Qt实现三次B样条算法

三次B样条算法是一种常用的曲线插值算法，可以用于实现平滑的曲线绘制。下面是使用Qt实现三次B样条算法的示例代码：

#include <QtGui>

class BSplineCurve : public QWidget
{
public:
    BSplineCurve(QWidget *parent = 0) : QWidget(parent)
    {
        setWindowTitle(tr("B-Spline Curve"));

        controlPoints << QPointF(50, 50)
                      << QPointF(150, 100)
                      << QPointF(250, 50)
                      << QPointF(350, 150)
                      << QPointF(450, 100);

        setFixedSize(500, 200);
    }

protected:
    void paintEvent(QPaintEvent *event)
    {
        QPainter painter(this);
        painter.setRenderHint(QPainter::Antialiasing);

        // 绘制控制点
        painter.setPen(Qt::blue);
        for (int i = 0; i < controlPoints.size(); ++i) {
            painter.drawEllipse(controlPoints[i], 5, 5);
        }

        // 绘制B样条曲线
        painter.setPen(Qt::red);
        for (int i = 0; i < controlPoints.size() - 3; ++i) {
            QPointF p1 = controlPoints[i];
            QPointF p2 = controlPoints[i+1];
            QPointF p3 = controlPoints[i+2];
            QPointF p4 = controlPoints[i+3];

            for (qreal t = 0; t <= 1; t += 0.1) {
                qreal x = (-t*t*t + 3*t*t - 3*t + 1)*p1.x()
                        + (3*t*t*t - 6*t*t + 4)*p2.x()
                        + (-3*t*t*t + 3*t*t + 3*t + 1)*p3.x()
                        + (t*t*t)*p4.x();
                qreal y = (-t*t*t + 3*t*t - 3*t + 1)*p1.y()
                        + (3*t*t*t - 6*t*t + 4)*p2.y()
                        + (-3*t*t*t + 3*t*t + 3*t + 1)*p3.y()
                        + (t*t*t)*p4.y();
                painter.drawPoint(x, y);
            }
        }
    }

private:
    QList<QPointF> controlPoints;
};

int main(int argc, char *argv[])
{
    QApplication app(argc, argv);

    BSplineCurve bspline;
    bspline.show();

    return app.exec();
}

在这个示例代码中，我们使用`QList<QPointF>`来存储控制点的坐标，然后在`paintEvent`函数中，使用`QPainter`来绘制控制点和B样条曲线。具体细节可以参考代码注释。