Piranesi's Perspective Trick (2019)
medium.comI'll take this opportunity to drop the fact that I'm kind of obsessed with the book "Piranesi", where the main character (named after the artist in the article) survives in a world which is just endless corridors of classical architecture, statues, and staircases.
It's an incredibly calming experience, I've listened to the audiobook over 10 times before sleep. Highly recommended.
A very different book, but I loved reading "Jonathan Strange & Mr Norrell" [0] as well by the same author.
[0] which used footnotes to great effect
This also has a great audiobook version. Simon Prebble really brings the characters to life.
I enjoyed the TV adaptation as well.
Indeed. It made long walks with my dog seem all too short.
Clicked the article for the book, stayed for the awesome explanation on how perspective works.
This must have been the inspiration for the Counter-Strike map de_piranesi !
No, the CS map predates the novel by almost 20 years. Almost certainly they were just both inspired by the same artist.
I second this review - Piranesi is a fantastic and inventive novel.
I remember being very frustrated with the main character while listening to the audio book. I enjoy the memory of the story a lot more than I remember actively listening to the story. I think I kept trying to "figure out" the world like it was a puzzle. I also find naive characters very frustrating. It wasn't until I finished the story that I really appreciated it.
"The House is valuable because it is the House. It is enough in and of itself."
So did you just spoil the ending for me?
Nope, that's a quote from early in the book.
Not even close
I think about this book ALL the time. It was way more terrifying than calming to me. But still absolutely love it / haunted by it.
A truly wonderful novel that I also opened the comments to shill.
we each enter the corridors for our own purposes and yet they are one
Loved the book. Bought it in hardcover, based just on the blurb, which sounded so futuristic and imaginative. Surprised me in ways I didn't expect.
I absolutely adored Johnathan Strange and Mr. Norrel, I don't read a _ton_ of fiction, but somehow stumbled into it and recommend it to anyone who will listen.
But I couldn't get into Piranesi at all. The first few chapters never seem to actually go anywhere. It got terrific reviews so maybe it's just too abstract for me.
It reads like a parable and you are right there isn’t a lot of action. I thought the imagery was very stark and the relation the main character had to the world is similar to an abuse victim rationalizing their situation.
Read the book once, will definitely check out the audiobook. I got in the habit of reading it before bed too, sounds perfect.
Absolute banger. I am convinced it will be held up as a true classic.
There are a few "wait what?" moments in the first half of the book that no other books have matched.
Sadly, the ending doesnt live up to the expectations, at least for me.
The paradox of mystery, when the mystery is too good that no ending can justify it.
Yes, could almost have been written for another story altogether.
Came here to say this. I loved the voice of the main character.
> By legibility I mean that the Piranesi distortion is easier to read, and that to anyone unfamiliar with photographs, that hasn’t grown up with TV, photographs and magazines, the Piranesi version would look much better, and the true perspective would look rather odd.
I think this is a key point that people are often unaware of. For instance, whenever I see a modern artist who has painted photorealistic art, I read discussion about how amazing it is that this artist can paint something so perfectly life-like, and the Renaissance artists were clearly inferior, since they couldn't paint with such skill.
Besides the obvious discussion about the purpose of art, the other question is whether a photorealistic painting is actually more "lifelike?"
Sure, it represents the world exactly the way that a camera sees it, but does it represent the world exactly as we see it? With our human brains we are filling in details, we are focused on the subject of the painting, we are distorting, we are re-mapping shades of color to what we know they ought to be. "Lens blur" in particular isn't remotely the way our eyes perceive the world: our eyes can never roam around the unfocused parts of our own image, rather we ignore the blurry parts unless we specifically try to notice them, and anything we try to focus on becomes sharp.
So I appreciate the authors recognition that Piranesi's perspective may indeed be closer to how we perceive the world than "correct" perspective.
> rather we ignore the blurry parts unless we specifically try to notice them, and anything we try to focus on becomes sharp.
Unrelated to perspective: Artists often put more detail in places that you're "supposed to" look at, and leave other things more as a blurry sketch, and our eyes naturally don't linger on those parts. What's interesting to me is that I can often recognize AI art by the way it doesn't make use of this, it tends to make everything equally detailed.
I learned this back when I used to make maps for Source games (Team Fortress 2, CS:Source, etc.) — at first I sprinkled props and detailed geometry equally throughout the level, but it's better (in terms of art direction, player attention, and performance optimization) to put details in places that "matter". Valve does this [0] in their official maps and it's actually hard to notice until you really pay attention to it.
One of the most dramatic things in this respect is to look at a photograph of a flame. Our lived experience of what flames look like is very different. The same is true of nearly any dynamic object in life (flowing water is another great example where the photograph doesn’t look like what we experience).
Those examples are very challenging because they are volumetric objects, in addition to being dynamic. The flame does not even have a well-defined surface. What you see as red/yellow in the flame is in fact just glowing soot particles, and the point where this disappears is just a temperature difference in the gas such that the soot stops glowing.
One of my favorite books is "Seeing Like a State"[1], which talks about how the modern world has transitioned from talking about things like distance and space in human terms ("an hour's walk", "six bushels' worth of crops") to a surveyor's terms ("3 miles", "5 acres"). In the modern world, we're very used to thinking about things as mediated by technology (maps, cameras, compasses), and that affects how we think about arts, as well - matching what a camera produces is "photorealistic", but isn't how we actually _see_ things. This is one example, another I've always found fascinating is that the large Chinese landscape paintings play a trick where the perspective shifts depending on where you're looking - the whole work does not share a single perspective point, but any given point on the scroll looks "correct" for that spot and its surroundings.
[1]https://bookshop.org/p/books/seeing-like-a-state-how-certain...
I strongly agree.
> The distinctive feature of Piranesi’s perspective trick is that when you have a series of similar objects receding into the distance, such as houses or arches in a bridge, the nearer versions are just drawn as larger versions of those in the distance
This makes so much sense. When nature presents me with a series of identical arches, that is how I'm going to interpret them. Not as the geometric shapes that are actually projected onto the backs of my eyes.
You make good points, but if we really perceived reality differently than cameras, someone would write an article about that - after all you can take a photo on your smartphone and compare to your IRL view. Yes it's hard to make it match but it's possible. Since no one made an experiment to show this, and since we understand pretty well the optics of a human eye, I think the cameras actually reproduce human vision decently. The aspect of a psychological bias and filling stuff in perhaps distorts in each possible way, so the camera shows the average human perception.
One thing that cameras can do that we can't do with our (unaided) eyes is change focal length. When a camera zooms in or zooms out, there is a change in the geometry of perspective. When zooming in, the change is difficult to see but is well documented. Portrait photographers are well aware of this because it tends to make people look better. When zooming out, especially when zooming out to a very wide field of view, the effect can be very noticeable. When people use a phone camera to take a picture of a group of people, the people at the edges of the photo can look very flattened and unnatural. Again, this effect is well known and very much discussed and written about in photography and art. In the article about Piranesi's work, we see a very interesting remedy to the perceived distortion of a wide view. Again, these works show a field of view, and therefore a focal length, that is not possible with our eyes. We can visualise in our mind's eye what the scene looks like but what our eyes are doing is moving around the scene while our visual cortex and ultimately our mind's eye construct a mental model. In our minds, we know that the arches of the bridge are the same size and shape despite being distorted by distance. We can look at what's in front of us and see that in the receding row of arches the nearest appears to be bigger than the farthest but we also know that's just an artefact of our point of view. Things are subtly different when we look with our eyes at a photograph, painting or drawing. It's not the same as when we see something in real life, we're looking at a 2 dimensional representation of a 3 dimensional scene. We do see the perspective in the picture - we don't see a bunch of lines on a two dimensional plane. Our brains are making that happen and are making some adjustments along the way. It just so happens that something we have difficulty adjusting so it "looks right" is a very wide angle scene. That's because we don't ever see a very wide angle scene in one glance in real life.
> When a camera zooms in or zooms out, there is a change in the geometry of perspective.
This is the opposite of what happens. The perspective is exactly the same, only cropped to a narrower field of view.
Changed perspective would be counteracting the lens zoom with foot zoom -- now this causes the change in perspective you talk about. But it's caused entirely by moving the camera. The zoom is just to preserve framing and could just as well be accomplished by cropping in post, assuming sufficient resolution.
You are 100% correct! I was unconsciously assuming the foot zooming. Thanks for picking that up!
I think foot zoom is the primary reason for faces looking weird (big noses) in smartphone selfies, while "a photograph occupying less of your FOV than the camera was capturing" is why people at the edge of a photo look distorted.
Just one well known difference: Human have two eyes and we use the difference to determine distances. A photo is flat.
Another difference: In human sigth you can only focus on the center of the vision field, while on a photograph you can look at unfocused points and observe the distortion on the edges of the picture. Human observation (like looking at the bridge in the pic) is really a series of observations where we move the focus.
Notably, photorealism is called photorealism because it deliberatley tries to reproduce photography, not because it tries to reproduce observable reality.
Panini projection is built into Unity and Unreal. From the documentation from the latter [0] you can see how it's essentially a cropped fisheye-ish projection. That doc also has (in my opinion) a clearer comparison on how the two projections differ, especially looking at the layout of the square tiles on the floor in the first set of pictures.
[0] https://dev.epicgames.com/documentation/en-us/unreal-engine/...
Wow, this is SO cool! It looks better because you can see the details of objects far from the 'camera'. This is basically what you do when you are there in reality, constantly refocusing on objects. This perspective trick to me is a map of zones on the picture on which I will focus.
I wonder what would happen if we'd render videos using it, and maybe games? Could this be a solution to better graphics? Would movement ruin it? Please tell me!
The panotools wiki has a good comparison of different projections of the same photo. Google Streetview uses equirectangular pictures to store 360° images. Panini is another type of equirectangular.
Examples
Panini: https://wiki.panotools.org/File:Ben_Equirectangular_panini.j...
Equirectangular: https://wiki.panotools.org/File:Big_ben_equirectangular.jpg
Full list: https://wiki.panotools.org/Projections
if you have any connection to the admins of that wiki, it would be great to get MultimediaViewer extension enabled - https://www.mediawiki.org/wiki/Extension:MultimediaViewer
they're on 1.35 right now which is a bit out of date (lifecycle - https://www.mediawiki.org/wiki/Version_lifecycle) but an older branch of MMV should work fine on 1.35
I hate this behavior on Wikipedia. Worst part is that people then share links to those views which don't work without running javashit.
If you have an account, you can disable it in preferences. Appearance -> Files -> "Enable Media Viewer" Toggle that off and it'll never happen again
Blocking the scripts in question works better for that without the need to make an account. But neither solves the problem of others sharing links to image views that won't work without scripts enabled.
You can still share a link directly to the file. For example:
* Page with images - https://support.wiki.gg/wiki/CSS * An image in media viewer - https://support.wiki.gg/wiki/CSS#/media/File:Css-wiki-body-b... * The image file page - https://support.wiki.gg/wiki/File:Css-wiki-body-background-i... * The direct image in question - https://support.wiki.gg/images/4/41/Css-wiki-body-background...
My theory is that most perceived perspective errors arise when a photograph captured with a wide field of view is shown in a narrower one; a perspective-"distorted" image looks more realistic if you put your nose up to the screen so the photograph fills more of your field of view (enlarging the center and eventually squashing the edges). And tricks like Panini projection and Piranesi's arches are ways of making features at the edge of the screen "take up" the correct amount of viewing angle (without bending straight lines) when the painting takes up less of your vision than the original scene.
> it isn’t possible to construct a camera or a computer program to render a view that does this
Hmmm
> The mathematics of this is quite simple
If so then surely a program could be written
Doing it with a camera/computer requires identifying the objects that need to be drawn in "Piranesi Perspective". The mathematics of laying out the objects is quite simple, but rendering a raster image into a view such that the key objects have this perspective probably isn't possible. You would need to vectorize the image in a general way. I don't know the state of the art in that field, but it sure seems hard.
He has written a program:
https://github.com/brunopostle/piranesi
The problem is that it is a method for projecting a rectangle, not a full 3D scene. I can imagine though that it could be extended to a full projection if you specify a central axis along which the perspective trick happens.
It confused me too, and maybe I am wrong, but I took it to mean, "can't render an existing (i.e. non-Piranesi) view into Piranesi perspective." Meaning, if you're an artist starting from scratch, you could do it (using the math given)--and some of those examples seem like aspects of one drawing employ Piranesi perspective while others don't.
So maybe the author was just saying if the work was drawn with "true" perspective throughout, there isn't a programmatic way of converting the entire thing over to Piranesi. That's at least how I read it, I'm curious about it too!
Yes, perhaps the computer needs information on which pixels belong to which buildings in order to apply perspective-per-object, rather than perspective-to-the-entire-image?
Something is up with that green building on the right, too. It's wider in the "true perspective" views, wider even than the ortho view
Here is the Panini projection paper, it's a good read[0].
Unreal Engine has support for it as a post-processing filter[1], but I don't know of any games using it.
[0]: http://tksharpless.net/vedutismo/Pannini/panini.pdf [1]: https://dev.epicgames.com/documentation/en-us/unreal-engine/...
Piranesi's imaginary prisons are worth a viewing. Great gothic prisons from a fever dream rendered in a similar fashion to these engravings.
Here you go: https://en.wikipedia.org/wiki/Carceri_d%27invenzione
Came expecting commentary on the POV used in the (excellent) novel, learned great stuff about visual arts and incidentally more context about the book. Thanks for posting!
In the image with the caption:
"Normal homography perspective transformation produced in GIMP. Note how squashed the buildings at the right and left are when taken in isolation"
It would have been nice to show a few more easy-to-understand comparisons. The "street view" image was nice, but blurry. Ditto with the map. I think if the last image of the two buildings had been shown side-by-side with the "correct" perspective, that might have helped explain the article.
This was a really cool article and I hope others read it through, but yes, it took me way too far into the article to "get" what he was saying was wrong with the perspective.
I wonder how hard it is to change a game engine to render images like this, and if the effect would be preserved while panning.
I think the difficulty comes from it being context dependent, it's not a consistent distortion of the true image the way most projections are, it identifies synthetic structures in the foreground and warps everything else (including similar structures in the background) around them. It should be possible for an AI filter though.
Yeah, I thought better (cleaner?) examples would have helped.
> The building at the right is not squashed ? It is wider than in the Piranesi picture above.
The building on the right is squashed, in isolation. When you take the building by itself (in isolation), it is indeed wider than the picture above, but it is also the same height, i.e., squashed.
They mean distorted, not squished for both.
This reminds me of an issue in vintage computer graphics. Say you have a game with some polygons happening, and they're nicely rendered in 3D perspective. You'd like to add some snazzy textures to them.
Here's a problem. The textures have to be put through a perspective projection. As in every pixel.
It's possible to cheat. You can simply use a bicubic stretch or even linear. It really shows up when the polygons are large and they rotate to create deep perspective. You see an artifact whereby the center of the texture does not stay centered on the polygon as it rotates.
Playstation 1 didn't do perspective correct texture mapping. If you scroll way down this WebGL tutorial page a few examples are shown:
https://webglfundamentals.org/webgl/lessons/webgl-3d-perspec...
If liked this, you might also like:
https://aaronhertzmann.com/2024/06/10/perspective-distortion...
https://aaronhertzmann.com/2024/09/09/dvc-multiperspective.h...
This is really interesting, I'd love to see this perspective incorporated into mapping software like google maps/streetview.
That's a really cool article!
TIL.
It makes absolute sense, but I never even thought about doing it that way. I was trained as an artist, and I always did perspective the "classic" way. It's entirely possible that this might not work on some subject matter, but it works great on buildings.
I half remember an articled or docu from a while ago where someone was analyzing the perspective in some studio Ghibli backgrounds, finding that many are artistically "distorted". When this was brought up to one of the artists, they responded along the lines of: "The western idea of 1, 2 and 3 point perspective is just one way of drawing perspective and not necessarily more 'correct'." (I guess that's true, even if you think of 1 and 2 point perspective as cropped versions of a 'true' perspective image, the lines wouldn't be completely straight in reality. It's all different kinds of artistic license).
A great example of something you can feel but I never had the words for.
> But here is the same elevation drawn using correct rectilinear perspective. I hope you will agree that the Piranesi version is much more legible, the furthest house above is easier to see and the nearest house isn’t horribly distorted as it is below.
The section with this bit has some pictures that really illustrate the effect.I wish there was an easy photoshop way to recreate this
Surely this introduces some curvature to the diagonals? I can't see how the perpendicular lines can be in correct perspective with the diagonals being parallel unless something is curving. I guess because it's preserving the perpendicular lines and the curvature is subtle, it's not very noticeable in typical architectural pictures.
Curvature maybe — "skew" seems more likely.
It's not a real projection as in a panosphere -> rectangle mapping but rather a local transformation of specific objects.
I think that this trick or something like it is used in ski mountain maps. For example: https://files.skimap.org/js03b74i9eokcg2y1iakwdtv2av6.pdf
I don't know how to confirm this; the distortion just feels similar to me.
I highly recommend to the people cross-interested in film theory, the Eisensteins book essay The philosophy of composition. At great length talking about Piranesi perspective.
Piranesi also made an amazing set of depictions of imaginary “dungeons”, sometimes using escher-like trick perspective.
Great article. And thanks for the correct OSM attribution in your map images. :)
Last Year at Marienbad (1961)
Lol, it's literally affine texture mapping.
Read the article and look at the examples - there still is perspective, just no perspective distortion (or the other way around, there is a perspective distortion to keep some lines parallel, where in normal view this wouldn't be the case).
I really hate it when a designer takes a perspective rendering with the camera really close, and then modifies the object so that it looks that way from a normal distance. Not sure if that's what happened here (can't read the article), but designers should not do that.
"So here is a general 2D remapping as a prototype replacement for the perspective tool in image editors (I have no ability to add this to GIMP, somebody else needs to step up)..."
Well given that this is HN, if there's any forum where somebody has experience contributing to GIMP, it should be here. Any takers?