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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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nasshu31's avatar

why is this harder than math


PatternSeeker86's avatar
Delightful. Thanks for sharing your beautiful work. 
SCBart's avatar
your tutorials are great!
ashbasher22's avatar
Looks great. Good way for cartoonists to learn about interesting perspectives and shots. :)
FantasyRebirth96's avatar
Sorta kinda confused on this still. Maybe I should re read this. But I'll give practicing some perspective shoots a try and do my best to grasp the idea of it.
yezzzsir's avatar
Great job on this. Thanks for taking the time to put it together.
askoldnemirov's avatar
broke my brain a bit, but got it! Thanks for your work! Would really like to buy your book, if u will ever write one! 
waltervan00's avatar
Yo, great eye-opening perspective discussion. Upon reading it, I immediately wanted to try and do it myself.
And, only naturally, questions arise.

The orientation and placement of the beholder was really well explained. However, when it came to the objects with the scene, I find it a little hard to apply the logic to it. Say, you are looking at a cube from a 2-point perspective base, how will the guidelines bend and distort? I tried to identify the plane of a wall seen from an oblique angle and trying to apply distortion from it. It was stuck on whether the guidelines would bend up or down (making the wall bulge in, out, or warp around the image). If my question didn't make quite any sense, then I would happily link a crude diagram of my issue. (this applies to ground planes as well).

Another question I have is about you demonstration of wrapping up a panorama into what I assume is 4 Point perspective. I sometimes wonder whether that scenario could just be done in a 1 Point perspective. Also, about the demonstration with the worm's eye view of the room, may I ask why the guidelines are bent as such? Looking from the other examples, it could be related to the beholder's height in the scene.

I do understand that there are six vanishing points and distortion could be used to bring more life to the straight and stiff perspective scenarios. (which sounds very rewarding).

Cheers. I look forward to seeing you reply, once you have the free time to do so, of course.
Nsio's avatar
Note that in 2 point perspective, there are only 2 vanishing points and no more. Thus, you cannot distort the guidelines, because there are no other vanishing points for them. If you apply distortion here, it´s no longer 2 point perspective, because the distortion suggests that the beholder is turning her eyes and, as a result, revealing the influence of other vanishing points.

You can check how things distort in perspective by holding something (like a book) close to your eyes and then watch what happens in your peripheral vision. The larger the object is, the easier it is to see the distortion. Basically the closest part of the objects seems to buldge towards you, while the edges seem to bend away from you.

No, the panorama view cannot be done with 1 point perspective. If you don´t acknowledge the other vanishing points on the left and right (or sometimes behind you) and keep the lines straight, you get the effect as seen on the first example of "unwrapping 3D" part. If you force things into 1 point perspective but apply distortion, then it´s no longer 1 points perspective, and it may not be consructed correctly if you don´t know how the others vanishing points affects the view.

The room looks distorted because you normally wouldnçt see the scene like that. Your brain will treat the lines straight, it doesn´t need to know that the view is actually bending. The height of the eye level on that scene only makes the distortion above more pronounced, because the ceiling is farther away from the eye level. As I said before, try seeing what´s going on in your peripheral vision, and you ought to see the bending.
Tsiternish's avatar
I saw that effect the most clear when I got myself the new glasses. They made my vision sort of... closer to what you get with the wide-angle lens. When I first wore them, I realised that what I was taught about perspective was not completely valid. But I guess the job of an art teacher (or any teacher, perhaps) is to teach students basic things and shortcuts and encourage them to explore the more advanced material on their own.
merser24's avatar
Wait so is this stuff supposed to be for everything? or drawings with distortion applied? First slide got me confused lol. 
Nsio's avatar
Basically, it's supposed to be for everything, if the goal is to achieve real and natural perspective. However, in many cases the distortion is so insignificant it can be ignored. Sometimes the effect isn't desirable at all.
AoiKen's avatar
this is very very hard for me to understand.... sigh... I can never be able to understand this...
AsjJohnson's avatar
I have noticed that curve kind'a thing before, like when you look at a tile floor, and follow it to where you're standing, and behind you, where the vanishing point's at both ends. But I wasn't really sure how to incorporate it in drawings, and in the past I've often done that building/cube you have as the first, wrong, example.
It's nice that someone else has noticed that type of thing. (...haven't looked at the whole tutorial yet, but I'll get back to it when I have time. I thought I'd mention this now)
Nsio's avatar
Yes, that's just the effect, on a tile floor it's very evident :D
AsjJohnson's avatar
yeah, tile floors, and also tile(ish?) ceilings. Probably ceilings more so. Then, there's also the issue with cameras, where if you take a photo in a small bedroom, all the walls are bowed. Or that panorama example you have (those can turn out not-quite-right with cameras, maybe partly because of the other vanishing point).
It seems like having the slight arcs in pictures can really help make them look more real or organic. I noticed that even in that little building example where you do it both ways. It might make the difference between a cityscape or inside of a building that looks grid-like and harsh, and one that looks 'right' and more inviting.
...but, I wonder why no one's come up with a better perspective theory before. I could tell something was a little off about it for a long time, but there didn't seem to be anything about it academically. I suppose it would've been harder to tell before cameras were invented, though. Or maybe the perspective lines were always meant to just be a rough guide instead of taken literally.
Nsio's avatar
The current theory of perspective just works so well and it's easy to construct. Since all lines are straight, it's easy to draw everything with a ruler, it's easy to set useful reference points and place the elements in perspective. When there are no straight lines, the benefits of perspective grids are lost. The perspective changes all the time so you can't use any ruler or define useful guidelines. From there on it's just about making decent guesses.

Anyway, the current theory isn't wrong by all means. It's just simplified and designed to work in certain situations where minor distortions don't really matter. The rules are the same with "real" perspective, it's just that the beholder acts more like a static camera with limited field of vision. All in all, perspective is just a tool and theory to simplify the reality and art is all about making convincing illusions, so it's not that important to follow everything literally (as long as the artist understand what she is doing).
You should change your name you humble intelligent organism lol :P
poodlelover162's avatar
Me: - prints this out - grabs hilighter - starts to take notes -
Nsio, am enjoying your tutorials and learning as well. These are very helpful. Especially the one on perspective answered questions that I have always had in mind. Still more to go as I practice. Also like your name ( NSIO : Not So Intelligent Organism :) ). Helps me remember as sometimes I do not remember if it was NSOI or NSIO... when I search for you on google/deviantart.

Contrary to your forte, I have never drawn females ! Hoping to learn with the help of your tutorials :)

Thank you again!
Holydiver79's avatar
Thank you thank you ♡
Love your Nsio Explains. Great tutorials!
dreama-draws's avatar
any books you recommend? 
Nsio's avatar
Not on this subject but "Making Comics" by Scott McCloud is pretty awesome book. Although it's aimed for comic artists, many things in it can be applied on any field of art.
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