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class view : public QGraphicsView
{
    Q_OBJECT
public:
    view(QWidget *parent = 0);
private:
    float scale;
protected:
    void drawBackground(QPainter *p, const QRectF &rect);
    void mouseMoveEvent(QMouseEvent *event);
    void wheelEvent(QWheelEvent *event);
    void keyPressEvent(QKeyEvent *e);
signals:
    
public slots:
    
};

void view::drawBackground(QPainter *p, const QRectF &rect)
{

    QPainter painter(viewport());
 ...  
//рисую qpainter-ом

}
//-------------------------------------------------------------------------------------------------
/*
void view::mouseMoveEvent(QMouseEvent *event)
{
//просто снимаю координаты курсора
...
}
*/
void view::keyPressEvent(QKeyEvent *e)
{
   ...
}

void view::wheelEvent(QWheelEvent *event)
{
   ...
   
}

class scene : public QGraphicsScene
{
    //Q_OBJECT
public:
    explicit scene(QObject *parent = 0);
private:
protected:
signals:   
public slots: 
};

scene::scene(QObject *parent) :
    QGraphicsScene(parent)
{
    setSceneRect(0,0,800,800);

     ...
    addItem(mf);
}