How vanishing points work (Part 2)

In the first part of this series, we came up with a rule for finding the location on the retina that corresponds to the vanishing point of a straight line in our field of view.

What if we have more than one straight line – will we need more than one vanishing point?

It depends!

Let’s consider two special cases. First, we’ll look at two parallel lines in our field of view. Imagine being back on our country road, and this time there is a fence on each side of the road:


The eye’s view of two parallel fences, as one might see on either side of a road. Should they both have the same vanishing point?

If we consider a single horizontal wire from each fence, we will have two lines that, in the real world, are parallel. The question is, do they have the same vanishing point? Well, let’s follow our rule on how to get the vanishing point from a line. We’ll apply it first to fence 1, then to fence 2.

First, fence 1:


In the above figure, I’ve drawn a line through the center of the eye that is parallel to fence 1. It hits the edge of the eye at the red “x”. But this is exactly where the vanishing point was for the fence we looked at in the first post. In fact, if we put the light ray drawings for the two fences together, we get:


The two fences have the same vanishing point. This gives us a second rule for vanishing points:

Any set of parallel lines has a single vanishing point.

(You might have noticed that I implicitly assumed this rule to be true when I showed the very first picture of the fence along the country road. The three horizontal wires in the fence, which are all parallel to one another, were assumed to have the same vanishing point. I didn’t have to make this assumption. I could have drawn the fence with only a single wire, and the result would have been the same. It just wouldn’t have looked much like a real fence!)

Here’s where I’d like to mention the direction that the eye is looking in. Notice, in the above figure, that the person is looking a little to the right of center (thick grey arrow). This means that the vanishing point of the two fences lies a little to the left of the center of her gaze. Looking back to the first image in this post, you’ll see that this is indeed the case. The vanishing point of the two fences is to the left of the figure’s center.

If the person were to move her eyes so that she was gazing in a different direction, the only thing we would have to change in the light ray diagram is the position of the thick gray arrow. For example, let’s say she looks sharply to the left. The light ray diagram now looks like this:


The only thing that’s changed is the direction of the thick grey arrow. But this now means that the vanishing point lies to the right of the center of gaze. To the viewer, then, the scene now looks something like this:


Now the vanishing point is to the right of the viewer’s field of view. It’s quite remarkable how much the scene changes due to the simple act of looking in a different direction. But I guess that’s really the point of looking in a different direction in the first place – to change the scene!

In the next post I’ll look at what happens when we have two perpendicular lines in our field of view.

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