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In class I stress
linear perspective
is one of many
depth cues.
And often
best done
a ruler.

You do want to study linear perspective but don’t treat it as obligatory in “good art”.

That’s a great way to build it up into something intimidating.

As in all things, overemphasis of Perfection is no friend.

I’ve long felt playing with distortion and smart use of the other tools we have at our disposal can give the most interesting results. Certainly the most Dynamic.

To illustrate that I’ve got a few things to show you here.

First i’ve embedded a set of animated “3D” Gifs I saw posted to Buzzfeed today! Why?

The Illusion of depth they so effectively trick you into seeing!

The 3D effect here is an optical illusionHere’s why it works.

There are atmospheric and scale related perspective cues in these. And movement is what makes these especially pop.

But the trick used in all very overtly is a framing device, and it’s one that can come into play in all visual Art.

In each the animators have put in three white bars, you noticed already right? They’re hard to miss. They all help set and establish the Midground!

There is a behind, a Background where everything starts.

And a Foreground, that the “3D” object ends up in, AFTER passing the Midground bars.

The bars never move. The moving objects overlap them as they travel. Again simply by being there, they establish a fixed Midground.

Your brain does the rest, accentuating awareness of the Foreground, and Background.

Combined here with movement scale and linear cues it induces greater depth perception. Brain Magic. Overlapping objects and having a Foreground, Midground and Background in all your art will do this even without animation.

11 anigif10 9 8 6 4 3 2 5
Via imgur: Via selfservicehope: Via chritphr: Via imgur: Via tugamaggie: Via fandom-pride: Via imgur.com: Via pgmcanalla: Via zsof


Now a little perspective on the history and multiple inventions of “Perspective”!

It’s often taught that we in the west invented liner perspective and did it in the Renaissance. This isn’t true though. In fact at that time italians reverse engineered it from arabic math on optics! And probably, ideas about it, a basic understanding was there already in some respects.

perspective basicsByzantine2wb

Before we ever developed complex theories or techniques, attempts to depict dimensional space came naturally to us. We drew what we thought we saw, and thanks to our binocular vision we see depth.

it’s debated how much our cave painting ancestors thought their animal drawings were really that life like. But we suspect they used some optical effects like patterns and dots, and the shapes of the rocks themselves, to help make their drawings more alive looking in the flickering light of their fires. Painting the shoulders or haunches of an animal over a bulge in the rock to add realism? So it’s not surprising we actually had started to develop liner perspective long before the Renaissance.

ancient Greek and Roman use of angler, fish bone, and even single point perspective!We know for certain we developed a working understanding of the geometry of perception and optics earlier than most people often realize. Roman’s used very sophisticated linear or near linear perspective sometimes.

Some of their work had a fishbone like vertical vanishing point, but some was even done using single point perspective, which again is often presented as an invention of the renaissance. Really it was a re-discovery, primed by the european introduction of the work of Ibn al-Haytham on the nature of light and optics.

Despite the western arts early use of optical perspective as seen in the Roman examples I gave, later Byzantine art & culture had a radically different idea about perspective in art, that led to the seemingly strange look of things in their Icons and paintings.

It was symbolism driven, Reversed Perspective. Rather than the picture plane serving as a window into space with a vanishing points in the far distance and all lines pointing to them; standing in front of Byzantine art, you are the vanishing point!

It’s designed to work with a viewer whose kneeling, praying or worshiping. They are the focal point of the viewing experience.

A prime example is seen here on the left. Note that there are some examples here of things appearing smaller as they become distant?

Trees and buildings? The road, a distant fortified wall. Also the haze of atmospheric perspective is employed as well.

But the angles of walls are all over the place, unless you think in terms of yourself as the focus point, rather than a point on the horizon. All the things are turning to address you the viewer.

People are sized as well not by distance, but based on importance in their society. Tinny workers on the oddly small symbolic cathedral, larger master masons on the left, a bigger forman, talking with the lords and leaders of the town?

Byzantine perspective was symbolic. Meant to give a more direct connection with the holy spirit, or communicate social order. Not simulate a realistic view of the world.

This approach still works to induce depth, it’s just strange now that we’re accustom to more naturalistic techniques. It’s kind of like a Bas-relief style of depth.

It still has powerful compositional uses today, you see it in less representational art along with a another common Byzantine stylization, radiant internal, and uniform frontal lighting. It creates a kind of “wood block” effect as some have described, that I enjoy in my own art.

All this is here aside from the value of the history lesson, is to underline the idea that Perspective, is a compositional tool, as much as it is a drawing technique.

It’s about arranging space just as much as the rule of thirds or any other compositional rule. consider that, and what the goals are of a given work, before assuming how you should approach the application of perspective.


 Illustration of distortion in Linear Perspective, by Hector Gonzalez Molina
Illustration of distortion in Linear Perspective, by Hector Gonzalez Molina

Notes about Linear Perspective
and distortion.

I touched on the in my post on Linear Perspective, but it’s worth underlining here again. One of the more common issues that comes up with perspective drawing is that many are unaware or mindful of the fact that you WILL create distortion if you have more than one vanishing point for a given object, inside the frame.

We often see demos showing two vanishing points at what would be right angles for a box, being drawn both inside the picture plane.

But if we do this, we’re compressing the object dramatically. See the example on the right [ from a great suport blog on perspective studies in spanish by Hector Gonzalez Molina ]

The spherical grid of Curvilinear Perspective

If our goal is to create a less distorted image, then you can only really have one of them inside the frame of the picture plane, and the others would live someplace off the canvas.

This presents complications in keeping track of those vanishing points. At one point when I was first starting out as a professional artist I had wood meter-sticks clamped to the back of my desk and sticking out each side, so I could use thumb tacks and string to measure vanishing points in naturalistic positions and rectilinear lines. That can be a hassle and I don’t do it anymore. Which brings me to the next important point. It’s not bad always, to have distortion. We can put two, or even 4, or 5 right angle vanishing points inside the frame!  The result is simply this spherical grid of Curvilinear Perspective.

Even if you stick to linear perspective with a rectilinear grid, and two or three vanishing points, there’s a lot of stretching and distortion that goes on when they all come into view. Just keep this in mind. If you don’t want the squish and distortion that brings, only have one vanishing point in the picture plane at a time.

That said, don’t be afraid of bending reality. Curvilinear Perspective describes well what wide-angle lenses see. The difference between undistorted Rectilinear Perspective, and Curvilinear Perspective, is mostly the allowing for curved lines in its geometry. You don’t always have to see the curve either, but it’s a lot more like how we really do see, and how lenses work, than Linear Perspective is.

We perceive the liner structures of most traditional buildings as Rectilinear, but this is in part an illusion, thanks to what I’ve come to think of as something like the error correction software of our visual cortex. Note the difference between looking at a building yourself, and looking at it via Google Earth, which maps its street view shots onto a Rectilinear grid rather than a Curvilinear one. Note the strait lines even at the edges of the shots.

Another effect of wide angle views/pulling more into the shot including those second and third vanishing points, is how it changes our perception of depth. The wider our view, the deeper the depth seems as well. The more narrow the view, typically things appear closer over all and to each other.

depthgiphyThis gif is a great way to illustrate that. It shows a telephoto lens dramatically changing focal length. The camera’s position does not change much as the lense shifts, but the amount of information that can fit in the frame does. When it pulls back to fit in more, we can see that the main subject of the concrete block in the mid ground more or less stays the same size, but objects in the background appear to become more distant/smaller, and note that some of the ground in the foreground ends up rushing towards us and getting cut off.

Also the concrete block if drawn, would have vanishing points BELOW the horizon line here, that’s why the angles appear to change on it as the focal length does.

The relative perspective is constant, but as the shot extends or compresses, it changes the angle of the vanishing point ‘lines’ that describe the sides of the block.

Now if we were to pull back even further, into a fish eye lense, we would eventually see what kind of distortion happens with an optical lense, when more than one vanishing point comes into view.  It starts to look a lot like Hector’s drawing doesn’t it? This image comes from a post here, author unknown.

You can see how both the vertical lines have begun to curve, and the horizontal lines that would describe the rows of desks starts to bend, so that the vanishing points to the left and right can come into the frame. And the back of the hall, appears to pull further away, just like with the depth of field change we see in the gif of the concrete block on the beach.

So that brings us to the next stop in exploring perspective…


What I enjoy using the most, is a form of Curvilinear Perspective. What I think of a Bifocal Perceptual Curvilinear Perspective.

I’ve uploaded three viewfinder frames to help illustrate this idea.

The first is symbolic of the structure of simple One Point, or Single Point Perspective.

But the fact is we don’t see with a single eye. We see with two, and the very complex visual processing power turns that into the seemingly uniform version of the world we assume we see.

So for my second viewfinder model, we add a vanishing point for the second eye about the same space apart as our eyes. and now we have two slightly different points of view.

This is the same effect drives 3D film or old school 3D art. Albert Sauteur, a painter in the EU, has patented his own version of what he calls Binocular Perspective complete with math to explain how and when you follow what vanishing point.

Last we see with wide-angle versions of the same viewfinder, showing something like the barrel distortion our brain edits out of the experience of seeing, but is innate in the mechanics I think, of our vision.

So the final viewfinder shows all three effects at play at once. I like to use this in my own art, but also twist and mold the space as a compositional tool.

What I often end up with looks like an irregular asymmetrical example of the ‘Mustache distortion‘.

Bifocal Perceptual Curvilinear Perspective, is my own made up fancy name for it. 🙂

2eyesgridSo here on the left is the Curvilinear Perspective grid-two of them superimposed on each other-illustrating the implications of this idea about Bifocal Perception.

Interesting eh?

The lower version fades out at the edges corresponding roughly to the average limits of the human field of view.

Ok, with this in mind In the next example I want to share with you is the work of an artist who I admire, and I think we aplications of the delightfully named ‘Mustache distortion’.

Intentional or not, I think illustrates how you can push and pull space around the idea of emulating Bifocal Perceptual Curvilinear Perspective.

Ultimately using the bending of reality, as a 3 dimensional compositional tool in 2 dimensional art!

I really love this drawing by Kim Jung Gi. I don’t know how much of this he did intentionally, or if he had the same ideas about optics and perception as I do behind it, but i’ve read him talk about how much he thinks about space & observing perspective in his interviews. In any case I’m confident he’s using the same kind of tools/ideas to compose space itself on the page much the same as I like to sometimes, and does such a daring and lovely job of it! It’s really kind of validating when you find people doing things you’ve been trying to, and making gorgeous art of it. Maybe you’re not so crazy! Maybe you need to be a bit more crazy.

I love that doesn’t just invite distortion, but uses it to create a more organic feeling space while leading your eye invisibly through it better. Suspecting what I felt, I traced over Kim’s art here to see if my gut was right and demonstrate what i mean.  To start, notice that it also has the two vanishing points directly out in space in front of the viewers point of view, but also two other vanishing points the help lead the eye up to the right, and then down.

The POV is of someone sitting up straight or slightly taller than most of the other seated people. The cabinets over the counters and kitchen shelves lift, pulling the space and eye up and to the left, then we drop into a well created by the mass of the patrons seated at the counter, who all have their own vanishing point a few feet lower. Creates and eye sink of depth. The walls in the right concave in rather than out, to push the eye back into the space and help create the circular movements I noted in this version of the image.

So we have a lot of depth, creating this very strong feeling of diving into the space and then warping of the space to get the reader to rotate around and keep the movement of your eye coming back to start the ride over. He uses great skill with paterns and structure to draw us as well. The banners, the story of the cooks, the folks sitting in the counter, they are showcased by having their own offset vanishing points, pushing out the space on the right. The displacement between the vertical center line of the image, the “fishbone”,and the narrative composition of the piece, creates a great deal of the movement we experience in reading the image. I seldom take this idea as far as I see it done in his lovely line drawings.

So here’s more amazing examples of Kim’s very expressive and loose use of space, where he even goes further with Anamorphic distortion, as well Bifocal Perceptual Curvilinear Perspective.


Jed Alexander [Dot.com – Twitter] is an Illustrator I’ve had the pleasure of getting to know online over the years.

A while back he shared a couple of great posts on his own explorations of things along similar lines of space bending passion. ‘Perspective your computer can’t do‘ & ‘Hippopotabus! Process and Influences‘. The set are a super fascinating informative look into his process.

The first about using organic forms of Curvilinear Perspective, and the later diving into more depth on the process behind this lovely illustration. As seen here broken out, it was built up out of layers of art drawing and washed on paper, mixed with digital rendering tools for the final result.


The Seahorse Smile

The Music Lesson by Johannes Vermeer c. 1662-1664 - Oil on canvas 73.3 x 64.5 cm. (28 7/8 x 25 3/8 in.) The Royal Collection, The Windsor Castle

This is a bit tangential to the topic but I watched Tim’s Vermeer and was excited to see the part where he discovered the Seahorse Smile! Tim Jenison in the course of reverse engineering the possible painting technique used by Johannes Vermeer, stumbled into some powerful evidence to back up the suspicions seeded by Hockney’s studies, for the use of optics in Vermeer’s work by nearly duplicating a “mistake” he then confirmed Vermeer made!

Reputedly the first record of anyone finding and “error” in Vermeer’s art like it in 350 years. Which underlines a point I make in my class about never feeling like you have to get perspective “perfect” to use it. Freehand has so much more compositional power for one thing, and the Seahorse Smile is evidence that a more expansive sense of space is what makes Vermeer’s work enveloping along with the colour and feeling of light. So what is the Seahorse Smile?

The Seahorse Smile: Tim Jenison first stumbled into the rediscovery/invention of using a concave mirror in place of a dark room in a camera obscura, to focus the light and detail of coincidently, the delicate seahorse pattern painted on the harpsichord of his loyal recreation. The previously presumed used technique of a camera obscura from the Hockney–Falco thesis just was not cutting it. By introducing a shaving mirror he solved it. It focused more light and resolved a clear image even in full daylight. Incidentally he was developing a way to match tone and colour, but inadvertently introduce a subtle wide-angle lens effect to the work.

A subtle curvilinear distortion which Vermeer and Jenison both tried to correct in the structure of the harpsichord in his painting by ruling its lines, but Tim discovered Vermeer left the distortion in the more detailed wood work & seahorse pattern on it’s face! I find you can see in the oblique angle shot of the painting — I frame grabbed from the film and posted below with notes and a photo of Tim’s drawing machine — that curvilinear distortion and perspective properties appear throughout all the lateral lines in the painting.

I think, this even very subtle rounding and curving of space, is part of what makes Vermeer’s work so enjoyable to look at. By both so loyally matching color and tone, as well as our perception of space, he hit on the exact formula for magical feeling art.



And now, a long desk side chat
while I apply some of these principles in my own work!

It took me a while but I’ve finally made a video talking about some of this while doing a drawing using it a little myself. You can watch it here, it’s just under 40 min.

Ok, to end the post, here’s a bunch of examples of my own work, where i frequently use of these techniques to depict space and combine them with strong lighting/shading for lots of depth! The tones are mostly rendered in ink wash or pencil, and digital gradations.

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