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#ifndef QBEZIER_P_H

#define QBEZIER_P_H

//

//  W A R N I N G

//  -------------

//

// This file is not part of the Qt API.  It exists for the convenience

// of other Qt classes.  This header file may change from version to

// version without notice, or even be removed.

//

// We mean it.

//

#include "QtCore/qpoint.h"

#include "QtCore/qline.h"

#include "QtCore/qrect.h"

#include "QtCore/qvector.h"

#include "QtCore/qlist.h"

#include "QtCore/qpair.h"

QT_BEGIN_NAMESPACE

class QPolygonF;

class Q_GUI_EXPORT QBezier

{

public:

    static QBezier fromPoints(const QPointF &p1, const QPointF &p2,

                              const QPointF &p3, const QPointF &p4);

    static void coefficients(qreal t, qreal &a, qreal &b, qreal &c, qreal &d);

    inline QPointF pointAt(qreal t) const;

    inline QPointF normalVector(qreal t) const;

    inline QPointF derivedAt(qreal t) const;

    inline QPointF secondDerivedAt(qreal t) const;

    QPolygonF toPolygon() const;

    void addToPolygon(QPolygonF *p) const;

    void addToPolygonIterative(QPolygonF *p) const;

    void addToPolygonMixed(QPolygonF *p) const;

    QRectF bounds() const;

    qreal length(qreal error = 0.01) const;

    void addIfClose(qreal *length, qreal error) const;

    qreal tAtLength(qreal len) const;

    int stationaryYPoints(qreal &t0, qreal &t1) const;

    qreal tForY(qreal t0, qreal t1, qreal y) const;

    QPointF pt1() const { return QPointF(x1, y1); }

    QPointF pt2() const { return QPointF(x2, y2); }

    QPointF pt3() const { return QPointF(x3, y3); }

    QPointF pt4() const { return QPointF(x4, y4); }

    inline QPointF midPoint() const;

    inline QLineF midTangent() const;

    inline QLineF startTangent() const;

    inline QLineF endTangent() const;

    inline void parameterSplitLeft(qreal t, QBezier *left);

    inline void split(QBezier *firstHalf, QBezier *secondHalf) const;

    int shifted(QBezier *curveSegments, int maxSegmets,

                qreal offset, float threshold) const;

    QVector< QList<QBezier> > splitAtIntersections(QBezier &a);

    QBezier bezierOnInterval(qreal t0, qreal t1) const;

    static QVector< QPair<qreal, qreal> > findIntersections(const QBezier &a,

                                                     const QBezier &b);

    static bool findIntersections(const QBezier &a, const QBezier &b,

                                  QVector<QPair<qreal, qreal> > *t);

    qreal x1, y1, x2, y2, x3, y3, x4, y4;

};

inline QPointF QBezier::midPoint() const

{

    return QPointF((x1 + x4 + 3*(x2 + x3))/8., (y1 + y4 + 3*(y2 + y3))/8.);

}

inline QLineF QBezier::midTangent() const

{

    QPointF mid = midPoint();

    QLineF dir(QLineF(x1, y1, x2, y2).pointAt(0.5), QLineF(x3, y3, x4, y4).pointAt(0.5));

    return QLineF(mid.x() - dir.dx(), mid.y() - dir.dy(),

                  mid.x() + dir.dx(), mid.y() + dir.dy());

}

inline QLineF QBezier::startTangent() const

{

    QLineF tangent(pt1(), pt2());

    if (tangent.isNull())

        tangent = QLineF(pt1(), pt3());

    if (tangent.isNull())

        tangent = QLineF(pt1(), pt4());

    return tangent;

}

inline QLineF QBezier::endTangent() const

{

    QLineF tangent(pt4(), pt3());

    if (tangent.isNull())

        tangent = QLineF(pt4(), pt2());

    if (tangent.isNull())

        tangent = QLineF(pt4(), pt1());

    return tangent;

}

inline void QBezier::coefficients(qreal t, qreal &a, qreal &b, qreal &c, qreal &d)

{

    qreal m_t = 1. - t;

    b = m_t * m_t;

    c = t * t;

    d = c * t;

    a = b * m_t;

    b *= 3. * t;

    c *= 3. * m_t;

}

inline QPointF QBezier::pointAt(qreal t) const

{

#if 1

    qreal a, b, c, d;

    coefficients(t, a, b, c, d);

    return QPointF(a*x1 + b*x2 + c*x3 + d*x4, a*y1 + b*y2 + c*y3 + d*y4);

#else

    // numerically more stable:

    qreal m_t = 1. - t;

    qreal a = x1*m_t + x2*t;

    qreal b = x2*m_t + x3*t;

    qreal c = x3*m_t + x4*t;

    a = a*m_t + b*t;

    b = b*m_t + c*t;

    qreal x = a*m_t + b*t;

    qreal a = y1*m_t + y2*t;

    qreal b = y2*m_t + y3*t;

    qreal c = y3*m_t + y4*t;

    a = a*m_t + b*t;

    b = b*m_t + c*t;

    qreal y = a*m_t + b*t;

    return QPointF(x, y);

#endif

}

inline QPointF QBezier::normalVector(qreal t) const

{

    qreal m_t = 1. - t;

    qreal a = m_t * m_t;

    qreal b = t * m_t;

    qreal c = t * t;

    return QPointF((y2-y1) * a + (y3-y2) * b + (y4-y3) * c,  -(x2-x1) * a - (x3-x2) * b - (x4-x3) * c);

}

inline QPointF QBezier::derivedAt(qreal t) const

{

    // p'(t) = 3 * (-(1-2t+t^2) * p0 + (1 - 4 * t + 3 * t^2) * p1 + (2 * t - 3 * t^2) * p2 + t^2 * p3)

    qreal m_t = 1. - t;

    qreal d = t * t;

    qreal a = -m_t * m_t;

    qreal b = 1 - 4 * t + 3 * d;

    qreal c = 2 * t - 3 * d;

    return 3 * QPointF(a * x1 + b * x2 + c * x3 + d * x4,

                       a * y1 + b * y2 + c * y3 + d * y4);

}

inline QPointF QBezier::secondDerivedAt(qreal t) const

{

    qreal a = 2. - 2. * t;

    qreal b = -4 + 6 * t;

    qreal c = 2 - 6 * t;

    qreal d = 2 * t;

    return 3 * QPointF(a * x1 + b * x2 + c * x3 + d * x4,

                       a * y1 + b * y2 + c * y3 + d * y4);

}

inline void QBezier::split(QBezier *firstHalf, QBezier *secondHalf) const

{

    Q_ASSERT(firstHalf);

    Q_ASSERT(secondHalf);

    qreal c = (x2 + x3)*.5;

    firstHalf->x2 = (x1 + x2)*.5;

    secondHalf->x3 = (x3 + x4)*.5;

    firstHalf->x1 = x1;

    secondHalf->x4 = x4;

    firstHalf->x3 = (firstHalf->x2 + c)*.5;

    secondHalf->x2 = (secondHalf->x3 + c)*.5;

    firstHalf->x4 = secondHalf->x1 = (firstHalf->x3 + secondHalf->x2)*.5;

    c = (y2 + y3)/2;

    firstHalf->y2 = (y1 + y2)*.5;

    secondHalf->y3 = (y3 + y4)*.5;

    firstHalf->y1 = y1;

    secondHalf->y4 = y4;

    firstHalf->y3 = (firstHalf->y2 + c)*.5;

    secondHalf->y2 = (secondHalf->y3 + c)*.5;

    firstHalf->y4 = secondHalf->y1 = (firstHalf->y3 + secondHalf->y2)*.5;

}

inline void QBezier::parameterSplitLeft(qreal t, QBezier *left)

{

    left->x1 = x1;

    left->y1 = y1;

    left->x2 = x1 + t * ( x2 - x1 );

    left->y2 = y1 + t * ( y2 - y1 );

    left->x3 = x2 + t * ( x3 - x2 ); // temporary holding spot

    left->y3 = y2 + t * ( y3 - y2 ); // temporary holding spot

    x3 = x3 + t * ( x4 - x3 );

    y3 = y3 + t * ( y4 - y3 );

    x2 = left->x3 + t * ( x3 - left->x3);

    y2 = left->y3 + t * ( y3 - left->y3);

    left->x3 = left->x2 + t * ( left->x3 - left->x2 );

    left->y3 = left->y2 + t * ( left->y3 - left->y2 );

    left->x4 = x1 = left->x3 + t * (x2 - left->x3);

    left->y4 = y1 = left->y3 + t * (y2 - left->y3);

}

QT_END_NAMESPACE

#endif // QBEZIER_P_H