But what located the specific vanishing point?« Across page we saw that the horizontal sight line aimed at infinity parallel to the tracks points to it. So, very simply: the vanishing point of the tracks is the point at which the sight line parallel to them intersects the picture plane. (The vanishing point essentially is this horizontal sight line seen from its end.) All lines parallel to the tracks will naturally also converge toward this same point.
IN OTHER WORDS THE OBSERVER SIMPLY "POINTED" WITH HIS EYES PARALLEL TO THE GIVEN SET OF LINES IN ORDER TO LOCATE THEIR VANISHING POINT
The following will show that this holds true regardless of the direction of the set of lines.
Here the tracks are at an angle to the picture plane.
The side view across page again applies, so we know that the infinite point of convergence (vanishing point) must be at eye level.
Now, looking at this new top view, we see that sight lines embracing the width of the foreground ties depart, as before, at a wide angle. For ties further away this angle gets progressively smaller and also aims more and more to the right. When the ties are finally viewed at infinity only a single sight line remains and it is virtually parallel to the tracks. Therefore, the sight line parallel to the tracks "points" to the tracks' vanishing point.
This little experiment would work for ANY set of parallel lines that appear to converge, regardless of whether they were horizontal, vertical or oblique, or whether the observer were looking up at them, straight out or down. Therefore the universal rule is: The vanishing point for any set of parallel lines is the point at which the sight line parallel to the set intersects the picture plane.
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