5 ms·

Yes! I was a bit disappointed when he explained it was just portals and a clever rendering hack rather than actually modeling non-Euclidean space natively, then

Yes! I was a bit disappointed when he explained it was just portals and a clever rendering hack rather than actually modeling non-Euclidean space natively, then I was delighted when he showed the room-scale VR example.

wcoenen 8y ago
> rather than actually modeling non-Euclidean space natively In mathematics such non-Euclidean spaces are called manifolds. A manifold is defined as a set of Euclidean-like regions that are connected by transition map functions. That formalism is basically the same thing as these portals. https://en.wikipedia.org/wiki/Manifold https://en.wikipedia.org/wiki/Manifold
- thfuran 8y ago
  Except that that method wouldn't let you have, for example, a hyperbolic plane that could be traversed without obstruction.
  - wcoenen 8y ago
    I think you could actually approximate an unobstructed hyperbolic plane to arbitrary precision with portals. In this game, the hyperbolic plane is represented as a tiling of hexagons and heptagons: https://www.youtube.com/watch?v=lX5eCfRSCKY&t=742s https://www.youtube.com/watch?v=lX5eCfRSCKY&t=742s If you take this model but upgrade each cell to a little 3D euclidean region, then you could completely surround it by portals that connect it to the neighbouring cells. The edges of the portals wouldn't be visible. The smaller the euclidean cells, the better the approximation to the hyperbolic plane.
    - zenorogue 8y ago
      For easy computations assume octagonal cells. Their vertices will have 135 degrees each. The edges of the portal will be visible because the left and right images do not match (since 3*135 ≠ 360). And a object (as long as it is modelled as an Euclidean 3D object, not a point) will not be able to go through such a vertex.
- DanielRibeiro 8y ago
  There is a game in development that uses these ideas too, and is aptly called Manifold Garden: https://store.steampowered.com/app/473950/Manifold_Garden/ https://store.steampowered.com/app/473950/Manifold_Garden/
- deleted 8y ago
  [deleted]
taneq 8y ago
What would count as "modeling non-Euclidean space natively"? I mean, these spaces are basically just piecewise-Euclidean spaces and the portals define how the pieces connect. Or did you mean smoothly curved space with wormholes (which I imagine would be confusing as heck)?
- potiuper 8y ago
  "modeling non-Euclidean space natively" could be done with something as simple as hyperbolic geometry. For "Piecewise-Euclidean spaces" see https://en.wikipedia.org/wiki/Piecewise_linear_manifold https://en.wikipedia.org/wiki/Piecewise_linear_manifold, https://en.wikipedia.org/wiki/PDIFF https://en.wikipedia.org/wiki/PDIFF (splines), and more generally https://en.wikipedia.org/wiki/Surgery_theory https://en.wikipedia.org/wiki/Surgery_theory.
- SiempreViernes 8y ago
  Is there much point in using weird geometries if you don't make confusing levels? Surely the point of using weird geometries is to expose the player to weird effects that aren't achievable by simple euclidean planes and a bit of trickery with perspective or colours?
  - taneq 8y ago
    There's a much more pragmatic use: Folding a large game level into the walkable area of a VR setup. There are a few people investigating games using this technique and apparently it's quite effective (eg. https://void-room.itch.io/tea-for-god https://void-room.itch.io/tea-for-god - I haven't tried it yet though.)
codeparade 8y ago
I did find this video which attempts 'continuous' non-euclidean spaces but the results are really disorienting: https://youtu.be/tl40xidKF-4?t=4m6s https://youtu.be/tl40xidKF-4?t=4m6s Instead, the goal my engine was to make the effect as subtle as possible, even unnoticeable.

wcoenen 8y ago

> rather than actually modeling non-Euclidean space natively In mathematics such non-Euclidean spaces are called manifolds. A manifold is defined as a set of Euclidean-like regions that are connected by transition map functions. That formalism is basically the same thing as these portals. https://en.wikipedia.org/wiki/Manifold https://en.wikipedia.org/wiki/Manifold

thfuran 8y ago
Except that that method wouldn't let you have, for example, a hyperbolic plane that could be traversed without obstruction.
- wcoenen 8y ago
  I think you could actually approximate an unobstructed hyperbolic plane to arbitrary precision with portals. In this game, the hyperbolic plane is represented as a tiling of hexagons and heptagons: https://www.youtube.com/watch?v=lX5eCfRSCKY&t=742s https://www.youtube.com/watch?v=lX5eCfRSCKY&t=742s If you take this model but upgrade each cell to a little 3D euclidean region, then you could completely surround it by portals that connect it to the neighbouring cells. The edges of the portals wouldn't be visible. The smaller the euclidean cells, the better the approximation to the hyperbolic plane.
  - zenorogue 8y ago
    For easy computations assume octagonal cells. Their vertices will have 135 degrees each. The edges of the portal will be visible because the left and right images do not match (since 3*135 ≠ 360). And a object (as long as it is modelled as an Euclidean 3D object, not a point) will not be able to go through such a vertex.
DanielRibeiro 8y ago
There is a game in development that uses these ideas too, and is aptly called Manifold Garden: https://store.steampowered.com/app/473950/Manifold_Garden/ https://store.steampowered.com/app/473950/Manifold_Garden/
deleted 8y ago
[deleted]

taneq 8y ago

What would count as "modeling non-Euclidean space natively"? I mean, these spaces are basically just piecewise-Euclidean spaces and the portals define how the pieces connect. Or did you mean smoothly curved space with wormholes (which I imagine would be confusing as heck)?

potiuper 8y ago
"modeling non-Euclidean space natively" could be done with something as simple as hyperbolic geometry. For "Piecewise-Euclidean spaces" see https://en.wikipedia.org/wiki/Piecewise_linear_manifold https://en.wikipedia.org/wiki/Piecewise_linear_manifold, https://en.wikipedia.org/wiki/PDIFF https://en.wikipedia.org/wiki/PDIFF (splines), and more generally https://en.wikipedia.org/wiki/Surgery_theory https://en.wikipedia.org/wiki/Surgery_theory.
SiempreViernes 8y ago
Is there much point in using weird geometries if you don't make confusing levels? Surely the point of using weird geometries is to expose the player to weird effects that aren't achievable by simple euclidean planes and a bit of trickery with perspective or colours?
- taneq 8y ago
  There's a much more pragmatic use: Folding a large game level into the walkable area of a VR setup. There are a few people investigating games using this technique and apparently it's quite effective (eg. https://void-room.itch.io/tea-for-god https://void-room.itch.io/tea-for-god - I haven't tried it yet though.)

codeparade 8y ago

I did find this video which attempts 'continuous' non-euclidean spaces but the results are really disorienting: https://youtu.be/tl40xidKF-4?t=4m6s https://youtu.be/tl40xidKF-4?t=4m6s Instead, the goal my engine was to make the effect as subtle as possible, even unnoticeable.