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Nsio Explains: Distortion in Perspective



It's been a while from my last tutorial. This is 14th in my "Nsio Explains" tutorial series. I'll be talking about perspective once again, because I'm not entirely satisfied in my perspective tutorial. I tried to explain it in a way I'm not really understanding it.

Unlearning misconceptions
Honestly speaking, I was (and still am) really bad at constructing perspective. I was using the system, but I didn't understand how it worked. I was using it because I was told that's how you should do it. Since I didn't understand it properly, I kept using it in wrong way and not realizing the issues. I trusted the system too much.

When I see perspective artist, I feel that most people have exactly the same issue I did: not really understanding how to work with perspective system. Another big mistake is to avoid doing perspective altogether. It's hard that's for sure, but the concept is actually really simple. Once you understand perspective, things start to make a lot of sense. It's like a snowball rolling downhill, the amount of things you can understand increases exponentially. That happened on my case at least as I'm basing most of my understanding on perspective and perception.

It wasn't until I got to study architecture at the university that I realized how perspective works. We had a lesson or two about perspective, but it was exact the same stuff I had been told already. I understood perspective while I was making 3D CAD models. I could orbit around the 3D models and I quickly realized the significance of the eye-level and the placement of the vanishing points and how the guidelines work from there.

When I was doing final renderings of my models I learned something rather annoying. All my visualizations had very unnatural perspective. For long I was trying to find the reason as to why they look so unnatural until I found out the problem. Perspective system doesn't take eye movement in account. That said, all lines are perfectly straight in constructed (or computer generated) perspective because the camera is static. You simply can't see the floor under you if you are looking at the wall in front of you. However, if you orbit around the model, everything looks very natural.

This is the reason that made me "abandon" constructed perspective and trust more on my perception instead.

The horizon line
The horizon in perspective is quite interesting thing. It's infinitely far away and everything you see recede towards it. The horizon isn't only in front of you, it's all around you. Thus you can consider that horizon line is actually a circle and you are in the middle of it. That's right, you as the beholder are the center point of whole perspective system, because it's your point of view that affects the perspective you perceive. In art, you determine where the beholder  is so that the viewers can then see what the beholder sees. I call this "global perspective".

Nsio explains: Perspective by Nsio

Why is horizon horizontal? That may sound stupid question, but it's not a coincidence to call it horizon. Horizon is horizontal because everything we see are somehow connected to the common reference plane, that happens to be the ground. We are all subject to gravitation that pulls us towards the center of the Earth. Although the Earth isn't flat as a pancake (dun dun duun!) it's safe to simplify it as a flat plane in most cases. That's what classical perspective system does and it gets the job done decently.

Btw, there is vertical "horizon" as well. It works just like a horizontal horizon, but it's vertical. It's not that common though, because it's usually more important to show what happens on our eye-level than high above or below it.

The vanishing points are always located on the horizon (also on the vertical one). But where are they exactly? How can you tell where they should be?

It's pretty simple actually. In 3D there are three dimensions: width, height and depth. Imagine three axes, X, Y and Z representing these directions. There is one vanishing point at both ends of each axis, which makes 6 vanishing points in total. That's only the start though.

A cube is very common 3D object. Each of the faces are perpendicular to it's respective axis, so if you look at one face directly in front of you, you are looking straight at the vanishing point related to that particular face. The faces on the left, right, above and below recede towards that vanishing point. However, that's only because you are looking there. In reality, the cube isn't receding anywhere.  It's just because of your vision that the cube will recede towards that vanishing point. If you turn and look another face, say, the face that was on the left, you are looking directly at another vanishing point. It works just like the first one, but it's not the same vanishing point. if you turn 180 degrees, you will be looking at the vanishing points at the other end of the respective axis. That vanishing point is there even when you aren't looking at it. That said, the sixth vanishing point is behind you and you can only see it if you turn to towards it. It's no longer behind you then though. In other words, you can never see the vanishing point behind you.

So, the vanishing points are related to your point of view and also on the object you are looking at. You aren't always looking straight on the front face of the cube. While all objects have their own set of vanishing points, most of the time they are tied on the ground plane, so it's relatively easy to place their vanishing points on the horizon(s). That's why classical perspective works so well. You just assume that all objects you are drawing (a street view with buildings on both sides for example) are all in the same orientation. Sometimes the objects aren't tied to global perspective and its horizon at all. Think about a dice you throw. While it's whirling in air, it has no constraints at all.

Unwrapping 3D
There is (at least) one major problem with classical perspective, or at least I find it very disturbing. The view point is static and, depending on situation, makes the perspective feel rather lifeless and unnatural. This has to do with limitations of the perspective system. Constructed perspective works well as long as you stay within the boundaries it works on.

The first limitation is that you can never really see more than one vanishing point. That's because the other vanishing points are well beyond your field of vision. Let's take the vanishing point on the left for example. It's on your left side and you can't see it unless you turn towards it. In classical perspective, that's not allowed. Let me demonstrate why. (see the deviation for picture examples)

Let's have a very simple room with 4 walls, a floor and a ceiling. The beholder is in the middle of the room. She is looking at wall one and her ultimate goal is to look directly at the wall 2 without moving her eyes. In other words, she has to see both of the faces directly from the front at the same time.

In one point perspective, you have only one vanishing point in front of you, no more. All horizontal and vertical lines are parallel. Now, everything is fine as long as you won't try to find the vanishing point on your left side, in other words, you don't try to see the wall on the left. If you extend the view to left, you will quickly see the problem with one point perspective. The room become excessively deep and the wall becomes skewed. Remember, you can never see more than is within your field of vision, so if you keep going, everything will look skewed. In one point perspective, you can't find other vanishing points.

In two point perspective, you now have the chances because now there is one vanishing point on the left. However you can't see both vanishing points at the same time. It's not possible, because you can't see both front and side face of a cube directly from the front at the same time. You can try to fake it by locating the vanishing points really far away on a canvas, so far that your lines are almost parallel. However, your drawing will get horribly skewed without you even realizing it. If you place both vanishing points within the canvas, you're screwed. If you have two vanishing points visible, you can't go beyond than that without breaking the system. In fact, the system is already pretty much broken if both vanishing points are visible and it shows as excessive depth.

I haven't discussed third vanishing point in the example, because it's basically the same as the one on the left, besides it's above or below the beholder. It won't help the beholder in her quest of seeing the wall 2 from the front.

The moment we introduce fourth vanishing point, we are moving beyond the field of classical perspective. At this point there are no straight lines anymore and it's really not possible to construct such perspective with straight ruler. The guidelines become arcs. So the only way to show both walls 1 and 2, you need separate frames for them.

So the problem is that on a flat canvas, you can never show what really is on the left side of the beholder. That's the limit of 2D. In order to show the second wall, you will need to apply perspective distortion that mimics eye movement. It's an illusion which works quite well. Panorama pictures are excellent examples of this.… this is my favorite panorama example. The road is straight, no matter how you brains try to tell you that it's arcing.

The reason that the example 4. in my tutorial looks weird is the fact that you normally can't see that much. When you move your eyes or turn your head, you won't even notice such distortion taking place. Your brains don't need that information. When you are presented such "unwrapped" perspective, your brains won't understand it naturally. However, if you re-wrap the perspective, you can see that it forms that familiar 3D illusion. I applied mesh transformation in Clip Studio Paint to reconstruct the unwrapped view.

Applying distortion
Distorted perspective can't show everything, but it can show more than classical perspective with straight guidelines. It's possible to draw 6-point perspective which includes the vanishing point behind the beholder, but it's not possible to draw it without discontinuity in some areas.… here is an example of such perspective. You need two 5-point perspectives to pull it off.

Fortunately, in most cases you don't need to show anything that's behind the beholder though.

Distorted perspective isn't easy to construct. But what's great about art is that it doesn't have to be perfectly executed in order to be convincing and believable. Careful amount of distortion really makes the difference. Although I mind the perspective system, I hardly ever really construct it. I want to trust my intuition and perception. I'm fairly good at figuring out the relationship between the beholder and the objects she sees, but I'm not perfect either. You can see an example about few imperfections in one of my example pictures.

TL;DR This tutorial was fun to compile because I had to make some studies about perspective. My goal was to tie my understanding to what I've been taught and this was excellent practice for that.

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