The Logic of Two Point Perspective

Welcome back! When we left off last time, we had just finished getting super deep into explaining one point perspective. It was way more information than necessary for most, to be honest, but I think actually understanding the ins and outs of how it works is kind of cool. Today, we’ll take a similar approach to two point perspective.

Let’s start by examining a brand new setup of our trusty camera and sticks:

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This time, our sticks aren’t simply moving straight away from our camera. Instead, note that they’re moving away at an angle and are arranged in a square angle relative to each other. Here’s the top view:

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From the side view, these sticks behave exactly like the ones in the last section. As they get farther away, we perceive them to shrink towards the horizon, until they’re just a little speck on the horizon.

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When we look at this setup from the top, however, things are slightly different. Let’s extend one set of our sticks way back and examine what happens to our lines of vision. In this example, the sticks always move the same amount every time, but as they get farther and farther they move less and less in the camera’s field of vision. To measure this, I’m going to look at the angles formed by the lines of vision of each additional stick as they go back.

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Check out how those angles get smaller and smaller as we go back. Eventually, if we go back far enough, that angle is going to be so small that it might as well not exist. It’s at that point that we can say that we’ve found our vanishing point.

Of course, the same thing holds true for the other set of sticks, going the other way.

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So now what? We’ve got two vanishing points that are off to the sides instead of one in the center. It’s time to start figuring out what this scene looks like from the point of view of the camera. Let’s start by drawing out our vanishing points and a couple of the sticks that are closest to us, and let’s connect them up.

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Now we can add the rest of the sticks in our scene using these connector lines as a guide.

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Note that any other rows of sticks going in the same direction as the ones we started with are going to end up at the same vanishing points.

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And there’s our two point perspective! Let’s try to build out some solid shapes with this knowledge. See if you can follow along with the logic.

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Though it is a logical step forward from one point perspective, it took quite a while for people to figure this stuff out.

While one point perspective had been pretty much mapped out in the mid 1400s, it wasn’t until the early 1500s when two point perspective was figured out by engineers and mathematicians. What’s more, it didn’t really show up in artwork until over a hundred years later in the mid 1600s. I wonder what took them so long.

Next time, we’ll be talking about three point perspective, and after that we’ll move on to construction!