How would one go about programming graphics in a non-euclidean space? For example:
- An area that looks like a plane.
- If you walk in a straight line you will end up where you started.
- There would be no portals/teleports.
- The area would look flat.
Or maybe if I wanted to have a room connected to another room with two parallel hallways so that one would be much longer than could fit there if you judged by the second one as if it were an euclidean space.
Do any graphics packages like OpenGL or DirectX support anything similar to what I described? Or do I have to manually calculate 3-dimensional projection for whatever space I mean by non-euclidean?
This guy, Alexander Bruce, did it with his Hazard: The Journey of Life. Not sure how, could just be portal/teleport stuff.
It sounds very interesting though, but I'm not sure how you'd go about doing it.
Maybe you could ask him about it?
There is no support for this kind of thing.
The only way it is physically possible is by portals, so I don't see why you even need to ask.
I mean how would you even work with non-euclidean geometry?
It might be possible if you map the plane to the surface of a 4 dimensional sphere or something. But this is way beyond my level of understanding.
You can't do it without the smoke and mirrors of 3D graphics; in this case, you want to use some [i]very[/i] seamless portals.
Spore did it... I think he means like wandering round a planet...
Well, with a big enough sphere, you could make it look like a seamless flat land, just like Earth.
Why not use portals?
Technically, it might be a portal/teleport, but just have a plane. When you reach the border render what would be on the other side.
[media]http://www.youtube.com/watch?v=4TIXt4Kb3PQ[/media]
Looks pretty good using portals.
Well, in this case you could just make the models far behind the "player" disappear, only to reappear again later, in front of him.
but... why? What are you planning to make?
Yeah, context would really help here.
[QUOTE=Nikita;23310539]How would one go about programming graphics in a non-euclidean space? For example:
- An area that looks like a plane.
- If you walk in a straight line you will end up where you started.
- There would be no portals/teleports.
- [b]The area would look flat.[/b]
Or maybe if I wanted to have a room connected to another room with two parallel hallways so that one would be much longer than could fit there if you judged by the second one as if it were an euclidean space.
Do any graphics packages like OpenGL or DirectX support anything similar to what I described? Or do I have to manually calculate 3-dimensional projection for whatever space I mean by non-euclidean?[/QUOTE]
No graphics package that I know of supports non-Euclidean geometry directly. As everyone is saying, you would have to use a bunch of tricks to give the illusion of non-Euclidean space using DirectX or openGL.
However non-Euclidean systems such as spherical and hyperbolic geometry are mathematically consistent, so there's no reason why you couldn't code a spherical geometry rendering engine. The only problem might be your last bullet point, since in non-Euclidean space the notion of "flat" often doesn't exist. It would be challenging, but extremely cool if someone were to develop a true non-Euclidean rendering engine that doesn't rely on Euclidean projections. It wouldn't be too hard in 2D (I think) but 3D could get a little bit mind-bending.
[QUOTE=Jallen;23311087]There is no support for this kind of thing.
The only way it is physically possible is by portals, so I don't see why you even need to ask.
I mean how would you even work with non-euclidean geometry?[/QUOTE]
I think you're being a little close-minded. Non-Euclidean geometry is just as valid as Euclidean - only less intuitive.
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