Qt開發之實作平滑曲線

前言

最近預研了幾個圖庫，感覺qcustomplot還蠻合适的。性能，互動，還可定制提供了極強的拓展性。

回到正題，Qt實作平滑曲線，很簡單，就是根據貝塞爾曲線算法計算出點,何為貝塞爾曲線？又稱貝茲曲線或貝濟埃曲線，是應用于二維圖形應用程式的數學曲線。一般的矢量圖形軟體通過它來精确畫出曲線，貝茲曲線由線段與節點組成，節點是可拖動的支點，線段像可伸縮的皮筋，我們在繪圖工具上看到的鋼筆工具就是來做這種矢量曲線的。貝塞爾曲線是計算機圖形學中相當重要的參數曲線，在一些比較成熟的位圖軟體中也有貝塞爾曲線工具，如PhotoShop等。在Flash4中還沒有完整的曲線工具，而在Flash5裡面已經提供出貝塞爾曲線工具。

提供代碼如下：

QVector<QPointF> QCPGraph::calculateControlPoints(const QVector<QPointF> &points) const
{
    QVector<QPointF> controlPoints;
    controlPoints.resize(points.count() * 2 - 2);

    int n = points.count() - 1;

    if (n == 1) {
        //for n==1
        controlPoints[0].setX((2 * points[0].x() + points[1].x()) / 3);
        controlPoints[0].setY((2 * points[0].y() + points[1].y()) / 3);
        controlPoints[1].setX(2 * controlPoints[0].x() - points[0].x());
        controlPoints[1].setY(2 * controlPoints[0].y() - points[0].y());
        return controlPoints;
    }

    // Calculate first Bezier control points
    // Set of equations for P0 to Pn points.
    //
    //  |   2   1   0   0   ... 0   0   0   ... 0   0   0   |   |   P1_1    |   |   P0 + 2 * P1             |
    //  |   1   4   1   0   ... 0   0   0   ... 0   0   0   |   |   P1_2    |   |   4 * P1 + 2 * P2         |
    //  |   0   1   4   1   ... 0   0   0   ... 0   0   0   |   |   P1_3    |   |   4 * P2 + 2 * P3         |
    //  |   .   .   .   .   .   .   .   .   .   .   .   .   |   |   ...     |   |   ...                     |
    //  |   0   0   0   0   ... 1   4   1   ... 0   0   0   | * |   P1_i    | = |   4 * P(i-1) + 2 * Pi     |
    //  |   .   .   .   .   .   .   .   .   .   .   .   .   |   |   ...     |   |   ...                     |
    //  |   0   0   0   0   0   0   0   0   ... 1   4   1   |   |   P1_(n-1)|   |   4 * P(n-2) + 2 * P(n-1) |
    //  |   0   0   0   0   0   0   0   0   ... 0   2   7   |   |   P1_n    |   |   8 * P(n-1) + Pn         |
    //
    QVector<qreal> vector;
    vector.resize(n);

    vector[0] = points[0].x() + 2 * points[1].x();


    for (int i = 1; i < n - 1; ++i)
        vector[i] = 4 * points[i].x() + 2 * points[i + 1].x();

    vector[n - 1] = (8 * points[n - 1].x() + points[n].x()) / 2.0;

    QVector<qreal> xControl = firstControlPoints(vector);

    vector[0] = points[0].y() + 2 * points[1].y();

    for (int i = 1; i < n - 1; ++i)
        vector[i] = 4 * points[i].y() + 2 * points[i + 1].y();

    vector[n - 1] = (8 * points[n - 1].y() + points[n].y()) / 2.0;

    QVector<qreal> yControl = firstControlPoints(vector);

    for (int i = 0, j = 0; i < n; ++i, ++j) {

        controlPoints[j].setX(xControl[i]);
        controlPoints[j].setY(yControl[i]);

        j++;

        if (i < n - 1) {
            controlPoints[j].setX(2 * points[i + 1].x() - xControl[i + 1]);
            controlPoints[j].setY(2 * points[i + 1].y() - yControl[i + 1]);
        } else {
            controlPoints[j].setX((points[n].x() + xControl[n - 1]) / 2);
            controlPoints[j].setY((points[n].y() + yControl[n - 1]) / 2);
        }
    }
    return controlPoints;
}

QVector<qreal> QCPGraph::firstControlPoints(const QVector<qreal> &vector) const
{
    QVector<qreal> result;

    int count = vector.count();
    result.resize(count);
    result[0] = vector[0] / 2.0;

    QVector<qreal> temp;
    temp.resize(count);
    temp[0] = 0;

    qreal b = 2.0;

    for (int i = 1; i < count; i++) {
        temp[i] = 1 / b;
        b = (i < count - 1 ? 4.0 : 3.5) - temp[i];
        result[i] = (vector[i] - result[i - 1]) / b;
    }

    for (int i = 1; i < count; i++)
        result[count - i - 1] -= temp[count - i] * result[count - i];

    return result;
}

//最後調用
QPainter painter;
QPainterPath splinePath;
int i = 0;
int pointSize = lines.size();
while (i < pointSize) {
   if (!qIsNaN(lines.at(i).y()) || !qIsNaN(lines.at(i).x()) || !qIsInf(lines.at(i).y()))     
   {
      if (lines.count() >= 2)
      {
         QVector<QPointF> controlPoints = calculateControlPoints(lines);
         splinePath.moveTo(lines.at(0));
         for (int i = 0; i < lines.size() - 1; ++i) {
             const QPointF &point = lines.at(i + 1);
             splinePath.cubicTo(controlPoints[2 * i], controlPoints[2 * i + 1], point);
         }
      }
   }
   i++;
}
painter.drawPath(splinePath);
           

調用可根據具體業務場景做适當調整。比如去掉while循環等。