Returns the sum of the absolute values of x() and y(),    traditionally known as the "Manhattan length" of the vector from    the origin to the point. For example:    \code        QPoint oldPosition;        MyWidget::mouseMoveEvent(QMouseEvent *event)        {            QPoint point = event->pos() - oldPosition;            if (point.manhattanLength() > 3)                // the mouse has moved more than 3 pixels since the oldPosition        }    \endcode    This is a useful, and quick to calculate, approximation to the    true length:    \code        int trueManhattenLength = sqrt(pow(x(), 2) + pow(y(), 2));    \endcode    The tradition of "Manhattan length" arises because such distances    apply to travelers who can only travel on a rectangular grid, like    the streets of Manhattan.*/int QPoint::manhattanLength() const{    return qAbs(x())+qAbs(y());}#ifndef QT_NO_DEBUG_STREAMQDebug operator<<(QDebug dbg, const QPoint &p) {    dbg.nospace() << "QPoint(" << p.x() << ',' << p.y() << ')';    return dbg.space();}QDebug operator<<(QDebug d, const QPointF &p){    d << "QPointF(" << p.x() << ", " << p.y() << ")";    return d;}#endif/*!    \class QPointF    \ingroup multimedia    \brief The QPointF class defines a point in the plane using    floating point precision.    A point is specified by a x coordinate and an y coordinate which    can be accessed using the x() and y() functions. The coordinates    of the point are specified using floating point numbers for    accuracy. The isNull() function returns true if both x and y are    set to 0.0. The coordinates can be set (or altered) using the setX()    and setY() functions, or alternatively the rx() and ry() functions which    return references to the coordinates (allowing direct    manipulation).    Given a point \e p, the following statements are all equivalent:    \code        QPointF p;        p.setX(p.x() + 1.0);        p += QPoint(1.0, 0.0);        p.rx()++;    \endcode    A QPointF object can also be used as a vector: Addition and    subtraction are defined as for vectors (each component is added    separately). A QPointF object can also be divided or multiplied by    an \c int or a \c qreal.    In addition, the QPointF class provides a constructor converting a    QPoint object into a QPointF object, and a corresponding toPoint()    function which returns a QPoint copy of \e this point. Finally,    QPointF objects can be streamed as well as compared.    \sa QPoint, QPolygonF*//*!    \fn QPointF::QPointF()    Constructs a null point, i.e. with coordinates (0.0, 0.0)    \sa isNull()*//*!    \fn QPointF::QPointF(const QPoint &point)    Constructs a copy of the given \a point.    \sa toPoint()*//*!    \fn QPointF::QPointF(qreal x, qreal y)    Constructs a point with the given coordinates (\a x, \a y).    \sa setX(), setY()*//*!    \fn bool QPointF::isNull() const    Returns true if both the x and y coordinates are set to 0.0,    otherwise returns false.*//*!    \fn qreal QPointF::x() const    Returns the x-coordinate of this point.    \sa setX(), rx()*//*!    \fn qreal QPointF::y() const    Returns the y-coordinate of this point.    \sa setY(), ry()*//*!    \fn void QPointF::setX(qreal x)    Sets the x coordinate of this point to the given \a x coordinate.    \sa x() setY()*//*!    \fn void QPointF::setY(qreal y)    Sets the y coordinate of this point to the given \a y coordinate.    \sa  y(), setX()*//*!    \fn qreal& QPointF::rx()    Returns a reference to the x coordinate of this point.    Using a reference makes it possible to directly manipulate x. For example:    \code         QPoint p(1.1, 2.5);         p.rx()--;   // p becomes (0.1, 2.5)    \endcode    \sa x(), setX()*//*!    \fn qreal& QPointF::ry()    Returns a reference to the y coordinate of this point.    Using a reference makes it possible to directly manipulate y. For example:    \code        QPoint p(1.1, 2.5);        p.ry()++;   // p becomes (1.1, 3.5)    \endcode    \sa y() setY()*//*!    \fn QPointF& QPointF::operator+=(const QPointF &point)    Adds the given \a point to this point and returns a reference to    this point. For example:    \code        QPoint p( 3.1, 7.1);        QPoint q(-1.0, 4.1);        p += q;    // p becomes (2.1, 11.2)    \endcode    \sa operator-=()*//*!    \fn QPointF& QPointF::operator-=(const QPointF &point)    Subtracts the given \a point from this point and returns a reference    to this point. For example:    \code        QPoint p( 3.1, 7.1);        QPoint q(-1.0, 4.1);        p -= q;    // p becomes (4.1, 3.0)    \endcode    \sa operator+=()*//*!    \fn QPointF& QPointF::operator*=(qreal factor)    Multiplies this point's coordinates by the given \a factor, and    returns a reference to this point. For example:    \code         QPoint p(-1.1, 4.1);         p *= 2.5;    // p becomes (-2.75,10.25)    \endcode    \sa operator/=()*//*!    \fn QPointF& QPointF::operator/=(qreal divisor)    Divides both x and y by the given \a divisor, and returns a reference    to this point. For example:    \code        QPoint p(-2.75, 10.25);        p /= 2.5;           // p becomes (-1.1,4.1)    \endcode    \sa operator*=()*//*!    \fn const QPointF operator+(const QPointF &p1, const QPointF &p2)    \relates QPointF    Returns a QPointF object that is the sum of the given points, \a p1    and \a p2; each component is added separately.    \sa QPointF::operator+=()*//*!    \fn const QPointF operator-(const QPointF &p1, const QPointF &p2)    \relates QPointF    Returns a QPointF object that is formed by subtracting \a p2 from \a p1;    each component is subtracted separately.    \sa QPointF::operator-=()*//*!    \fn const QPointF operator*(const QPointF &point, qreal factor)    \relates QPointF    Returns a copy of the given \a point,  multiplied by the given \a factor.    \sa QPointF::operator*=()*//*!    \fn const QPointF operator*(qreal factor, const QPointF &point)    \relates QPointF    \overload    Returns a copy of the given \a point, multiplied by the given \a factor.*//*!    \fn const QPointF operator-(const QPointF &point)    \relates QPointF    \overload    Returns a QPointF object that is formed by changing the sign of    both components of the given \a point.    Equivalent to \c {QPointF(0,0) - point}.*//*!    \fn const QPointF operator/(const QPointF &point, qreal divisor)    \relates QPointF    Returns the QPointF object formed by dividing both components of    the given \a point by the given \a divisor.    \sa QPointF::operator/=()*//*!    \fn QPoint QPointF::toPoint() const    Rounds the coordinates of this point to the nearest integer, and    returns a QPoint object with the rounded coordinates.    \sa QPointF()*//*!    \fn bool operator==(const QPointF &p1, const QPointF &p2)    \relates QPointF    Returns true if \a p1 is equal to \a p2; otherwise returns false.*//*!    \fn bool operator!=(const QPointF &p1, const QPointF &p2);    \relates QPointF    Returns true if \a p1 is not equal to \a p2; otherwise returns false.*/#ifndef QT_NO_DATASTREAM/*!    \fn QDataStream &operator<<(QDataStream &stream, const QPointF &point)    \relates QPointF    Writes the given \a point to the given \a stream and returns a    reference to the stream.    \sa {Format of the QDataStream Operators}*/QDataStream &operator<<(QDataStream &s, const QPointF &p){    s << double(p.x()) << double(p.y());    return s;}/*!    \fn QDataStream &operator>>(QDataStream &stream, QPointF &point)    \relates QPointF    Reads a point from the given \a stream into the given \a point    and returns a reference to the stream.    \sa {Format of the QDataStream Operators}*/QDataStream &operator>>(QDataStream &s, QPointF &p){    double x, y;    s >> x;    s >> y;    p.setX(qreal(x));    p.setY(qreal(y));    return s;}#endif // QT_NO_DATASTREAM