问如何在QT中画出一条经过多个点的平滑曲线？

EN

namespace
{
    float distance(const QPointF& pt1, const QPointF& pt2)
    {
        float hd = (pt1.x() - pt2.x()) * (pt1.x() - pt2.x());
        float vd = (pt1.y() - pt2.y()) * (pt1.y() - pt2.y());
        return std::sqrt(hd + vd);
    }

    QPointF getLineStart(const QPointF& pt1, const QPointF& pt2)
    {
        QPointF pt;
        float rat = 10.0 / distance(pt1, pt2);
        if (rat > 0.5) {
            rat = 0.5;
        }
        pt.setX((1.0 - rat) * pt1.x() + rat * pt2.x());
        pt.setY((1.0 - rat) * pt1.y() + rat * pt2.y());
        return pt;
    }

    QPointF getLineEnd(const QPointF& pt1, const QPointF& pt2)
    {
        QPointF pt;
        float rat = 10.0 / distance(pt1, pt2);
        if (rat > 0.5) {
            rat = 0.5;
        }
        pt.setX(rat * pt1.x() + (1.0 - rat)*pt2.x());
        pt.setY(rat * pt1.y() + (1.0 - rat)*pt2.y());
        return pt;
    }

}

void PainterPath::smoothOut(const float& factor)
{
    QList<QPointF> points;
    QPointF p;
    for (int i = 0; i < mPath->elementCount() - 1; i++) {
        p = QPointF(mPath->elementAt(i).x, mPath->elementAt(i).y);

        // Except for first and last points, check what the distance between two
        // points is and if its less then min, don't add them to the list.
        if (points.count() > 1 && (i < mPath->elementCount() - 2) && (distance(points.last(), p) < factor)) {
            continue;
        }
        points.append(p);
    }

    // Don't proceed if we only have 3 or less points.
    if (points.count() < 3) {
        return;
    }

    QPointF pt1;
    QPointF pt2;
    QPainterPath* path = new QPainterPath();
    for (int i = 0; i < points.count() - 1; i++) {
        pt1 = getLineStart(points[i], points[i + 1]);
        if (i == 0) {
            path->moveTo(pt1);
        } else {
            path->quadTo(points[i], pt1);
        }
        pt2 = getLineEnd(points[i], points[i + 1]);
        path->lineTo(pt2);
    }

    delete mPath;
    mPath = path;
    prepareGeometryChange();
}