Join 3,558 readers in helping fund MetaFilter (Hide)


The nightmare corpse-city of R'lyeh was built in measureless eons behind history by the vast, loathsome shapes that seeped down from the dark stars.
April 25, 2012 10:56 AM   Subscribe

Have you ever wondered what non-euclidean geometry actually looks like? This video uses a custom ray tracer for the Minecraft engine to give some examples.
posted by codacorolla (33 comments total) 17 users marked this as a favorite

 
Apparently I've spent many long hours staring at the ceiling in a non-euclidean world, waiting to return to my world so that I might finally sleep.
posted by neuromodulator at 11:02 AM on April 25, 2012 [1 favorite]


1:41: Longer than you think, Dad! It's longer than you think!
posted by Faint of Butt at 11:02 AM on April 25, 2012 [7 favorites]


Disappointingly, neither eldritch nor particularly cyclopean.
posted by Sing Or Swim at 11:04 AM on April 25, 2012 [8 favorites]


Needs more thin monotonous whine of accursed flutes.
posted by KokuRyu at 11:07 AM on April 25, 2012 [8 favorites]


LSD does this without all the coding.
posted by jnnla at 11:09 AM on April 25, 2012 [5 favorites]


I have some code that does ray tracing around spinning black holes. I really want to merge that in to this.
posted by kiltedtaco at 11:09 AM on April 25, 2012 [1 favorite]


Oh, sure, it starts like that, then you're hitting the hard stuff and waking ancient evils from the nether end of time, signing the book of Azathoth or a rat claws it's way out of your heart.
posted by Artw at 11:10 AM on April 25, 2012 [1 favorite]


Needs more thin monotonous whine of accursed flutes.

Didn't.. didn't you hear them?
posted by curious nu at 11:10 AM on April 25, 2012 [11 favorites]


A more subtle version of this sort of technology could be quite useful. Within games, building exteriors that look correctly sized result in interiors that feel too small. Traditionally this gets dealt with by putting loading screens between the exterior and interior of significant spaces (Skyrim, for example). Rockstar's open world games are notable for often allowing seamless exterior-to-interior transitions, but even then their interiors feel weirdly cavernous, their doors oddly cyclopean.
posted by GameDesignerBen at 11:15 AM on April 25, 2012 [3 favorites]


By necessity this is a little how sectors worked in the Build engine (a commenter at the FPP link mentions this, and is shot down by the uploader - but I think he's essentially right). Since it's not a true 3D engine you can't have rooms over rooms. To get around this the engine has a system called 'sectors' which are really just warps to different points. So you would go up a staircase and seamlessly warp to the room one floor over where you were. I don't think it was used often in the games that came out for the engine (probably because they wanted things to be realistic) but it would allow you to make rooms which were longer than they were supposed to be, or at least give that illusion. This custom map plays with sectors to achieve some cool effects, and there's actually a secret level in Duke3D which uses weird sector warping to disorient the player, but I can't remember which one off the top of my head.
posted by codacorolla at 11:23 AM on April 25, 2012 [1 favorite]


What exactly does this guy mean when he says "non-euclidian"? Minecraft worlds are set in euclidean geometry, so what does it mean to say that he's "ray-tracing in non-euclidian geometry" It makes no sense at all.

I think what he means is that the rays of light go in curves rather then straight lines. But it still doesn't make all that much sense.

Anyway, there are some better examples of trippy stuff being done using geometry shaders and Minecraft.

Anyway, true non-euclidean geometry wouldn't have these weird warping effects. the universe itself is non-euclidean (or believed to be), but at a very great scale, as well as being warped by relativity around planets. You do have gravitational lensing but nothing super-trippy like in the video.
posted by delmoi at 11:29 AM on April 25, 2012 [4 favorites]


Oh man, here's a crosseyed 3D video of that acid shader, if you really want to make yourself throw up.
posted by delmoi at 11:34 AM on April 25, 2012


codacorolla: " This custom map plays with sectors to achieve some cool effects."

Dang that's pretty dang dope! I would play that game.
posted by rebent at 11:35 AM on April 25, 2012


I don't know anything about this, but I hope someone builds a TARDIS.
posted by ADent at 11:38 AM on April 25, 2012 [3 favorites]


codacorolla: " This custom map plays with sectors to achieve some cool effects"

Oh, man... I so want to make a L4D2 or TF2 map like this now. O_O
Ellis: Safe house ahea---oh, crap.
posted by xedrik at 11:48 AM on April 25, 2012


I don't know anything about this, but I hope someone builds a TARDIS.

Then build R'lyeh. Then put R'lyeh inside the TARDIS!

Ahahahahaha! All it's insides would be outside!
posted by GenjiandProust at 11:49 AM on April 25, 2012 [3 favorites]


Good, so now you Aporkalypse Ankh-Morpork people can get to work on L-Space!
posted by robocop is bleeding at 11:50 AM on April 25, 2012 [1 favorite]


be right back, need to go write up a Kickstarter for a House of Leaves RPG
posted by The demon that lives in the air at 12:02 PM on April 25, 2012 [7 favorites]


1:41: Longer than you think, Dad! It's longer than you think!

Oh thanks. I totally needed that story brought back to mind after last night's King thread already me thinking about. Of all the stories in the world, this is the one I wish I could unread.
posted by DU at 12:03 PM on April 25, 2012


Anyway, true non-euclidean geometry wouldn't have these weird warping effects.

What does this statement mean? I don't know how you can rule out a particular non-Euclidian geometry (which this clearly is) as being not a "true" non-Euclidian geometry. It's not one that we would expect to exist physically, but there's nothing wrong with it. I actually think it's a great way to show what a non-trivial curvature would "feel" like; much better than resorting to the same analogies of "imagine an ant on a balloon".

I think what he means is that the rays of light go in curves rather then straight lines.

Light travels along geodesics. They only appear "curved" if you imagine that they're travelling in a Euclidian 3-space, which they're not, but we're pretty used to imagining that that they are. So really I think it's more accurate to say that the rays of light are traveling along straight lines, but the notion of straight in this geometry is completely foreign to us, so they appear curved to our brain.
posted by kiltedtaco at 12:26 PM on April 25, 2012 [3 favorites]


I wanted to see a guy fall into a convex corner.
posted by Mister Moofoo at 12:41 PM on April 25, 2012 [1 favorite]


I'm fairly certain the Morgan Av. MTA platform employs some sort of abominable non-Euclidean space in its construction. That station is build like a Mystery Spot.
posted by modernserf at 1:09 PM on April 25, 2012


What does this statement mean? I don't know how you can rule out a particular non-Euclidian geometry (which this clearly is) as being not a "true" non-Euclidian geometry. It's not one that we would expect to exist physically, but there's nothing wrong with it.
A non-euclidian geometry is one in which all the axioms of regular geometry are true, except for the one about parallel lines. As far as I know, the eliptic/hyperbolic ones are the only ones that exist.

How can you render euclidian space in a non-euclidian way? It makes no sense.
Light travels along geodesics. They only appear "curved" if you imagine that they're travelling in a Euclidian 3-space
Light travels in straight lines in euclidean geometry. Non-euclidean geometry would mean... something else.

But the problem is that the world of minecraft is based on euclidean world broken up into voxels along parallel planes along 3 axises.

So, if the world is made up of parallel planes, is he transforming it into non-euclidean terms by converting planes that don't touch into curves that don't touch? I doubt it.

Anyway, you also have the word "imagine" in there - you can create an isomorphism between euclidean and non-euclidean geometry if you want, and what's a line/plane in one can be considered a curve in the other. But since this was on a computer, I'm guessing he was actually using euclidean geometry - and simply having his light rays travel around in curves.
posted by delmoi at 1:25 PM on April 25, 2012


be right back, need to go write up a Kickstarter for a House of Leaves RPG

War of the Shadow of the God of the Five & 1/2 Minute Hallway of Blood
posted by byanyothername at 3:34 PM on April 25, 2012


Oh a more concise way of illustrating why this isn't non-euclidean geometry the parallel lines axiom is not just undefined, but considered false.

So in other words, if you have a line, and a point not on that line - in euclidean geometry there is exactly one line in the same plane that will never intersect it.

In non-euclidean geometry the line will intersect it. Clearly, you can see where you can have two lines (in the same plane) that would not intersect in this world, thus it's not really non-euclidean.
Ahhh, he wasn't able to show mind-bending impossible geometry on a reality-based computer, but rather an approximation of it. Wow, this guy must be reading this thread literally sobbing saying "jesus... jesus delmoi, you've destroyed me." I can't even say how thankful I am that you were here to post literal paragraphs about how wrong this guy was...
1) We live in non-euclidean geometry, so any reality based computer is also already non-euclidean. It's just not noticeable at human scales.

2) it's entirely possible to simulate true non-euclidean geometry on a computer, without approximating anything.

3) What are you talking about?
posted by delmoi at 3:54 PM on April 25, 2012


The most merciful thing in the world, I think, is the inability of the human mind to correlate all its contents. We live on a placid island of ignorance in the midst of black seas of infinity, and it was not meant that we should voyage far. The sciences, each straining in its own direction, have hitherto harmed us little; but some day the piecing together of dissociated knowledge will open up such terrifying vistas of reality, and of our frightful position therein, that we shall either go mad from the revelation or flee from the light into the peace and safety of a new dark age.
posted by Scoo at 4:50 PM on April 25, 2012 [2 favorites]


[Few comments removed. MetaTalk is an option for people who can't interact civilly with people on MeFi but otherwise remember what it says beneath the box and be cool. Thanks.]
posted by jessamyn at 5:07 PM on April 25, 2012


Let me summarize: thanks for ruining another thread by being a tedious know-it-all!

Pff...and here I was just about to agree with delmoi. This point he made is actually a really good one:

1) We live in non-euclidean geometry, so any reality based computer is also already non-euclidean. It's just not noticeable at human scales.

There is a trivially simple answer to the question, "What would a non-Euclidean geometry even look like?" The answer is: exactly like the actual world. (In fact, a couple centuries before Einstein, Thomas Reid argued that the world as we see it would be non-Euclidean because of the curvature of the eye and its parts. Even setting aside the fact that the space itself is non-Euclidean, we would still perceive it as such!) So what are people really looking for when they do stuff like this?
posted by voltairemodern at 5:10 PM on April 25, 2012


So in other words, if you have a line, and a point not on that line - in euclidean geometry there is exactly one line in the same plane that will never intersect it. In non-euclidean geometry the line will intersect it.

Not in the case of negative curvature.

Anyways, if the point of all this is just to point out that the term "non-Euclidian" in math specifically means spaces with either hyperbolic or elliptical curvature uniformly everywhere, then I think that point could have been made much more easily by just acknowledging that this is a terminology thing rather than calling the whole exercise into question. I don't think it was that hard to understand that the author meant "non-Cartesian 3-space" (or whatever you want to call it) when they called it non-Euclidian.


We live in non-euclidean geometry

If you want to stick with the math definition, no we don't, we live in a universe that has a complex curvature shaped by the matter in it. And, on the flip side, on the gigaparsec scale we have no evidence that the universe as a whole is anything other than flat. But those are pedantic points that I wouldn't bring up normally. I still like this video because it gives you a sense of what interacting with complex, non-uniform curvature and distortion would be like. I honestly can't see any problems with it beyond semantics.
posted by kiltedtaco at 5:52 PM on April 25, 2012 [3 favorites]


Bernhard Riemann was a pimp.
posted by bardic at 11:34 PM on April 25, 2012


If you want to stick with the math definition, no we don't, we live in a universe that has a complex curvature shaped by the matter in it. And, on the flip side, on the gigaparsec scale we have no evidence that the universe as a whole is anything other than flat.
Yeah, that's right. On small scales physicists use a metric space, which is neither a euclidean geometry or a non-euclidean geometry, since the axioms that change are not the parallel line one.

I saw this great video a while back about the history of cosmology. It used to be thought that an expanding universe meant a hyperbolic geometry, And now we know it is expanding, but it turns out to have a flat geometry anyway (at least that's my impression of where things stand, I'm hardly an expert)

Anyway, obviously the geometry that a computer sits in isn't really relevant to the kinds of things that it computes, I just thought it was an interesting point.

If you want an example of what a 'normal' hyperbolic geometry looks like MC Escher did a bunch of tilings in hyperbolic geometry using a projection into euclidean 2-space. You can have weird things like squares where five meet up at a corner, rather then 4. It's pretty interesting.
posted by delmoi at 2:08 AM on April 26, 2012


Somebody could make a video game using technology like this.

Te presento a mi amigo Antichamber.
posted by Peevish at 5:07 AM on April 26, 2012


So, when is this guy getting shuffled off to The Laundry?
posted by Orb2069 at 4:10 AM on April 27, 2012


« Older Leverage the power of CLOUD COMPUTING using standa...  |  All The Wild Horses is a portr... Newer »


This thread has been archived and is closed to new comments