This post and the forthcoming ones are for anyone who has had perspective explained to them, but found that their brain started to close down causing them to feel an irresistible urge to get as far away from the person explaining as possible and have a quiet coffee and read OK magazine because it is certain there will be no article on perspective in it. Every now and again I am in the position of the abandoned explainee when I have to explain some of the finer points of perspective to a fellow painter. It starts off fine when I say, “Hold up your brush as close as you can and as level as you can, right in front of your eyes.” They do this and I pronounce. “You see where it cuts across your vision, that is always the Horizon line.” Over the years I have mastered the skill of saying horizon with a capital ‘H’.
They mostly just accept this, but some say, “What about if you are up a mountain, won’t it be lower?”
Fixing an irritatingly patronising smirk on my features I reply,”No, if you hold up your brush when you are on the very top of mount Everest it will still mark the horizon.”
“What about in space?” The smart-arses come back.
My smirk slightly morphs into a pout at this point…”When exactly are you going to paint in space…?” I enquire.
“So it doesn’t always work! What is the use of that then?”
So there we are, the rules of perspective are rules that don’t always look right on the page when you follow them. In actuality, as I have written in other posts, the whole business of linear perspective is a crude approximation of what and how we actually see. It is convenient I suppose that one point perspective is fairly easy to explain, with railway tracks meeting at the horizon etc. However once you are in the territory of 2 and 3 point perspective and quite wide angles of view your explanations gain an ever increasing degree of complexity which are going to glaze over most painter’s eyes. Also linear perspective assumes you only have one eye and a flat retina. Also it is taken for granted that neither your head or your peepers can swivel. I don’t know about you, but when I paint something I do a fair amount of swivelling and general rubbernecking!
Many artists avoid the whole thing by never doing town or cityscapes at all, or if they do they look way off into the distance which is where linear flattens out into cardboard cutouts. Most of us who don’t avoid such subjects stick to the safe territory of one point perspective and a tight view. Where it all falls apart though is when we take that slightly wider view.
Time for one of those diagrams, but don’t click away, there will be no equations or hyperbolic geometry.
Here we are in a town with mostly one point perspective, there are only a few bits of sticky-out shop and rooflines that don’t recede from us. The rest tapers off to meet at the point on the horizon in the middle of the street. I’ve gone quite wide too and all seems well. I have cheated a bit though. If I had stuck to the constructed rules of perspective the shop on the far right would be sort of stretched out; indeed in a photo that is just what happens. So a skinny man standing in the middle of a photograph will look like a fat man if he goes to the far side of the frame. We are so used to this effect in photos we no longer notice the distortion. Just for fun below is an image where those perspective rules that you have never quite understood start falling apart.
The wide-angleness of this image is not far off a point and click camera or your phone. As you see we have a straight row of perfectly identical computer generated men. Well call me picky, but to my eye the chap on the far right has had a few more iced buns in the last month than his friend in the middle… but they are identical models just duplicated, the distortion is purely caused by using the rules of linear perspective. To make it worse the chap on the right is about twice as far away from you the as chap in the middle… now I always thought the “rules” said things got smaller as they got further away. The blimps in the sky, by the way, are all perfect spheres… it is a property of spheres that they always have a circular outline wherever they are in your field of view. These appear to break that rule with enthusiasm. To recap, if you got a set of bald grey elevenplets (rarer that triplets I hear) and stood them in a line in front of your point and snap this is how they would look in your photo.
Here we are back in our city. We have stepped back a bit and widened the view. This is version one. At first glance this looks sort of OK. However the building on the far left has a corner that should be closer to you than the point at which it leaves the picture on the left of the frame. Yet following the rules of linear perspective it causes that face of the building to get taller as it gets more distant. The very opposite of what our eyes see in reality. Below is my guestimate fix.
Take a moment to compare versions one and two. I have made two simple adjustments one quite obvious, one less so. Firstly can you see that this looks more likely than the first version? If not can I suggest a quick coffee and a copy of OK? Ahem… the big change is on the left. The vanishing point has flipped from right to left so the building goes away from you as it should, you might also notice that the chimney stacks and the zebra crossing make more sense and the corner feels properly square. The other change is to the shop corner to the right of the picture. I have slightly curved and flattened the angle of the perspective as the lines reach the square corner. This helps the building on the left fit in better, though beware if you over do it things start to look bendy!
Linear perspective is fine as a starting point, but you do have to make subtle corrections to make up for its considerable deficiencies. Essentially you need to make some straight lines a bit bendy in order to get things to make better sense. My own take is to not over do it and get into fisheye territory, but to do the least possible to reduce any inconsistencies. I do get asked, “How can straight lines be bendy?” they will often hold their ruler against the offending roofline and go, “See it’s straight.” Instead of telling them the unwelcome fact that they are seeing their ruler bendy too, I usually suggest a coffee…
I am doing these little tutorials in small bites to make them a bit more digestible. If people have perspective questions post them below and I will try and cover them in future posts.
Ok Rob, I will be the first to bite! This one had me thinking a bit. As someone entirely self-taught in the matter of perspective, to my eyes the first of the latter two street scenes is wrong because there should be a vanishing point somehwere off to the left of the picture, as well as one to the right.This is what your guesstimate approximates to- if anything, the ground level line should be sloping slightly up from R to L in the building on the left, assuming your eye level is same as the man on the zebra crossing. I had in my possession a couple of large (A1 or A0) perspective sheets which would make the whole thing a lot easier- I assume these were originally produced for architects. Nowadays, you can print off A4 sheets from the internet which give the same effect, although less useful for setting out a large painting.
I dont know if you have already seen, but your blog has been rated as one of the world’s most influential art blogs- congratulations!
Comment by Karl — February 17, 2017 @ 5:53 pm
Karl, at first, my reaction was exactly yours. This is because we both adapt the “rules”to suit ourselves. But actually Rob’s first perspective drawing is exactly how you would render it if you follow the taught rules. The buildings facing us on the left are, after all, parallel to those that recede facing us on the right. So they must share a VP. I think in practice most of us use a blend of the strict rules of linear perspective and a commonsense “tweak”. So, ahem, you’re not wrong, but Rob is spot on.
Comment by Colin — February 18, 2017 @ 12:04 am
Thanks Colin, I am feeling better about having missed a formal art education! I can see a thread developing on “what they teach you wrong at art school”
Comment by karl — February 18, 2017 @ 9:37 am
Hi Karl, here is a simpler layout. We are looking straight down the street but not quite down the middle as you can see I am imagining standing to the Right of the white line. The streets by the way are in a rectangular grid. I think you can see the corner on the left looks square but the corner on the right doesn’t. If I changed my position to the Left the VP would flip to the other side and the lefthand corner would look wrong. So my cheat is to combine the view standing a yard to the left with the one standing a yard to the right.
As you see we now feel all the corners could be square and the streets are believably in a rectangular grid a state of affairs that was not entirely clear when using just one VP. I should perhaps add you could get the same effect by standing right on the white line with your camera and turning a little to the left and right. If you take a picture in each position, print them out, slice them vertically in half and then join the two halves that look best from each picture then this is roughly the result you would get.
Comment by Rob Adams — February 18, 2017 @ 10:44 am
Thanks Rob, this makes sense. It seems to me to be an argument for intuition rather than following rules to the letter .
Comment by Karl — February 18, 2017 @ 11:27 am
Thanks for this – really does help !
Comment by vonnie — February 18, 2017 @ 8:06 pm
Hi Karl, I try and consider all these “rules” (the rule of thirds is another) as a useful starting point. They get you into a place from where you can make better choices to move forward. The difficulty occurs if you think of them as final answers to problems to be followed without further examination. Knowing roughly the rules of linear perspective is very useful, but understanding them is a step further. If you grasp how the system works you can “reverse engineer” a photograph to look more how it would seem to the eye if you paint from it. Part of what we pick up on with plein air paintings vs ones from photo ref is that the camera sees by the rules of perspective but our eyes don’t.
Comment by Rob Adams — February 19, 2017 @ 10:15 am
I am studing about perspective, and i like this video (Denis Mandarino), about quadridimensional perspective, for panoramic image or painting
https://www.youtube.com/watch?v=iggFZNCt1vo
And this link (Yvonne Tessuto Tavares), about quadrilateral perspective, for ambients. Yvonne Tessuto Tavares wrote a book about it.
http://www.quadrilateralperspective.com/english/default.asp
Isbel
Comment by Isbel — March 3, 2017 @ 6:17 pm
Yes multiple viewpoints are well known, Escher was the real master of it often moving the viewpoint from exterior to interior in the same drawing. Adding temporal events is very common in comic strips that have a panorama split into sections with the same characters in each describing the action.
I did a post on spherical hyperbolic perspective that has an example of perspective with a temporal shift as well.
Comment by Rob Adams — March 4, 2017 @ 10:51 am
Your posts are very interesting, and study them is a privilege.
Thanks a lot!
Comment by Isbel — March 7, 2017 @ 1:18 pm
It’s worth remembering that your position relative to a painting when viewing it is also a factor. E.g. If done right the fat guy would appear thin again.
Also perspective works just as well in space. There’s nothing special about the horizon it’s just that we make floors of buildings parallel to the ground.
Comment by Benjamin — March 8, 2017 @ 6:51 am
Hi Ben I had to think about that a moment but not sure if it is true or not, the problem being that your camera and your perspective construction both have perfect peripheral vision. We on the other hand scan with eye movement using our fovea. I suspect that as soon as you turn your eyeball or your head you are swinging your picture plane too. I shall have to test it in the computer to see! That is something that it is hard to explain to people that the horizon would be better described as eye line as it is really marking the centre of the lens and the attitude of the viewing mechanism rather than something in the exterior world.
Comment by Rob Adams — March 8, 2017 @ 8:32 am
A quick test, yes you are right if you put your head very close to the screen and just use one eye the fat man is put on a diet. Presumably the point is when the horizontal angle of view matches the original.
Comment by Rob Adams — March 8, 2017 @ 8:43 am
Indeed that’s why the model as often discussed is incomplete. I would go as far as to say that the model—or trick—works perfectly for the very specific thing it is designed to achieve, namely reproduce the light passing through a 2D slice (some distance, d, in front of you) into *one* of your eyes. What people forget is that for the trick to work perfectly you must then also stand a distance d from it and look at it with one eye (with the painting hung so that your eye level matches the horizon). In other words the canvas must then match the exact position of that 2D slice. Then all the distortion produced by the eye on the original scene is also imposed on the lights rays coming from the painting and the man-fattening effects etc. to which you refer are also offset.
So I’m always a little wary about referring to it as an approximation when it absolutely is correct for the one specific trick it is pulling off.
The more important point is that using it or having knowledge of it doesn’t necessarily result in the best art. And it is an approximate tool if you’re interested in something slightly different to the rather rigid system just described.
Comment by Benjamin — March 8, 2017 @ 8:46 am
Yes I tend to do things by what feels right and then use perspective rules to sort out bits that don’t quite work, rather than establishing a perspective grid in the first place. Really I suppose a painting, especially a cityscape, is a montage of viewpoints rather than a single one.
Comment by Rob Adams — March 8, 2017 @ 8:56 am
I often do something similar especially since over-construction can lead to too much respect for the lines (and thus more of a coloured in drawing).
“Experimental error” is also a huge factor given that a small change of angle can result in huge changes in linear distance. I see the process of using linear perspective en plein air as a bit like solving a set of equations iteratively.
The 2D slice thing is a very useful image to hold in your mind. Your eye can’t tell whether a ray of light has reached it via bouncing off the surface of a canvas or from some point, P, 100m behind the canvas if the direction of the ray impinges on the eye at the same angle. So if the position of the paint representing point P is at the point where the light from P intersects the 2D plane, the eye can’t register the difference. Apply this across the plane and then hang & view the resulting canvas in the way I described and you realise why it must be right for this specific illusion.
The really cool thing is that the rules of perspective that we know and love can be derived mathematically from this construction. (It’s fun – I’ve done it – but you need that coffee)
Comment by Benjamin — March 8, 2017 @ 9:45 am
Really the math and the geometry is describes is quite straightforward especially for straight line perspective. Working out the proofs for hyperbolic geometry in curved perspective is beyond my pay grade though! I suppose one thing I would prefer is the method to be invisible to the viewer, there is a point where bending stuff becomes intrusive. I quite like travelling perspective which is used for film storyboards a lot, there both the viewpoint and VP height move across the composition. Hugh Ferriss is an interesting 1920’s artist who uses mixes of curved and linear.
Comment by Rob Adams — March 8, 2017 @ 7:41 pm
You’re right it is on the whole relatively trivial but there are some results that require some thought to prove rigorously – e.g. the formula for the convergence of equally spaced points.
Time to dig out me old notes on hyperbolic geometry…
Comment by Benjamin — March 8, 2017 @ 8:52 pm