/src/qt/qtbase/src/gui/painting/qpainterpath.cpp

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#include "qpainterpath.h"
#include "qpainterpath_p.h"

#include <qbitmap.h>
#include <qdebug.h>
#include <qiodevice.h>
#include <qlist.h>
#include <qmatrix.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

struct QPainterPathPrivateDeleter
{
    static inline void cleanup(QPainterPathPrivate *d)
    {
        // note - we must up-cast to QPainterPathData since QPainterPathPrivate
        // has a non-virtual destructor!
        if (d && !d->ref.deref())
            delete static_cast<QPainterPathData *>(d);
    }
};

// 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

/*!
    \class QPainterPath
    \ingroup painting
    \ingroup shared
    \inmodule QtGui

    \brief The QPainterPath class provides a container for painting operations,
    enabling graphical shapes to be constructed and reused.

    A painter path is an object composed of a number of graphical
    building blocks, such as rectangles, ellipses, lines, and curves.
    Building blocks can be joined in closed subpaths, for example as a
    rectangle or an ellipse. A closed path has coinciding start and
    end points. Or they can exist independently as unclosed subpaths,
    such as lines and curves.

    A QPainterPath object can be used for filling, outlining, and
    clipping. To generate fillable outlines for a given painter path,
    use the QPainterPathStroker class.  The main advantage of painter
    paths over normal drawing operations is that complex shapes only
    need to be created once; then they can be drawn many times using
    only calls to the QPainter::drawPath() function.

    QPainterPath provides a collection of functions that can be used
    to obtain information about the path and its elements. In addition
    it is possible to reverse the order of the elements using the
    toReversed() function. There are also several functions to convert
    this painter path object into a polygon representation.

    \tableofcontents

    \section1 Composing a QPainterPath

    A QPainterPath object can be constructed as an empty path, with a
    given start point, or as a copy of another QPainterPath object.
    Once created, lines and curves can be added to the path using the
    lineTo(), arcTo(), cubicTo() and quadTo() functions. The lines and
    curves stretch from the currentPosition() to the position passed
    as argument.

    The currentPosition() of the QPainterPath object is always the end
    position of the last subpath that was added (or the initial start
    point). Use the moveTo() function to move the currentPosition()
    without adding a component. The moveTo() function implicitly
    starts a new subpath, and closes the previous one.  Another way of
    starting a new subpath is to call the closeSubpath() function
    which closes the current path by adding a line from the
    currentPosition() back to the path's start position. Note that the
    new path will have (0, 0) as its initial currentPosition().

    QPainterPath class also provides several convenience functions to
    add closed subpaths to a painter path: addEllipse(), addPath(),
    addRect(), addRegion() and addText(). The addPolygon() function
    adds an \e unclosed subpath. In fact, these functions are all
    collections of moveTo(), lineTo() and cubicTo() operations.

    In addition, a path can be added to the current path using the
    connectPath() function. But note that this function will connect
    the last element of the current path to the first element of given
    one by adding a line.

    Below is a code snippet that shows how a QPainterPath object can
    be used:

    \table 100%
    \row
    \li \inlineimage qpainterpath-construction.png
    \li
    \snippet code/src_gui_painting_qpainterpath.cpp 0
    \endtable

    The painter path is initially empty when constructed. We first add
    a rectangle, which is a closed subpath. Then we add two bezier
    curves which together form a closed subpath even though they are
    not closed individually. Finally we draw the entire path. The path
    is filled using the default fill rule, Qt::OddEvenFill. Qt
    provides two methods for filling paths:

    \table
    \header
    \li Qt::OddEvenFill
    \li Qt::WindingFill
    \row
    \li \inlineimage qt-fillrule-oddeven.png
    \li \inlineimage qt-fillrule-winding.png
    \endtable

    See the Qt::FillRule documentation for the definition of the
    rules. A painter path's currently set fill rule can be retrieved
    using the fillRule() function, and altered using the setFillRule()
    function.

    \section1 QPainterPath Information

    The QPainterPath class provides a collection of functions that
    returns information about the path and its elements.

    The currentPosition() function returns the end point of the last
    subpath that was added (or the initial start point). The
    elementAt() function can be used to retrieve the various subpath
    elements, the \e number of elements can be retrieved using the
    elementCount() function, and the isEmpty() function tells whether
    this QPainterPath object contains any elements at all.

    The controlPointRect() function returns the rectangle containing
    all the points and control points in this path. This function is
    significantly faster to compute than the exact boundingRect()
    which returns the bounding rectangle of this painter path with
    floating point precision.

    Finally, QPainterPath provides the contains() function which can
    be used to determine whether a given point or rectangle is inside
    the path, and the intersects() function which determines if any of
    the points inside a given rectangle also are inside this path.

    \section1 QPainterPath Conversion

    For compatibility reasons, it might be required to simplify the
    representation of a painter path: QPainterPath provides the
    toFillPolygon(), toFillPolygons() and toSubpathPolygons()
    functions which convert the painter path into a polygon. The
    toFillPolygon() returns the painter path as one single polygon,
    while the two latter functions return a list of polygons.

    The toFillPolygons() and toSubpathPolygons() functions are
    provided because it is usually faster to draw several small
    polygons than to draw one large polygon, even though the total
    number of points drawn is the same. The difference between the two
    is the \e number of polygons they return: The toSubpathPolygons()
    creates one polygon for each subpath regardless of intersecting
    subpaths (i.e. overlapping bounding rectangles), while the
    toFillPolygons() functions creates only one polygon for
    overlapping subpaths.

    The toFillPolygon() and toFillPolygons() functions first convert
    all the subpaths to polygons, then uses a rewinding technique to
    make sure that overlapping subpaths can be filled using the
    correct fill rule. Note that rewinding inserts additional lines in
    the polygon so the outline of the fill polygon does not match the
    outline of the path.

    \section1 Examples

    Qt provides the \l {painting/painterpaths}{Painter Paths Example}
    and the \l {painting/deform}{Vector Deformation example} which are
    located in Qt's example directory.

    The \l {painting/painterpaths}{Painter Paths Example} shows how
    painter paths can be used to build complex shapes for rendering
    and lets the user experiment with the filling and stroking.  The
    \l {painting/deform}{Vector Deformation Example} shows how to use
    QPainterPath to draw text.

    \table
    \header
    \li \l {painting/painterpaths}{Painter Paths Example}
    \li \l {painting/deform}{Vector Deformation Example}
    \row
    \li \inlineimage qpainterpath-example.png
    \li \inlineimage qpainterpath-demo.png
    \endtable

    \sa QPainterPathStroker, QPainter, QRegion, {Painter Paths Example}
*/

/*!
    \enum QPainterPath::ElementType

    This enum describes the types of elements used to connect vertices
    in subpaths.

    Note that elements added as closed subpaths using the
    addEllipse(), addPath(), addPolygon(), addRect(), addRegion() and
    addText() convenience functions, is actually added to the path as
    a collection of separate elements using the moveTo(), lineTo() and
    cubicTo() functions.

    \value MoveToElement          A new subpath. See also moveTo().
    \value LineToElement            A line. See also lineTo().
    \value CurveToElement         A curve. See also cubicTo() and quadTo().
    \value CurveToDataElement  The extra data required to describe a curve in
                                               a CurveToElement element.

    \sa elementAt(), elementCount()
*/

/*!
    \class QPainterPath::Element
    \inmodule QtGui

    \brief The QPainterPath::Element class specifies the position and
    type of a subpath.

    Once a QPainterPath object is constructed, subpaths like lines and
    curves can be added to the path (creating
    QPainterPath::LineToElement and QPainterPath::CurveToElement
    components).

    The lines and curves stretch from the currentPosition() to the
    position passed as argument. The currentPosition() of the
    QPainterPath object is always the end position of the last subpath
    that was added (or the initial start point). The moveTo() function
    can be used to move the currentPosition() without adding a line or
    curve, creating a QPainterPath::MoveToElement component.

    \sa QPainterPath
*/

/*!
    \variable QPainterPath::Element::x
    \brief the x coordinate of the element's position.

    \sa {operator QPointF()}
*/

/*!
    \variable QPainterPath::Element::y
    \brief the y coordinate of the element's position.

    \sa {operator QPointF()}
*/

/*!
    \variable QPainterPath::Element::type
    \brief the type of element

    \sa isCurveTo(), isLineTo(), isMoveTo()
*/

/*!
    \fn bool QPainterPath::Element::operator==(const Element &other) const
    \since 4.2

    Returns \c true if this element is equal to \a other;
    otherwise returns \c false.

    \sa operator!=()
*/

/*!
    \fn bool QPainterPath::Element::operator!=(const Element &other) const
    \since 4.2

    Returns \c true if this element is not equal to \a other;
    otherwise returns \c false.

    \sa operator==()
*/

/*!
    \fn bool QPainterPath::Element::isCurveTo () const

    Returns \c true if the element is a curve, otherwise returns \c false.

    \sa type, QPainterPath::CurveToElement
*/

/*!
    \fn bool QPainterPath::Element::isLineTo () const

    Returns \c true if the element is a line, otherwise returns \c false.

    \sa type, QPainterPath::LineToElement
*/

/*!
    \fn bool QPainterPath::Element::isMoveTo () const

    Returns \c true if the element is moving the current position,
    otherwise returns \c false.

    \sa type, QPainterPath::MoveToElement
*/

/*!
    \fn QPainterPath::Element::operator QPointF () const

    Returns the element's position.

    \sa x, y
*/

/*!
    \fn void QPainterPath::addEllipse(qreal x, qreal y, qreal width, qreal height)
    \overload

    Creates an ellipse within the bounding rectangle defined by its top-left
    corner at (\a x, \a y), \a width and \a height, and adds it to the
    painter path as a closed subpath.
*/

/*!
    \since 4.4

    \fn void QPainterPath::addEllipse(const QPointF &center, qreal rx, qreal ry)
    \overload

    Creates an ellipse positioned at \a{center} with radii \a{rx} and \a{ry},
    and adds it to the painter path as a closed subpath.
*/

/*!
    \fn void QPainterPath::addText(qreal x, qreal y, const QFont &font, const QString &text)
    \overload

    Adds the given \a text to this path as a set of closed subpaths created
    from the \a font supplied. The subpaths are positioned so that the left
    end of the text's baseline lies at the point specified by (\a x, \a y).
*/

/*!
    \fn int QPainterPath::elementCount() const

    Returns the number of path elements in the painter path.

    \sa ElementType, elementAt(), isEmpty()
*/

int QPainterPath::elementCount() const
{
    return d_ptr ? d_ptr->elements.size() : 0;
}

/*!
    \fn QPainterPath::Element QPainterPath::elementAt(int index) const

    Returns the element at the given \a index in the painter path.

    \sa ElementType, elementCount(), isEmpty()
*/

QPainterPath::Element QPainterPath::elementAt(int i) const
{
    Q_ASSERT(d_ptr);
    Q_ASSERT(i >= 0 && i < elementCount());
    return d_ptr->elements.at(i);
}

/*!
    \fn void QPainterPath::setElementPositionAt(int index, qreal x, qreal y)
    \since 4.2

    Sets the x and y coordinate of the element at index \a index to \a
    x and \a y.
*/

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.
*/

/*!
    Constructs an empty QPainterPath object.
*/
QPainterPath::QPainterPath()
    : d_ptr(0)
{
}

/*!
    \fn QPainterPath::QPainterPath(const QPainterPath &path)

    Creates a QPainterPath object that is a copy of the given \a path.

    \sa operator=()
*/
QPainterPath::QPainterPath(const QPainterPath &other)
    : d_ptr(other.d_ptr.data())
{
    if (d_ptr)
        d_ptr->ref.ref();
}

/*!
    Creates a QPainterPath object with the given \a startPoint as its
    current position.
*/

QPainterPath::QPainterPath(const QPointF &startPoint)
    : d_ptr(new QPainterPathData)
{
    Element e = { startPoint.x(), startPoint.y(), MoveToElement };
    d_func()->elements << e;
}

void QPainterPath::detach()
{
    if (d_ptr->ref.load() != 1)
        detach_helper();
    setDirty(true);
}

/*!
    \internal
*/
void QPainterPath::detach_helper()
{
    QPainterPathPrivate *data = new QPainterPathData(*d_func());
    d_ptr.reset(data);
}

/*!
    \internal
*/
void QPainterPath::ensureData_helper()
{
    QPainterPathPrivate *data = new QPainterPathData;
    data->elements.reserve(16);
    QPainterPath::Element e = { 0, 0, QPainterPath::MoveToElement };
    data->elements << e;
    d_ptr.reset(data);
    Q_ASSERT(d_ptr != 0);
}

/*!
    \fn QPainterPath &QPainterPath::operator=(const QPainterPath &path)

    Assigns the given \a path to this painter path.

    \sa QPainterPath()
*/
QPainterPath &QPainterPath::operator=(const QPainterPath &other)
{
    if (other.d_func() != d_func()) {
        QPainterPathPrivate *data = other.d_func();
        if (data)
            data->ref.ref();
        d_ptr.reset(data);
    }
    return *this;
}

/*!
    \fn QPainterPath &QPainterPath::operator=(QPainterPath &&other)

    Move-assigns \a other to this QPainterPath instance.

    \since 5.2
*/

/*!
    \fn void QPainterPath::swap(QPainterPath &other)
    \since 4.8

    Swaps painter path \a other with this painter path. This operation is very
    fast and never fails.
*/

/*!
    Destroys this QPainterPath object.
*/
QPainterPath::~QPainterPath()
{
}

/*!
    Closes the current subpath by drawing a line to the beginning of
    the subpath, automatically starting a new path. The current point
    of the new path is (0, 0).

    If the subpath does not contain any elements, this function does
    nothing.

    \sa moveTo(), {QPainterPath#Composing a QPainterPath}{Composing
    a QPainterPath}
 */
void QPainterPath::closeSubpath()
{
#ifdef QPP_DEBUG
    printf("QPainterPath::closeSubpath()\n");
#endif
    if (isEmpty())
        return;
    detach();

    d_func()->close();
}

/*!
    \fn void QPainterPath::moveTo(qreal x, qreal y)

    \overload

    Moves the current position to (\a{x}, \a{y}) and starts a new
    subpath, implicitly closing the previous path.
*/

/*!
    \fn void QPainterPath::moveTo(const QPointF &point)

    Moves the current point to the given \a point, implicitly starting
    a new subpath and closing the previous one.

    \sa closeSubpath(), {QPainterPath#Composing a
    QPainterPath}{Composing a QPainterPath}
*/
void QPainterPath::moveTo(const QPointF &p)
{
#ifdef QPP_DEBUG
    printf("QPainterPath::moveTo() (%.2f,%.2f)\n", p.x(), p.y());
#endif

    if (!qt_is_finite(p.x()) || !qt_is_finite(p.y())) {
#ifndef QT_NO_DEBUG
        qWarning("QPainterPath::moveTo: Adding point where x or y is NaN or Inf, ignoring call");
#endif
        return;
    }

    ensureData();
    detach();

    QPainterPathData *d = d_func();
    Q_ASSERT(!d->elements.isEmpty());

    d->require_moveTo = false;

    if (d->elements.last().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;
}

/*!
    \fn void QPainterPath::lineTo(qreal x, qreal y)

    \overload

    Draws a line from the current position to the point (\a{x},
    \a{y}).
*/

/*!
    \fn void QPainterPath::lineTo(const QPointF &endPoint)

    Adds a straight line from the current position to the given \a
    endPoint.  After the line is drawn, the current position is updated
    to be at the end point of the line.

    \sa addPolygon(), addRect(), {QPainterPath#Composing a
    QPainterPath}{Composing a QPainterPath}
 */
void QPainterPath::lineTo(const QPointF &p)
{
#ifdef QPP_DEBUG
    printf("QPainterPath::lineTo() (%.2f,%.2f)\n", p.x(), p.y());
#endif

    if (!qt_is_finite(p.x()) || !qt_is_finite(p.y())) {
#ifndef QT_NO_DEBUG
        qWarning("QPainterPath::lineTo: Adding point where x or y is NaN or Inf, ignoring call");
#endif
        return;
    }

    ensureData();
    detach();

    QPainterPathData *d = d_func();
    Q_ASSERT(!d->elements.isEmpty());
    d->maybeMoveTo();
    if (p == QPointF(d->elements.last()))
        return;
    Element elm = { p.x(), p.y(), LineToElement };
    d->elements.append(elm);

    d->convex = d->elements.size() == 3 || (d->elements.size() == 4 && d->isClosed());
}

/*!
    \fn void QPainterPath::cubicTo(qreal c1X, qreal c1Y, qreal c2X,
    qreal c2Y, qreal endPointX, qreal endPointY);

    \overload

    Adds a cubic Bezier curve between the current position and the end
    point (\a{endPointX}, \a{endPointY}) with control points specified
    by (\a{c1X}, \a{c1Y}) and (\a{c2X}, \a{c2Y}).
*/

/*!
    \fn void QPainterPath::cubicTo(const QPointF &c1, const QPointF &c2, const QPointF &endPoint)

    Adds a cubic Bezier curve between the current position and the
    given \a endPoint using the control points specified by \a c1, and
    \a c2.

    After the curve is added, the current position is updated to be at
    the end point of the curve.

    \table 100%
    \row
    \li \inlineimage qpainterpath-cubicto.png
    \li
    \snippet code/src_gui_painting_qpainterpath.cpp 1
    \endtable

    \sa quadTo(), {QPainterPath#Composing a QPainterPath}{Composing
    a QPainterPath}
*/
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 (!qt_is_finite(c1.x()) || !qt_is_finite(c1.y()) || !qt_is_finite(c2.x()) || !qt_is_finite(c2.y())
        || !qt_is_finite(e.x()) || !qt_is_finite(e.y())) {
#ifndef QT_NO_DEBUG
        qWarning("QPainterPath::cubicTo: Adding point where x or y is NaN or Inf, ignoring call");
#endif
        return;
    }

    ensureData();
    detach();

    QPainterPathData *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.last() == 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;
}

/*!
    \fn void QPainterPath::quadTo(qreal cx, qreal cy, qreal endPointX, qreal endPointY);

    \overload

    Adds a quadratic Bezier curve between the current point and the endpoint
    (\a{endPointX}, \a{endPointY}) with the control point specified by
    (\a{cx}, \a{cy}).
*/

/*!
    \fn void QPainterPath::quadTo(const QPointF &c, const QPointF &endPoint)

    Adds a quadratic Bezier curve between the current position and the
    given \a endPoint with the control point specified by \a c.

    After the curve is added, the current point is updated to be at
    the end point of the curve.

    \sa cubicTo(), {QPainterPath#Composing a QPainterPath}{Composing a
    QPainterPath}
*/
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 (!qt_is_finite(c.x()) || !qt_is_finite(c.y()) || !qt_is_finite(e.x()) || !qt_is_finite(e.y())) {
#ifndef QT_NO_DEBUG
        qWarning("QPainterPath::quadTo: Adding point where x or y is NaN or Inf, 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);
}

/*!
    \fn void QPainterPath::arcTo(qreal x, qreal y, qreal width, qreal
    height, qreal startAngle, qreal sweepLength)

    \overload

    Creates an arc that occupies the rectangle QRectF(\a x, \a y, \a
    width, \a height), beginning at the specified \a startAngle and
    extending \a sweepLength degrees counter-clockwise.

*/

/*!
    \fn void QPainterPath::arcTo(const QRectF &rectangle, qreal startAngle, qreal sweepLength)

    Creates an arc that occupies the given \a rectangle, beginning at
    the specified \a startAngle and extending \a sweepLength degrees
    counter-clockwise.

    Angles are specified in degrees. Clockwise arcs can be specified
    using negative angles.

    Note that this function connects the starting point of the arc to
    the current position if they are not already connected. After the
    arc has been added, the current position is the last point in
    arc. To draw a line back to the first point, use the
    closeSubpath() function.

    \table 100%
    \row
    \li \inlineimage qpainterpath-arcto.png
    \li
    \snippet code/src_gui_painting_qpainterpath.cpp 2
    \endtable

    \sa arcMoveTo(), addEllipse(), QPainter::drawArc(), QPainter::drawPie(),
    {QPainterPath#Composing a QPainterPath}{Composing a
    QPainterPath}
*/
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 ((!qt_is_finite(rect.x()) && !qt_is_finite(rect.y())) || !qt_is_finite(rect.width()) || !qt_is_finite(rect.height())
        || !qt_is_finite(startAngle) || !qt_is_finite(sweepLength)) {
#ifndef QT_NO_DEBUG
        qWarning("QPainterPath::arcTo: Adding arc where a parameter is NaN or Inf, 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());
    }

}


/*!
    \fn void QPainterPath::arcMoveTo(qreal x, qreal y, qreal width, qreal height, qreal angle)
    \overload
    \since 4.2

    Creates a move to that lies on the arc that occupies the
    QRectF(\a x, \a y, \a width, \a height) at \a angle.
*/


/*!
    \fn void QPainterPath::arcMoveTo(const QRectF &rectangle, qreal angle)
    \since 4.2

    Creates a move to that lies on the arc that occupies the given \a
    rectangle at \a angle.

    Angles are specified in degrees. Clockwise arcs can be specified
    using negative angles.

    \sa moveTo(), arcTo()
*/

void QPainterPath::arcMoveTo(const QRectF &rect, qreal angle)
{
    if (rect.isNull())
        return;

    QPointF pt;
    qt_find_ellipse_coords(rect, angle, 0, &pt, 0);
    moveTo(pt);
}



/*!
    \fn QPointF QPainterPath::currentPosition() const

    Returns the current position of the path.
*/
QPointF QPainterPath::currentPosition() const
{
    return !d_ptr || d_func()->elements.isEmpty()
        ? QPointF()
        : QPointF(d_func()->elements.last().x, d_func()->elements.last().y);
}


/*!
    \fn void QPainterPath::addRect(qreal x, qreal y, qreal width, qreal height)

    \overload

    Adds a rectangle at position (\a{x}, \a{y}), with the given \a
    width and \a height, as a closed subpath.
*/

/*!
    \fn void QPainterPath::addRect(const QRectF &rectangle)

    Adds the given \a rectangle to this path as a closed subpath.

    The \a rectangle is added as a clockwise set of lines. The painter
    path's current position after the \a rectangle has been added is
    at the top-left corner of the rectangle.

    \table 100%
    \row
    \li \inlineimage qpainterpath-addrectangle.png
    \li
    \snippet code/src_gui_painting_qpainterpath.cpp 3
    \endtable

    \sa addRegion(), lineTo(), {QPainterPath#Composing a
    QPainterPath}{Composing a QPainterPath}
*/
void QPainterPath::addRect(const QRectF &r)
{
    if (!qt_is_finite(r.x()) || !qt_is_finite(r.y()) || !qt_is_finite(r.width()) || !qt_is_finite(r.height())) {
#ifndef QT_NO_DEBUG
        qWarning("QPainterPath::addRect: Adding rect where a parameter is NaN or Inf, ignoring call");
#endif
        return;
    }

    if (r.isNull())
        return;

    ensureData();
    detach();

    bool first = d_func()->elements.size() < 2;

    d_func()->elements.reserve(d_func()->elements.size() + 5);
    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;
}

/*!
    Adds the given \a polygon to the path as an (unclosed) subpath.

    Note that the current position after the polygon has been added,
    is the last point in \a polygon. To draw a line back to the first
    point, use the closeSubpath() function.

    \table 100%
    \row
    \li \inlineimage qpainterpath-addpolygon.png
    \li
    \snippet code/src_gui_painting_qpainterpath.cpp 4
    \endtable

    \sa lineTo(), {QPainterPath#Composing a QPainterPath}{Composing
    a QPainterPath}
*/
void QPainterPath::addPolygon(const QPolygonF &polygon)
{
    if (polygon.isEmpty())
        return;

    ensureData();
    detach();

    d_func()->elements.reserve(d_func()->elements.size() + polygon.size());

    moveTo(polygon.first());
    for (int i=1; i<polygon.size(); ++i) {
        Element elm = { polygon.at(i).x(), polygon.at(i).y(), LineToElement };
        d_func()->elements << elm;
    }
}

/*!
    \fn void QPainterPath::addEllipse(const QRectF &boundingRectangle)

    Creates an ellipse within the specified \a boundingRectangle
    and adds it to the painter path as a closed subpath.

    The ellipse is composed of a clockwise curve, starting and
    finishing at zero degrees (the 3 o'clock position).

    \table 100%
    \row
    \li \inlineimage qpainterpath-addellipse.png
    \li
    \snippet code/src_gui_painting_qpainterpath.cpp 5
    \endtable

    \sa arcTo(), QPainter::drawEllipse(), {QPainterPath#Composing a
    QPainterPath}{Composing a QPainterPath}
*/
void QPainterPath::addEllipse(const QRectF &boundingRect)
{
    if (!qt_is_finite(boundingRect.x()) || !qt_is_finite(boundingRect.y())
        || !qt_is_finite(boundingRect.width()) || !qt_is_finite(boundingRect.height())) {
#ifndef QT_NO_DEBUG
        qWarning("QPainterPath::addEllipse: Adding ellipse where a parameter is NaN or Inf, ignoring call");
#endif
        return;
    }

    if (boundingRect.isNull())
        return;

    ensureData();
    detach();

    Q_D(QPainterPath);
    bool first = d_func()->elements.size() < 2;
    d->elements.reserve(d->elements.size() + 13);

    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;
}

/*!
    \fn void QPainterPath::addText(const QPointF &point, const QFont &font, const QString &text)

    Adds the given \a text to this path as a set of closed subpaths
    created from the \a font supplied. The subpaths are positioned so
    that the left end of the text's baseline lies at the specified \a
    point.

    \table 100%
    \row
    \li \inlineimage qpainterpath-addtext.png
    \li
    \snippet code/src_gui_painting_qpainterpath.cpp 6
    \endtable

    \sa QPainter::drawText(), {QPainterPath#Composing a
    QPainterPath}{Composing a QPainterPath}
*/
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);
    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[i].analysis.bidiLevel;
    QTextEngine::bidiReorder(nItems, levels.data(), visualOrder.data());

    for (int i = 0; i < nItems; ++i) {
        int item = visualOrder[i];
        QScriptItem &si = eng->layoutData->items[item];

        if (si.analysis.flags < QScriptAnalysis::TabOrObject) {
            QGlyphLayout glyphs = eng->shapedGlyphs(&si);
            QFontEngine *fe = f.d->engineForScript(si.analysis.script);
            Q_ASSERT(fe);
            fe->addOutlineToPath(x, y, glyphs, this,
                                 si.analysis.bidiLevel % 2
                                 ? QTextItem::RenderFlags(QTextItem::RightToLeft)
                                 : QTextItem::RenderFlags(0));

            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();
    }
}

/*!
    \fn void QPainterPath::addPath(const QPainterPath &path)

    Adds the given \a path to \e this path as a closed subpath.

    \sa connectPath(), {QPainterPath#Composing a
    QPainterPath}{Composing a QPainterPath}
*/
void QPainterPath::addPath(const QPainterPath &other)
{
    if (other.isEmpty())
        return;

    ensureData();
    detach();

    QPainterPathData *d = reinterpret_cast<QPainterPathData *>(d_func());
    // Remove last moveto so we don't get multiple moveto's
    if (d->elements.last().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();
}


/*!
    \fn void QPainterPath::connectPath(const QPainterPath &path)

    Connects the given \a path to \e this path by adding a line from the
    last element of this path to the first element of the given path.

    \sa addPath(), {QPainterPath#Composing a QPainterPath}{Composing
    a QPainterPath}
*/
void QPainterPath::connectPath(const QPainterPath &other)
{
    if (other.isEmpty())
        return;

    ensureData();
    detach();

    QPainterPathData *d = reinterpret_cast<QPainterPathData *>(d_func());
    // Remove last moveto so we don't get multiple moveto's
    if (d->elements.last().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[first]) == QPointF(d->elements[first - 1])) {
        d->elements.remove(first--);
        --cStart;
    }

    if (cStart != first)
        d->cStart = cStart;
}

/*!
    Adds the given \a region to the path by adding each rectangle in
    the region as a separate closed subpath.

    \sa addRect(), {QPainterPath#Composing a QPainterPath}{Composing
    a QPainterPath}
*/
void QPainterPath::addRegion(const QRegion &region)
{
    ensureData();
    detach();

    QVector<QRect> rects = region.rects();
    d_func()->elements.reserve(rects.size() * 5);
    for (int i=0; i<rects.size(); ++i)
        addRect(rects.at(i));
}


/*!
    Returns the painter path's currently set fill rule.

    \sa setFillRule()
*/
Qt::FillRule QPainterPath::fillRule() const
{
    return isEmpty() ? Qt::OddEvenFill : d_func()->fillRule;
}

/*!
    \fn void QPainterPath::setFillRule(Qt::FillRule fillRule)

    Sets the fill rule of the painter path to the given \a
    fillRule. Qt provides two methods for filling paths:

    \table
    \header
    \li Qt::OddEvenFill (default)
    \li Qt::WindingFill
    \row
    \li \inlineimage qt-fillrule-oddeven.png
    \li \inlineimage qt-fillrule-winding.png
    \endtable

    \sa 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);
}

/*!
    Returns the bounding rectangle of this painter path as a rectangle with
    floating point precision.

    \sa controlPointRect()
*/
QRectF QPainterPath::boundingRect() const
{
    if (!d_ptr)
        return QRectF();
    QPainterPathData *d = d_func();

    if (d->dirtyBounds)
        computeBoundingRect();
    return d->bounds;
}

/*!
    Returns the rectangle containing all the points and control points
    in this path.

    This function is significantly faster to compute than the exact
    boundingRect(), and the returned rectangle is always a superset of
    the rectangle returned by boundingRect().

    \sa boundingRect()
*/
QRectF QPainterPath::controlPointRect() const
{
    if (!d_ptr)
        return QRectF();
    QPainterPathData *d = d_func();

    if (d->dirtyControlBounds)
        computeControlPointRect();
    return d->controlBounds;
}


/*!
    \fn bool QPainterPath::isEmpty() const

    Returns \c true if either there are no elements in this path, or if the only
    element is a MoveToElement; otherwise returns \c false.

    \sa elementCount()
*/

bool QPainterPath::isEmpty() const
{
    return !d_ptr || (d_ptr->elements.size() == 1 && d_ptr->elements.first().type == MoveToElement);
}

/*!
    Creates and returns a reversed copy of the path.

    It is the order of the elements that is reversed: If a
    QPainterPath is composed by calling the moveTo(), lineTo() and
    cubicTo() functions in the specified order, the reversed copy is
    composed by calling cubicTo(), lineTo() and moveTo().
*/
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;
}

/*!
    Converts the path into a list of polygons using the QTransform
    \a matrix, and returns the list.

    This function creates one polygon for each subpath regardless of
    intersecting subpaths (i.e. overlapping bounding rectangles). To
    make sure that such overlapping subpaths are filled correctly, use
    the toFillPolygons() function instead.

    \sa toFillPolygons(), toFillPolygon(), {QPainterPath#QPainterPath
    Conversion}{QPainterPath Conversion}
*/
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;
}

/*!
  \overload
 */
QList<QPolygonF> QPainterPath::toSubpathPolygons(const QMatrix &matrix) const
{
    return toSubpathPolygons(QTransform(matrix));
}

/*!
    Converts the path into a list of polygons using the
    QTransform \a matrix, and returns the list.

    The function differs from the toFillPolygon() function in that it
    creates several polygons. It is provided because it is usually
    faster to draw several small polygons than to draw one large
    polygon, even though the total number of points drawn is the same.

    The toFillPolygons() function differs from the toSubpathPolygons()
    function in that it create only polygon for subpaths that have
    overlapping bounding rectangles.

    Like the toFillPolygon() function, this function uses a rewinding
    technique to make sure that overlapping subpaths can be filled
    using the correct fill rule. Note that rewinding inserts addition
    lines in the polygons so the outline of the fill polygon does not
    match the outline of the path.

    \sa toSubpathPolygons(), toFillPolygon(),
    {QPainterPath#QPainterPath Conversion}{QPainterPath Conversion}
*/
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;
    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

    QVector< 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][