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
 
#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
 
QQuickPath::QQuickPath(QObject *parent)
 : QObject(*(new QQuickPathPrivate), parent)
{
}
 
QQuickPath::QQuickPath(QQuickPathPrivate &dd, QObject *parent)
    : QObject(dd, parent)
{
}
 
QQuickPath::~QQuickPath()
{
}
 
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();
}
 
bool QQuickPath::isClosed() const
{
    Q_D(const QQuickPath);
    return d->closed;
}
 
QQmlListProperty<QQuickPathElement> QQuickPath::pathElements()
{
    return QQmlListProperty<QQuickPathElement>(this,
                                               nullptr,
                                               pathElements_append,
                                               pathElements_count,
                                               pathElements_at,
                                               pathElements_clear);
}
 
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);
    QQuickPath *path = static_cast<QQuickPath*>(property->object);
 
    d->_pathElements.append(pathElement);
 
    if (d->componentComplete) {
        QQuickCurve *curve = qobject_cast<QQuickCurve *>(pathElement);
        if (curve)
            d->_pathCurves.append(curve);
        else if (QQuickPathText *text = qobject_cast<QQuickPathText *>(pathElement))
            d->_pathTexts.append(text);
        else {
            QQuickPathAttribute *attribute = qobject_cast<QQuickPathAttribute *>(pathElement);
            if (attribute && !d->_attributes.contains(attribute->name()))
                d->_attributes.append(attribute->name());
        }
 
        path->processPath();
 
        connect(pathElement, SIGNAL(changed()), path, SLOT(processPath()));
    }
}
 
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);
    QQuickPath *path = static_cast<QQuickPath*>(property->object);
 
    path->disconnectPathElements();
    d->_pathElements.clear();
    d->_pathCurves.clear();
    d->_pointCache.clear();
    d->_pathTexts.clear();
}
 
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;
 
    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;
    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;
        } 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());
        } 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());
            usesPercent = true;
        } else if (QQuickPathText *text = qobject_cast<QQuickPathText *>(pathElement)) {
            text->addToPath(path);
        }
    }
 
    // 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;
    for (QQuickCurve *curve : std::as_const(d->_pathCurves)) {
        QQuickPathData data;
        data.index = index;
        data.endPoint = endPoint;
        data.curves = d->_pathCurves;
        curve->addToPath(path, data);
        ++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: Length of paths inside ShapePath is not used, so currently
    // length is always 0. This avoids potentially heavy path.length()
    //pathLength = path.length();
    pathLength = 0;
 
    return path;
}
 
void QQuickPath::classBegin()
{
    Q_D(QQuickPath);
    d->componentComplete = false;
}
 
void QQuickPath::disconnectPathElements()
{
    Q_D(const QQuickPath);
 
    for (QQuickPathElement *pathElement : d->_pathElements)
        disconnect(pathElement, SIGNAL(changed()), this, SLOT(processPath()));
}
 
void QQuickPath::connectPathElements()
{
    Q_D(const QQuickPath);
 
    for (QQuickPathElement *pathElement : d->_pathElements)
        connect(pathElement, SIGNAL(changed()), this, SLOT(processPath()));
}
 
void QQuickPath::gatherAttributes()
{
    Q_D(QQuickPath);
 
    QSet<QString> attributes;
 
    // 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;
 
    gatherAttributes();
 
    processPath();
 
    connectPathElements();
}
 
QPainterPath QQuickPath::path() const
{
    Q_D(const QQuickPath);
    return d->_path;
}
 
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;
}
 
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;
}
 
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);
}
 
QPointF QQuickPath::pointAtPercent(qreal t) const
{
    Q_D(const QQuickPath);
    if (d->isShapePath)                     // this since ShapePath does not calculate the length at all,
        return d->_path.pointAtPercent(t);  // in order to be faster.
 
    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();
}
 
/****************************************************************************/
 
QString QQuickPathAttribute::name() const
{
    return _name;
}
 
void QQuickPathAttribute::setName(const QString &name)
{
    if (_name == name)
        return;
     _name = name;
    emit nameChanged();
}
 
qreal QQuickPathAttribute::value() const
{
    return _value;
}
 
void QQuickPathAttribute::setValue(qreal value)
{
    if (_value != value) {
        _value = value;
        emit valueChanged();
        emit changed();
    }
}
 
/****************************************************************************/
 
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()));
}
 
/****************************************************************************/
 
void QQuickPathMove::addToPath(QPainterPath &path, const QQuickPathData &data)
{
    path.moveTo(positionForCurve(data, path.currentPosition()));
}
 
/****************************************************************************/
 
qreal QQuickPathQuad::controlX() const
{
    return _controlX;
}
 
void QQuickPathQuad::setControlX(qreal x)
{
    if (_controlX != x) {
        _controlX = x;
        emit controlXChanged();
        emit changed();
    }
}
 
 
qreal QQuickPathQuad::controlY() const
{
    return _controlY;
}
 
void QQuickPathQuad::setControlY(qreal y)
{
    if (_controlY != y) {
        _controlY = y;
        emit controlYChanged();
        emit changed();
    }
}
 
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()));
}
 
/****************************************************************************/
 
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();
    }
}
 
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();
    }
}
 
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()));
}
 
/****************************************************************************/
 
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);
}
 
/****************************************************************************/
 
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();
}
 
bool QQuickPathArc::useLargeArc() const
{
    return _useLargeArc;
}
 
void QQuickPathArc::setUseLargeArc(bool largeArc)
{
    if (_useLargeArc == largeArc)
        return;
 
    _useLargeArc = largeArc;
    emit useLargeArcChanged();
    emit changed();
}
 
QQuickPathArc::ArcDirection QQuickPathArc::direction() const
{
    return _direction;
}
 
void QQuickPathArc::setDirection(ArcDirection direction)
{
    if (_direction == direction)
        return;
 
    _direction = direction;
    emit directionChanged();
    emit changed();
}
 
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());
}
 
/****************************************************************************/
 
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();
}
 
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();
}
 
qreal QQuickPathAngleArc::startAngle() const
{
    return _startAngle;
}
 
void QQuickPathAngleArc::setStartAngle(qreal angle)
{
    if (_startAngle == angle)
        return;
 
    _startAngle = angle;
    emit startAngleChanged();
    emit changed();
}
 
qreal QQuickPathAngleArc::sweepAngle() const
{
    return _sweepAngle;
}
 
void QQuickPathAngleArc::setSweepAngle(qreal angle)
{
    if (_sweepAngle == angle)
        return;
 
    _sweepAngle = angle;
    emit sweepAngleChanged();
    emit changed();
}
 
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);
}
 
/****************************************************************************/
 
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);
}
 
/****************************************************************************/
 
qreal QQuickPathPercent::value() const
{
    return _value;
}
 
void QQuickPathPercent::setValue(qreal value)
{
    if (_value != value) {
        _value = value;
        emit valueChanged();
        emit changed();
    }
}
 
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<QVector<QPointF>>()) {
        setPath(path.value<QVector<QPointF>>());
    } else if (path.canConvert<QVariantList>()) {
        // This handles cases other than QPolygonF or QVector<QPointF>, such as
        // QList<QPointF>, QVector<QPoint>, QVariantList of QPointF, QVariantList of QPoint.
        QVector<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<QSequentialIterable>() 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 QVector<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));
}
 
 
QQuickPathMultiline::QQuickPathMultiline(QObject *parent) : QQuickCurve(parent)
{
}
 
QVariant QQuickPathMultiline::paths() const
{
    return QVariant::fromValue(m_paths);
}
 
void QQuickPathMultiline::setPaths(const QVariant &paths)
{
    if (paths.canConvert<QVector<QPolygonF>>()) {
        const QVector<QPolygonF> pathPolygons = paths.value<QVector<QPolygonF>>();
        QVector<QVector<QPointF>> pathVectors;
        for (const QPolygonF &p : pathPolygons)
            pathVectors << p;
        setPaths(pathVectors);
    } else if (paths.canConvert<QVector<QVector<QPointF>>>()) {
        setPaths(paths.value<QVector<QVector<QPointF>>>());
    } else if (paths.canConvert<QVariantList>()) {
        // This handles cases other than QVector<QPolygonF> or QVector<QVector<QPointF>>, such as
        // QList<QVector<QPointF>>, QList<QList<QPointF>>, QVariantList of QVector<QPointF>,
        // QVariantList of QVariantList of QPointF, QVector<QList<QPoint>> etc.
        QVector<QVector<QPointF>> pathsList;
        QVariantList vll = paths.value<QVariantList>();
        for (const QVariant &v : vll) {
            // If we bind a QVector<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>();
                QVector<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(QVector<QVector<QPointF>>());
    }
}
 
void QQuickPathMultiline::setPaths(const QVector<QVector<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 QVector<QPointF> &p: m_paths) {
        path.moveTo(p.first());
        for (int i = 1; i < p.size(); ++i)
            path.lineTo(p.at(i));
    }
}
 
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"