#define TOLERANCE 1.0e-3
  int main(int argc, char *argv[])
  {
  QApplication a(argc, argv);
QGraphicsView view;
  QGraphicsScene *scene = new QGraphicsScene;
  view.setScene(scene);
  view.setHorizontalScrollBarPolicy(Qt::ScrollBarAlwaysOff);
  view.setVerticalScrollBarPolicy(Qt::ScrollBarAlwaysOff);
// line 1
  QPointF p1( 0.0, 0.0 );
  QPointF p2( 200.0, 0.0 );
  QPainterPath smallRectPath1;
  smallRectPath1.addRect( QRectF( p1.x() - TOLERANCE, p1.y() - TOLERANCE, 2 * TOLERANCE, 2 * TOLERANCE ) );
QPainterPath path1;
  path1.addPolygon( QPolygonF() << p1 << p2 );
  path1.connectPath( smallRectPath1 ); // construce a closed trajectory with small rectangle
// line 2
  QPointF p3( 0.0, -100.0 );
  QPointF p4( 200.0, 100.0 );
  QPainterPath smallRectPath2;
  smallRectPath2.addRect( QRectF( p3.x() - TOLERANCE, p3.y() - TOLERANCE, 2 * TOLERANCE, 2 * TOLERANCE ) );
QPainterPath path2;
  path2.addPolygon( QPolygonF() << p3 << p4 ); // slope is -1.0
  path2.connectPath( smallRectPath2 ); // construce a closed trajectory with small rectangle
// path1 intersected path2 is null path
  qDebug() << path1.intersected( path2 );
// line 3
  QPointF p5( 200.0, 200.0 );
QPainterPath path3;
  path3.addPolygon( QPolygonF() << p3 << p5 ); // slope is not -1.0
  path3.connectPath( smallRectPath2 ); // construce a closed trajectory with small rectangle
// path1 intersected path3 is not null path
  qDebug() << path1.intersected( path3 );
scene->addPath( path1 );
  scene->addPath( path2 );
  scene->addPath( path3 );
view.show();
  return a.exec();
  }