Qt在Widget上绘制矩形

Question

我需要在作为mainWindow的子项的小部件上绘制矩形。但是下面的代码在绘制Widget时没有成功，它是在父屏幕上绘制的。

mainwindow.cpp

MainWindow::MainWindow(QWidget *parent) :
    QMainWindow(parent),
    ui(new Ui::MainWindow)
{

    ui->setupUi(this);
}

void MainWindow::paintEvent (QPaintEvent *e)
{
 QPainter *painter = new QPainter (ui->widget);
 painter->begin (this);
 painter->drawRect(e->rect());
 painter->end ();
}

void MainWindow::mouseMoveEvent(QMouseEvent *event){

    update((QRect(LastPoint,event->pos())));
}

void MainWindow::mousePressEvent(QMouseEvent *event)
{
    if (event->button() == Qt::LeftButton) {
        LastPoint = event->pos();
    }
}

MainWindow::~MainWindow()
{
    delete ui;
}

mainwindow.hpp

namespace Ui {
class MainWindow;
}

class MainWindow : public QMainWindow
{
    Q_OBJECT

public:
    explicit MainWindow(QWidget *parent = 0);
    void paintEvent (QPaintEvent *e);
    void mouseMoveEvent(QMouseEvent *event);
    void mousePressEvent(QMouseEvent *event);
    QPoint LastPoint;

    ~MainWindow();

private:
    Ui::MainWindow *ui;
};

我附上了设计师的截图。