) {
        qreal percent = p;
        const AttributePoint &point = attributePoints.at(ii);
        const AttributePoint &prevPoint = attributePoints.at(ii-1);
        if (percent > prevPoint.percent || ii == 1) {
            qreal elementPercent = (percent - prevPoint.percent);
 
            qreal spc = prevPoint.origpercent + elementPercent * point.scale;
 
            while (spc < epc) {
                Q_ASSERT(!(currElement < firstElement));
                Q_UNUSED(firstElement);
                currBez = nextBezier(path, &currElement, &bezLength, true /*reverse*/);
                //special case for first element is to avoid floating point math
                //causing an epc that never hits 0.
                currLength = (currElement == firstElement) ? bezLength : prevLength;
                prevLength = currLength - bezLength;
                epc = prevLength / pathLength;
            }
            prevBez.element = currElement;
            prevBez.bezLength = bezLength;
            prevBez.currLength = currLength;
            prevBez.bezier = currBez;
            prevBez.p = p;
            prevBez.isValid = true;
 
            qreal realT = (pathLength * spc - (currLength - bezLength)) / bezLength;
 
            if (angle) {
                qreal m1 = slopeAt(realT, currBez.x1, currBez.x2, currBez.x3, currBez.x4);
                qreal m2 = slopeAt(realT, currBez.y1, currBez.y2, currBez.y3, currBez.y4);
                *angle = QLineF(0, 0, m1, m2).angle();
            }
 
            return currBez.pointAt(qBound(qreal(0), realT, qreal(1)));
        }
    }
 
    return QPointF(0,0);
}
 
/*!
   \qmlmethod point Path::pointAtPercent(real t)
 
    Returns the point at the percentage \a t of the current path.
    The argument \a t has to be between 0 and 1.
 
    \note Similarly to other percent methods in \l QPainterPath,
    the percentage measurement is not linear with regards to the length,
    if curves are present in the path.
    When curves are present, the percentage argument is mapped to the \c t
    parameter of the Bezier equations.
 
   \sa QPainterPath::pointAtPercent()
 
   \since QtQuick 2.14
*/
QPointF QQuickPath::pointAtPercent(qreal t) const
{
    Q_D(const QQuickPath);
    if (d->isShapePath)
        return d->_path.pointAtPercent(t); // ShapePath has QPainterPath computation caching
 
    if (d->_pointCache.isEmpty()) {
        createPointCache();
        if (d->_pointCache.isEmpty())
            return QPointF();
    }
 
    const int segmentCount = d->_pointCache.size() - 1;
    qreal idxf = t*segmentCount;
    int idx1 = qFloor(idxf);
    qreal delta = idxf - idx1;
    if (idx1 > segmentCount)
        idx1 = segmentCount;
    else if (idx1 < 0)
        idx1 = 0;
 
    if (delta == 0.0)
        return d->_pointCache.at(idx1);
 
    // interpolate between the two points.
    int idx2 = qCeil(idxf);
    if (idx2 > segmentCount)
        idx2 = segmentCount;
    else if (idx2 < 0)
        idx2 = 0;
 
    QPointF p1 = d->_pointCache.at(idx1);
    QPointF p2 = d->_pointCache.at(idx2);
    QPointF pos = p1 * (1.0-delta) + p2 * delta;
 
    return pos;
}
 
qreal QQuickPath::attributeAt(const QString &name, qreal percent) const
{
    Q_D(const QQuickPath);
    if (percent < 0 || percent > 1)
        return 0;
 
    for (int ii = 0; ii < d->_attributePoints.size(); ++ii) {
        const AttributePoint &point = d->_attributePoints.at(ii);
 
        if (point.percent == percent) {
            return point.values.value(name);
        } else if (point.percent > percent) {
            qreal lastValue =
                ii?(d->_attributePoints.at(ii - 1).values.value(name)):0;
            qreal lastPercent =
                ii?(d->_attributePoints.at(ii - 1).percent):0;
            qreal curValue = point.values.value(name);
            qreal curPercent = point.percent;
 
            return lastValue + (curValue - lastValue) * (percent - lastPercent) / (curPercent - lastPercent);
        }
    }
 
    return 0;
}
 
/****************************************************************************/
 
qreal QQuickCurve::x() const
{
    return _x.isValid() ? _x.value() : 0;
}
 
void QQuickCurve::setX(qreal x)
{
    if (!_x.isValid() || _x != x) {
        _x = x;
        emit xChanged();
        emit changed();
    }
}
 
bool QQuickCurve::hasX()
{
    return _x.isValid();
}
 
qreal QQuickCurve::y() const
{
    return _y.isValid() ? _y.value() : 0;
}
 
void QQuickCurve::setY(qreal y)
{
    if (!_y.isValid() || _y != y) {
        _y = y;
        emit yChanged();
        emit changed();
    }
}
 
bool QQuickCurve::hasY()
{
    return _y.isValid();
}
 
qreal QQuickCurve::relativeX() const
{
    return _relativeX;
}
 
void QQuickCurve::setRelativeX(qreal x)
{
    if (!_relativeX.isValid() || _relativeX != x) {
        _relativeX = x;
        emit relativeXChanged();
        emit changed();
    }
}
 
bool QQuickCurve::hasRelativeX()
{
    return _relativeX.isValid();
}
 
qreal QQuickCurve::relativeY() const
{
    return _relativeY;
}
 
void QQuickCurve::setRelativeY(qreal y)
{
    if (!_relativeY.isValid() || _relativeY != y) {
        _relativeY = y;
        emit relativeYChanged();
        emit changed();
    }
}
 
bool QQuickCurve::hasRelativeY()
{
    return _relativeY.isValid();
}
 
#ifndef QT_NO_DEBUG_STREAM
QDebug operator<<(QDebug debug, const QQuickCurve *curve)
{
    QDebugStateSaver saver(debug);
    debug.nospace() << curve->metaObject()->className() << '(' << (const void *)curve;
    if (!curve->objectName().isEmpty())
        debug << " name=" << curve->objectName();
    debug << " x=" << curve->x();
    debug << " y=" << curve->y();
    debug << " relativeX=" << curve->relativeX();
    debug << " relativeY=" << curve->relativeY();
    debug << ')';
    return debug;
}
#endif
 
/****************************************************************************/
 
/*!
    \qmltype PathAttribute
    \nativetype QQuickPathAttribute
    \inqmlmodule QtQuick
    \ingroup qtquick-animation-paths
    \brief Specifies how to set an attribute at a given position in a Path.
 
    The PathAttribute object allows attributes consisting of a name and
    a value to be specified for various points along a path.  The
    attributes are exposed to the delegate as
    \l{Attached Properties and Attached Signal Handlers} {Attached Properties}.
    The value of an attribute at any particular point along the path is interpolated
    from the PathAttributes bounding that point.
 
    The example below shows a path with the items scaled to 30% with
    opacity 50% at the top of the path and scaled 100% with opacity
    100% at the bottom.  Note the use of the PathView.iconScale and
    PathView.iconOpacity attached properties to set the scale and opacity
    of the delegate.
 
    \table
    \row
    \li \image declarative-pathattribute.png
    \li
    \snippet qml/pathview/pathattributes.qml 0
    (see the PathView documentation for the specification of ContactModel.qml
     used for ContactModel above.)
    \endtable
 
 
    \sa Path
*/
 
/*!
    \class QQuickPathAttribute
    \inmodule QtQuick
    \internal
*/
 
/*!
    \qmlproperty string QtQuick::PathAttribute::name
    This property holds the name of the attribute to change.
 
    This attribute will be available to the delegate as PathView.<name>
 
    Note that using an existing Item property name such as "opacity" as an
    attribute is allowed.  This is because path attributes add a new
    \l{Attached Properties and Attached Signal Handlers} {Attached Property}
    which in no way clashes with existing properties.
*/
 
/*!
    the name of the attribute to change.
*/
 
QString QQuickPathAttribute::name() const
{
    return _name;
}
 
void QQuickPathAttribute::setName(const QString &name)
{
    if (_name == name)
        return;
     _name = name;
    emit nameChanged();
}
 
/*!
   \qmlproperty real QtQuick::PathAttribute::value
   This property holds the value for the attribute.
 
   The value specified can be used to influence the visual appearance
   of an item along the path. For example, the following Path specifies
   an attribute named \e itemRotation, which has the value \e 0 at the
   beginning of the path, and the value 90 at the end of the path.
 
   \qml
   Path {
       startX: 0
       startY: 0
       PathAttribute { name: "itemRotation"; value: 0 }
       PathLine { x: 100; y: 100 }
       PathAttribute { name: "itemRotation"; value: 90 }
   }
   \endqml
 
   In our delegate, we can then bind the \e rotation property to the
   \l{Attached Properties and Attached Signal Handlers} {Attached Property}
   \e PathView.itemRotation created for this attribute.
 
   \qml
   Rectangle {
       width: 10; height: 10
       rotation: PathView.itemRotation
   }
   \endqml
 
   As each item is positioned along the path, it will be rotated accordingly:
   an item at the beginning of the path with be not be rotated, an item at
   the end of the path will be rotated 90 degrees, and an item mid-way along
   the path will be rotated 45 degrees.
*/
 
/*!
    the new value of the attribute.
*/
qreal QQuickPathAttribute::value() const
{
    return _value;
}
 
void QQuickPathAttribute::setValue(qreal value)
{
    if (_value != value) {
        _value = value;
        emit valueChanged();
        emit changed();
    }
}
 
/****************************************************************************/
 
/*!
    \qmltype PathLine
    \nativetype QQuickPathLine
    \inqmlmodule QtQuick
    \ingroup qtquick-animation-paths
    \brief Defines a straight line.
 
    The example below creates a path consisting of a straight line from
    0,100 to 200,100:
 
    \qml
    Path {
        startX: 0; startY: 100
        PathLine { x: 200; y: 100 }
    }
    \endqml
 
    \sa Path, PathQuad, PathCubic, PathArc, PathAngleArc, PathCurve, PathSvg, PathMove, PathPolyline, PathRectangle
*/
 
/*!
    \qmlproperty real QtQuick::PathLine::x
    \qmlproperty real QtQuick::PathLine::y
 
    Defines the end point of the line.
 
    \sa relativeX, relativeY
*/
 
/*!
    \qmlproperty real QtQuick::PathLine::relativeX
    \qmlproperty real QtQuick::PathLine::relativeY
 
    Defines the end point of the line relative to its start.
 
    If both a relative and absolute end position are specified for a single axis, the relative
    position will be used.
 
    Relative and absolute positions can be mixed, for example it is valid to set a relative x
    and an absolute y.
 
    \sa x, y
*/
 
inline QPointF positionForCurve(const QQuickPathData &data, const QPointF &prevPoint)
{
    QQuickCurve *curve = data.curves.at(data.index);
    bool isEnd = data.index == data.curves.size() - 1;
    return QPointF(curve->hasRelativeX() ? prevPoint.x() + curve->relativeX() : !isEnd || curve->hasX() ? curve->x() : data.endPoint.x(),
                   curve->hasRelativeY() ? prevPoint.y() + curve->relativeY() : !isEnd || curve->hasY() ? curve->y() : data.endPoint.y());
}
 
void QQuickPathLine::addToPath(QPainterPath &path, const QQuickPathData &data)
{
    path.lineTo(positionForCurve(data, path.currentPosition()));
}
 
/****************************************************************************/
 
/*!
    \qmltype PathMove
    \nativetype QQuickPathMove
    \inqmlmodule QtQuick
    \ingroup qtquick-animation-paths
    \brief Moves the Path's position.
 
    The example below creates a path consisting of two horizontal lines with
    some empty space between them. All three segments have a width of 100:
 
    \qml
    Path {
        startX: 0; startY: 100
        PathLine { relativeX: 100; y: 100 }
        PathMove { relativeX: 100; y: 100 }
        PathLine { relativeX: 100; y: 100 }
    }
    \endqml
 
    \note PathMove should not be used in a Path associated with a PathView. Use
    PathLine instead. For ShapePath however it is important to distinguish
    between the operations of drawing a straight line and moving the path
    position without drawing anything.
 
    \sa Path, PathQuad, PathCubic, PathArc, PathAngleArc, PathCurve, PathSvg, PathLine
*/
 
/*!
    \qmlproperty real QtQuick::PathMove::x
    \qmlproperty real QtQuick::PathMove::y
 
    Defines the position to move to.
 
    \sa relativeX, relativeY
*/
 
/*!
    \qmlproperty real QtQuick::PathMove::relativeX
    \qmlproperty real QtQuick::PathMove::relativeY
 
    Defines the position to move to relative to its start.
 
    If both a relative and absolute end position are specified for a single axis, the relative
    position will be used.
 
    Relative and absolute positions can be mixed, for example it is valid to set a relative x
    and an absolute y.
 
    \sa x, y
*/
 
void QQuickPathMove::addToPath(QPainterPath &path, const QQuickPathData &data)
{
    path.moveTo(positionForCurve(data, path.currentPosition()));
}
 
/****************************************************************************/
 
/*!
    \qmltype PathQuad
    \nativetype QQuickPathQuad
    \inqmlmodule QtQuick
    \ingroup qtquick-animation-paths
    \brief Defines a quadratic Bezier curve with a control point.
 
    The following QML produces the path shown below:
    \table
    \row
    \li \image declarative-pathquad.png
    \li
    \qml
    Path {
        startX: 0; startY: 0
        PathQuad { x: 200; y: 0; controlX: 100; controlY: 150 }
    }
    \endqml
    \endtable
 
    \sa Path, PathCubic, PathLine, PathArc, PathAngleArc, PathCurve, PathSvg
*/
 
/*!
    \class QQuickPathQuad
    \inmodule QtQuick
    \internal
*/
 
/*!
    \qmlproperty real QtQuick::PathQuad::x
    \qmlproperty real QtQuick::PathQuad::y
 
    Defines the end point of the curve.
 
    \sa relativeX, relativeY
*/
 
/*!
    \qmlproperty real QtQuick::PathQuad::relativeX
    \qmlproperty real QtQuick::PathQuad::relativeY
 
    Defines the end point of the curve relative to its start.
 
    If both a relative and absolute end position are specified for a single axis, the relative
    position will be used.
 
    Relative and absolute positions can be mixed, for example it is valid to set a relative x
    and an absolute y.
 
    \sa x, y
*/
 
/*!
   \qmlproperty real QtQuick::PathQuad::controlX
   \qmlproperty real QtQuick::PathQuad::controlY
 
   Defines the position of the control point.
*/
 
/*!
    the x position of the control point.
*/
qreal QQuickPathQuad::controlX() const
{
    return _controlX;
}
 
void QQuickPathQuad::setControlX(qreal x)
{
    if (_controlX != x) {
        _controlX = x;
        emit controlXChanged();
        emit changed();
    }
}
 
 
/*!
    the y position of the control point.
*/
qreal QQuickPathQuad::controlY() const
{
    return _controlY;
}
 
void QQuickPathQuad::setControlY(qreal y)
{
    if (_controlY != y) {
        _controlY = y;
        emit controlYChanged();
        emit changed();
    }
}
 
/*!
   \qmlproperty real QtQuick::PathQuad::relativeControlX
   \qmlproperty real QtQuick::PathQuad::relativeControlY
 
    Defines the position of the control point relative to the curve's start.
 
    If both a relative and absolute control position are specified for a single axis, the relative
    position will be used.
 
    Relative and absolute positions can be mixed, for example it is valid to set a relative control x
    and an absolute control y.
 
    \sa controlX, controlY
*/
 
qreal QQuickPathQuad::relativeControlX() const
{
    return _relativeControlX;
}
 
void QQuickPathQuad::setRelativeControlX(qreal x)
{
    if (!_relativeControlX.isValid() || _relativeControlX != x) {
        _relativeControlX = x;
        emit relativeControlXChanged();
        emit changed();
    }
}
 
bool QQuickPathQuad::hasRelativeControlX()
{
    return _relativeControlX.isValid();
}
 
qreal QQuickPathQuad::relativeControlY() const
{
    return _relativeControlY;
}
 
void QQuickPathQuad::setRelativeControlY(qreal y)
{
    if (!_relativeControlY.isValid() || _relativeControlY != y) {
        _relativeControlY = y;
        emit relativeControlYChanged();
        emit changed();
    }
}
 
bool QQuickPathQuad::hasRelativeControlY()
{
    return _relativeControlY.isValid();
}
 
void QQuickPathQuad::addToPath(QPainterPath &path, const QQuickPathData &data)
{
    const QPointF &prevPoint = path.currentPosition();
    QPointF controlPoint(hasRelativeControlX() ? prevPoint.x() + relativeControlX() : controlX(),
                         hasRelativeControlY() ? prevPoint.y() + relativeControlY() : controlY());
    path.quadTo(controlPoint, positionForCurve(data, path.currentPosition()));
}
 
/****************************************************************************/
 
/*!
    \qmltype PathCubic
    \nativetype QQuickPathCubic
    \inqmlmodule QtQuick
    \ingroup qtquick-animation-paths
    \brief Defines a cubic Bezier curve with two control points.
 
    The following QML produces the path shown below:
    \table
    \row
    \li \image declarative-pathcubic.png
    \li
    \qml
    Path {
        startX: 20; startY: 0
        PathCubic {
            x: 180; y: 0
            control1X: -10; control1Y: 90
            control2X: 210; control2Y: 90
        }
    }
    \endqml
    \endtable
 
    \sa Path, PathQuad, PathLine, PathArc, PathAngleArc, PathCurve, PathSvg, PathRectangle
*/
 
/*!
    \qmlproperty real QtQuick::PathCubic::x
    \qmlproperty real QtQuick::PathCubic::y
 
    Defines the end point of the curve.
 
    \sa relativeX, relativeY
*/
 
/*!
    \qmlproperty real QtQuick::PathCubic::relativeX
    \qmlproperty real QtQuick::PathCubic::relativeY
 
    Defines the end point of the curve relative to its start.
 
    If both a relative and absolute end position are specified for a single axis, the relative
    position will be used.
 
    Relative and absolute positions can be mixed, for example it is valid to set a relative x
    and an absolute y.
 
    \sa x, y
*/
 
/*!
   \qmlproperty real QtQuick::PathCubic::control1X
   \qmlproperty real QtQuick::PathCubic::control1Y
 
    Defines the position of the first control point.
*/
qreal QQuickPathCubic::control1X() const
{
    return _control1X;
}
 
void QQuickPathCubic::setControl1X(qreal x)
{
    if (_control1X != x) {
        _control1X = x;
        emit control1XChanged();
        emit changed();
    }
}
 
qreal QQuickPathCubic::control1Y() const
{
    return _control1Y;
}
 
void QQuickPathCubic::setControl1Y(qreal y)
{
    if (_control1Y != y) {
        _control1Y = y;
        emit control1YChanged();
        emit changed();
    }
}
 
/*!
   \qmlproperty real QtQuick::PathCubic::control2X
   \qmlproperty real QtQuick::PathCubic::control2Y
 
    Defines the position of the second control point.
*/
qreal QQuickPathCubic::control2X() const
{
    return _control2X;
}
 
void QQuickPathCubic::setControl2X(qreal x)
{
    if (_control2X != x) {
        _control2X = x;
        emit control2XChanged();
        emit changed();
    }
}
 
qreal QQuickPathCubic::control2Y() const
{
    return _control2Y;
}
 
void QQuickPathCubic::setControl2Y(qreal y)
{
    if (_control2Y != y) {
        _control2Y = y;
        emit control2YChanged();
        emit changed();
    }
}
 
/*!
   \qmlproperty real QtQuick::PathCubic::relativeControl1X
   \qmlproperty real QtQuick::PathCubic::relativeControl1Y
   \qmlproperty real QtQuick::PathCubic::relativeControl2X
   \qmlproperty real QtQuick::PathCubic::relativeControl2Y
 
    Defines the positions of the control points relative to the curve's start.
 
    If both a relative and absolute control position are specified for a control point's axis, the relative
    position will be used.
 
    Relative and absolute positions can be mixed, for example it is valid to set a relative control1 x
    and an absolute control1 y.
 
    \sa control1X, control1Y, control2X, control2Y
*/
 
qreal QQuickPathCubic::relativeControl1X() const
{
    return _relativeControl1X;
}
 
void QQuickPathCubic::setRelativeControl1X(qreal x)
{
    if (!_relativeControl1X.isValid() || _relativeControl1X != x) {
        _relativeControl1X = x;
        emit relativeControl1XChanged();
        emit changed();
    }
}
 
bool QQuickPathCubic::hasRelativeControl1X()
{
    return _relativeControl1X.isValid();
}
 
qreal QQuickPathCubic::relativeControl1Y() const
{
    return _relativeControl1Y;
}
 
void QQuickPathCubic::setRelativeControl1Y(qreal y)
{
    if (!_relativeControl1Y.isValid() || _relativeControl1Y != y) {
        _relativeControl1Y = y;
        emit relativeControl1YChanged();
        emit changed();
    }
}
 
bool QQuickPathCubic::hasRelativeControl1Y()
{
    return _relativeControl1Y.isValid();
}
 
qreal QQuickPathCubic::relativeControl2X() const
{
    return _relativeControl2X;
}
 
void QQuickPathCubic::setRelativeControl2X(qreal x)
{
    if (!_relativeControl2X.isValid() || _relativeControl2X != x) {
        _relativeControl2X = x;
        emit relativeControl2XChanged();
        emit changed();
    }
}
 
bool QQuickPathCubic::hasRelativeControl2X()
{
    return _relativeControl2X.isValid();
}
 
qreal QQuickPathCubic::relativeControl2Y() const
{
    return _relativeControl2Y;
}
 
void QQuickPathCubic::setRelativeControl2Y(qreal y)
{
    if (!_relativeControl2Y.isValid() || _relativeControl2Y != y) {
        _relativeControl2Y = y;
        emit relativeControl2YChanged();
        emit changed();
    }
}
 
bool QQuickPathCubic::hasRelativeControl2Y()
{
    return _relativeControl2Y.isValid();
}
 
void QQuickPathCubic::addToPath(QPainterPath &path, const QQuickPathData &data)
{
    const QPointF &prevPoint = path.currentPosition();
    QPointF controlPoint1(hasRelativeControl1X() ? prevPoint.x() + relativeControl1X() : control1X(),
                          hasRelativeControl1Y() ? prevPoint.y() + relativeControl1Y() : control1Y());
    QPointF controlPoint2(hasRelativeControl2X() ? prevPoint.x() + relativeControl2X() : control2X(),
                          hasRelativeControl2Y() ? prevPoint.y() + relativeControl2Y() : control2Y());
    path.cubicTo(controlPoint1, controlPoint2, positionForCurve(data, path.currentPosition()));
}
 
/****************************************************************************/
 
/*!
    \qmltype PathCurve
    \nativetype QQuickPathCatmullRomCurve
    \inqmlmodule QtQuick
    \ingroup qtquick-animation-paths
    \brief Defines a point on a Catmull-Rom curve.
 
    PathCurve provides an easy way to specify a curve passing directly through a set of points.
    Typically multiple PathCurves are used in a series, as the following example demonstrates:
 
    \snippet qml/path/basiccurve.qml 0
 
    This example produces the following path (with the starting point and PathCurve points
    highlighted in red):
 
    \image declarative-pathcurve.png
 
    \sa Path, PathLine, PathQuad, PathCubic, PathArc, PathSvg
*/
 
/*!
    \qmlproperty real QtQuick::PathCurve::x
    \qmlproperty real QtQuick::PathCurve::y
 
    Defines the end point of the curve.
 
    \sa relativeX, relativeY
*/
 
/*!
    \qmlproperty real QtQuick::PathCurve::relativeX
    \qmlproperty real QtQuick::PathCurve::relativeY
 
    Defines the end point of the curve relative to its start.
 
    If both a relative and absolute end position are specified for a single axis, the relative
    position will be used.
 
    Relative and absolute positions can be mixed, for example it is valid to set a relative x
    and an absolute y.
 
    \sa x, y
*/
 
inline QPointF previousPathPosition(const QPainterPath &path)
{
    int count = path.elementCount();
    if (count < 1)
        return QPointF();
 
    int index = path.elementAt(count-1).type == QPainterPath::CurveToDataElement ? count - 4 : count - 2;
    return index > -1 ? QPointF(path.elementAt(index)) : path.pointAtPercent(0);
}
 
void QQuickPathCatmullRomCurve::addToPath(QPainterPath &path, const QQuickPathData &data)
{
    //here we convert catmull-rom spline to bezier for use in QPainterPath.
    //basic conversion algorithm:
    //  catmull-rom points * inverse bezier matrix * catmull-rom matrix = bezier points
    //each point in the catmull-rom spline produces a bezier endpoint + 2 control points
    //calculations for each point use a moving window of 4 points
    //  (previous 2 points + current point + next point)
    QPointF prevFar, prev, point, next;
 
    //get previous points
    int index = data.index - 1;
    QQuickCurve *curve = index == -1 ? 0 : data.curves.at(index);
    if (qobject_cast<QQuickPathCatmullRomCurve*>(curve)) {
        prev = path.currentPosition();
        prevFar = previousPathPosition(path);
    } else {
        prev = path.currentPosition();
        bool prevFarSet = false;
        if (index == -1 && data.curves.size() > 1) {
            if (qobject_cast<QQuickPathCatmullRomCurve*>(data.curves.at(data.curves.size()-1))) {
                //TODO: profile and optimize
                QPointF pos = prev;
                QQuickPathData loopData;
                loopData.endPoint = data.endPoint;
                loopData.curves = data.curves;
                for (int i = data.index; i < data.curves.size(); ++i) {
                    loopData.index = i;
                    pos = positionForCurve(loopData, pos);
                    if (i == data.curves.size()-2)
                        prevFar = pos;
                }
                if (pos == QPointF(path.elementAt(0))) {
                    //this is a closed path starting and ending with catmull-rom segments.
                    //we try to smooth the join point
                    prevFarSet = true;
                }
            }
        }
        if (!prevFarSet)
            prevFar = prev;
    }
 
    //get current point
    point = positionForCurve(data, path.currentPosition());
 
    //get next point
    index = data.index + 1;
    if (index < data.curves.size() && qobject_cast<QQuickPathCatmullRomCurve*>(data.curves.at(index))) {
        QQuickPathData nextData;
        nextData.index = index;
        nextData.endPoint = data.endPoint;
        nextData.curves = data.curves;
        next = positionForCurve(nextData, point);
    } else {
        if (point == QPointF(path.elementAt(0)) && qobject_cast<QQuickPathCatmullRomCurve*>(data.curves.at(0)) && path.elementCount() >= 3) {
            //this is a closed path starting and ending with catmull-rom segments.
            //we try to smooth the join point
            next = QPointF(path.elementAt(3));  //the first catmull-rom point
        } else
            next = point;
    }
 
    /*
        full conversion matrix (inverse bezier * catmull-rom):
        0.000,  1.000,  0.000,  0.000,
        -0.167,  1.000,  0.167,  0.000,
        0.000,  0.167,  1.000, -0.167,
        0.000,  0.000,  1.000,  0.000
 
        conversion doesn't require full matrix multiplication,
        so below we simplify
    */
    QPointF control1(prevFar.x() * qreal(-0.167) +
                     prev.x() +
                     point.x() * qreal(0.167),
                     prevFar.y() * qreal(-0.167) +
                     prev.y() +
                     point.y() * qreal(0.167));
 
    QPointF control2(prev.x() * qreal(0.167) +
                     point.x() +
                     next.x() * qreal(-0.167),
                     prev.y() * qreal(0.167) +
                     point.y() +
                     next.y() * qreal(-0.167));
 
    path.cubicTo(control1, control2, point);
}
 
/****************************************************************************/
 
/*!
    \qmltype PathArc
    \nativetype QQuickPathArc
    \inqmlmodule QtQuick
    \ingroup qtquick-animation-paths
    \brief Defines an arc with the given radius.
 
    PathArc provides a simple way of specifying an arc that ends at a given position
    and uses the specified radius. It is modeled after the SVG elliptical arc command.
 
    The following QML produces the path shown below:
    \table
    \row
    \li \image declarative-patharc.png
    \li \snippet qml/path/basicarc.qml 0
    \endtable
 
    Note that a single PathArc cannot be used to specify a circle. Instead, you can
    use two PathArc elements, each specifying half of the circle.
 
    \sa Path, PathLine, PathQuad, PathCubic, PathAngleArc, PathCurve, PathSvg
*/
 
/*!
    \qmlproperty real QtQuick::PathArc::x
    \qmlproperty real QtQuick::PathArc::y
 
    Defines the end point of the arc.
 
    \sa relativeX, relativeY
*/
 
/*!
    \qmlproperty real QtQuick::PathArc::relativeX
    \qmlproperty real QtQuick::PathArc::relativeY
 
    Defines the end point of the arc relative to its start.
 
    If both a relative and absolute end position are specified for a single axis, the relative
    position will be used.
 
    Relative and absolute positions can be mixed, for example it is valid to set a relative x
    and an absolute y.
 
    \sa x, y
*/
 
/*!
    \qmlproperty real QtQuick::PathArc::radiusX
    \qmlproperty real QtQuick::PathArc::radiusY
 
    Defines the radius of the arc.
 
    The following QML demonstrates how different radius values can be used to change
    the shape of the arc:
    \table
    \row
    \li \image declarative-arcradius.png
    \li \snippet qml/path/arcradius.qml 0
    \endtable
*/
 
qreal QQuickPathArc::radiusX() const
{
    return _radiusX;
}
 
void QQuickPathArc::setRadiusX(qreal radius)
{
    if (_radiusX == radius)
        return;
 
    _radiusX = radius;
    emit radiusXChanged();
    emit changed();
}
 
qreal QQuickPathArc::radiusY() const
{
    return _radiusY;
}
 
void QQuickPathArc::setRadiusY(qreal radius)
{
    if (_radiusY == radius)
        return;
 
    _radiusY = radius;
    emit radiusYChanged();
    emit changed();
}
 
/*!
    \qmlproperty bool QtQuick::PathArc::useLargeArc
    Whether to use a large arc as defined by the arc points.
 
    Given fixed start and end positions, radius, and direction,
    there are two possible arcs that can fit the data. useLargeArc
    is used to distinguish between these. For example, the following
    QML can produce either of the two illustrated arcs below by
    changing the value of useLargeArc.
 
    \table
    \row
    \li \image declarative-largearc.png
    \li \snippet qml/path/largearc.qml 0
    \endtable
 
    The default value is false.
*/
 
bool QQuickPathArc::useLargeArc() const
{
    return _useLargeArc;
}
 
void QQuickPathArc::setUseLargeArc(bool largeArc)
{
    if (_useLargeArc == largeArc)
        return;
 
    _useLargeArc = largeArc;
    emit useLargeArcChanged();
    emit changed();
}
 
/*!
    \qmlproperty enumeration QtQuick::PathArc::direction
 
    Defines the direction of the arc. Possible values are
    PathArc.Clockwise (default) and PathArc.Counterclockwise.
 
    The following QML can produce either of the two illustrated arcs below
    by changing the value of direction.
    \table
    \row
    \li \image declarative-arcdirection.png
    \li \snippet qml/path/arcdirection.qml 0
    \endtable
 
    \sa useLargeArc
*/
 
QQuickPathArc::ArcDirection QQuickPathArc::direction() const
{
    return _direction;
}
 
void QQuickPathArc::setDirection(ArcDirection direction)
{
    if (_direction == direction)
        return;
 
    _direction = direction;
    emit directionChanged();
    emit changed();
}
 
/*!
    \qmlproperty real QtQuick::PathArc::xAxisRotation
 
    Defines the rotation of the arc, in degrees. The default value is 0.
 
    An arc is a section of circles or ellipses. Given the radius and the start
    and end points, there are two ellipses that connect the points. This
    property defines the rotation of the X axis of these ellipses.
 
    \note The value is only useful when the x and y radius differ, meaning the
    arc is a section of ellipses.
 
    The following QML demonstrates how different radius values can be used to change
    the shape of the arc:
    \table
    \row
    \li \image declarative-arcrotation.png
    \li \snippet qml/path/arcrotation.qml 0
    \endtable
*/
 
qreal QQuickPathArc::xAxisRotation() const
{
    return _xAxisRotation;
}
 
void QQuickPathArc::setXAxisRotation(qreal rotation)
{
    if (_xAxisRotation == rotation)
        return;
 
    _xAxisRotation = rotation;
    emit xAxisRotationChanged();
    emit changed();
}
 
void QQuickPathArc::addToPath(QPainterPath &path, const QQuickPathData &data)
{
    const QPointF &startPoint = path.currentPosition();
    const QPointF &endPoint = positionForCurve(data, startPoint);
    QQuickSvgParser::pathArc(path,
            _radiusX,
            _radiusY,
            _xAxisRotation,
            _useLargeArc,
            _direction == Clockwise ? 1 : 0,
            endPoint.x(),
            endPoint.y(),
            startPoint.x(), startPoint.y());
}
 
/****************************************************************************/
 
/*!
    \qmltype PathAngleArc
    \nativetype QQuickPathAngleArc
    \inqmlmodule QtQuick
    \ingroup qtquick-animation-paths
    \brief Defines an arc with the given radii and center.
 
    PathAngleArc provides a simple way of specifying an arc. While PathArc is designed
    to work as part of a larger path (specifying start and end), PathAngleArc is designed
    to make a path where the arc is primary (such as a circular progress indicator) more intuitive.
 
    \sa Path, PathLine, PathQuad, PathCubic, PathCurve, PathSvg, PathArc, PathRectangle
*/
 
/*!
    \qmlproperty real QtQuick::PathAngleArc::centerX
    \qmlproperty real QtQuick::PathAngleArc::centerY
 
    Defines the center of the arc.
*/
 
qreal QQuickPathAngleArc::centerX() const
{
    return _centerX;
}
 
void QQuickPathAngleArc::setCenterX(qreal centerX)
{
    if (_centerX == centerX)
        return;
 
    _centerX = centerX;
    emit centerXChanged();
    emit changed();
}
 
qreal QQuickPathAngleArc::centerY() const
{
    return _centerY;
}
 
void QQuickPathAngleArc::setCenterY(qreal centerY)
{
    if (_centerY == centerY)
        return;
 
    _centerY = centerY;
    emit centerYChanged();
    emit changed();
}
 
/*!
    \qmlproperty real QtQuick::PathAngleArc::radiusX
    \qmlproperty real QtQuick::PathAngleArc::radiusY
 
    Defines the radii of the ellipse of which the arc is part.
*/
 
qreal QQuickPathAngleArc::radiusX() const
{
    return _radiusX;
}
 
void QQuickPathAngleArc::setRadiusX(qreal radius)
{
    if (_radiusX == radius)
        return;
 
    _radiusX = radius;
    emit radiusXChanged();
    emit changed();
}
 
qreal QQuickPathAngleArc::radiusY() const
{
    return _radiusY;
}
 
void QQuickPathAngleArc::setRadiusY(qreal radius)
{
    if (_radiusY == radius)
        return;
 
    _radiusY = radius;
    emit radiusYChanged();
    emit changed();
}
 
/*!
    \qmlproperty real QtQuick::PathAngleArc::startAngle
 
    Defines the start angle of the arc.
 
    The start angle is reported clockwise, with zero degrees at the 3 o'clock position.
*/
 
qreal QQuickPathAngleArc::startAngle() const
{
    return _startAngle;
}
 
void QQuickPathAngleArc::setStartAngle(qreal angle)
{
    if (_startAngle == angle)
        return;
 
    _startAngle = angle;
    emit startAngleChanged();
    emit changed();
}
 
/*!
    \qmlproperty real QtQuick::PathAngleArc::sweepAngle
 
    Defines the sweep angle of the arc.
 
    The arc will begin at startAngle and continue sweepAngle degrees, with a value of 360
    resulting in a full circle. Positive numbers are clockwise and negative numbers are counterclockwise.
*/
 
qreal QQuickPathAngleArc::sweepAngle() const
{
    return _sweepAngle;
}
 
void QQuickPathAngleArc::setSweepAngle(qreal angle)
{
    if (_sweepAngle == angle)
        return;
 
    _sweepAngle = angle;
    emit sweepAngleChanged();
    emit changed();
}
 
/*!
    \qmlproperty bool QtQuick::PathAngleArc::moveToStart
 
    Whether this element should be disconnected from the previous Path element (or startX/Y).
 
    The default value is true. If set to false, the previous element's end-point
    (or startX/Y if PathAngleArc is the first element) will be connected to the arc's
    start-point with a straight line.
*/
 
bool QQuickPathAngleArc::moveToStart() const
{
    return _moveToStart;
}
 
void QQuickPathAngleArc::setMoveToStart(bool move)
{
    if (_moveToStart == move)
        return;
 
    _moveToStart = move;
    emit moveToStartChanged();
    emit changed();
}
 
void QQuickPathAngleArc::addToPath(QPainterPath &path, const QQuickPathData &)
{
    qreal x = _centerX - _radiusX;
    qreal y = _centerY - _radiusY;
    qreal width = _radiusX * 2;
    qreal height = _radiusY * 2;
    if (_moveToStart)
        path.arcMoveTo(x, y, width, height, -_startAngle);
    path.arcTo(x, y, width, height, -_startAngle, -_sweepAngle);
}
 
/****************************************************************************/
 
/*!
    \qmltype PathSvg
    \nativetype QQuickPathSvg
    \inqmlmodule QtQuick
    \ingroup qtquick-animation-paths
    \brief Defines a path using an SVG path data string.
 
    The following QML produces the path shown below:
    \table
    \row
    \li \image declarative-pathsvg.png
    \li
    \qml
    Path {
        startX: 50; startY: 50
        PathSvg { path: "L 150 50 L 100 150 z" }
    }
    \endqml
    \endtable
 
    \sa Path, PathLine, PathQuad, PathCubic, PathArc, PathAngleArc, PathCurve
*/
 
/*!
    \qmlproperty string QtQuick::PathSvg::path
 
    The SVG path data string specifying the path.
 
    See \l {http://www.w3.org/TR/SVG/paths.html#PathData}{W3C SVG Path Data}
    for more details on this format.
*/
 
QString QQuickPathSvg::path() const
{
    return _path;
}
 
void QQuickPathSvg::setPath(const QString &path)
{
    if (_path == path)
        return;
 
    _path = path;
    emit pathChanged();
    emit changed();
}
 
void QQuickPathSvg::addToPath(QPainterPath &path, const QQuickPathData &)
{
    QQuickSvgParser::parsePathDataFast(_path, path);
}
 
/****************************************************************************/
 
/*!
    \qmltype PathRectangle
    \nativetype QQuickPathRectangle
    \inqmlmodule QtQuick
    \ingroup qtquick-animation-paths
    \brief Defines a rectangle with optionally rounded corners.
    \since QtQuick 6.8
 
    PathRectangle provides an easy way to specify a rectangle, optionally with
    rounded or beveled corners. The API corresponds to that of the \l Rectangle
    item.
 
    \image pathrectangle-bevel.png
 
    \snippet qml/pathrectangle/pathrectangle-bevel.qml shape
 
    \sa Path, PathLine, PathQuad, PathCubic, PathArc, PathAngleArc, PathCurve, PathSvg
*/
 
/*!
    \qmlproperty real QtQuick::PathRectangle::x
    \qmlproperty real QtQuick::PathRectangle::y
 
    Defines the top left corner of the rectangle.
 
    Unless that corner is rounded, this will also be the start and end point of the path.
 
    \sa relativeX, relativeY
*/
 
/*!
    \qmlproperty real QtQuick::PathRectangle::relativeX
    \qmlproperty real QtQuick::PathRectangle::relativeY
 
    Defines the top left corner of the rectangle relative to the path's start point.
 
    If both a relative and absolute end position are specified for a single axis, the relative
    position will be used.
 
    Relative and absolute positions can be mixed, for example it is valid to set a relative x
    and an absolute y.
 
    \sa x, y
*/
 
/*!
    \qmlproperty real QtQuick::PathRectangle::width
    \qmlproperty real QtQuick::PathRectangle::height
 
    Defines the width and height of the rectangle.
 
    \sa x, y
*/
 
qreal QQuickPathRectangle::width() const
{
    return _width;
}
 
void QQuickPathRectangle::setWidth(qreal width)
{
    if (_width == width)
        return;
 
    _width = width;
    emit widthChanged();
    emit changed();
}
 
qreal QQuickPathRectangle::height() const
{
    return _height;
}
 
void QQuickPathRectangle::setHeight(qreal height)
{
    if (_height == height)
        return;
 
    _height = height;
    emit heightChanged();
    emit changed();
}
 
/*!
    \qmlproperty real QtQuick::PathRectangle::strokeAdjustment
 
    This property defines the stroke width adjustment to the rectangle coordinates.
 
    When used in a \l ShapePath with stroking enabled, the actual stroked rectangle will by default
    extend beyond the defined rectangle by half the stroke width on all sides. This is the expected
    behavior since the path defines the midpoint line of the stroking, and corresponds to QPainter
    and SVG rendering.
 
    If one instead wants the defined rectangle to be the outer edge of the stroked rectangle, like
    a \l Rectangle item with a border, one can set strokeAdjustment to the stroke width. This will
    effectively shift all edges inwards by half the stroke width. Like in the following example:
 
    \qml
    ShapePath {
        id: myRec
        fillColor: "white"
        strokeColor: "black"
        strokeWidth: 16
        joinStyle: ShapePath.MiterJoin
 
        PathRectangle { x: 10; y: 10; width: 200; height: 100; strokeAdjustment: myRec.strokeWidth }
    }
    \endqml
*/
 
qreal QQuickPathRectangle::strokeAdjustment() const
{
    return _strokeAdjustment;
}
 
void QQuickPathRectangle::setStrokeAdjustment(qreal newStrokeAdjustment)
{
    if (_strokeAdjustment == newStrokeAdjustment)
        return;
    _strokeAdjustment = newStrokeAdjustment;
    emit strokeAdjustmentChanged();
    emit changed();
}
 
/*!
    \include pathrectangle.qdocinc {radius-property} {QtQuick::PathRectangle}
 
    The default value is \c 0.
*/
 
qreal QQuickPathRectangle::radius() const
{
    return _extra.isAllocated() ? _extra->radius : 0;
}
 
void QQuickPathRectangle::setRadius(qreal newRadius)
{
    if (_extra.value().radius == newRadius)
        return;
    _extra->radius = newRadius;
    emit radiusChanged();
    if (!(_extra->isRadiusSet(Qt::TopLeftCorner)))
        emit topLeftRadiusChanged();
    if (!(_extra->isRadiusSet(Qt::TopRightCorner)))
        emit topRightRadiusChanged();
    if (!(_extra->isRadiusSet(Qt::BottomLeftCorner)))
        emit bottomLeftRadiusChanged();
    if (!(_extra->isRadiusSet(Qt::BottomRightCorner)))
        emit bottomRightRadiusChanged();
    emit changed();
}
 
/*!
    \include pathrectangle.qdocinc {radius-properties} {PathRectangle} {qml/pathrectangle/pathrectangle.qml} {shape}
*/
 
qreal QQuickPathRectangle::cornerRadius(Qt::Corner corner) const
{
    if (_extra.isAllocated())
        return (_extra->isRadiusSet(corner)) ? _extra->cornerRadii[corner] : _extra->radius;
    else
        return 0;
}
 
void QQuickPathRectangle::setCornerRadius(Qt::Corner corner, qreal newCornerRadius)
{
    if (_extra.value().cornerRadii[corner] == newCornerRadius
        && (_extra->isRadiusSet(corner)))
        return;
    _extra->cornerRadii[corner] = newCornerRadius;
    _extra->cornerProperties |= (1 << corner);
 
    emitCornerRadiusChanged(corner);
}
 
void QQuickPathRectangle::resetCornerRadius(Qt::Corner corner)
{
    if (!_extra.isAllocated() || !(_extra->isRadiusSet(corner)))
        return;
    _extra->cornerProperties &= ~(1 << corner);
    emitCornerRadiusChanged(corner);
}
 
void QQuickPathRectangle::emitCornerRadiusChanged(Qt::Corner corner)
{
    switch (corner) {
    case Qt::TopLeftCorner:
        emit topLeftRadiusChanged();
        break;
    case Qt::TopRightCorner:
        emit topRightRadiusChanged();
        break;
    case Qt::BottomLeftCorner:
        emit bottomLeftRadiusChanged();
        break;
    case Qt::BottomRightCorner:
        emit bottomRightRadiusChanged();
        break;
    }
    emit changed();
}
 
/*!
    \include pathrectangle.qdocinc {bevel-property}
        {QtQuick::PathRectangle}{qml/pathrectangle/pathrectangle-bevel.qml}
        {shape}
    \since 6.10
*/
 
bool QQuickPathRectangle::hasBevel() const
{
    return _extra.isAllocated() ? (_extra->cornerProperties & (1 << 8)) != 0 : false;
}
 
void QQuickPathRectangle::setBevel(bool bevel)
{
    if (((_extra.value().cornerProperties & (1 << 8)) != 0) == bevel)
        return;
    if (bevel)
        _extra->cornerProperties |= (1 << 8);
    else
        _extra->cornerProperties &= ~(1 << 8);
 
    emit bevelChanged();
    if (!(_extra->isBevelSet(Qt::TopLeftCorner)))
        emit topLeftBevelChanged();
    if (!(_extra->isBevelSet(Qt::TopRightCorner)))
        emit topRightBevelChanged();
    if (!(_extra->isBevelSet(Qt::BottomLeftCorner)))
        emit bottomLeftBevelChanged();
    if (!(_extra->isBevelSet(Qt::BottomRightCorner)))
        emit bottomRightBevelChanged();
    emit changed();
}
/*!
    \include pathrectangle.qdocinc {bevel-properties}
        {QtQuick::PathRectangle} {qml/pathrectangle/pathrectangle.qml} {shape}
*/
 
bool QQuickPathRectangle::cornerBevel(Qt::Corner corner) const
{
    if (_extra.isAllocated())
        return _extra->isBevelSet(corner);
    else
        return false;
}
 
void QQuickPathRectangle::setCornerBevel(Qt::Corner corner, bool newCornerBevel)
{
    if ((_extra.value().isBevelSet(corner)) == newCornerBevel)
        return;
    if (!newCornerBevel) {
        resetCornerBevel(corner);
        return;
    }
    _extra->cornerProperties |= (1 << (corner + 4));
    emitCornerBevelChanged(corner);
}
 
void QQuickPathRectangle::resetCornerBevel(Qt::Corner corner)
{
    if (!_extra.isAllocated() || !(_extra->isBevelSet(corner)))
        return;
    _extra->cornerProperties &= ~(1 << (corner + 4));
    emitCornerBevelChanged(corner);
}
 
void QQuickPathRectangle::emitCornerBevelChanged(Qt::Corner corner)
{
    switch (corner) {
    case Qt::TopLeftCorner:
        emit topLeftBevelChanged();
        break;
    case Qt::TopRightCorner:
        emit topRightBevelChanged();
        break;
    case Qt::BottomLeftCorner:
        emit bottomLeftBevelChanged();
        break;
    case Qt::BottomRightCorner:
        emit bottomRightBevelChanged();
        break;
    }
    emit changed();
}
 
void QQuickPathRectangle::addToPath(QPainterPath &path, const QQuickPathData &data)
{
    QRectF rect(positionForCurve(data, path.currentPosition()), QSizeF(_width, _height));
 
    qreal halfStroke = _strokeAdjustment * 0.5;
    rect.adjust(halfStroke, halfStroke, -halfStroke, -halfStroke);
    if (rect.isEmpty())
        return;
 
    if (!_extra.isAllocated()) {
        // No rounded corners
        path.addRect(rect);
    } else {
        // Radii must not exceed half of the width or half of the height
        const qreal maxDiameter = qMin(rect.width(), rect.height());
        const qreal generalDiameter = qMax(qreal(0), qMin(maxDiameter, 2 * _extra->radius));
        auto effectiveDiameter = [&](Qt::Corner corner) {
            qreal radius = _extra->cornerRadii[corner];
            return (_extra->isRadiusSet(corner)) ? qMin(maxDiameter, 2 * radius) : generalDiameter;
        };
        const qreal diamTL = effectiveDiameter(Qt::TopLeftCorner);
        const qreal diamTR = effectiveDiameter(Qt::TopRightCorner);
        const qreal diamBL = effectiveDiameter(Qt::BottomLeftCorner);
        const qreal diamBR = effectiveDiameter(Qt::BottomRightCorner);
 
        path.moveTo(rect.left() + diamTL * 0.5, rect.top());
        if (diamTR) {
            if (!cornerBevel(Qt::TopRightCorner)) {
                // Rounded corners.
                path.arcTo(QRectF(QPointF(rect.right() - diamTR, rect.top()), QSizeF(diamTR, diamTR)), 90, -90);
            } else {
                // Beveled corners.
                path.lineTo(QPointF(rect.right() - diamTR * 0.5, rect.top()));
                path.lineTo(QPointF(rect.right(), rect.top() + diamTR * 0.5));
            }
        } else {
            // Regular corners.
            path.lineTo(rect.topRight());
        }
 
        if (diamBR) {
            if (!cornerBevel(Qt::BottomRightCorner)) {
                path.arcTo(QRectF(QPointF(rect.right() - diamBR, rect.bottom() - diamBR), QSizeF(diamBR, diamBR)), 0, -90);
            } else {
                path.lineTo(QPointF(rect.right(), rect.bottom() - diamBR * 0.5));
                path.lineTo(QPointF(rect.right() - diamBR * 0.5, rect.bottom()));
            }
        } else {
            path.lineTo(rect.bottomRight());
        }
 
        if (diamBL) {
            if (!cornerBevel(Qt::BottomLeftCorner)) {
                path.arcTo(QRectF(QPointF(rect.left(), rect.bottom() - diamBL), QSizeF(diamBL, diamBL)), 270, -90);
            } else {
                path.lineTo(QPointF(rect.left() + diamBL * 0.5, rect.bottom()));
                path.lineTo(QPointF(rect.left(), rect.bottom() - diamBL * 0.5));
            }
        } else {
            path.lineTo(rect.bottomLeft());
        }
 
        if (diamTL) {
            if (!cornerBevel(Qt::TopLeftCorner))
                path.arcTo(QRectF(rect.topLeft(), QSizeF(diamTL, diamTL)), 180, -90);
            else
                path.lineTo(QPointF(rect.left(), rect.top() + diamTL * 0.5));
        } else {
            path.lineTo(rect.topLeft());
        }
        path.closeSubpath();
    }
}
 
/****************************************************************************/
 
/*!
    \qmltype PathPercent
    \nativetype QQuickPathPercent
    \inqmlmodule QtQuick
    \ingroup qtquick-animation-paths
    \brief Manipulates the way a path is interpreted.
 
    PathPercent allows you to manipulate the spacing between items on a
    PathView's path. You can use it to bunch together items on part of
    the path, and spread them out on other parts of the path.
 
    The examples below show the normal distribution of items along a path
    compared to a distribution which places 50% of the items along the
    PathLine section of the path.
    \table
    \row
    \li \image declarative-nopercent.png
    \li
    \qml
    PathView {
        // ...
        Path {
            startX: 20; startY: 0
            PathQuad { x: 50; y: 80; controlX: 0; controlY: 80 }
            PathLine { x: 150; y: 80 }
            PathQuad { x: 180; y: 0; controlX: 200; controlY: 80 }
        }
    }
    \endqml
    \row
    \li \image declarative-percent.png
    \li
    \qml
    PathView {
        // ...
        Path {
            startX: 20; startY: 0
            PathQuad { x: 50; y: 80; controlX: 0; controlY: 80 }
            PathPercent { value: 0.25 }
            PathLine { x: 150; y: 80 }
            PathPercent { value: 0.75 }
            PathQuad { x: 180; y: 0; controlX: 200; controlY: 80 }
            PathPercent { value: 1 }
        }
    }
    \endqml
    \endtable
 
    \sa Path
*/
 
/*!
    \qmlproperty real QtQuick::PathPercent::value
    The proportion of items that should be laid out up to this point.
 
    This value should always be higher than the last value specified
    by a PathPercent at a previous position in the Path.
 
    In the following example we have a Path made up of three PathLines.
    Normally, the items of the PathView would be laid out equally along
    this path, with an equal number of items per line segment. PathPercent
    allows us to specify that the first and third lines should each hold
    10% of the laid out items, while the second line should hold the remaining
    80%.
 
    \qml
    PathView {
        // ...
        Path {
            startX: 0; startY: 0
            PathLine { x:100; y: 0; }
            PathPercent { value: 0.1 }
            PathLine { x: 100; y: 100 }
            PathPercent { value: 0.9 }
            PathLine { x: 100; y: 0 }
            PathPercent { value: 1 }
        }
    }
    \endqml
*/
 
qreal QQuickPathPercent::value() const
{
    return _value;
}
 
void QQuickPathPercent::setValue(qreal value)
{
    if (_value != value) {
        _value = value;
        emit valueChanged();
        emit changed();
    }
}
 
/*!
    \qmltype PathPolyline
    \nativetype QQuickPathPolyline
    \inqmlmodule QtQuick
    \ingroup qtquick-animation-paths
    \brief Defines a polyline through a list of coordinates.
    \since QtQuick 2.14
 
    The example below creates a triangular path consisting of four vertices
    on the edge of the containing Shape's bounding box.
    Through the containing shape's \l {QtQuick::Path::}{scale} property,
    the path will be rescaled together with its containing shape.
 
    \qml
    PathPolyline {
        id: ppl
        path: [ Qt.point(0.0, 0.0),
                Qt.point(1.0, 0.0),
                Qt.point(0.5, 1.0),
                Qt.point(0.0, 0.0)
              ]
    }
    \endqml
 
    \sa Path, PathQuad, PathCubic, PathArc, PathAngleArc, PathCurve, PathSvg, PathMove
*/
 
/*!
    \qmlproperty point QtQuick::PathPolyline::start
 
    This read-only property contains the beginning of the polyline.
*/
 
/*!
    \qmlproperty list<point> QtQuick::PathPolyline::path
 
    This property defines the vertices of the polyline.
 
    It can be a JS array of points constructed with \c Qt.point(),
    a QList or QVector of QPointF, or QPolygonF.
    If you are binding this to a custom property in some C++ object,
    QPolygonF is the most appropriate type to use.
*/
 
QQuickPathPolyline::QQuickPathPolyline(QObject *parent) : QQuickCurve(parent)
{
}
 
QVariant QQuickPathPolyline::path() const
{
    return QVariant::fromValue(m_path);
}
 
void QQuickPathPolyline::setPath(const QVariant &path)
{
    if (path.userType() == QMetaType::QPolygonF) {
        setPath(path.value<QPolygonF>());
    } else if (path.canConvert<QList<QPointF>>()) {
        setPath(path.value<QList<QPointF>>());
    } else if (path.canConvert<QVariantList>()) {
        // This handles cases other than QPolygonF or QList<QPointF>, such as
        // QList<QPointF>, QList<QPoint>, QVariantList of QPointF, QVariantList of QPoint.
        QList<QPointF> pathList;
        QVariantList vl = path.value<QVariantList>();
        // If path is a QJSValue, e.g. coming from a JS array of Qt.point() in QML,
        // then path.value<QVariantList>() is inefficient.
        // TODO We should be able to iterate over path.value<QMetaSequence::Iterable>() eventually
        for (const QVariant &v : vl)
            pathList.append(v.toPointF());
        setPath(pathList);
    } else {
        qWarning() << "PathPolyline: path of type" << path.userType() << "not supported";
    }
}
 
void QQuickPathPolyline::setPath(const QList<QPointF> &path)
{
    if (m_path != path) {
        const QPointF &oldStart = start();
        m_path = path;
        const QPointF &newStart = start();
        emit pathChanged();
        if (oldStart != newStart)
            emit startChanged();
        emit changed();
    }
}
 
QPointF QQuickPathPolyline::start() const
{
    if (m_path.size()) {
        const QPointF &p = m_path.first();
        return p;
    }
    return QPointF();
}
 
void QQuickPathPolyline::addToPath(QPainterPath &path, const QQuickPathData &/*data*/)
{
    if (m_path.size() < 2)
        return;
 
    path.moveTo(m_path.first());
    for (int i = 1; i < m_path.size(); ++i)
        path.lineTo(m_path.at(i));
}
 
 
/*!
    \qmltype PathMultiline
    \nativetype QQuickPathMultiline
    \inqmlmodule QtQuick
    \ingroup qtquick-animation-paths
    \brief Defines a set of polylines through a list of lists of coordinates.
    \since QtQuick 2.14
 
    This element allows to define a list of polylines at once.
    Each polyline in the list will be preceded by a \l{QPainterPath::moveTo}{moveTo}
    command, effectively making each polyline a separate one.
    The polylines in this list are supposed to be non-intersecting with each other.
    In any case, when used in conjunction with a \l ShapePath, the containing ShapePath's
    \l ShapePath::fillRule applies.
    That is, with the default \c OddEvenFill and non intersecting shapes, the largest shape in the list defines an area to be filled;
    areas where two shapes overlap are holes; areas where three shapes overlap are filled areas inside holes, etc.
 
    The example below creates a high voltage symbol by adding each path
    of the symbol to the list of paths.
    The coordinates of the vertices are normalized, and through the containing shape's
    \l {QtQuick::Path::}{scale} property, the path will be rescaled together with its containing shape.
 
    \qml
    PathMultiline {
        paths: [
                [Qt.point(0.5,     0.06698),
                 Qt.point(1,       0.93301),
                 Qt.point(0,       0.93301),
                 Qt.point(0.5,     0.06698)],
 
                [Qt.point(0.5,     0.12472),
                 Qt.point(0.95,    0.90414),
                 Qt.point(0.05,    0.90414),
                 Qt.point(0.5,     0.12472)],
 
                [Qt.point(0.47131, 0.32986),
                 Qt.point(0.36229, 0.64789),
                 Qt.point(0.51492, 0.58590),
                 Qt.point(0.47563, 0.76014),
                 Qt.point(0.44950, 0.73590),
                 Qt.point(0.46292, 0.83392),
                 Qt.point(0.52162, 0.75190),
                 Qt.point(0.48531, 0.76230),
                 Qt.point(0.57529, 0.53189),
                 Qt.point(0.41261, 0.59189),
                 Qt.point(0.53001, 0.32786),
                 Qt.point(0.47131, 0.32986)]
               ]
    }
    \endqml
 
    \sa Path, QPainterPath::setFillRule, PathPolyline, PathQuad, PathCubic, PathArc, PathAngleArc, PathCurve, PathSvg, PathMove
*/
 
/*!
    \qmlproperty point QtQuick::PathMultiline::start
 
    This read-only property contains the beginning of the polylines.
*/
 
/*!
    \qmlproperty list<list<point>> QtQuick::PathMultiline::paths
 
    This property defines the vertices of the polylines.
 
    It can be a JS array of JS arrays of points constructed with \c Qt.point(),
    a QList or QVector of QPolygonF, or QList<QList<QPointF>>.
    If you are binding this to a custom property in some C++ object,
    QList<QPolygonF> or QList<QList<QPointF>> is the most
    appropriate type to use.
*/
 
QQuickPathMultiline::QQuickPathMultiline(QObject *parent) : QQuickCurve(parent)
{
}
 
QVariant QQuickPathMultiline::paths() const
{
    return QVariant::fromValue(m_paths);
}
 
void QQuickPathMultiline::setPaths(const QVariant &paths)
{
    if (paths.canConvert<QList<QPolygonF>>()) {
        const QList<QPolygonF> pathPolygons = paths.value<QList<QPolygonF>>();
        QList<QList<QPointF>> pathVectors;
        for (const QPolygonF &p : pathPolygons)
            pathVectors << p;
        setPaths(pathVectors);
    } else if (paths.canConvert<QList<QList<QPointF>>>()) {
        setPaths(paths.value<QList<QList<QPointF>>>());
    } else if (paths.canConvert<QVariantList>()) {
        // This handles cases other than QList<QPolygonF> or QList<QList<QPointF>>, such as
        // QList<QList<QPointF>>, QList<QList<QPointF>>, QVariantList of QList<QPointF>,
        // QVariantList of QVariantList of QPointF, QList<QList<QPoint>> etc.
        QList<QList<QPointF>> pathsList;
        QVariantList vll = paths.value<QVariantList>();
        for (const QVariant &v : vll) {
            // If we bind a QList<QPolygonF> property directly, rather than via QVariant,
            // it will come through as QJSValue that can be converted to QVariantList of QPolygonF.
            if (v.canConvert<QPolygonF>()) {
                pathsList.append(v.value<QPolygonF>());
            } else {
                QVariantList vl = v.value<QVariantList>();
                QList<QPointF> l;
                for (const QVariant &point : vl) {
                    if (point.canConvert<QPointF>())
                        l.append(point.toPointF());
                }
                if (l.size() >= 2)
                    pathsList.append(l);
            }
        }
        setPaths(pathsList);
    } else {
        qWarning() << "PathMultiline: paths of type" << paths.userType() << "not supported";
        setPaths(QList<QList<QPointF>>());
    }
}
 
void QQuickPathMultiline::setPaths(const QList<QList<QPointF>> &paths)
{
    if (m_paths != paths) {
        const QPointF &oldStart = start();
        m_paths = paths;
        const QPointF &newStart = start();
        emit pathsChanged();
        if (oldStart != newStart)
            emit startChanged();
        emit changed();
    }
}
 
QPointF QQuickPathMultiline::start() const
{
    if (m_paths.size())
        return m_paths.first().first();
    return QPointF();
}
 
void QQuickPathMultiline::addToPath(QPainterPath &path, const QQuickPathData &)
{
    if (!m_paths.size())
        return;
    for (const QList<QPointF> &p: m_paths) {
        path.moveTo(p.first());
        for (int i = 1; i < p.size(); ++i)
            path.lineTo(p.at(i));
    }
}
 
/*!
    \qmltype PathText
    \nativetype QQuickPathText
    \inqmlmodule QtQuick
    \ingroup qtquick-animation-paths
    \brief Defines a string in a specified font.
    \since QtQuick 2.15
 
    This element defines the shape of a specified string in a specified font. The text's
    baseline will be translated to the x and y coordinates, and the outlines from the font
    will be added to the path accordingly.
 
    When used to render texts in a Shape item, note the following:
    \list
        \li For correct fill, the ShapePath's fillRule should be set to ShapePath.WindingFill.
        \li Not all fonts provide a nice outline suitable for stroking. If you want a stroked
            outline and are getting unsatisfactory results, try a different font.
    \endlist
 
    \qml
    PathText {
        x: 0
        y: font.pixelSize
        font.family: "Arial"
        font.pixelSize: 100
        text: "Foobar"
    }
    \endqml
 
    \sa Path, QPainterPath::setFillRule, PathPolyline, PathQuad, PathCubic, PathArc, PathAngleArc, PathCurve, PathSvg, PathMove
*/
 
/*!
    \qmlproperty real QtQuick::PathText::x
 
    The horizontal position of the PathText's baseline.
*/
 
/*!
    \qmlproperty real QtQuick::PathText::y
 
    The vertical position of the PathText's baseline.
 
    \note This property refers to the position of the baseline of the text, not the top of its bounding box. This may
    cause some confusion, e.g. when using the PathText with Qt Quick Shapes. See \l FontMetrics for information on how to
    get the ascent of a font, which can be used to translate the text into the expected position.
*/
 
/*!
    \qmlproperty string QtQuick::PathText::text
 
    The text for which this PathText should contain the outlines.
*/
 
/*!
    \qmlproperty string QtQuick::PathText::font.family
 
    Sets the family name of the font.
 
    \include qmltypereference.qdoc qml-font-family
*/
 
/*!
    \qmlproperty string QtQuick::PathText::font.styleName
 
    Sets the style name of the font.
 
    The style name is case insensitive. If set, the font will be matched against style name instead
    of the font properties \l font.weight, \l font.bold and \l font.italic.
*/
 
/*!
    \qmlproperty bool QtQuick::PathText::font.bold
 
    Sets whether the font weight is bold.
*/
 
/*!
    \qmlproperty int QtQuick::PathText::font.weight
 
    Sets the font's weight.
 
    The weight can be one of:
 
    \value Font.Thin        100
    \value Font.ExtraLight  200
    \value Font.Light       300
    \value Font.Normal      400 (default)
    \value Font.Medium      500
    \value Font.DemiBold    600
    \value Font.Bold        700
    \value Font.ExtraBold   800
    \value Font.Black       900
 
    \qml
    PathText { text: "Hello"; font.weight: Font.DemiBold }
    \endqml
*/
 
/*!
    \qmlproperty bool QtQuick::PathText::font.italic
 
    Sets whether the font has an italic style.
*/
 
/*!
    \qmlproperty bool QtQuick::PathText::font.underline
 
    Sets whether the text is underlined.
*/
 
/*!
    \qmlproperty bool QtQuick::PathText::font.strikeout
 
    Sets whether the font has a strikeout style.
*/
 
/*!
    \qmlproperty real QtQuick::PathText::font.pointSize
 
    Sets the font size in points. The point size must be greater than zero.
*/
 
/*!
    \qmlproperty int QtQuick::PathText::font.pixelSize
 
    Sets the font size in pixels.
 
    Using this function makes the font device dependent.
    Use \c pointSize to set the size of the font in a device independent manner.
*/
 
/*!
    \qmlproperty real QtQuick::PathText::font.letterSpacing
 
    Sets the letter spacing for the font.
 
   \include qmltypereference.qdoc qml-font-letter-spacing
*/
 
/*!
    \qmlproperty real QtQuick::PathText::font.wordSpacing
 
    Sets the word spacing for the font.
 
    \include qmltypereference.qdoc qml-font-word-spacing
*/
 
/*!
    \qmlproperty enumeration QtQuick::PathText::font.capitalization
 
    Sets the capitalization for the text.
 
    \include qmltypereference.qdoc qml-font-capitalization
*/
 
/*!
    \qmlproperty bool QtQuick::PathText::font.kerning
 
    \include qmltypereference.qdoc qml-font-kerning
*/
 
/*!
    \qmlproperty bool QtQuick::PathText::font.preferShaping
 
    \include qmltypereference.qdoc qml-font-prefer-shaping
*/
 
/*!
    \qmlproperty object QtQuick::PathText::font.variableAxes
    \since 6.7
 
    \include qmltypereference.qdoc qml-font-variable-axes
*/
 
/*!
    \qmlproperty object QtQuick::PathText::font.features
    \since 6.6
 
    \include qmltypereference.qdoc qml-font-features
*/
 
/*!
    \qmlproperty bool QtQuick::PathText::font.contextFontMerging
    \since 6.8
 
    \include qmltypereference.qdoc qml-font-context-font-merging
*/
 
/*!
    \qmlproperty bool QtQuick::PathText::font.preferTypoLineMetrics
    \since 6.8
 
    \include qmltypereference.qdoc qml-font-prefer-typo-line-metrics
*/
void QQuickPathText::updatePath() const
{
    if (!_path.isEmpty())
        return;
 
    _path.addText(0.0, 0.0, _font, _text);
 
    // Account for distance from baseline to top, since addText() takes baseline position
    QRectF brect = _path.boundingRect();
    _path.translate(_x, _y - brect.y());
}
 
void QQuickPathText::addToPath(QPainterPath &path)
{
    if (_text.isEmpty())
        return;
    updatePath();
    path.addPath(_path);
}
 
QT_END_NAMESPACE
 
#include "moc_qquickpath_p.cpp"