Non-euclidean geometry in 3D games

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Adamo
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Non-euclidean geometry in 3D games

Post by Adamo »

like on this example:
http://www.youtube.com/watch?feature=iv ... ion_143076
A non-euclidean geometry is something that I always liked to see in DM style games without using ordinary teleporters - it would confuse player the most.
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Re: Non-euclidean geometry in 3D games

Post by Joramun »

Well, in DM teleporters would be the easiest way to do that !
Actually, I was planning on doing a non-euclidian dungeon.
It ended up being a very small puzzle dungeon, that I will release as a curiosity for DSB.
Check it !

Also: Did you ever play "Portal" from Half-Life 2 ? It's a great game, with a lot of non-euclidian thinking required to solve puzzle. Too bad it's only used as platform gymnastics.
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Re: Non-euclidean geometry in 3D games

Post by Jan »

This youtube video looks more like the Clockwise-Anticlockwise puzzle. :)
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Re: Non-euclidean geometry in 3D games

Post by Gambit37 »

Nice use of portals. Quite messes with your head, doesn't it :-) A shame about the flicker when he crosses the sector line though, you'd need to get rid of that to make it really effective.
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Re: Non-euclidean geometry in 3D games

Post by zoom »

Personally I would only use that in some kind of wizard´s castle with abundant magic or maybe an enchanted forest.
For a Labyrinth something like that would probably be too harsh and drive bonkers..

I would not use these weird shortcuts and shiftings throughout a complete game.(that is: simply not everywhere)

For Multiplayer maps it could be a fresh addition.
Nice.
Thanks for posting Adamo, have not seen anything like it before :)
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Re: Non-euclidean geometry in 3D games

Post by Trantor »

I'm not sure if "non-Euclidian" is a term I would use for this (stupid mathematicians, I know)...

Anyway, I can only support zoom: Don't do this everywhere in a whole dungeon. It could quickly become annoying and brain-hurting.

And Portal (which is a truly marvelous game) is quite different. It uses perfectly normal Euclidian geometry, only with two connected teleporters which you can set up (almost) anywhere you want. But the architecture itself is perfectly possible.
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Re: Non-euclidean geometry in 3D games

Post by Sophia »

I agree with the prevailing sentiment. A setup like this would make a good puzzle (like the "Clockwise" room) but would quickly get confusing, tiring, and frustrating if it existed in the whole dungeon. :)
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Re: Non-euclidean geometry in 3D games

Post by Paul Stevens »

It seems perfectly Euclidian. Just as Pits and stairs
add a 3rd dimension these 'portals' add
a dimension. And, just as pits are
one-way portals into the 3rd dimension, the
portals can be one-way.

I think the clockwise puzzle can be thought of
as a three-dimensional puzzle on a torus.
I forget exactly....might be a pretzel.
Nothing non-Euclidian about that.

But then, it is now believed that our entire
universe is a two-dimensional hologram on the
surface of a sphere. A holographic dungeon.
That should attract interest.
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Re: Non-euclidean geometry in 3D games

Post by Zyx »

Since the torus has a curvature, is it still an euclidian world?
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Re: Non-euclidean geometry in 3D games

Post by Paul Stevens »

I think 'Euclidian' is the wrong word in
a technical sense.

We live in a Euclidian 3-D world (at least
pretty close). I meant that I can draw the
topology of these dungeons in that world.
They don't necessarily require a Klein bottle
or two infinite, non-intersecting 3-D spaces
or something that is impossible to construct
in our world.
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Re: Non-euclidean geometry in 3D games

Post by Zyx »

With the technique seen in the video, can't you build a Klein bottle? Imagine a 3x3 room with a door in a central pilar leading to the 3x3 room from outside.
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Re: Non-euclidean geometry in 3D games

Post by Joramun »

Well the examples above are locally euclidian but with a sudden scratch in their space time.
If you try to transform them into a flat space without breaking or tearing them, you'll see that you can't.
So they're not really euclidian, if by that you mean flat (they're flat except at the transition surface)
and simply connex (=there is no loop that can't be reduced to a point by a continuous transformation, and a loop going through the portal is not reducible except by tearing the space apart...).
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Re: Non-euclidean geometry in 3D games

Post by Bit »

In 'The wheel of time' was a mirror (flat as always, and you could walk around), and inside the mirror you could see the next level. A nice effect.

I always thought about a computer game with uncommon physics! But - it isn't easy to generate such one (or even imagine it!).
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Re: Non-euclidean geometry in 3D games

Post by Zyx »

Yes, I meant flat markovian space. Why isn't it easy? Isn't simulating anything non-linear already non-classic physic? Aren't teleporters and windows enough to connect unconnected spaces? Can't you entangle arbitrarily distant spaces? Can't you memorize machine-states or predict machine states and jump to them, fiddling with the flow of time? Can't you design an engine with only reversible algorithms? With imaginary roots? With imaginary consequences?
With DSAs in CSBwin you can make themselves aware of their own state and parameters and of other DSAs. A virtual computing machine. DSA can communicate with messages with up to 100 parameters, so you can create some agent engines and neuronal nets with creativity, achieving very singular states, almost conscious, with some sort of metadimension affecting the data and behaviour of the whole dungeon through those omnipotent, omniscient DSAs.
In the latest conflux beta they form a neural net for simulating fluid mechanics, on a very primitive algorithm, but it's just the proof of concept that anything can be constructed, even some heuristic search for a meta-meaning.
There is also a helm delivering some random text. A DSA could even compose des cadavres exquis. So it could contain some random meaning to the player, thus influenciating him. A special statistical DSA could note when the player stop damaging a monster or going deeper, which could be a criterion for "losing the game" from the dungeon's point of view. After hundreds of thousands of uttered words in different context, some statistical correlations would appear. Like "wait" or "secret here" would incite the player to stop what he was doing against the dungeon. Refining the context associated with this interesting attitude, the DSA could end up realizing that putting some fake wall or unlocking mechanism most of the time will incite the player to search for the prophetized "secret", thus linking a positive word with concrete contexts that the DSA would then proceed to feed to the player, just to bribe him. But then the player would get smarter or greedy and would be wanting more and the AI would still have to find new strategies for this new context which would be an adaptive response to its adaptive response to the player, thus adding an incredible layer of complexity.
Allowing superposition or not like for elementary particules in quantics would be doable too.
I'm not sure the DM engine is the best platform to design such a world though, but it could prove that it's not so complicated, though awfully slow.

EDIT: spelling
Last edited by Zyx on Fri Dec 10, 2010 6:50 pm, edited 2 times in total.
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Re: Non-euclidean geometry in 3D games

Post by Gambit37 »

My brain hurts.
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Re: Non-euclidean geometry in 3D games

Post by ChristopheF »

Gumbyt37 ?
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Re: Non-euclidean geometry in 3D games

Post by Gambit37 »

I was aiming for an entry in Forum Quote of the Week. I thought a 3 word response to Zyx's unfathomable* science was rather amusing ;-)

*unfathomable to me at any rate.
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Re: Non-euclidean geometry in 3D games

Post by beowuuf »

Sorry, I think zyx would win it. After the brain hurting ideas, the phrase 'edit: spelling' is very amusing.

At some point when my brain is back to working again, I might try and follow the actual post.
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Re: Non-euclidean geometry in 3D games

Post by Gambit37 »

Yeah, but he edited it 6 hours after I replied ;) *First!* *runs*
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Re: Non-euclidean geometry in 3D games

Post by Paul Stevens »

Yes, I meant flat markovian space.
I think we are in agreement.
My first post was really not at all what
I wanted to say. I was responding to
It could quickly become annoying and brain-hurting
and I wanted to say that what I saw in the video was
nothing I couldn't get my mind around in the context
of our usual 3D space. All of us do it all the time when
we encounter a teleporter. The video made it perhaps easier
by showing you where the teleporter exited and, it appeared,
that most teleporters were 2-way.
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Re: Non-euclidean geometry in 3D games

Post by Sphenx »

I fear that Zyx is growing the idea of building a DSA monster over the original engine to build its markovian-klein space to stuck the player within, along the idea of that the dungeon is alive (Dungeon Keeper symptom), I would call the resulting environment "the Matrix". Maybe one with a brownian motion may escape this terrible space - or ... just remember this : the cake is a lie.
I think the distorsion is to build the 'dungeon' in a specific space then display it in another (standard 3D euclidean space).
By the way, the display in original DM is not even euclidean with its special perspective and 'wall changes' when turning.
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Re: Non-euclidean geometry in 3D games

Post by Zyx »

Well, if I had time, my next dungeon would be much more abstract in its behavior. It would adapt to the player with a certain personality. The game would be as much to survive as to understand the mind of the dungeon, and manage to dialog and "tame" it.
I mean that the dungeon would react with discomfort, fear, degenerescence, anger or cowardice under certain conditions structured by a hidden logic with progressive, hierarchical steps with a few "AND/OR" twists.
Symmetrically it would be at ease and pleased, even "smiling" or pleasing under other circumstances also secretly structured, according to rules similar to those of a human mood.
By learning what it likes and dislikes, and what it wants from you, you would be able to negotiate, ie, obtain some things slightly desagreable for it to yield in exchange of greater benefit. The better the object targetted (ie, powerful weapon), the more negative for it to give access, the more you have to treat it kindly and offer great relieve. Or you could use threats and bad treatment to subjugate the dungeon...
The levels would have an organic design and with areas, wall items and floor items functionally linked between them and with some inner values (pleasure/pain) associated with some of their states or modes. Thus, the whole dungeon would be a closed ecosystem and a body. The generation of monsters, food, items, etc. would be a by-product of its existence. The walls wouldn't be static and the big hollow dungeon-entity would move through stone, altering its shape.

The basic, corporeal missions for the player would thus to treat diseases, prurit, hunger, etc., of the dungeon.
But I would try to set a few rules for achieving some more spiritual meta-missions too.

Something that I think would be interesting would be to put this "body" in a spatial context. (like, you finally discover that the everchanging dungeon has struck a vein of magma and is now too hot and uncomfortable, so you must teach it to avoid it and stop the flooding. Or similar scenario but this time the dungeon, once a happy surface dweller, dug into the ocean which started pouring into it, making it heavier and slower, and it is sinking into the ocean. So you must empty it by several means (evaporate, fill the breaches, sever flooded section, close important doors, destroy water elementals, pump water out, augment the dungeon volume, create a balloon room at the top, etc.).

However those metamissions would need a more versatile interface, probably making the actions menu behaving as tree of choices. Everything seems doable by DSA but it would take a year or two to research everything, so if anyone is interested by the idea, don't wait for me.

Anyway, going back to the topic started by the non-euclidian link of Adamo. I've been wondering for a while now... why was this concept not new to me? And then I remembered it, it was an animation I was watching when I was around 3 years old (and now showing to my 5-months son :wink: ):
http://www.youtube.com/watch?v=v45qOGNsrbw
(at 0:37)

There was some non-euclidian geometry in the episodes: ubiquity, worm tunnels, inner space bigger than outer volume, discontinuity, etc.
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Re: Non-euclidean geometry in 3D games

Post by Adamo »

Zyx wrote:
Well, if I had time, my next dungeon would be much more abstract in its behavior. It would adapt to the player with a certain personality. The game would be as much to survive as to understand the mind of the dungeon, and manage to dialog and "tame" it.
I mean that the dungeon would react with discomfort, fear, degenerescence, anger or cowardice under certain conditions structured by a hidden logic with progressive, hierarchical steps with a few "AND/OR" twists.
Do you mean something like the "gods" in crawl?
http://r1gm.free.fr/Crawl/crawlSS_052_gods.txt
"gods" in DCSS actively reacts to player`s actions rewarding or punishing him for several activities (unless you`re not religios).

Anyway, in your game, for example, "a dungeon" might "punish" you like for killing too much screamers for food by generating spiders (something like that was in CSB I think).. But it wouldn`t be done using actuators that recognizes the screamer slices dropped on a floor (and generating spider), but using more complex DSA structures, right?

That way, exaples (what I can think of now) of "bad" indirect dungeon reactions would be (I`ll use DCSS gods examples):
- rotting some of your food (a player gets a message like "Elyvilon decided to take his tribute of food"),
- rusting some of your weapon,
- cursing some of your clothes,
- generating more monsters on level x... (a player gets a message like "Trog got furious at you"),
- halving some of your stats,
- causing diseases,
- teleporting some less important stuff (no keys nor other important items) from your backpack to different locations,
- "turning off" the light,
- resurrecting some of killed monsters (if only there are remainings on the floor left, like it`s in lates Conflux version),
- causing temporary invicibileness of some monsters (that`d be cruel!),
- adding 50% strenght to all monsters on level y...,
- etc.

"Good" dungeon reactions would be pretty much the same (but reversed), plus some like:
- giving regular or special (very rarely!) weapons, food, clothes etc.,
- curing diseases,
- adding some points to the stats,
- healing during the fight (in response of character being attacked by a monster; "Elyvilon decided to save you"),
- regenerating used (empty) staffes,
- resurrecting dead characters,
- adding experience levels ("Okawaru grants you a gift"),
- immediatelly killing monsters in front of you (a player gets a message like "Yredelemnul now decided to help you" etc),
- making all fake walls visible on this level (a player gets a message like "Okawaru decided to reveal his secrets to you"),
- etc., etc.

All the good or bad actions would have to be more or less random so the player never knows when it happens.. Even if you do something "bad" you could never be sure if you get a "punishement". Same for "good" actions. DCSS "good" gods/"good" actions might be replaced by Lord Order and "bad" gods/"bad" actions might be replaced by "Lord Chaos" messages for example. Or something like.
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Re: Non-euclidean geometry in 3D games

Post by Zyx »

Those are possible events, but the causes would not be from a moral perspective but rather from a functional point of view.
The dungeon would work as an organism. Each area and elements of the dungeon would participate to the whole. If something is missing or malfunctioning, then the dungeon is disturbed and starts reacting to correct its internal state.
The party would thus be like a virus.
But then, the dungeon would also be disturbed by other factors, so the player could help fixing.

The organic functions would be abstract and generic. The dungeon would procedurally determine what it needs to do applying the survival functions to its current state, a little like a chess program. There would be some random flavor so the personality of the dungeon would not be the same for each game.

An example:
the body of the dungeon could exist thank to digging monsters and filling monsters. Let's call them dwarves.
Those dwarves require food, water, and room to survive.
The food could be obtained through another race of hunters in exchange of the gems the dwarves find.
Those hunters would need specific grounds to find their preys and weapons.
The grounds would need to be watered and with flora to sustain animal life.
The water would come from subterranean rivers that can be diverted from their course through walls, pits and traps.
The flora would come from seeds and would automatically have life cycle when the conditions are met (watered floor).
The animal life would spontaneously appear, from little things to bigger, when the conditions are met.
The hunters would buy their weapons to merchants with coins.
They could obtain coins by selling the gems to jewelers.
The merchants would need room for the supply, which is what a digging dwarf can do, etc.
Etc.

This way, the whole design of the dungeon would be dynamically made by its hosts. If one of the components is blocked, the chain starts crumbling, the species become aggressive, they start abnormal or desperate actions to find what they need, etc.

The body of the dungeon would be an ecosystem.

As for the mind:
Let's list all the situations that could be relevant for the dungeon. Let's divide them between pleasure and pain: this would be the personality of the dungeon. What it wants and doesn't want. The game would be to understand what it wants and give it (maybe in exchange of a reward).
One possible scenario would be to have two separate dungeons in the same file. Both want to merge and grow. However, direct, unprepared contact would just cause disruption. So the player would have to teleport back and forth to understand what works and what doesn't and thus prepare the surface of contact. The player could explore tendrils which already made contact and try to understand what went wrong. An example: a tendril filled with lava is in contact with the watered part of the other dungeon: the water evaporates, destroying the base the whole watered ecosystem; the lava cools, destroying the lava-based ecosystem. The player would need to find where to direct the lava into the dungeon so that it finds a place where both the lava and the recipient experiment synergy or pleasure, thus allowing a new kind of ecosystem, a successful hybrid. Both dungeons would have different ecosystems.
Each tendril of each dungeon should be solved this way in order for both dungeons to be pleased.

It's not so complicated to design as it seems, in fact I think it's all doable with DSA:
Each tile could adopt a tileskin.
Skins (wall and floor) would have:
- a visual aspect
- exclusive conditions of birth: like threshold for a dry tile to become wet, or for a wet tile to become wet-lichened, etc.
- specific properties (humidity, heat) radiating to neighbors
- rules of yielding (items, monsters, events)

Some items like seeds would behave like those skins but would be transportable.

Anyway, I may be OT here.
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Re: Non-euclidean geometry in 3D games

Post by Sophia »

I don't know if it was intentional or not but you pretty much just described Dwarf Fortress. :P
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Re: Non-euclidean geometry in 3D games

Post by beowuuf »

I suspect nothing but deliberate intent from the creator of Conflux :)
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Re: Non-euclidean geometry in 3D games

Post by Zyx »

Yes, I took the dwarf example on purpose.
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Re: Non-euclidean geometry in 3D games

Post by Tom Hatfield »

Regarding the OP: there was a deathmatch level like this in Duke Nukem 3D called Lunatic Fringe. It was basically a double-layered outer ring with a hollow center section that led to different parts of the ring.
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