I'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.

> 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.

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

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

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.

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"

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.

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.

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)

https://en.m.wikipedia.org/wiki/Last_Year_at_Marienbad

Lol, it's literally affine texture mapping.

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?