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Imagine the fun of walking or flying through a faithfully reproduced Escher world.
I’ve always wanted to explore Escher’s worlds and walk through those impossible constructs in person. With today’s technology, we can do that by building virtual worlds whose physical laws allow such structures to
exist.
Today, many 3D game editors allow considerable freedom and tools to build entire buildings and levels. But so far, they've tried to simulate the real world and its physical laws. Some editors have bent rules such as gravitation, but none so far have sought to allow the creation of impossible, paradoxical structures that break the rules of 3D space.
Perhaps someone can write a program or game editor that allows this? It should also allow gravity to be manipulated locally, so that people can walk up, down or sideways along Escher’s floating stair-cases, for instance. And allow light to move in curves so that we can play tricks on the perspective.
A good program should allow us to do more than that. We should be able to construct virtual worlds in four or more dimensions. Although we can only view the construct from our limited 3-dimensional perspective, the underlying program can simulate what happens to our perspective when we move in a 4th-dimensional direction, and allow us to see different 3-dimensional slices in a 4-dimensional space.
Escher World
http://www.halfbake...idea/Escher_20World
[phoenix, Apr 11 2002]
"Ascending and Descending"
http://www.worldofe...ngDescendingLg.html
[waugsqueke, Apr 11 2002]
"Waterfall"
http://www.worldofe...ry/WaterfallLg.html
[waugsqueke, Apr 11 2002]
(?) Impossible triangle
http://www.sandlots...s/Triangle_plan.htm
Not the curvy one I was looking for... [st3f, Apr 11 2002, last modified Oct 21 2004]
(?) An embryonic whitepaper on an Escher shader for Maya
http://mfadt.parson...hilmc/Escherian.htm
Well, somebody was thinking along these lines but it looks like they threw in the towel. [bristolz, Apr 11 2002, last modified Oct 21 2004]
(?) Hyperbolic Manifolds
http://www.concentr...eph0/cs/hyperbolic/
"Standing in such a space, you would be able to see many copies of yourself off in the distance, each image corresponding to one way that a light ray can loop back to you by following the wraparound topology of the space." [prometheus, Apr 11 2002, last modified Oct 21 2004]
Cool Escher Link
http://escherdroste.math.leidenuniv.nl/
Mathematician who worked out the transformations in one Escher print. Be sure to watch the movie version! [krelnik, Oct 23 2002, last modified Oct 21 2004]
why we suck, supposedly
http://www.livejour...alewolf/103450.html
[egnor, Oct 04 2004, last modified Oct 21 2004]
Escher's "Reptiles" rendered
http://graphics.sta...n/cs348b-01/escher/
Not a particularly impossible image, though. [egnor, Oct 04 2004, last modified Oct 21 2004]
(?) simple example (ut2003)
http://www.ikkitous...files/utstuff/maps/
well you want "dm-escher.ut2", but you need to have reatil ut2003 to see it (and dont expect all that much :P) [Chester, Oct 04 2004, last modified Oct 21 2004]
[link]
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Computer programs are rule based. It's the fundamental principle of building any application. And yet you want one that builds a 3D world AND "break[s] the rules of 3D space". Escher only works because its 2D, you can't build an Escher model from one of his drawings. WIBNI/magic [marked-for-deletion]. |
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Right. Most of Escher's works are point-of-view illusions (eg. the neverending staircase, or the self-feeding waterfall) that vanish when the perspective is changed. |
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The effect would be similar to the experience of entering one of those specially constructed forced-perspective rooms where one person appears to be a giant, and the other tiny. The effect is lost when not at the proper POV. |
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While computer programs have to be rule-based, it doesn't have to be the rules of this world. It could be the rules of Escher's world, or some other set of rules that are *internally* consistent. |
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It's perfectly possible, for instance, to programme a virtual environment like a spiral staircase that loops back to itself, remniscent of the Escher classic stairs. |
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I don't agree that Escher only works in 2D. Although he draws in 2D we visualise it in 3D and it works because of unusual deviations from the way 3D space works in our universe. |
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In a computer-created virtual world, any set of rules is possible. When I say "breaks the rules" of 3D space, I don't mean computer-based rules but the physical characteristics of 3D space. |
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[waugsqueke]: It seems to me that Escher's absurdities and paradoxes work from different perspectives. Although his chosen perspective sometimes does enhance the absurdity, such absurdity is inherent in the shapes and structure of his constructs rather than the perspective. |
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For instance, the endless stairs is still endless whichever angle you look at it from, and the painting with the many stairs can be hung in any direction, and it is equally conceivable that there will be other such confusing stairs if you place your perspective elsewhere in the painting. |
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Counter-intuitively, I have to agree with [baboo]. A first-person perspective would be attainable (I believe) and fun. |
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// the endless stairs is still endless whichever angle you look at it from // |
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Look at the picture (linked). Trace the ledge that runs along the southeast wall, just below the stairs... up and around where it meets the northeast rampart. The bottom corner of the staircase cannot be both lower and higher than the top corner. That is an paradoxically impossible illusion that even falls apart from this angle if examined too closely. |
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"Waterfall" is even more clearly impossible. Several of the support structures have bases attached on one level while supporting sluices on another level and completely different physical location. This is an impossible construction... essentially a more complex version of the impossible triangle. |
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its not perspective, but the water canals and never-ending stairs are forming a moebius loop. likewise with the structure of the house of 3 dimensions.
I, particularly like the little lizards that come creeping to life out of the paper drawings. |
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True baboo, computational rules don't have to be those of the real world. They do however have to be internally consistant. Escher's drawings are not this, because they are 2D illusions - you *cannot* render a 3D environment where one object is infront of another object, and behind it at the same time. This would require some way of mapping a pixel/object to one x-y-z position, mapping it to another different x-y-z position, *and* make them exactly the same. |
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mcscotland: I agree with you for some of Escher's drawings. Others are internally consistent and could be rendered. |
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Even those those that fail in 3D could be possible described as 4 or 5 dimensional images which get rendered into 2D. |
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Even the impossible triangle has been constructed. (All the lines that look straight are made as curves so that it works). |
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Escher was an architect originally, wasn't he? I read that his fascination with illusionary geometric art was probably a disatisfaction with the limits forced on architecture by only having 3 dimensions, and that darn gravity thing. |
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Hmmm. Verrry interesting. [Waugs], while Escher's work is clearly viewpoint dependent, do you think that he could have created the "Waterfall" piece from several viewpoints? Sure, the exact illusion would change given the changing viewpoints and center-of-projection, but don't you think that each 2D projection (viewpoint) could be Escher-esque and entertaining?
[mcscotland] Maybe the 3D model requires internal consistency but I don't think the rendered 2D projection requires consistency at all. It can be non-photo realistic. After-all, isn't the 2D projection the same space that Escher worked his magic in? Suppose some clever person wrote a (render) shader that applied "Escher Sensibility Rules" regardless of the camera viewpoint (perhaps with camera-path constraints that provide the optimum illusion from any point along the path). Sure, the illusion might be profoundly different from different centers-of-projection, but don't you think that the resulting imagery could be fun to look at?
If the modeler was also optimized to understand the shader rules, perhaps the various models in a given environment could be imbued with user-definable behaviors that cause them to be rendered in Escher-like ways. As environments were being constructed the modeler could provide hinting to the user as to the Escher-ness of the results. Such a modeling environment would probably require a new vocabulary to describe the various unorthodox parameters a user would have to work with.
One thing that I think might not ever be gotten away from, though, is that the illusion would likely "pop" from one paradox to the next. This would mean that smooth, sustained Escherness, with the camera in motion, probably wouldn't be possible. The best that could be done might be Myst-like nodal navigation, with each node optimized (albeit by the shader) for Escherness.
Of course, maybe I am mis-thinking all of this and need to have some more coffee and ponder. |
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"Escherness"... terrific. |
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Thinking about "Waterfall" from various POVs, it seems that the effect could probably be taken the same from any surrounding point provided the vertical angle of view was the same. One could imagine a 360° line at any point along which the illusion would hold up, but above or below this line, the illusion falls apart. Is this what you were getting at with the reference to constrained camera-paths? |
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Yes. (be glad I didn't opt for "Escherality.") |
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I have to vote for this idea, even if it isn't feasible. I mean seriously how cool would it actually be to wander around one of Eschers landscapes? |
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Anyone played myst? (evil, evil, game) You could use that kind of (anoying because it limits freedom of movement) movement system where there are only a certain number of places you can go... |
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You would not be able to interact directly with the imposible geometry but it would still be there... |
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You mean "Myst-like nodal navigation?" Someone mentioned that a few annos back . . . |
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I think Myst is charming, rather than evil. |
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Myst (and Riven) look incredible, but I have no patience for games like that. The kids love 'em though. |
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Just designing a game with an escher feel would be good; whole corridors decorated on every surface with birds tesselating into fish, A giant stature of a hand drawing its elf, A FPS weapon that is a reflective sphere that you hold in your hand. |
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On the topic of games that do 'Escherness' a little already;
Douglas Adams' 'Starship Titanic', has a weird upside-down room in it that you get to by walking up a staricase that gets increasingly steep.
'Thief: the dark project' has a level which, though using normal rules of physics, you are moving around a house designed by a crazy person, where the corridors twist and at times it seems like you are standing on the ceiling/walls. |
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Lots of games have already done something similar to what baboo is proposing (albeit in a much more simplistic way). |
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"Adventure" for the Atari 2600 had a world consisting of only a few 2D rooms. If you mapped out where each room's doors led, you'd quickly find they did not follow paths typical to a 2D world. Going north AND south from one room might lead you to the same second room. |
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In more modern gaming times, I recall playing a custom level in Lucasarts' "Dark Forces" that contained impossible rooms. The level included impossibilities like walking down a corridor with only two or three 90 degree left turns in it that still somehow ended up where it began. My favorite was a room with only a thin wall standing freely in the middle of it. A door in the wall allowed you to pass into an huge room that surely didn't exist in the oiginal nearly empty room. |
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Anyhow, I think this is a great idea. Although I don't know who is going to invest the time in creating it ... and for what purpose other than eye-candy. |
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Some of Escher's pieces, like Relativity, do not depend upon tricks of perspective and could easily be worked into a first-person shooter. Indeed, anyone who's played Q*Bert probably remembers something very similar. |
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Other pieces would be much trickier. Something like the never-ending staircase can be done if the player is restricted from looking 'across' it (whether because of a wall, or fog, or whatever). The trick there would be to have everything the player can see move as a unit, and have things the player can't see move--though not as a unit--so as to maintain proper consistency. |
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For example, one could have an endless "spiral" staircase which looped back on itself. One would always see steps going up in one direction, and down in the other. There would be a 'seam' on the staircase 180 degrees from the player's current position, but since that spot would not be visible it wouldn't affect the consistency of the player's world view. |
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The "relativity" is probably the coolest concept, though, especially if there were player controls that could rotate the player's apparent gravity to any axis. |
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I think it would have the sort of appeal that those old text-based adventure games (like Zork) had. You would explore a completely unknown world, and you had to piece it together, slowly--sort of like learning about the world as a kid. A wonderful experience. |
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OK who's been playing Puzzle Donkey then????!!
ps stuck on 2.2...any help appreciated. |
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Baked using a portal-rendering engine. |
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I've seen people create 4-d worlds for the game of Descent, where rooms overlapped in mapspace but didn't at all in flight. |
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Once you leave the 3-D rendering space behind, I see no reason why a computer which knows nothing of dimensions would be restricted to a Euclidean 3-d environment. Use a fluid 1'st person perspective for the display and the view wouldn't necessarily have to 'trip' over the impossibilities. |
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most of the pics would defenitly be impossable, especaily the intresting ones
but some stuff could be done a bit better than some of you expect! (i have you point you to TerranFury im just repeating him with more detail, i think) |
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Check out the "warpzones" in ut2003, they effectivly create a sheet, which links to another sheet (like a wormhole?) |
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infiinate spiral steps are defeitay possable, but not from a birds eye view, like then orignal pic |
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well ive made a map which though very simple (and not al that echer like) does demonstrate a good deal of the uses ofn warpzones (more stuff can be done, but it would talke more than the minimal effort provided by me, like a window in the middle of the air should be possable (similer to those in "his dark materials" i suppose(should i go this deep in brackets?))) |
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anyways check the link (simple example (ut2003)) to see the map, i made it quite a while ago, and i know its are simple and has probs, but worth a look.
you need a retail copy of ut2003 to play/see |
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I can almost visualize what you are talking about. I think many of the naysayer arguments here are falling into the trap of thinking in 3D. |
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If we are restricted to 3 dimensions, then yes many of those drawings could only exist from one perspective, but if we work with more than three dimensions you could end up with a situation where two points are diverging from a 3D point of view, but converging in other dimensions. |
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Space would end up being contorted in some very strange ways that I don't even want to imagine this late at night, but I think it sounds very plausible. |
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[admin: I, too, disagree with the MFD - and while I may yet be wrong, I think it's at least worth leaving up!] |
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I just look really really closely at my eyeball for my V.E.E. |
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The skull is just _there_. |
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I think the recently released "portal" is doing this kind of thing with great flair. |
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It's a puzzle game set in a regular 3D world, but you can make a kind of worm hole between two surfaces that instantaneously transports objects from one end to the other, rotating their momentum as necessary. |
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But, even in the portal game, bless it's heart, you can change neither the speed of light nor the mass of the strange quark. [+] (Though the present idea lacks a description of malleable laws, besides gravity) |
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And remember, shine a photon through two slits and it will split (as long as you're not looking). <--condensed quantum mechanics |
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