An observer approaching a high pole
The picture above illustrates a high pole with six marks. Each mark has a light body and a circle of sight corresponding to its height. The mark 1 has the smallest circle, the mark 6 has the biggest circle of sight.
The picture above shows an observer with a relatively small circle of sight approaching the pole. At this point, the pole is entirely below the horizon line of the observer.
As the observer continues to approach the pole, his light body intersects the circle of sight of the 6th , the highest mark. The mark 6 appears on the horizon of the observer, but remains partly obscured by the horizon line as long as the observer does not cross the circle of sight of the 6th mark.
As the observer crosses the circle of sight of the 6th mark, it becomes entirely visible. Furthermore, his circle of sight now intersects the circle of the 5th mark. At this point, the mark 6 is entirely visible, and the mark 5 is partly visible.
The observer crosses the circle of sight of the 5th mark while his circle of sight intersects the circle of the 4th mark. He has a full view on the marks 5 and 6, while the mark 4 is only partly visible.
The observer crosses the circle of the 4th mark. He now has a full view on the marks 6,5,4. The mark 3 is only partly visible as his circle of sight intersects the circle of the 3rd mark but the observer has not yet crossed it.
The observer crosses the circle of the 2nd mark. The marks 6,5,4,3,2 are entirely visible, while the mark 1 is only partly visible. The bottom of the pole remains obscured by the horizon line as long as the circle of sight of the observer has not reached the pole.
Now the light body, or circle of sight, of the observer covers the entire pole, from top to bottom. The bottom of the pole is now visible as it is covered by the circle of sight of the observer.
As the observer moves on, the pylon disappears below the horizon, bottom first. At this point, he still has a full view on the marks 6,5,4; the marks 1 and 2 are entirely below his horizon line, while the mark 3 is partly visible.
As the light body and circle of sight of the observer withdraws from the outer circle of the pylon, the pylon completely disappears below his horizon line. At this point, the observer no longer sees the pylon as his light body is no longer intersecting the light body of the pylon. There is no curvature between them.