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void MainWindow::paintEvent(QPaintEvent *  /*event*/ ) 
{ 
    QPainter painter(this); 
    painter.setRenderHint(QPainter::Antialiasing, true); 
    QRect BackgroundRect(0, 0, 800,600); 
    painter.setBrush(QBrush(Qt::black, Qt::SolidPattern)); 
    painter.drawRect( BackgroundRect ); 
} 

    painter.setRenderHint(QPainter::Antialiasing, true); 

void MainWindow::paintEvent(QPaintEvent *  /*event*/ ) 
{ 
    QPainter painter(this); 
    painter.setRenderHint(QPainter::Antialiasing, true); 
    QRect BackgroundRect(0, 0, 800,600); 
    painter.setBrush(QBrush(Qt::black, Qt::SolidPattern)); 
    painter.drawRect( BackgroundRect ); 
}

void MainWindow::paintEvent(QPaintEvent *  event ) 
{ 
    QPainter painter(this); 
    painter.setRenderHint(QPainter::Antialiasing, true); 
    QRect BackgroundRect = event->rect(); 
    painter.setBrush(QBrush(Qt::black, Qt::SolidPattern)); 
    painter.drawRect( BackgroundRect ); 
}

void MainWindow::paintEvent(QPaintEvent *  event ) 
{ 
    QPainter painter(this); 
    QRect BackgroundRect = event->rect(); 
    painter.setBrush(QBrush(Qt::black, Qt::SolidPattern)); 
    painter.drawRect( BackgroundRect ); 

    painter.setRenderHint(QPainter::Antialiasing, true); 
    ...
    // а тут желательно рисовать в пределах BackgroundRect
}

painter.setClipRegion(event->region());

    painter.setBrush(QBrush(Qt::red, Qt::SolidPattern));
    painter.drawRoundRect( MainRect, 3, 3);

void QGLFormat::setDoubleBuffer ( bool enable )

void MainWindow::paintEvent(QPaintEvent *  event ) 
{ 
    QPainter painter(this); 
    QRect r = event->rect(); 
    painter.drawPixmap(r.topLeft(), bgPixmap, r);
}

void TestWidget::paintEvent(QPaintEvent * paintEvent)
{
	QPainter painter(this);
	draw();
	painter.drawPixmap(paintEvent->rect(), bufferPixmap);
	painter.end();
}

void TestWidget::draw()
{
	bufferPixmap = QPixmap(size());
	bufferPixmap.fill(Qt::transparent);
	QPainter painter(&bufferPixmap);
	painter.setRenderHint(QPainter::Antialiasing, true);
	QPolygon polyline;
	const int N = 40;
	for(int i = 0; i < N; i++)
	{
		polyline.append(QPoint(i*width()/N, height()*(i%2)));
	}
	painter.setPen(QPen(Qt::black, 1, Qt::SolidLine));
	painter.drawPolyline(polyline);
}