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qline.cpp

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#include "qline.h"
#include "qdebug.h"
#include "qdatastream.h"
#include <private/qnumeric_p.h>

#include <math.h>

/*!
    \class QLine
    \ingroup multimedia

    \brief The QLine class provides a two-dimensional vector using
    integer precision.

    A QLine describes a finite length line (or a line segment) on a
    two-dimensional surface. The start and end points of the line are
    specified using integer point accuracy for coordinates. Use the
    QLineF constructor to retrieve a floating point copy.

    \table
    \row
        \o \inlineimage qline-point.png
        \o \inlineimage qline-coordinates.png
    \endtable

    The positions of the line's start and end points can be retrieved
    using the p1(), x1(), y1(), p2(), x2(), and y2() functions. The
    dx() and dy() functions return the horizontal and vertical
    components of the line. Use isNull() to determine whether the
    QLine represents a valid line or a null line.

    Finally, the line can be translated a given offset using the
    translate() function.

    \sa QLineF, QPolygon, QRect
*/

/*!
    \fn QLine::QLine()

    Constructs a null line.
*/

/*!
    \fn QLine::QLine(const QPoint &p1, const QPoint &p2)

    Constructs a line object that represents the line between \a p1 and
    \a p2.
*/

/*!
    \fn QLine::QLine(int x1, int y1, int x2, int y2)

    Constructs a line object that represents the line between (\a x1, \a y1) and
    (\a x2, \a y2).
*/

/*!
    \fn bool QLine::isNull() const

    Returns true if the line is not set up with valid start and end point;
    otherwise returns false.
*/

/*!
    \fn QPoint QLine::p1() const

    Returns the line's start point.

    \sa x1(), y1(), p2()
*/

/*!
    \fn QPoint QLine::p2() const

    Returns the line's end point.

    \sa x2(), y2(), p1()
*/

/*!
    \fn int QLine::x1() const

    Returns the x-coordinate of the line's start point.

    \sa p1()
*/

/*!
    \fn int QLine::y1() const

    Returns the y-coordinate of the line's start point.

    \sa p1()
*/

/*!
    \fn int QLine::x2() const

    Returns the x-coordinate of the line's end point.

    \sa p2()
*/

/*!
    \fn int QLine::y2() const

    Returns the y-coordinate of the line's end point.

    \sa p2()
*/

/*!
    \fn int QLine::dx() const

    Returns the horizontal component of the line's vector.

    \sa dy()
*/

/*!
    \fn int QLine::dy() const

    Returns the vertical component of the line's vector.

    \sa dx()
*/

/*!
    \fn bool QLine::operator!=(const QLine &line) const

    Returns true if the given \a line is not the same as \e this line.

    A line is different from another line if any of their start or
    end points differ, or the internal order of the points is different.
*/

/*!
    \fn bool QLine::operator==(const QLine &line) const

    Returns true if the given \a line is the same as \e this line.

    A line is identical to another line if the start and end points
    are identical, and the internal order of the points is the same.
*/

/*!
    \fn void QLine::translate(const QPoint &offset)

    Translates this line by the given \a offset.
*/

/*!
    \fn void QLine::translate(int dx, int dy)
    \overload

    Translates this line the distance specified by \a dx and \a dy.
*/

#ifndef QT_NO_DEBUG_STREAM
QDebug operator<<(QDebug d, const QLine &p)
{
    d << "QLine(" << p.p1() << "," << p.p2() << ")";
    return d;
}
#endif

#ifndef QT_NO_DATASTREAM
/*!
    \relates QLine

    Writes the given \a line to the given \a stream and returns a
    reference to the stream.

    \sa {Format of the QDataStream Operators}
*/

00201 QDataStream &operator<<(QDataStream &stream, const QLine &line)
{
    stream << line.p1() << line.p2();
    return stream;
}

/*!
    \relates QLine

    Reads a line from the given \a stream into the given \a line and
    returns a reference to the stream.

    \sa {Format of the QDataStream Operators}
*/

00216 QDataStream &operator>>(QDataStream &stream, QLine &line)
{
    QPoint p1, p2;
    stream >> p1;
    stream >> p2;
    line = QLine(p1, p2);

    return stream;
}

#endif // QT_NO_DATASTREAM


#ifndef M_2PI
#define M_2PI 6.28318530717958647692528676655900576
#endif

/*!
    \class QLineF
    \ingroup multimedia

    \brief The QLineF class provides a two-dimensional vector using
    floating point precision.

    A QLineF describes a finite length line (or line segment) on a
    two-dimensional surface. QLineF defines the start and end points
    of the line using floating point accuracy for coordinates.  Use
    the toLine() function to retrieve an integer based copy of this
    line.

    \table
    \row
        \o \inlineimage qline-point.png
        \o \inlineimage qline-coordinates.png
    \endtable

    The positions of the line's start and end points can be retrieved
    using the p1(), x1(), y1(), p2(), x2(), and y2() functions. The
    dx() and dy() functions return the horizontal and vertical
    components of the line, respectively.

    The line's length can be retrieved using the length() function,
    and altered using the setLength() function.  Use the isNull()
    function to determine whether the QLineF represents a valid line
    or a null line.

    The intersect() function determines the IntersectType for this
    line and a given line, while the angle() function returns the
    angle between the lines. In addition, the unitVector() function
    returns a line that has the same starting point as this line, but
    with a length of only 1, while the normalVector() function returns
    a line that is perpendicular to this line with the same starting
    point and length.

    Finally, the line can be translated a given offset using the
    translate() function, and can be traversed using the pointAt()
    function.

    \sa QLine, QPolygonF, QRectF
*/

/*!
    \enum QLineF::IntersectType

    Describes the intersection between two lines.

    \table
    \row
    \o \inlineimage qlinef-unbounded.png
    \o \inlineimage qlinef-bounded.png
    \row
    \o QLineF::UnboundedIntersection
    \o QLineF::BoundedIntersection
    \endtable

    \value NoIntersection Indicates that the lines do not intersect;
    i.e. they are parallel.

    \value UnboundedIntersection The two lines intersect,
    but not within the range defined by their lengths. This will be
    the case if the lines are not parallel.

    \value BoundedIntersection The two lines intersect with each other
    within the start and end points of each line.

    \sa intersect()
*/

/*!
    \fn QLineF::QLineF()

    Constructs a null line.
*/

/*!
    \fn QLineF::QLineF(const QPointF &p1, const QPointF &p2)

    Constructs a line object that represents the line between \a p1 and
    \a p2.
*/

/*!
    \fn QLineF::QLineF(qreal x1, qreal y1, qreal x2, qreal y2)

    Constructs a line object that represents the line between (\a x1, \a y1) and
    (\a x2, \a y2).
*/

/*!
    \fn QLineF::QLineF(const QLine &line)

    Construct a QLineF object from the given integer-based \a line.

    \sa toLine()
*/

/*!
    Returns true if the line is not set up with valid start and end point;
    otherwise returns false.
*/

00337 bool QLineF::isNull() const
{
    return (qFuzzyCompare(pt1.x(), pt2.x()) && qFuzzyCompare(pt1.y(), pt2.y())) ? true : false;
}


/*!
    \fn QPointF QLineF::p1() const

    Returns the line's start point.

    \sa x1(), y1(), p2()
*/

/*!
    \fn QPointF QLineF::p2() const

    Returns the line's end point.

    \sa x2(), y2(), p1()
*/

/*!
    \fn QLine QLineF::toLine() const

    Returns an integer based copy of this line.

    Note that the returned line's start and end points are rounded to
    the nearest integer.

    \sa QLineF()
*/
/*!
    \fn qreal QLineF::x1() const

    Returns the x-coordinate of the line's start point.

    \sa p1()
*/

/*!
    \fn qreal QLineF::y1() const

    Returns the y-coordinate of the line's start point.

    \sa p1()
*/

/*!
    \fn qreal QLineF::x2() const

    Returns the x-coordinate of the line's end point.

    \sa p2()
*/

/*!
    \fn qreal QLineF::y2() const

    Returns the y-coordinate of the line's end point.

    \sa p2()
*/

/*!
    \fn qreal QLineF::dx() const

    Returns the horizontal component of the line's vector.

    \sa dy(), pointAt()
*/

/*!
    \fn qreal QLineF::dy() const

    Returns the vertical component of the line's vector.

    \sa dx(), pointAt()
*/

/*!
    \fn QLineF::setLength(qreal length)

    Sets the length of the line to the given \a length. If the line is a
    null line, the length will remain zero regardless of the length
    specified.

    \sa length(), isNull()
*/

/*!
    \fn QLineF QLineF::normalVector() const

    Returns a line that is perpendicular to this line with the same starting
    point and length.

    \image qlinef-normalvector.png

    \sa unitVector()
*/

/*!
    \fn bool QLineF::operator!=(const QLineF &line) const

    Returns true if the given \a line is not the same as \e this line.

    A line is different from another line if their start or end points
    differ, or the internal order of the points is different.
*/

/*!
    \fn bool QLineF::operator==(const QLineF &line) const

    Returns true if the given \a line is the same as this line.

    A line is identical to another line if the start and end points
    are identical, and the internal order of the points is the same.
*/

/*!
  \fn qreal QLineF::pointAt(qreal t) const

  Returns the point at the parameterized position specified by \a
  t. The function returns the line's start point if t = 0, and its end
  point if t = 1.

  \sa dx(), dy()
*/

/*!
    Returns the length of the line.

    \sa setLength()
*/
00471 qreal QLineF::length() const
{
    qreal x = pt2.x() - pt1.x();
    qreal y = pt2.y() - pt1.y();
    return sqrt(x*x + y*y);
}


/*!
    Returns the unit vector for this line, i.e a line starting at the
    same point as \e this line with a length of 1.0.

    \sa normalVector()
*/
00485 QLineF QLineF::unitVector() const
{
    qreal x = pt2.x() - pt1.x();
    qreal y = pt2.y() - pt1.y();

    qreal len = sqrt(x*x + y*y);
    QLineF f(p1(), QPointF(pt1.x() + x/len, pt1.y() + y/len));

#ifndef QT_NO_DEBUG
    if (qAbs(f.length() - 1) >= 0.001)
        qWarning("QLine::unitVector: New line does not have unit length");
#endif

    return f;
}

#define SAME_SIGNS(a, b) ((a) * (b) >= 0)

// Line intersection algorithm, copied from Graphics Gems II
static bool qt_linef_intersect(qreal x1, qreal y1, qreal x2, qreal y2,
                               qreal x3, qreal y3, qreal x4, qreal y4)
{
    qreal a1, a2, b1, b2, c1, c2; /* Coefficients of line eqns. */
    qreal r1, r2, r3, r4;         /* 'Sign' values */

    a1 = y2 - y1;
    b1 = x1 - x2;
    c1 = x2 * y1 - x1 * y2;

    r3 = a1 * x3 + b1 * y3 + c1;
    r4 = a1 * x4 + b1 * y4 + c1;

    if ( r3 != 0 && r4 != 0 && SAME_SIGNS( r3, r4 ))
        return false;

    a2 = y4 - y3;
    b2 = x3 - x4;
    c2 = x4 * y3 - x3 * y4;

    r1 = a2 * x1 + b2 * y1 + c2;
    r2 = a2 * x2 + b2 * y2 + c2;

    if ( r1 != 0 && r2 != 0 && SAME_SIGNS( r1, r2 ))
        return false;

    return true;
}

/*!
    \fn QLineF::IntersectType QLineF::intersect(const QLineF &line, QPointF *intersectionPoint) const

    Returns a value indicating whether or not \e this line intersects
    with the given \a line.

    The actual intersection point is extracted to \a intersectionPoint
    (if the pointer is valid). If the lines are parallel, the
    intersection point is undefined.
*/

00544 QLineF::IntersectType QLineF::intersect(const QLineF &l, QPointF *intersectionPoint) const
{
    if (isNull() || l.isNull()
        || !qIsFinite(pt1.x()) || !qIsFinite(pt1.y()) || !qIsFinite(pt2.x()) || !qIsFinite(pt2.y())
        || !qIsFinite(l.pt1.x()) || !qIsFinite(l.pt1.y()) || !qIsFinite(l.pt2.x()) || !qIsFinite(l.pt2.y()))
        return NoIntersection;

    QPointF isect;
    IntersectType type = qt_linef_intersect(pt1.x(), pt1.y(), pt2.x(), pt2.y(),
                                            l.x1(), l.y1(), l.x2(), l.y2())
                         ? BoundedIntersection : UnboundedIntersection;

    // For special case where one of the lines are vertical
    if (dx() == 0 && l.dx() == 0) {
        type = NoIntersection;
    } else if (dx() == 0) {
        qreal la = l.dy() / l.dx();
        isect = QPointF(pt1.x(), la * pt1.x() + l.y1() - la*l.x1());
    } else if (l.dx() == 0) {
        qreal ta = dy() / dx();
        isect = QPointF(l.x1(), ta * l.x1() + y1() - ta*x1());
    } else {
        qreal ta = dy()/dx();
        qreal la = l.dy()/l.dx();
        if (ta == la) // no intersection
            return NoIntersection;

        qreal x = ( - l.y1() + la * l.x1() + pt1.y() - ta * pt1.x() ) / (la - ta);
        isect = QPointF(x, ta*(x - pt1.x()) + pt1.y());
    }
    if (intersectionPoint)
        *intersectionPoint = isect;
    return type;
}

/*!
    \fn void QLineF::translate(const QPointF &offset)

    Translates this line by the given \a offset.
*/

/*!
    \fn void QLineF::translate(qreal dx, qreal dy)
    \overload

    Translates this line the distance specified by \a dx and \a dy.
*/

/*!
  \fn qreal QLineF::angle(const QLineF &line) const

  Returns the angle (in degrees) between this line and the given \a
  line, taking the direction of the lines into account. If the lines
  do not intersect within their range, it is the intersection point of
  the extended lines that serves as origo (see
  QLineF::UnboundedIntersection).

  \table
  \row
  \o \inlineimage qlinef-angle-identicaldirection.png
  \o \inlineimage qlinef-angle-oppositedirection.png
  \endtable

  When the lines are parallel, this function returns 0 if they have
  the same direction; otherwise it returns 180.

  \sa intersect()
*/
00612 qreal QLineF::angle(const QLineF &l) const
{
    if (isNull() || l.isNull())
        return 0;
    qreal cos_line = (dx()*l.dx() + dy()*l.dy()) / (length()*l.length());
    qreal rad = 0;
    // only accept cos_line in the range [-1,1], if it is outside, use 0 (we return 0 rather than PI for those cases)
    if (cos_line >= -1.0 && cos_line <= 1.0) rad = acos( cos_line );
    return rad * 360 / M_2PI;
}


#ifndef QT_NO_DEBUG_STREAM
QDebug operator<<(QDebug d, const QLineF &p)
{
    d << "QLineF(" << p.p1() << "," << p.p2() << ")";
    return d;
}
#endif

#ifndef QT_NO_DATASTREAM
/*!
    \relates QLineF

    Writes the given \a line to the given \a stream and returns a
    reference to the stream.

    \sa {Format of the QDataStream Operators}
*/

00642 QDataStream &operator<<(QDataStream &stream, const QLineF &line)
{
    stream << line.p1() << line.p2();
    return stream;
}

/*!
    \relates QLineF

    Reads a line from the given \a stream into the given \a line and
    returns a reference to the stream.

    \sa {Format of the QDataStream Operators}
*/

00657 QDataStream &operator>>(QDataStream &stream, QLineF &line)
{
    QPointF start, end;
    stream >> start;
    stream >> end;
    line = QLineF(start, end);

    return stream;
}

#endif // QT_NO_DATASTREAM

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