The intersection rectangle can be retrieved using the intersected()    function.    \sa  contains()*/bool QRect::intersects(const QRect &r) const{    if (isNull() || r.isNull())        return false;    QRect r1 = normalized();    QRect r2 = r.normalized();    return (qMax(r1.x1, r2.x1) <= qMin(r1.x2, r2.x2) &&             qMax(r1.y1, r2.y1) <= qMin(r1.y2, r2.y2));}/*!    \fn bool operator==(const QRect &r1, const QRect &r2)    \relates QRect    Returns true if the rectangles \a r1 and \a r2 are equal,    otherwise returns false.*//*!    \fn bool operator!=(const QRect &r1, const QRect &r2)    \relates QRect    Returns true if the rectangles \a r1 and \a r2 are different, otherwise    returns false.*//*****************************************************************************  QRect stream functions *****************************************************************************/#ifndef QT_NO_DATASTREAM/*!    \fn QDataStream &operator<<(QDataStream &stream, const QRect &rectangle)    \relates QRect    Writes the given \a rectangle to the given \a stream, and returns    a reference to the stream.    \sa {Format of the QDataStream Operators}*/QDataStream &operator<<(QDataStream &s, const QRect &r){    if (s.version() == 1)        s << (qint16)r.left() << (qint16)r.top()          << (qint16)r.right() << (qint16)r.bottom();    else        s << (qint32)r.left() << (qint32)r.top()          << (qint32)r.right() << (qint32)r.bottom();    return s;}/*!    \fn QDataStream &operator>>(QDataStream &stream, QRect &rectangle)    \relates QRect    Reads a rectangle from the given \a stream into the given \a    rectangle, and returns a reference to the stream.    \sa {Format of the QDataStream Operators}*/QDataStream &operator>>(QDataStream &s, QRect &r){    if (s.version() == 1) {        qint16 x1, y1, x2, y2;        s >> x1; s >> y1; s >> x2; s >> y2;        r.setCoords(x1, y1, x2, y2);    }    else {        qint32 x1, y1, x2, y2;        s >> x1; s >> y1; s >> x2; s >> y2;        r.setCoords(x1, y1, x2, y2);    }    return s;}#endif // QT_NO_DATASTREAM#ifndef QT_NO_DEBUG_STREAMQDebug operator<<(QDebug dbg, const QRect &r) {    dbg.nospace() << "QRect(" << r.x() << ',' << r.y() << ' '                  << r.width() << 'x' << r.height() << ')';    return dbg.space();}#endif/*!    \class QRectF    \ingroup multimedia    \brief The QRectF class defines a rectangle in the plane using floating    point precision.    A rectangle is normally expressed as an upper-left corner and a    size.  The size (width and height) of a QRectF is always equivalent    to the mathematical rectangle that forms the basis for its    rendering.    A QRectF can be constructed with a set of left, top, width and    height integers, or from a QPoint and a QSize.  The following code    creates two identical rectangles.    \code        QRectF r1(100, 200, 11, 16);        QRectF r2(QPoint(100, 200), QSize(11, 16));    \endcode    There is also a third constructor creating a QRectF from a QRect,    and a corresponding toRect() function that returns a QRect object    based on the values of this rectangle (note that the coordinates    in the returned rectangle are rounded to the nearest integer).    The QRectF class provides a collection of functions that return    the various rectangle coordinates, and enable manipulation of    these. QRectF also provide functions to move the rectangle    relative to the various coordinates. In addition there is a    moveTo() function that moves the rectangle, leaving its top left    corner at the given coordinates. Alternatively, the translate()    function moves the rectangle the given offset relative to the    current position, and the translated() function returns a    translated copy of this rectangle.    The size() function returns the rectange's dimensions as a    QSize. The dimensions can also be retrieved separately using the    width() and height() functions. To manipulate the dimensions use    the setSize(), setWidth() or setHeight() functions. Alternatively,    the size can be changed by applying either of the functions    setting the rectangle coordinates, for example, setBottom() or    setRight().    The contains() function tells whether a given point is inside the    rectangle or not, and the intersects() function returns true if    this rectangle intersects with a given rectangle (otherwise    false). The QRectF class also provides the intersected() function    which returns the intersection rectangle, and the united() function    which returns the rectangle that encloses the given rectangle and    this:    \table    \row    \o \inlineimage qrect-intersect.png    \o \inlineimage qrect-unite.png    \row    \o intersected()    \o united()    \endtable    The isEmpty() function returns true if the rectangle's width or    height is less than, or equal to, 0. Note that an empty rectangle    is not valid: The isValid() function returns true if both width    and height is larger than 0. A null rectangle (isNull() == true)    on the other hand, has both width and height set to 0.    Finally, QRectF objects can be streamed as well as compared.    \tableofcontents    \section1 Rendering    When using an \l {QPainter::Antialiasing}{anti-aliased} painter,    the boundary line of a QRectF will be rendered symmetrically on both    sides of the mathematical rectangle's boundary line. But when    using an aliased painter (the default) other rules apply.    Then, when rendering with a one pixel wide pen the QRectF's boundary    line will be rendered to the right and below the mathematical    rectangle's boundary line.    When rendering with a two pixels wide pen the boundary line will    be split in the middle by the mathematical rectangle. This will be    the case whenever the pen is set to an even number of pixels,    while rendering with a pen with an odd number of pixels, the spare    pixel will be rendered to the right and below the mathematical    rectangle as in the one pixel case.    \table    \row        \o \inlineimage qrect-diagram-zero.png        \o \inlineimage qrectf-diagram-one.png    \row        \o Logical representation        \o One pixel wide pen    \row        \o \inlineimage qrectf-diagram-two.png        \o \inlineimage qrectf-diagram-three.png    \row        \o Two pixel wide pen        \o Three pixel wide pen    \endtable    \section1 Coordinates    The QRectF class provides a collection of functions that return    the various rectangle coordinates, and enable manipulation of    these. QRectF also provide functions to move the rectangle    relative to the various coordinates.    For example: the bottom(), setBottom() and moveBottom() functions:    bottom() returns the y-coordinate of the rectangle's bottom edge,    setBottom() sets the bottom edge of the rectangle to the given y    coordinate (it may change the height, but will never change the    rectangle's top edge) and moveBottom() moves the entire rectangle    vertically, leaving the rectangle's bottom edge at the given y    coordinate and its size unchanged.    \image qrectf-coordinates.png    It is also possible to add offsets to this rectangle's coordinates    using the adjust() function, as well as retrieve a new rectangle    based on adjustments of the original one using the adjusted()    function. If either of the width and height is negative, use the    normalized() function to retrieve a rectangle where the corners    are swapped.    In addition, QRectF provides the getCoords() function which extracts    the position of the rectangle's top-left and bottom-right corner,    and the getRect() function which extracts the rectangle's top-left    corner, width and height. Use the setCoords() and setRect()    function to manipulate the rectangle's coordinates and dimensions    in one go.    \sa QRect, QRegion*//*****************************************************************************  QRectF member functions *****************************************************************************//*!    \fn QRectF::QRectF()    Constructs a null rectangle.    \sa isNull()*//*!    \fn QRectF::QRectF(const QPointF &topLeft, const QSizeF &size)    Constructs a rectangle with the given \a topLeft corner and the given \a size.    \sa setTopLeft(), setSize()*//*!    \fn QRectF::QRectF(qreal x, qreal y, qreal width, qreal height)    Constructs a rectangle with (\a x, \a y) as its top-left corner    and the given \a width and \a height.    \sa setRect()*//*!    \fn QRectF::QRectF(const QRect &rectangle)    Constructs a QRectF rectangle from the given QRect \a rectangle.    \sa toRect()*//*!    \fn bool QRectF::isNull() const    Returns true if the rectangle is a null rectangle, otherwise returns false.    A null rectangle has both the width and the height set to 0. A    null rectangle is also empty, and hence not valid.    \sa isEmpty(), isValid()*//*!    \fn bool QRectF::isEmpty() const    Returns true if the rectangle is empty, otherwise returns false.    An empty rectangle has width() <= 0 or height() <= 0.  An empty    rectangle is not valid (i.e isEmpty() == !isValid()).    Use the normalized() function to retrieve a rectangle where the    corners are swapped.    \sa isNull(),  isValid(),  normalized()*//*!    \fn bool QRectF::isValid() const    Returns true if the rectangle is valid, otherwise returns false.    A valid rectangle has a width() > 0 and height() > 0. Note that    non-trivial operations like intersections are not defined for    invalid rectangles. A valid rectangle is not empty (i.e. isValid()    == !isEmpty()).    \sa isNull(), isEmpty(), normalized()*//*!    Returns a normalized rectangle; i.e. a rectangle that has a    non-negative width and height.    If width() < 0 the function swaps the left and right corners, and    it swaps the top and bottom corners if height() < 0.    \sa isValid(), isEmpty()*/QRectF QRectF::normalized() const{    QRectF r = *this;    if (r.w < 0) {        r.xp = r.xp + r.w;        r.w = -r.w;    }    if (r.h < 0) {        r.yp = r.yp + r.h;        r.h = -r.h;    }    return r;}/*!    \fn qreal QRectF::x() const    Returns the x-coordinate of the rectangle's left edge. Equivalent    to left().    \sa setX(), y(), topLeft()*//*!    \fn qreal QRectF::y() const    Returns the y-coordinate of the rectangle's top edge. Equivalent    to top().    \sa setY(), x(),  topLeft()*//*!    \fn void QRectF::setLeft(qreal x)    Sets the left edge of the rectangle to the given \a x    coordinate. May change the width, but will never change the right    edge of the rectangle.    Equivalent to setX().    \sa left(), moveLeft()*//*!    \fn void QRectF::setTop(qreal y)    Sets the top edge of the rectangle to the given \a y coordinate. May    change the height, but will never change the bottom edge of the    rectangle.    Equivalent to setY().    \sa top(), moveTop()*//*!    \fn void QRectF::setRight(qreal x)    Sets the right edge of the rectangle to the given \a x    coordinate. May change the width, but will never change the left    edge of the rectangle.    \sa right(), moveRight()*//*!    \fn void QRectF::setBottom(qreal y)    Sets the bottom edge of the rectangle to the given \a y    coordinate. May change the height, but will never change the top    edge of the rectangle.    \sa bottom(), moveBottom()*//*!    \fn void QRectF::setX(qreal x)    Sets the left edge of the rectangle to the given \a x    coordinate. May change the width, but will never change the right    edge of the rectangle.    Equivalent to setLeft().    \sa x(), setY(), setTopLeft()*//*!    \fn void QRectF::setY(qreal y)    Sets the top edge of the rectangle to the given \a y    coordinate. May change the height, but will never change the    bottom edge of the rectangle.    Equivalent to setTop().    \sa y(), setX(), setTopLeft()*//*!    \fn void QRectF::setTopLeft(const QPointF &position)    Set the top-left corner of the rectangle to the given \a    position. May change the size, but will the never change the    bottom-right corner of the rectangle.    \sa topLeft(), moveTopLeft()*//*!    \fn void QRectF::setBottomRight(const QPointF &position)    Set the top-right corner of the rectangle to the given \a    position. May change the size, but will the never change the    top-left corner of the rectangle.    \sa bottomRight(), moveBottomRight()*//*!    \fn void QRectF::setTopRight(const QPointF &position)    Set the top-right corner of the rectangle to the given \a    position. May change the size, but will the never change the    bottom-left corner of the rectangle.    \sa topRight(), moveTopRight()*//*!    \fn void QRectF::setBottomLeft(const QPointF &position)    Set the bottom-left corner of the rectangle to the given \a    position. May change the size, but will the never change the    top-right corner of the rectangle.    \sa bottomLeft(), moveBottomLeft()*//*!    \fn QPointF QRectF::center() const    Returns the center point of the rectangle.    \sa moveCenter()*//*!    \fn void QRectF::getRect(qreal *x, qreal *y, qreal *width, qreal *height) const    Extracts the position of the rectangle's top-left corner to *\a x and    *\a y, and its dimensions to *\a width and *\a height.    \sa setRect(), getCoords()*//*!    \fn void QRectF::getCoords(qreal *x1, qreal *y1, qreal *x2, qreal *y2) const    Extracts the position of the rectangle's top-left corner to *\a x1    and *\a y1, and the position of the bottom-right corner to *\a x2 and    *\a y2.    \sa setCoords(), getRect()*//*!    \fn void QRectF::moveLeft(qreal x)    Moves the rectangle horizontally, leaving the rectangle's left    edge at the given \a x coordinate. The rectangle's size is    unchanged.    \sa left(), setLeft(), moveRight()*//*!    \fn void QRectF::moveTop(qreal y)    Moves the rectangle vertically, leaving the rectangle's top line    at the given \a y coordinate. The rectangle's size is unchanged.    \sa top(), setTop(), moveBottom()*//*!    \fn void QRectF::moveRight(qreal x)    Moves the rectangle horizontally, leaving the rectangle's right    edge at the given \a x coordinate. The rectangle's size is    unchanged.    \sa right(), setRight(), moveLeft()*//*!    \fn void QRectF::moveBottom(qreal y)    Moves the rectangle vertically, leaving the rectangle's bottom