How do I paint with QPainter?

I have started learning Qt recently.
I did not get quite clear how can I paint using QPainter class. Let`s say I want just to place a few points in the window:

class PointDrawer: public QWidget {
    Q_OBJECT
private:
    QPainter p;
public:
    PointDrawer(QWidget* obj=0): QWidget(obj), p(this) {}
    virtual void paintEvent(QPaintEvent*) {
        p.setPen(QPen(Qt::black, 3));
        int n = 8;
        while(...) {
            qreal fAngle = 2 * 3.14 * i / n;
            qreal x = 50 + cos(fAngle) * 40;
            qreal y = 50 + sin(fAngle) * 40;
            p.drawPoint(QPointF(x, y));
                        i++;
        }
    }
}

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

    drawer.resize(200, 200);
    drawer.show();

    return app.exec();
}

And after that, I got nothing!
Can you please tell me where I am wrong?