qpainterpath.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 "qpainterpath.h"
#include "qpainterpath_p.h"
 
#include <qbitmap.h>
#include <qdebug.h>
#include <qiodevice.h>
#include <qlist.h>
#include <qpen.h>
#include <qpolygon.h>
#include <qtextlayout.h>
#include <qvarlengtharray.h>
#include <qmath.h>
 
#include <private/qbezier_p.h>
#include <private/qfontengine_p.h>
#include <private/qnumeric_p.h>
#include <private/qobject_p.h>
#include <private/qpathclipper_p.h>
#include <private/qstroker_p.h>
#include <private/qtextengine_p.h>
 
#include <limits.h>
 
#if 0
#include <performance.h>
#else
#define PM_INIT
#define PM_MEASURE(x)
#define PM_DISPLAY
#endif
 
QT_BEGIN_NAMESPACE
 
static inline bool isValidCoord(qreal c)
{
    if (sizeof(qreal) >= sizeof(double))
        return qIsFinite(c) && fabs(c) < 1e128;
    else
        return qIsFinite(c) && fabsf(float(c)) < 1e16f;
}
 
static bool hasValidCoords(QPointF p)
{
    return isValidCoord(p.x()) && isValidCoord(p.y());
}
 
static bool hasValidCoords(QRectF r)
{
    return isValidCoord(r.x()) && isValidCoord(r.y()) && isValidCoord(r.width()) && isValidCoord(r.height());
}
 
// This value is used to determine the length of control point vectors
// when approximating arc segments as curves. The factor is multiplied
// with the radius of the circle.
 
// #define QPP_DEBUG
// #define QPP_STROKE_DEBUG
//#define QPP_FILLPOLYGONS_DEBUG
 
QPainterPath qt_stroke_dash(const QPainterPath &path, qreal *dashes, int dashCount);
 
void qt_find_ellipse_coords(const QRectF &r, qreal angle, qreal length,
                            QPointF* startPoint, QPointF *endPoint)
{
    if (r.isNull()) {
        if (startPoint)
            *startPoint = QPointF();
        if (endPoint)
            *endPoint = QPointF();
        return;
    }
 
    qreal w2 = r.width() / 2;
    qreal h2 = r.height() / 2;
 
    qreal angles[2] = { angle, angle + length };
    QPointF *points[2] = { startPoint, endPoint };
 
    for (int i = 0; i < 2; ++i) {
        if (!points[i])
            continue;
 
        qreal theta = angles[i] - 360 * qFloor(angles[i] / 360);
        qreal t = theta / 90;
        // truncate
        int quadrant = int(t);
        t -= quadrant;
 
        t = qt_t_for_arc_angle(90 * t);
 
        // swap x and y?
        if (quadrant & 1)
            t = 1 - t;
 
        qreal a, b, c, d;
        QBezier::coefficients(t, a, b, c, d);
        QPointF p(a + b + c*QT_PATH_KAPPA, d + c + b*QT_PATH_KAPPA);
 
        // left quadrants
        if (quadrant == 1 || quadrant == 2)
            p.rx() = -p.x();
 
        // top quadrants
        if (quadrant == 0 || quadrant == 1)
            p.ry() = -p.y();
 
        *points[i] = r.center() + QPointF(w2 * p.x(), h2 * p.y());
    }
}
 
#ifdef QPP_DEBUG
static void qt_debug_path(const QPainterPath &path)
{
    const char *names[] = {
        "MoveTo     ",
        "LineTo     ",
        "CurveTo    ",
        "CurveToData"
    };
 
    printf("\nQPainterPath: elementCount=%d\n", path.elementCount());
    for (int i=0; i<path.elementCount(); ++i) {
        const QPainterPath::Element &e = path.elementAt(i);
        Q_ASSERT(e.type >= 0 && e.type <= QPainterPath::CurveToDataElement);
        printf(" - %3d:: %s, (%.2f, %.2f)\n", i, names[e.type], e.x, e.y);
    }
}
#endif
 
int QPainterPath::elementCount() const
{
    return d_ptr ? d_ptr->elements.size() : 0;
}
 
QPainterPath::Element QPainterPath::elementAt(int i) const
{
    Q_ASSERT(d_ptr);
    Q_ASSERT(i >= 0 && i < elementCount());
    return d_ptr->elements.at(i);
}
 
void QPainterPath::setElementPositionAt(int i, qreal x, qreal y)
{
    Q_ASSERT(d_ptr);
    Q_ASSERT(i >= 0 && i < elementCount());
    detach();
    QPainterPath::Element &e = d_ptr->elements[i];
    e.x = x;
    e.y = y;
}
 
 
/*###
    \fn QPainterPath &QPainterPath::operator +=(const QPainterPath &other)
 
    Appends the \a other painter path to this painter path and returns a
    reference to the result.
*/
 
QPainterPath::QPainterPath() noexcept
    : d_ptr(nullptr)
{
}
 
QPainterPath::QPainterPath(const QPainterPath &other) = default;
 
QPainterPath::QPainterPath(const QPointF &startPoint)
    : d_ptr(new QPainterPathPrivate(startPoint))
{
}
 
void QPainterPath::detach()
{
    d_ptr.detach();
    setDirty(true);
}
 
void QPainterPath::ensureData_helper()
{
    QPainterPathPrivate *data = new QPainterPathPrivate;
    data->elements.reserve(16);
    QPainterPath::Element e = { 0, 0, QPainterPath::MoveToElement };
    data->elements << e;
    d_ptr.reset(data);
    Q_ASSERT(d_ptr != nullptr);
}
 
QPainterPath &QPainterPath::operator=(const QPainterPath &other)
{
    QPainterPath copy(other);
    swap(copy);
    return *this;
}
 
QPainterPath::~QPainterPath()
{
}
 
void QPainterPath::clear()
{
    if (!d_ptr)
        return;
 
    detach();
    d_func()->clear();
    d_func()->elements.append( {0, 0, MoveToElement} );
}
 
void QPainterPath::reserve(int size)
{
    Q_D(QPainterPath);
    if ((!d && size > 0) || (d && d->elements.capacity() < size)) {
        ensureData();
        detach();
        d_func()->elements.reserve(size);
    }
}
 
int QPainterPath::capacity() const
{
    Q_D(QPainterPath);
    if (d)
        return d->elements.capacity();
 
    return 0;
}
 
void QPainterPath::closeSubpath()
{
#ifdef QPP_DEBUG
    printf("QPainterPath::closeSubpath()\n");
#endif
    if (isEmpty())
        return;
    detach();
 
    d_func()->close();
}
 
void QPainterPath::moveTo(const QPointF &p)
{
#ifdef QPP_DEBUG
    printf("QPainterPath::moveTo() (%.2f,%.2f)\n", p.x(), p.y());
#endif
 
    if (!hasValidCoords(p)) {
#ifndef QT_NO_DEBUG
        qWarning("QPainterPath::moveTo: Adding point with invalid coordinates, ignoring call");
#endif
        return;
    }
 
    ensureData();
    detach();
 
    QPainterPathPrivate *d = d_func();
    Q_ASSERT(!d->elements.isEmpty());
 
    d->require_moveTo = false;
 
    if (d->elements.constLast().type == MoveToElement) {
        d->elements.last().x = p.x();
        d->elements.last().y = p.y();
    } else {
        Element elm = { p.x(), p.y(), MoveToElement };
        d->elements.append(elm);
    }
    d->cStart = d->elements.size() - 1;
}
 
void QPainterPath::lineTo(const QPointF &p)
{
#ifdef QPP_DEBUG
    printf("QPainterPath::lineTo() (%.2f,%.2f)\n", p.x(), p.y());
#endif
 
    if (!hasValidCoords(p)) {
#ifndef QT_NO_DEBUG
        qWarning("QPainterPath::lineTo: Adding point with invalid coordinates, ignoring call");
#endif
        return;
    }
 
    ensureData();
    detach();
 
    QPainterPathPrivate *d = d_func();
    Q_ASSERT(!d->elements.isEmpty());
    d->maybeMoveTo();
    if (p == QPointF(d->elements.constLast()))
        return;
    Element elm = { p.x(), p.y(), LineToElement };
    d->elements.append(elm);
 
    d->convex = d->elements.size() == 3 || (d->elements.size() == 4 && d->isClosed());
}
 
void QPainterPath::cubicTo(const QPointF &c1, const QPointF &c2, const QPointF &e)
{
#ifdef QPP_DEBUG
    printf("QPainterPath::cubicTo() (%.2f,%.2f), (%.2f,%.2f), (%.2f,%.2f)\n",
           c1.x(), c1.y(), c2.x(), c2.y(), e.x(), e.y());
#endif
 
    if (!hasValidCoords(c1) || !hasValidCoords(c2) || !hasValidCoords(e)) {
#ifndef QT_NO_DEBUG
        qWarning("QPainterPath::cubicTo: Adding point with invalid coordinates, ignoring call");
#endif
        return;
    }
 
    ensureData();
    detach();
 
    QPainterPathPrivate *d = d_func();
    Q_ASSERT(!d->elements.isEmpty());
 
 
    // Abort on empty curve as a stroker cannot handle this and the
    // curve is irrelevant anyway.
    if (d->elements.constLast() == c1 && c1 == c2 && c2 == e)
        return;
 
    d->maybeMoveTo();
 
    Element ce1 = { c1.x(), c1.y(), CurveToElement };
    Element ce2 = { c2.x(), c2.y(), CurveToDataElement };
    Element ee = { e.x(), e.y(), CurveToDataElement };
    d->elements << ce1 << ce2 << ee;
}
 
void QPainterPath::quadTo(const QPointF &c, const QPointF &e)
{
#ifdef QPP_DEBUG
    printf("QPainterPath::quadTo() (%.2f,%.2f), (%.2f,%.2f)\n",
           c.x(), c.y(), e.x(), e.y());
#endif
 
    if (!hasValidCoords(c) || !hasValidCoords(e)) {
#ifndef QT_NO_DEBUG
        qWarning("QPainterPath::quadTo: Adding point with invalid coordinates, ignoring call");
#endif
        return;
    }
 
    ensureData();
    detach();
 
    Q_D(QPainterPath);
    Q_ASSERT(!d->elements.isEmpty());
    const QPainterPath::Element &elm = d->elements.at(elementCount()-1);
    QPointF prev(elm.x, elm.y);
 
    // Abort on empty curve as a stroker cannot handle this and the
    // curve is irrelevant anyway.
    if (prev == c && c == e)
        return;
 
    QPointF c1((prev.x() + 2*c.x()) / 3, (prev.y() + 2*c.y()) / 3);
    QPointF c2((e.x() + 2*c.x()) / 3, (e.y() + 2*c.y()) / 3);
    cubicTo(c1, c2, e);
}
 
void QPainterPath::arcTo(const QRectF &rect, qreal startAngle, qreal sweepLength)
{
#ifdef QPP_DEBUG
    printf("QPainterPath::arcTo() (%.2f, %.2f, %.2f, %.2f, angle=%.2f, sweep=%.2f\n",
           rect.x(), rect.y(), rect.width(), rect.height(), startAngle, sweepLength);
#endif
 
    if (!hasValidCoords(rect) || !isValidCoord(startAngle) || !isValidCoord(sweepLength)) {
#ifndef QT_NO_DEBUG
        qWarning("QPainterPath::arcTo: Adding point with invalid coordinates, ignoring call");
#endif
        return;
    }
 
    if (rect.isNull())
        return;
 
    ensureData();
    detach();
 
    int point_count;
    QPointF pts[15];
    QPointF curve_start = qt_curves_for_arc(rect, startAngle, sweepLength, pts, &point_count);
 
    lineTo(curve_start);
    for (int i=0; i<point_count; i+=3) {
        cubicTo(pts[i].x(), pts[i].y(),
                pts[i+1].x(), pts[i+1].y(),
                pts[i+2].x(), pts[i+2].y());
    }
 
}
 
 
void QPainterPath::arcMoveTo(const QRectF &rect, qreal angle)
{
    if (rect.isNull())
        return;
 
    QPointF pt;
    qt_find_ellipse_coords(rect, angle, 0, &pt, nullptr);
    moveTo(pt);
}
 
 
 
QPointF QPainterPath::currentPosition() const
{
    return !d_ptr || d_func()->elements.isEmpty()
        ? QPointF()
        : QPointF(d_func()->elements.constLast().x, d_func()->elements.constLast().y);
}
 
 
void QPainterPath::addRect(const QRectF &r)
{
    if (!hasValidCoords(r)) {
#ifndef QT_NO_DEBUG
        qWarning("QPainterPath::addRect: Adding point with invalid coordinates, ignoring call");
#endif
        return;
    }
 
    if (r.isNull())
        return;
 
    ensureData();
    detach();
 
    bool first = d_func()->elements.size() < 2;
 
    moveTo(r.x(), r.y());
 
    Element l1 = { r.x() + r.width(), r.y(), LineToElement };
    Element l2 = { r.x() + r.width(), r.y() + r.height(), LineToElement };
    Element l3 = { r.x(), r.y() + r.height(), LineToElement };
    Element l4 = { r.x(), r.y(), LineToElement };
 
    d_func()->elements << l1 << l2 << l3 << l4;
    d_func()->require_moveTo = true;
    d_func()->convex = first;
}
 
void QPainterPath::addPolygon(const QPolygonF &polygon)
{
    if (polygon.isEmpty())
        return;
 
    ensureData();
    detach();
 
    moveTo(polygon.constFirst());
    for (int i=1; i<polygon.size(); ++i) {
        Element elm = { polygon.at(i).x(), polygon.at(i).y(), LineToElement };
        d_func()->elements << elm;
    }
}
 
void QPainterPath::addEllipse(const QRectF &boundingRect)
{
    if (!hasValidCoords(boundingRect)) {
#ifndef QT_NO_DEBUG
        qWarning("QPainterPath::addEllipse: Adding point with invalid coordinates, ignoring call");
#endif
        return;
    }
 
    if (boundingRect.isNull())
        return;
 
    ensureData();
    detach();
 
    bool first = d_func()->elements.size() < 2;
 
    QPointF pts[12];
    int point_count;
    QPointF start = qt_curves_for_arc(boundingRect, 0, -360, pts, &point_count);
 
    moveTo(start);
    cubicTo(pts[0], pts[1], pts[2]);           // 0 -> 270
    cubicTo(pts[3], pts[4], pts[5]);           // 270 -> 180
    cubicTo(pts[6], pts[7], pts[8]);           // 180 -> 90
    cubicTo(pts[9], pts[10], pts[11]);         // 90 - >0
    d_func()->require_moveTo = true;
 
    d_func()->convex = first;
}
 
void QPainterPath::addText(const QPointF &point, const QFont &f, const QString &text)
{
    if (text.isEmpty())
        return;
 
    ensureData();
    detach();
 
    QTextLayout layout(text, f);
    layout.setCacheEnabled(true);
 
    QTextOption opt = layout.textOption();
    opt.setUseDesignMetrics(true);
    layout.setTextOption(opt);
 
    QTextEngine *eng = layout.engine();
    layout.beginLayout();
    QTextLine line = layout.createLine();
    Q_UNUSED(line);
    layout.endLayout();
    const QScriptLine &sl = eng->lines[0];
    if (!sl.length || !eng->layoutData)
        return;
 
    int nItems = eng->layoutData->items.size();
 
    qreal x(point.x());
    qreal y(point.y());
 
    QVarLengthArray<int> visualOrder(nItems);
    QVarLengthArray<uchar> levels(nItems);
    for (int i = 0; i < nItems; ++i)
        levels[i] = eng->layoutData->items.at(i).analysis.bidiLevel;
    QTextEngine::bidiReorder(nItems, levels.data(), visualOrder.data());
 
    for (int i = 0; i < nItems; ++i) {
        int item = visualOrder[i];
        const QScriptItem &si = eng->layoutData->items.at(item);
 
        if (si.analysis.flags < QScriptAnalysis::TabOrObject) {
            QGlyphLayout glyphs = eng->shapedGlyphs(&si);
            QFontEngine *fe = eng->fontEngine(si);
            Q_ASSERT(fe);
            fe->addOutlineToPath(x, y, glyphs, this,
                                 si.analysis.bidiLevel % 2
                                 ? QTextItem::RenderFlags(QTextItem::RightToLeft)
                                 : QTextItem::RenderFlags{});
 
            const qreal lw = fe->lineThickness().toReal();
            if (f.d->underline) {
                qreal pos = fe->underlinePosition().toReal();
                addRect(x, y + pos, si.width.toReal(), lw);
            }
            if (f.d->overline) {
                qreal pos = fe->ascent().toReal() + 1;
                addRect(x, y - pos, si.width.toReal(), lw);
            }
            if (f.d->strikeOut) {
                qreal pos = fe->ascent().toReal() / 3;
                addRect(x, y - pos, si.width.toReal(), lw);
            }
        }
        x += si.width.toReal();
    }
}
 
void QPainterPath::addPath(const QPainterPath &other)
{
    if (other.isEmpty())
        return;
 
    ensureData();
    detach();
 
    QPainterPathPrivate *d = d_func();
    // Remove last moveto so we don't get multiple moveto's
    if (d->elements.constLast().type == MoveToElement)
        d->elements.remove(d->elements.size()-1);
 
    // Locate where our own current subpath will start after the other path is added.
    int cStart = d->elements.size() + other.d_func()->cStart;
    d->elements += other.d_func()->elements;
    d->cStart = cStart;
 
    d->require_moveTo = other.d_func()->isClosed();
}
 
 
void QPainterPath::connectPath(const QPainterPath &other)
{
    if (other.isEmpty())
        return;
 
    ensureData();
    detach();
 
    QPainterPathPrivate *d = d_func();
    // Remove last moveto so we don't get multiple moveto's
    if (d->elements.constLast().type == MoveToElement)
        d->elements.remove(d->elements.size()-1);
 
    // Locate where our own current subpath will start after the other path is added.
    int cStart = d->elements.size() + other.d_func()->cStart;
    int first = d->elements.size();
    d->elements += other.d_func()->elements;
 
    if (first != 0)
        d->elements[first].type = LineToElement;
 
    // avoid duplicate points
    if (first > 0 && QPointF(d->elements.at(first)) == QPointF(d->elements.at(first - 1))) {
        d->elements.remove(first--);
        --cStart;
    }
 
    if (cStart != first)
        d->cStart = cStart;
}
 
void QPainterPath::addRegion(const QRegion &region)
{
    ensureData();
    detach();
 
    for (const QRect &rect : region)
        addRect(rect);
}
 
 
Qt::FillRule QPainterPath::fillRule() const
{
    return !d_func() ? Qt::OddEvenFill : d_func()->fillRule;
}
 
void QPainterPath::setFillRule(Qt::FillRule fillRule)
{
    ensureData();
    if (d_func()->fillRule == fillRule)
        return;
    detach();
 
    d_func()->fillRule = fillRule;
}
 
#define QT_BEZIER_A(bezier, coord) 3 * (-bezier.coord##1 \
                                        + 3*bezier.coord##2 \
                                        - 3*bezier.coord##3 \
                                        +bezier.coord##4)
 
#define QT_BEZIER_B(bezier, coord) 6 * (bezier.coord##1 \
                                        - 2*bezier.coord##2 \
                                        + bezier.coord##3)
 
#define QT_BEZIER_C(bezier, coord) 3 * (- bezier.coord##1 \
                                        + bezier.coord##2)
 
#define QT_BEZIER_CHECK_T(bezier, t) \
    if (t >= 0 && t <= 1) { \
        QPointF p(b.pointAt(t)); \
        if (p.x() < minx) minx = p.x(); \
        else if (p.x() > maxx) maxx = p.x(); \
        if (p.y() < miny) miny = p.y(); \
        else if (p.y() > maxy) maxy = p.y(); \
    }
 
 
static QRectF qt_painterpath_bezier_extrema(const QBezier &b)
{
    qreal minx, miny, maxx, maxy;
 
    // initialize with end points
    if (b.x1 < b.x4) {
        minx = b.x1;
        maxx = b.x4;
    } else {
        minx = b.x4;
        maxx = b.x1;
    }
    if (b.y1 < b.y4) {
        miny = b.y1;
        maxy = b.y4;
    } else {
        miny = b.y4;
        maxy = b.y1;
    }
 
    // Update for the X extrema
    {
        qreal ax = QT_BEZIER_A(b, x);
        qreal bx = QT_BEZIER_B(b, x);
        qreal cx = QT_BEZIER_C(b, x);
        // specialcase quadratic curves to avoid div by zero
        if (qFuzzyIsNull(ax)) {
 
            // linear curves are covered by initialization.
            if (!qFuzzyIsNull(bx)) {
                qreal t = -cx / bx;
                QT_BEZIER_CHECK_T(b, t);
            }
 
        } else {
            const qreal tx = bx * bx - 4 * ax * cx;
 
            if (tx >= 0) {
                qreal temp = qSqrt(tx);
                qreal rcp = 1 / (2 * ax);
                qreal t1 = (-bx + temp) * rcp;
                QT_BEZIER_CHECK_T(b, t1);
 
                qreal t2 = (-bx - temp) * rcp;
                QT_BEZIER_CHECK_T(b, t2);
            }
        }
    }
 
    // Update for the Y extrema
    {
        qreal ay = QT_BEZIER_A(b, y);
        qreal by = QT_BEZIER_B(b, y);
        qreal cy = QT_BEZIER_C(b, y);
 
        // specialcase quadratic curves to avoid div by zero
        if (qFuzzyIsNull(ay)) {
 
            // linear curves are covered by initialization.
            if (!qFuzzyIsNull(by)) {
                qreal t = -cy / by;
                QT_BEZIER_CHECK_T(b, t);
            }
 
        } else {
            const qreal ty = by * by - 4 * ay * cy;
 
            if (ty > 0) {
                qreal temp = qSqrt(ty);
                qreal rcp = 1 / (2 * ay);
                qreal t1 = (-by + temp) * rcp;
                QT_BEZIER_CHECK_T(b, t1);
 
                qreal t2 = (-by - temp) * rcp;
                QT_BEZIER_CHECK_T(b, t2);
            }
        }
    }
    return QRectF(minx, miny, maxx - minx, maxy - miny);
}
 
QRectF QPainterPath::boundingRect() const
{
    if (!d_ptr)
        return QRectF();
    QPainterPathPrivate *d = d_func();
 
    if (d->dirtyBounds)
        computeBoundingRect();
    return d->bounds;
}
 
QRectF QPainterPath::controlPointRect() const
{
    if (!d_ptr)
        return QRectF();
    QPainterPathPrivate *d = d_func();
 
    if (d->dirtyControlBounds)
        computeControlPointRect();
    return d->controlBounds;
}
 
 
bool QPainterPath::isEmpty() const
{
    return !d_ptr || (d_ptr->elements.size() == 1 && d_ptr->elements.constFirst().type == MoveToElement);
}
 
QPainterPath QPainterPath::toReversed() const
{
    Q_D(const QPainterPath);
    QPainterPath rev;
 
    if (isEmpty()) {
        rev = *this;
        return rev;
    }
 
    rev.moveTo(d->elements.at(d->elements.size()-1).x, d->elements.at(d->elements.size()-1).y);
 
    for (int i=d->elements.size()-1; i>=1; --i) {
        const QPainterPath::Element &elm = d->elements.at(i);
        const QPainterPath::Element &prev = d->elements.at(i-1);
        switch (elm.type) {
        case LineToElement:
            rev.lineTo(prev.x, prev.y);
            break;
        case MoveToElement:
            rev.moveTo(prev.x, prev.y);
            break;
        case CurveToDataElement:
            {
                Q_ASSERT(i>=3);
                const QPainterPath::Element &cp1 = d->elements.at(i-2);
                const QPainterPath::Element &sp = d->elements.at(i-3);
                Q_ASSERT(prev.type == CurveToDataElement);
                Q_ASSERT(cp1.type == CurveToElement);
                rev.cubicTo(prev.x, prev.y, cp1.x, cp1.y, sp.x, sp.y);
                i -= 2;
                break;
            }
        default:
            Q_ASSERT(!"qt_reversed_path");
            break;
        }
    }
    //qt_debug_path(rev);
    return rev;
}
 
QList<QPolygonF> QPainterPath::toSubpathPolygons(const QTransform &matrix) const
{
 
    Q_D(const QPainterPath);
    QList<QPolygonF> flatCurves;
    if (isEmpty())
        return flatCurves;
 
    QPolygonF current;
    for (int i=0; i<elementCount(); ++i) {
        const QPainterPath::Element &e = d->elements.at(i);
        switch (e.type) {
        case QPainterPath::MoveToElement:
            if (current.size() > 1)
                flatCurves += current;
            current.clear();
            current.reserve(16);
            current += QPointF(e.x, e.y) * matrix;
            break;
        case QPainterPath::LineToElement:
            current += QPointF(e.x, e.y) * matrix;
            break;
        case QPainterPath::CurveToElement: {
            Q_ASSERT(d->elements.at(i+1).type == QPainterPath::CurveToDataElement);
            Q_ASSERT(d->elements.at(i+2).type == QPainterPath::CurveToDataElement);
            QBezier bezier = QBezier::fromPoints(QPointF(d->elements.at(i-1).x, d->elements.at(i-1).y) * matrix,
                                       QPointF(e.x, e.y) * matrix,
                                       QPointF(d->elements.at(i+1).x, d->elements.at(i+1).y) * matrix,
                                                 QPointF(d->elements.at(i+2).x, d->elements.at(i+2).y) * matrix);
            bezier.addToPolygon(&current);
            i+=2;
            break;
        }
        case QPainterPath::CurveToDataElement:
            Q_ASSERT(!"QPainterPath::toSubpathPolygons(), bad element type");
            break;
        }
    }
 
    if (current.size()>1)
        flatCurves += current;
 
    return flatCurves;
}
 
QList<QPolygonF> QPainterPath::toFillPolygons(const QTransform &matrix) const
{
 
    QList<QPolygonF> polys;
 
    QList<QPolygonF> subpaths = toSubpathPolygons(matrix);
    int count = subpaths.size();
 
    if (count == 0)
        return polys;
 
    QList<QRectF> bounds;
    bounds.reserve(count);
    for (int i=0; i<count; ++i)
        bounds += subpaths.at(i).boundingRect();
 
#ifdef QPP_FILLPOLYGONS_DEBUG
    printf("QPainterPath::toFillPolygons, subpathCount=%d\n", count);
    for (int i=0; i<bounds.size(); ++i)
        qDebug() << " bounds" << i << bounds.at(i);
#endif
 
    QList< QList<int> > isects;
    isects.resize(count);
 
    // find all intersections
    for (int j=0; j<count; ++j) {
        if (subpaths.at(j).size() <= 2)
            continue;
        QRectF cbounds = bounds.at(j);
        for (int i=0; i<count; ++i) {
            if (cbounds.intersects(bounds.at(i))) {
                isects[j] << i;
            }
        }
    }
 
#ifdef QPP_FILLPOLYGONS_DEBUG
    printf("Intersections before flattening:\n");
    for (int i = 0; i < count; ++i) {
        printf("%d: ", i);
        for (int j = 0; j < isects[i].size(); ++j) {
            printf("%d ", isects[i][j]);
        }
        printf("\n");
    }
#endif
 
    // flatten the sets of intersections
    for (int i=0; i<count; ++i) {
        const QList<int> &current_isects = isects.at(i);
        for (int j=0; j<current_isects.size(); ++j) {
            int isect_j = current_isects.at(j);
            if (isect_j == i)
                continue;
            const QList<int> &isects_j = isects.at(isect_j);
            for (int k = 0, size = isects_j.size(); k < size; ++k) {
                int isect_k = isects_j.at(k);
                if (isect_k != i && !isects.at(i).contains(isect_k)) {
                    isects[i] += isect_k;
                }
            }
            isects[isect_j].clear();
        }
    }
 
#ifdef QPP_FILLPOLYGONS_DEBUG
    printf("Intersections after flattening:\n");
    for (int i = 0; i < count; ++i) {
        printf("%d: ", i);
        for (int j = 0; j < isects[i].size(); ++j) {
            printf("%d ", isects[i][j]);
        }
        printf("\n");
    }
#endif
 
    // Join the intersected subpaths as rewinded polygons
    for (int i=0; i<count; ++i) {
        const QList<int> &subpath_list = isects.at(i);
        if (!subpath_list.isEmpty()) {
            QPolygonF buildUp;
            for (int j=0; j<subpath_list.size(); ++j) {
                const QPolygonF &subpath = subpaths.at(subpath_list.at(j));
                buildUp += subpath;
                if (!subpath.isClosed())
                    buildUp += subpath.first();
                if (!buildUp.isClosed())
                    buildUp += buildUp.constFirst();
            }
            polys += buildUp;
        }
    }
 
    return polys;
}
 
//same as qt_polygon_isect_line in qpolygon.cpp
static void qt_painterpath_isect_line(const QPointF &p1,
                                      const QPointF &p2,
                                      const QPointF &pos,
                                      int *winding)
{
    qreal x1 = p1.x();
    qreal y1 = p1.y();
    qreal x2 = p2.x();
    qreal y2 = p2.y();
    qreal y = pos.y();
 
    int dir = 1;
 
    if (qFuzzyCompare(y1, y2)) {
        // ignore horizontal lines according to scan conversion rule
        return;
    } else if (y2 < y1) {
        qreal x_tmp = x2; x2 = x1; x1 = x_tmp;
        qreal y_tmp = y2; y2 = y1; y1 = y_tmp;
        dir = -1;
    }
 
    if (y >= y1 && y < y2) {
        qreal x = x1 + ((x2 - x1) / (y2 - y1)) * (y - y1);
 
        // count up the winding number if we're
        if (x<=pos.x()) {
            (*winding) += dir;
        }
    }
}
 
static void qt_painterpath_isect_curve(const QBezier &bezier, const QPointF &pt,
                                       int *winding, int depth = 0)
{
    qreal y = pt.y();
    qreal x = pt.x();
    QRectF bounds = bezier.bounds();
 
    // potential intersection, divide and try again...
    // Please note that a sideeffect of the bottom exclusion is that
    // horizontal lines are dropped, but this is correct according to
    // scan conversion rules.
    if (y >= bounds.y() && y < bounds.y() + bounds.height()) {
 
        // hit lower limit... This is a rough threshold, but its a
        // tradeoff between speed and precision.
        const qreal lower_bound = qreal(.001);
        if (depth == 32 || (bounds.width() < lower_bound && bounds.height() < lower_bound)) {
            // We make the assumption here that the curve starts to
            // approximate a line after while (i.e. that it doesn't
            // change direction drastically during its slope)
            if (bezier.pt1().x() <= x) {
                (*winding) += (bezier.pt4().y() > bezier.pt1().y() ? 1 : -1);
            }
            return;
        }
 
        // split curve and try again...
        const auto halves = bezier.split();
        qt_painterpath_isect_curve(halves.first,  pt, winding, depth + 1);
        qt_painterpath_isect_curve(halves.second, pt, winding, depth + 1);
    }
}
 
bool QPainterPath::contains(const QPointF &pt) const
{
    if (isEmpty() || !controlPointRect().contains(pt))
        return false;
 
    QPainterPathPrivate *d = d_func();
 
    int winding_number = 0;
 
    QPointF last_pt;
    QPointF last_start;
    for (int i=0; i<d->elements.size(); ++i) {
        const Element &e = d->elements.at(i);
 
        switch (e.type) {
 
        case MoveToElement:
            if (i > 0) // implicitly close all paths.
                qt_painterpath_isect_line(last_pt, last_start, pt, &winding_number);
            last_start = last_pt = e;
            break;
 
        case LineToElement:
            qt_painterpath_isect_line(last_pt, e, pt, &winding_number);
            last_pt = e;
            break;
 
        case CurveToElement:
            {
                const QPainterPath::Element &cp2 = d->elements.at(++i);
                const QPainterPath::Element &ep = d->elements.at(++i);
                qt_painterpath_isect_curve(QBezier::fromPoints(last_pt, e, cp2, ep),
                                           pt, &winding_number);
                last_pt = ep;
 
            }
            break;
 
        default:
            break;
        }
    }
 
    // implicitly close last subpath
    if (last_pt != last_start)
        qt_painterpath_isect_line(last_pt, last_start, pt, &winding_number);
 
    return (d->fillRule == Qt::WindingFill
            ? (winding_number != 0)
            : ((winding_number % 2) != 0));
}
 
enum PainterDirections { Left, Right, Top, Bottom };
 
static bool qt_painterpath_isect_line_rect(qreal x1, qreal y1, qreal x2, qreal y2,
                                           const QRectF &rect)
{
    qreal left = rect.left();
    qreal right = rect.right();
    qreal top = rect.top();
    qreal bottom = rect.bottom();
 
    // clip the lines, after cohen-sutherland, see e.g. http://www.nondot.org/~sabre/graphpro/line6.html
    int p1 = ((x1 < left) << Left)
             | ((x1 > right) << Right)
             | ((y1 < top) << Top)
             | ((y1 > bottom) << Bottom);
    int p2 = ((x2 < left) << Left)
             | ((x2 > right) << Right)
             | ((y2 < top) << Top)
             | ((y2 > bottom) << Bottom);
 
    if (p1 & p2)
        // completely inside
        return false;
 
    if (p1 | p2) {
        qreal dx = x2 - x1;
        qreal dy = y2 - y1;
 
        // clip x coordinates
        if (x1 < left) {
            y1 += dy/dx * (left - x1);
            x1 = left;
        } else if (x1 > right) {
            y1 -= dy/dx * (x1 - right);
            x1 = right;
        }
        if (x2 < left) {
            y2 += dy/dx * (left - x2);
            x2 = left;
        } else if (x2 > right) {
            y2 -= dy/dx * (x2 - right);
            x2 = right;
        }
 
        p1 = ((y1 < top) << Top)
             | ((y1 > bottom) << Bottom);
        p2 = ((y2 < top) << Top)
             | ((y2 > bottom) << Bottom);
 
        if (p1 & p2)
            return false;
 
        // clip y coordinates
        if (y1 < top) {
            x1 += dx/dy * (top - y1);
            y1 = top;
        } else if (y1 > bottom) {
            x1 -= dx/dy * (y1 - bottom);
            y1 = bottom;
        }
        if (y2 < top) {
            x2 += dx/dy * (top - y2);
            y2 = top;
        } else if (y2 > bottom) {
            x2 -= dx/dy * (y2 - bottom);
            y2 = bottom;
        }
 
        p1 = ((x1 < left) << Left)
             | ((x1 > right) << Right);
        p2 = ((x2 < left) << Left)
             | ((x2 > right) << Right);
 
        if (p1 & p2)
            return false;
 
        return true;
    }
    return false;
}
 
static bool qt_isect_curve_horizontal(const QBezier &bezier, qreal y, qreal x1, qreal x2, int depth = 0)
{
    QRectF bounds = bezier.bounds();
 
    if (y >= bounds.top() && y < bounds.bottom()
        && bounds.right() >= x1 && bounds.left() < x2) {
        const qreal lower_bound = qreal(.01);
        if (depth == 32 || (bounds.width() < lower_bound && bounds.height() < lower_bound))
            return true;
 
        const auto halves = bezier.split();
        if (qt_isect_curve_horizontal(halves.first, y, x1, x2, depth + 1)
            || qt_isect_curve_horizontal(halves.second, y, x1, x2, depth + 1))
            return true;
    }
    return false;
}
 
static bool qt_isect_curve_vertical(const QBezier &bezier, qreal x, qreal y1, qreal y2, int depth = 0)
{
    QRectF bounds = bezier.bounds();
 
    if (x >= bounds.left() && x < bounds.right()
        && bounds.bottom() >= y1 && bounds.top() < y2) {
        const qreal lower_bound = qreal(.01);
        if (depth == 32 || (bounds.width() < lower_bound && bounds.height() < lower_bound))
            return true;
 
        const auto halves = bezier.split();
        if (qt_isect_curve_vertical(halves.first, x, y1, y2, depth + 1)
            || qt_isect_curve_vertical(halves.second, x, y1, y2, depth + 1))
            return true;
    }
     return false;
}
 
static bool pointOnEdge(const QRectF &rect, const QPointF &point)
{
    if ((point.x() == rect.left() || point.x() == rect.right()) &&
        (point.y() >= rect.top() && point.y() <= rect.bottom()))
        return true;
    if ((point.y() == rect.top() || point.y() == rect.bottom()) &&
        (point.x() >= rect.left() && point.x() <= rect.right()))
        return true;
    return false;
}
 
/*
    Returns \c true if any lines or curves cross the four edges in of rect
*/
static bool qt_painterpath_check_crossing(const QPainterPath *path, const QRectF &rect)
{
    QPointF last_pt;
    QPointF last_start;
    enum { OnRect, InsideRect, OutsideRect} edgeStatus = OnRect;
    for (int i=0; i<path->elementCount(); ++i) {
        const QPainterPath::Element &e = path->elementAt(i);
 
        switch (e.type) {
 
        case QPainterPath::MoveToElement:
            if (i > 0
                && qFuzzyCompare(last_pt.x(), last_start.x())
                && qFuzzyCompare(last_pt.y(), last_start.y())
                && qt_painterpath_isect_line_rect(last_pt.x(), last_pt.y(),
                                                  last_start.x(), last_start.y(), rect))
                return true;
            last_start = last_pt = e;
            break;
 
        case QPainterPath::LineToElement:
            if (qt_painterpath_isect_line_rect(last_pt.x(), last_pt.y(), e.x, e.y, rect))
                return true;
            last_pt = e;
            break;
 
        case QPainterPath::CurveToElement:
            {
                QPointF cp2 = path->elementAt(++i);
                QPointF ep = path->elementAt(++i);
                QBezier bezier = QBezier::fromPoints(last_pt, e, cp2, ep);
                if (qt_isect_curve_horizontal(bezier, rect.top(), rect.left(), rect.right())
                    || qt_isect_curve_horizontal(bezier, rect.bottom(), rect.left(), rect.right())
                    || qt_isect_curve_vertical(bezier, rect.left(), rect.top(), rect.bottom())
                    || qt_isect_curve_vertical(bezier, rect.right(), rect.top(), rect.bottom()))
                    return true;
                last_pt = ep;
            }
            break;
 
        default:
            break;
        }
        // Handle crossing the edges of the rect at the end-points of individual sub-paths.
        // A point on on the edge itself is considered neither inside nor outside for this purpose.
        if (!pointOnEdge(rect, last_pt)) {
            bool contained = rect.contains(last_pt);
            switch (edgeStatus) {
            case OutsideRect:
                if (contained)
                    return true;
                break;
            case InsideRect:
                if (!contained)
                    return true;
                break;
            case OnRect:
                edgeStatus = contained ? InsideRect : OutsideRect;
                break;
            }
        } else {
            if (last_pt == last_start)
                edgeStatus = OnRect;
        }
    }
 
    // implicitly close last subpath
    if (last_pt != last_start
        && qt_painterpath_isect_line_rect(last_pt.x(), last_pt.y(),
                                          last_start.x(), last_start.y(), rect))
        return true;
 
    return false;
}
 
bool QPainterPath::intersects(const QRectF &rect) const
{
    if (elementCount() == 1 && rect.contains(elementAt(0)))
        return true;
 
    if (isEmpty())
        return false;
 
    QRectF cp = controlPointRect();
    QRectF rn = rect.normalized();
 
    // QRectF::intersects returns false if one of the rects is a null rect
    // which would happen for a painter path consisting of a vertical or
    // horizontal line
    if (qMax(rn.left(), cp.left()) > qMin(rn.right(), cp.right())
        || qMax(rn.top(), cp.top()) > qMin(rn.bottom(), cp.bottom()))
        return false;
 
    // If any path element cross the rect its bound to be an intersection
    if (qt_painterpath_check_crossing(this, rect))
        return true;
 
    if (contains(rect.center()))
        return true;
 
    Q_D(QPainterPath);
 
    // Check if the rectangle surrounds any subpath...
    for (int i=0; i<d->elements.size(); ++i) {
        const Element &e = d->elements.at(i);
        if (e.type == QPainterPath::MoveToElement && rect.contains(e))
            return true;
    }
 
    return false;
}
 
void QPainterPath::translate(qreal dx, qreal dy)
{
    if (!d_ptr || (dx == 0 && dy == 0))
        return;
 
    int elementsLeft = d_ptr->elements.size();
    if (elementsLeft <= 0)
        return;
 
    detach();
    QPainterPath::Element *element = d_func()->elements.data();
    Q_ASSERT(element);
    while (elementsLeft--) {
        element->x += dx;
        element->y += dy;
        ++element;
    }
}
 
QPainterPath QPainterPath::translated(qreal dx, qreal dy) const
{
    QPainterPath copy(*this);
    copy.translate(dx, dy);
    return copy;
}
 
bool QPainterPath::contains(const QRectF &rect) const
{
    Q_D(QPainterPath);
 
    // the path is empty or the control point rect doesn't completely
    // cover the rectangle we abort stratight away.
    if (isEmpty() || !controlPointRect().contains(rect))
        return false;
 
    // if there are intersections, chances are that the rect is not
    // contained, except if we have winding rule, in which case it
    // still might.
    if (qt_painterpath_check_crossing(this, rect)) {
        if (fillRule() == Qt::OddEvenFill) {
            return false;
        } else {
            // Do some wague sampling in the winding case. This is not
            // precise but it should mostly be good enough.
            if (!contains(rect.topLeft()) ||
                !contains(rect.topRight()) ||
                !contains(rect.bottomRight()) ||
                !contains(rect.bottomLeft()))
                return false;
        }
    }
 
    // If there exists a point inside that is not part of the path its
    // because: rectangle lies completely outside path or a subpath
    // excludes parts of the rectangle. Both cases mean that the rect
    // is not contained
    if (!contains(rect.center()))
        return false;
 
    // If there are any subpaths inside this rectangle we need to
    // check if they are still contained as a result of the fill
    // rule. This can only be the case for WindingFill though. For
    // OddEvenFill the rect will never be contained if it surrounds a
    // subpath. (the case where two subpaths are completely identical
    // can be argued but we choose to neglect it).
    for (int i=0; i<d->elements.size(); ++i) {
        const Element &e = d->elements.at(i);
        if (e.type == QPainterPath::MoveToElement && rect.contains(e)) {
            if (fillRule() == Qt::OddEvenFill)
                return false;
 
            bool stop = false;
            for (; !stop && i<d->elements.size(); ++i) {
                const Element &el = d->elements.at(i);
                switch (el.type) {
                case MoveToElement:
                    stop = true;
                    break;
                case LineToElement:
                    if (!contains(el))
                        return false;
                    break;
                case CurveToElement:
                    if (!contains(d->elements.at(i+2)))
                        return false;
                    i += 2;
                    break;
                default:
                    break;
                }
            }
 
            // compensate for the last ++i in the inner for
            --i;
        }
    }
 
    return true;
}
 
static inline bool epsilonCompare(const QPointF &a, const QPointF &b, const QSizeF &epsilon)
{
    return qAbs(a.x() - b.x()) <= epsilon.width()
        && qAbs(a.y() - b.y()) <= epsilon.height();
}
 
bool QPainterPath::operator==(const QPainterPath &path) const
{
    QPainterPathPrivate *d = d_func();
    QPainterPathPrivate *other_d = path.d_func();
    if (other_d == d) {
        return true;
    } else if (!d || !other_d) {
        if (!other_d && isEmpty() && elementAt(0) == QPointF() && d->fillRule == Qt::OddEvenFill)
            return true;
        if (!d && path.isEmpty() && path.elementAt(0) == QPointF() && other_d->fillRule == Qt::OddEvenFill)
            return true;
        return false;
    }
    else if (d->fillRule != other_d->fillRule)
        return false;
    else if (d->elements.size() != other_d->elements.size())
        return false;
 
    const qreal qt_epsilon = sizeof(qreal) == sizeof(double) ? 1e-12 : qreal(1e-5);
 
    QSizeF epsilon = boundingRect().size();
    epsilon.rwidth() *= qt_epsilon;
    epsilon.rheight() *= qt_epsilon;
 
    for (int i = 0; i < d->elements.size(); ++i)
        if (d->elements.at(i).type != other_d->elements.at(i).type
            || !epsilonCompare(d->elements.at(i), other_d->elements.at(i), epsilon))
            return false;
 
    return true;
}
 
bool QPainterPath::operator!=(const QPainterPath &path) const
{
    return !(*this==path);
}
 
QPainterPath QPainterPath::operator&(const QPainterPath &other) const
{
    return intersected(other);
}
 
QPainterPath QPainterPath::operator|(const QPainterPath &other) const
{
    return united(other);
}
 
QPainterPath QPainterPath::operator+(const QPainterPath &other) const
{
    return united(other);
}
 
QPainterPath QPainterPath::operator-(const QPainterPath &other) const
{
    return subtracted(other);
}
 
QPainterPath &QPainterPath::operator&=(const QPainterPath &other)
{
    return *this = (*this & other);
}
 
QPainterPath &QPainterPath::operator|=(const QPainterPath &other)
{
    return *this = (*this | other);
}
 
QPainterPath &QPainterPath::operator+=(const QPainterPath &other)
{
    return *this = (*this + other);
}
 
QPainterPath &QPainterPath::operator-=(const QPainterPath &other)
{
    return *this = (*this - other);
}
 
#ifndef QT_NO_DATASTREAM
QDataStream &operator<<(QDataStream &s, const QPainterPath &p)
{
    if (p.isEmpty()) {
        s << 0;
        return s;
    }
 
    s << p.elementCount();
    for (int i=0; i < p.d_func()->elements.size(); ++i) {
        const QPainterPath::Element &e = p.d_func()->elements.at(i);
        s << int(e.type);
        s << double(e.x) << double(e.y);
    }
    s << p.d_func()->cStart;
    s << int(p.d_func()->fillRule);
    return s;
}
 
QDataStream &operator>>(QDataStream &s, QPainterPath &p)
{
    bool errorDetected = false;
    int size;
    s >> size;
 
    if (size == 0) {
        p = {};
        return s;
    }
 
    p.ensureData(); // in case if p.d_func() == 0
    p.detach();
    p.d_func()->elements.clear();
    for (int i=0; i<size; ++i) {
        int type;
        double x, y;
        s >> type;
        s >> x;
        s >> y;
        Q_ASSERT(type >= 0 && type <= 3);
        if (!isValidCoord(qreal(x)) || !isValidCoord(qreal(y))) {
#ifndef QT_NO_DEBUG
            qWarning("QDataStream::operator>>: Invalid QPainterPath coordinates read, skipping it");
#endif
            errorDetected = true;
            continue;
        }
        QPainterPath::Element elm = { qreal(x), qreal(y), QPainterPath::ElementType(type) };
        p.d_func()->elements.append(elm);
    }
    s >> p.d_func()->cStart;
    int fillRule;
    s >> fillRule;
    Q_ASSERT(fillRule == Qt::OddEvenFill || fillRule == Qt::WindingFill);
    p.d_func()->fillRule = Qt::FillRule(fillRule);
    if (errorDetected || p.d_func()->elements.isEmpty())
        p = QPainterPath();  // Better than to return path with possibly corrupt datastructure, which would likely cause crash
    return s;
}
#endif // QT_NO_DATASTREAM
 
 
/*******************************************************************************
 * class QPainterPathStroker
 */
 
void qt_path_stroke_move_to(qfixed x, qfixed y, void *data)
{
    ((QPainterPath *) data)->moveTo(qt_fixed_to_real(x), qt_fixed_to_real(y));
}
 
void qt_path_stroke_line_to(qfixed x, qfixed y, void *data)
{
    ((QPainterPath *) data)->lineTo(qt_fixed_to_real(x), qt_fixed_to_real(y));
}
 
void qt_path_stroke_cubic_to(qfixed c1x, qfixed c1y,
                             qfixed c2x, qfixed c2y,
                             qfixed ex, qfixed ey,
                             void *data)
{
    ((QPainterPath *) data)->cubicTo(qt_fixed_to_real(c1x), qt_fixed_to_real(c1y),
                                     qt_fixed_to_real(c2x), qt_fixed_to_real(c2y),
                                     qt_fixed_to_real(ex), qt_fixed_to_real(ey));
}
 
QPainterPathStrokerPrivate::QPainterPathStrokerPrivate()
    : dashOffset(0)
{
    stroker.setMoveToHook(qt_path_stroke_move_to);
    stroker.setLineToHook(qt_path_stroke_line_to);
    stroker.setCubicToHook(qt_path_stroke_cubic_to);
}
 
QPainterPathStroker::QPainterPathStroker()
    : d_ptr(new QPainterPathStrokerPrivate)
{
}
 
QPainterPathStroker::QPainterPathStroker(const QPen &pen)
    : d_ptr(new QPainterPathStrokerPrivate)
{
    setWidth(pen.widthF());
    setCapStyle(pen.capStyle());
    setJoinStyle(pen.joinStyle());
    setMiterLimit(pen.miterLimit());
    setDashOffset(pen.dashOffset());
 
    if (pen.style() == Qt::CustomDashLine)
        setDashPattern(pen.dashPattern());
    else
        setDashPattern(pen.style());
}
 
QPainterPathStroker::~QPainterPathStroker()
{
}
 
 
QPainterPath QPainterPathStroker::createStroke(const QPainterPath &path) const
{
    QPainterPathStrokerPrivate *d = const_cast<QPainterPathStrokerPrivate *>(d_func());
    QPainterPath stroke;
    if (path.isEmpty())
        return path;
    if (d->dashPattern.isEmpty()) {
        d->stroker.strokePath(path, &stroke, QTransform());
    } else {
        QDashStroker dashStroker(&d->stroker);
        dashStroker.setDashPattern(d->dashPattern);
        dashStroker.setDashOffset(d->dashOffset);
        dashStroker.setClipRect(d->stroker.clipRect());
        dashStroker.strokePath(path, &stroke, QTransform());
    }
    stroke.setFillRule(Qt::WindingFill);
    return stroke;
}
 
void QPainterPathStroker::setWidth(qreal width)
{
    Q_D(QPainterPathStroker);
    if (width <= 0)
        width = 1;
    d->stroker.setStrokeWidth(qt_real_to_fixed(width));
}
 
qreal QPainterPathStroker::width() const
{
    return qt_fixed_to_real(d_func()->stroker.strokeWidth());
}
 
 
void QPainterPathStroker::setCapStyle(Qt::PenCapStyle style)
{
    d_func()->stroker.setCapStyle(style);
}
 
 
Qt::PenCapStyle QPainterPathStroker::capStyle() const
{
    return d_func()->stroker.capStyle();
}
 
void QPainterPathStroker::setJoinStyle(Qt::PenJoinStyle style)
{
    d_func()->stroker.setJoinStyle(style);
}
 
Qt::PenJoinStyle QPainterPathStroker::joinStyle() const
{
    return d_func()->stroker.joinStyle();
}
 
void QPainterPathStroker::setMiterLimit(qreal limit)
{
    d_func()->stroker.setMiterLimit(qt_real_to_fixed(limit));
}
 
qreal QPainterPathStroker::miterLimit() const
{
    return qt_fixed_to_real(d_func()->stroker.miterLimit());
}
 
 
void QPainterPathStroker::setCurveThreshold(qreal threshold)
{
    d_func()->stroker.setCurveThreshold(qt_real_to_fixed(threshold));
}
 
qreal QPainterPathStroker::curveThreshold() const
{
    return qt_fixed_to_real(d_func()->stroker.curveThreshold());
}
 
void QPainterPathStroker::setDashPattern(Qt::PenStyle style)
{
    d_func()->dashPattern = QDashStroker::patternForStyle(style);
}
 
void QPainterPathStroker::setDashPattern(const QList<qreal> &dashPattern)
{
    d_func()->dashPattern.clear();
    for (int i=0; i<dashPattern.size(); ++i)
        d_func()->dashPattern << qt_real_to_fixed(dashPattern.at(i));
}
 
QList<qreal> QPainterPathStroker::dashPattern() const
{
    return d_func()->dashPattern;
}
 
qreal QPainterPathStroker::dashOffset() const
{
    return d_func()->dashOffset;
}
 
void QPainterPathStroker::setDashOffset(qreal offset)
{
    d_func()->dashOffset = offset;
}
 
QPolygonF QPainterPath::toFillPolygon(const QTransform &matrix) const
{
    const QList<QPolygonF> flats = toSubpathPolygons(matrix);
    QPolygonF polygon;
    if (flats.isEmpty())
        return polygon;
    QPointF first = flats.first().first();
    for (int i=0; i<flats.size(); ++i) {
        polygon += flats.at(i);
        if (!flats.at(i).isClosed())
            polygon += flats.at(i).first();
        if (i > 0)
            polygon += first;
    }
    return polygon;
}
 
//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);
}
 
qreal QPainterPath::length() const
{
    Q_D(QPainterPath);
    if (isEmpty())
        return 0;
 
    qreal len = 0;
    for (int i=1; i<d->elements.size(); ++i) {
        const Element &e = d->elements.at(i);
 
        switch (e.type) {
        case MoveToElement:
            break;
        case LineToElement:
        {
            len += QLineF(d->elements.at(i-1), e).length();
            break;
        }
        case CurveToElement:
        {
            QBezier b = QBezier::fromPoints(d->elements.at(i-1),
                                            e,
                                            d->elements.at(i+1),
                                            d->elements.at(i+2));
            len += b.length();
            i += 2;
            break;
        }
        default:
            break;
        }
    }
    return len;
}
 
qreal QPainterPath::percentAtLength(qreal len) const
{
    Q_D(QPainterPath);
    if (isEmpty() || len <= 0)
        return 0;
 
    qreal totalLength = length();
    if (len > totalLength)
        return 1;
 
    qreal curLen = 0;
    for (int i=1; i<d->elements.size(); ++i) {
        const Element &e = d->elements.at(i);
 
        switch (e.type) {
        case MoveToElement:
            break;
        case LineToElement:
        {
            QLineF line(d->elements.at(i-1), e);
            qreal llen = line.length();
            curLen += llen;
            if (curLen >= len) {
                return len/totalLength ;
            }
 
            break;
        }
        case CurveToElement:
        {
            QBezier b = QBezier::fromPoints(d->elements.at(i-1),
                                            e,
                                            d->elements.at(i+1),
                                            d->elements.at(i+2));
            qreal blen = b.length();
            qreal prevLen = curLen;
            curLen += blen;
 
            if (curLen >= len) {
                qreal res = b.tAtLength(len - prevLen);
                return (res * blen + prevLen)/totalLength;
            }
 
            i += 2;
            break;
        }
        default:
            break;
        }
    }
 
    return 0;
}
 
static inline QBezier bezierAtT(const QPainterPath &path, qreal t, qreal *startingLength, qreal *bezierLength)
{
    *startingLength = 0;
    if (t > 1)
        return QBezier();
 
    qreal curLen = 0;
    qreal totalLength = path.length();
 
    const int lastElement = path.elementCount() - 1;
    for (int i=0; i <= lastElement; ++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);
            qreal llen = line.length();
            curLen += llen;
            if (i == lastElement || curLen/totalLength >= t) {
                *bezierLength = llen;
                QPointF a = path.elementAt(i-1);
                QPointF delta = e - a;
                return QBezier::fromPoints(a, a + delta / 3, a + 2 * delta / 3, e);
            }
            break;
        }
        case QPainterPath::CurveToElement:
        {
            QBezier b = QBezier::fromPoints(path.elementAt(i-1),
                                            e,
                                            path.elementAt(i+1),
                                            path.elementAt(i+2));
            qreal blen = b.length();
            curLen += blen;
 
            if (i + 2 == lastElement || curLen/totalLength >= t) {
                *bezierLength = blen;
                return b;
            }
 
            i += 2;
            break;
        }
        default:
            break;
        }
        *startingLength = curLen;
    }
    return QBezier();
}
 
QPointF QPainterPath::pointAtPercent(qreal t) const
{
    if (t < 0 || t > 1) {
        qWarning("QPainterPath::pointAtPercent accepts only values between 0 and 1");
        return QPointF();
    }
 
    if (!d_ptr || d_ptr->elements.size() == 0)
        return QPointF();
 
    if (d_ptr->elements.size() == 1)
        return d_ptr->elements.at(0);
 
    qreal totalLength = length();
    qreal curLen = 0;
    qreal bezierLen = 0;
    QBezier b = bezierAtT(*this, t, &curLen, &bezierLen);
    qreal realT = (totalLength * t - curLen) / bezierLen;
 
    return b.pointAt(qBound(qreal(0), realT, qreal(1)));
}
 
qreal QPainterPath::angleAtPercent(qreal t) const
{
    if (t < 0 || t > 1) {
        qWarning("QPainterPath::angleAtPercent accepts only values between 0 and 1");
        return 0;
    }
 
    qreal totalLength = length();
    qreal curLen = 0;
    qreal bezierLen = 0;
    QBezier bez = bezierAtT(*this, t, &curLen, &bezierLen);
    qreal realT = (totalLength * t - curLen) / bezierLen;
 
    qreal m1 = slopeAt(realT, bez.x1, bez.x2, bez.x3, bez.x4);
    qreal m2 = slopeAt(realT, bez.y1, bez.y2, bez.y3, bez.y4);
 
    return QLineF(0, 0, m1, m2).angle();
}
 
 
qreal QPainterPath::slopeAtPercent(qreal t) const
{
    if (t < 0 || t > 1) {
        qWarning("QPainterPath::slopeAtPercent accepts only values between 0 and 1");
        return 0;
    }
 
    qreal totalLength = length();
    qreal curLen = 0;
    qreal bezierLen = 0;
    QBezier bez = bezierAtT(*this, t, &curLen, &bezierLen);
    qreal realT = (totalLength * t - curLen) / bezierLen;
 
    qreal m1 = slopeAt(realT, bez.x1, bez.x2, bez.x3, bez.x4);
    qreal m2 = slopeAt(realT, bez.y1, bez.y2, bez.y3, bez.y4);
    //tangent line
    qreal slope = 0;
 
    if (m1)
        slope = m2/m1;
    else {
        if (std::numeric_limits<qreal>::has_infinity) {
            slope = (m2  < 0) ? -std::numeric_limits<qreal>::infinity()
                              : std::numeric_limits<qreal>::infinity();
        } else {
            if (sizeof(qreal) == sizeof(double)) {
                return 1.79769313486231570e+308;
            } else {
                return ((qreal)3.40282346638528860e+38);
            }
        }
    }
 
    return slope;
}
 
void QPainterPath::addRoundedRect(const QRectF &rect, qreal xRadius, qreal yRadius,
                                  Qt::SizeMode mode)
{
    QRectF r = rect.normalized();
 
    if (r.isNull())
        return;
 
    if (mode == Qt::AbsoluteSize) {
        qreal w = r.width() / 2;
        qreal h = r.height() / 2;
 
        if (w == 0) {
            xRadius = 0;
        } else {
            xRadius = 100 * qMin(xRadius, w) / w;
        }
        if (h == 0) {
            yRadius = 0;
        } else {
            yRadius = 100 * qMin(yRadius, h) / h;
        }
    } else {
        if (xRadius > 100)                          // fix ranges
            xRadius = 100;
 
        if (yRadius > 100)
            yRadius = 100;
    }
 
    if (xRadius <= 0 || yRadius <= 0) {             // add normal rectangle
        addRect(r);
        return;
    }
 
    qreal x = r.x();
    qreal y = r.y();
    qreal w = r.width();
    qreal h = r.height();
    qreal rxx2 = w*xRadius/100;
    qreal ryy2 = h*yRadius/100;
 
    ensureData();
    detach();
 
    bool first = d_func()->elements.size() < 2;
 
    arcMoveTo(x, y, rxx2, ryy2, 180);
    arcTo(x, y, rxx2, ryy2, 180, -90);
    arcTo(x+w-rxx2, y, rxx2, ryy2, 90, -90);
    arcTo(x+w-rxx2, y+h-ryy2, rxx2, ryy2, 0, -90);
    arcTo(x, y+h-ryy2, rxx2, ryy2, 270, -90);
    closeSubpath();
 
    d_func()->require_moveTo = true;
    d_func()->convex = first;
}
 
QPainterPath QPainterPath::united(const QPainterPath &p) const
{
    if (isEmpty() || p.isEmpty())
        return isEmpty() ? p : *this;
    QPathClipper clipper(*this, p);
    return clipper.clip(QPathClipper::BoolOr);
}
 
QPainterPath QPainterPath::intersected(const QPainterPath &p) const
{
    if (isEmpty() || p.isEmpty())
        return QPainterPath();
    QPathClipper clipper(*this, p);
    return clipper.clip(QPathClipper::BoolAnd);
}
 
QPainterPath QPainterPath::subtracted(const QPainterPath &p) const
{
    if (isEmpty() || p.isEmpty())
        return *this;
    QPathClipper clipper(*this, p);
    return clipper.clip(QPathClipper::BoolSub);
}
 
QPainterPath QPainterPath::simplified() const
{
    if (isEmpty())
        return *this;
    QPathClipper clipper(*this, QPainterPath());
    return clipper.clip(QPathClipper::Simplify);
}
 
bool QPainterPath::intersects(const QPainterPath &p) const
{
    if (p.elementCount() == 1)
        return contains(p.elementAt(0));
    if (isEmpty() || p.isEmpty())
        return false;
    QPathClipper clipper(*this, p);
    return clipper.intersect();
}
 
bool QPainterPath::contains(const QPainterPath &p) const
{
    if (p.elementCount() == 1)
        return contains(p.elementAt(0));
    if (isEmpty() || p.isEmpty())
        return false;
    QPathClipper clipper(*this, p);
    return clipper.contains();
}
 
void QPainterPath::setDirty(bool dirty)
{
    d_func()->dirtyBounds        = dirty;
    d_func()->dirtyControlBounds = dirty;
    d_func()->pathConverter.reset();
    d_func()->convex = false;
}
 
void QPainterPath::computeBoundingRect() const
{
    QPainterPathPrivate *d = d_func();
    d->dirtyBounds = false;
    if (!d_ptr) {
        d->bounds = QRect();
        return;
    }
 
    qreal minx, maxx, miny, maxy;
    minx = maxx = d->elements.at(0).x;
    miny = maxy = d->elements.at(0).y;
    for (int i=1; i<d->elements.size(); ++i) {
        const Element &e = d->elements.at(i);
 
        switch (e.type) {
        case MoveToElement:
        case LineToElement:
            if (e.x > maxx) maxx = e.x;
            else if (e.x < minx) minx = e.x;
            if (e.y > maxy) maxy = e.y;
            else if (e.y < miny) miny = e.y;
            break;
        case CurveToElement:
            {
                QBezier b = QBezier::fromPoints(d->elements.at(i-1),
                                                e,
                                                d->elements.at(i+1),
                                                d->elements.at(i+2));
                QRectF r = qt_painterpath_bezier_extrema(b);
                qreal right = r.right();
                qreal bottom = r.bottom();
                if (r.x() < minx) minx = r.x();
                if (right > maxx) maxx = right;
                if (r.y() < miny) miny = r.y();
                if (bottom > maxy) maxy = bottom;
                i += 2;
            }
            break;
        default:
            break;
        }
    }
    d->bounds = QRectF(minx, miny, maxx - minx, maxy - miny);
}
 
 
void QPainterPath::computeControlPointRect() const
{
    QPainterPathPrivate *d = d_func();
    d->dirtyControlBounds = false;
    if (!d_ptr) {
        d->controlBounds = QRect();
        return;
    }
 
    qreal minx, maxx, miny, maxy;
    minx = maxx = d->elements.at(0).x;
    miny = maxy = d->elements.at(0).y;
    for (int i=1; i<d->elements.size(); ++i) {
        const Element &e = d->elements.at(i);
        if (e.x > maxx) maxx = e.x;
        else if (e.x < minx) minx = e.x;
        if (e.y > maxy) maxy = e.y;
        else if (e.y < miny) miny = e.y;
    }
    d->controlBounds = QRectF(minx, miny, maxx - minx, maxy - miny);
}
 
#ifndef QT_NO_DEBUG_STREAM
QDebug operator<<(QDebug s, const QPainterPath &p)
{
    s.nospace() << "QPainterPath: Element count=" << p.elementCount() << Qt::endl;
    const char *types[] = {"MoveTo", "LineTo", "CurveTo", "CurveToData"};
    for (int i=0; i<p.elementCount(); ++i) {
        s.nospace() << " -> " << types[p.elementAt(i).type] << "(x=" << p.elementAt(i).x << ", y=" << p.elementAt(i).y << ')' << Qt::endl;
 
    }
    return s;
}
#endif
 
QT_END_NAMESPACE