一个qt/c++ demo,用于显示 Apollonian Gasket（阿波罗尼恩镂垫） 分形图

#include <QtWidgets>

class ApollonianGasketFractal : public QWidget    
{
public:
    ApollonianGasketFractal(QWidget *parent = 0);

protected:
    void paintEvent(QPaintEvent *);

private:
    void drawFractal(QPainter& painter, qreal x1, qreal y1, qreal x2, qreal y2,
                     qreal x3, qreal y3, int depth);
};

ApollonianGasketFractal::ApollonianGasketFractal(QWidget *parent)
    : QWidget(parent)
{   
    setFixedSize(500, 500);
}

void ApollonianGasketFractal::paintEvent(QPaintEvent *)
{
    QPainter painter(this);

    painter.setPen(Qt::transparent);
    painter.setBrush(QBrush(Qt::black));

    qreal x1 = 50.0;
    qreal y1 = 250.0;
    qreal x2 = 450.0;
    qreal y2 = 250.0;
    qreal x3 = 250.0;
    qreal y3 = 26.6;

    drawFractal(painter, x1, y1, x2, y2, x3, y3, 7);
}

void ApollonianGasketFractal::drawFractal(QPainter& painter, qreal x1, qreal y1, qreal x2, qreal y2,
                                           qreal x3, qreal y3, int depth)
{
    if (depth <= 0)
        return;

    // 计算内切圆的半径和位置
    qreal r = qSqrt((x1-x2)*(x1-x2) + (y1-y2)*(y1-y2))/2.0;
    qreal x = (x1 + x2)/2.0;
    qreal y = (y1 + y2)/2.0;

    // 绘制内切圆
    painter.drawEllipse(QPointF(x, y), r, r);

    // 递归绘制内切圆和外切圆之间的三个内切圆
    drawFractal(painter, x1, y1, x, y+r, x3, y3, depth-1);
    drawFractal(painter, x, y+r, x2, y2, x3, y3, depth-1);
    drawFractal(painter, x, y-r, x3, y3, x2, y2, depth-1);
}

int main(int argc, char *argv[])
{
    QApplication a(argc, argv);    
    ApollonianGasketFractal w;
    w.show();

    return a.exec();
}