Post by YellowAfterlife in A little portal platformer comments

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Thank you! It is not geometry (and I don’t call it geometry once), but portals allow for local violations of Euclidean geometry axioms - for example, there can be more than one straight line connecting two points. I was originally intending to do more things with portals (like passing through pairs of different-sized portals to adjust the player’s size or maintaining perceived gravity direction when exiting through a flipped portal), but ran into a lot of issues with getting portals to work well in Godot (see blog post).

As for rotation, hard to tell - ultimately that’s on Godot’s end. So long as you’ve clicked to lock the mouse cursor, should act normal.

Zeno Rogue3 years ago(+1)(-1)

Not sure what you mean -- with portals you still get locally Euclidean space -- "locally" usually means "in a sufficiently small neighborhood", and even if you are on a portal, you cannot tell from a small neighborhood, all the points in that small neighborhood will have only one straight line connecting them through the neighborhood, and all the small triangles will add to 180 degrees.

It does not make much sense to say that a game is non-Euclidean just because it violates some Euclid's axioms -- then you could say that any game taking place in a bounded world is non-Euclidean because Euclid's axioms say that lines can be extended infinitely, or any grid-based game, or any game with no space at all, or any 3D game because Euclid's axioms are for planar geometry, etc.

The interesting thing is replacing Euclid's parallel axiom while all the remaining ones remain unchanged. (Likewise when you say "irrational number" you still mean a real number, not anything that is a number and not rational.) Euclid thought that this was impossible (and that the parallel axiom actually follows from the other ones), so did people for 2000 years, and when it was discovered this was possible, this was called "non-Euclidean geometry". Later extended to other things similar in style, but portals do something totally different.

ThisSignGames3 years ago (1 edit) (-2)

No.

A non-Euclidean geometry is just a geometry in which not all Euclidean postulates are honoured. Wikipedia gives "replacing the parallel postulate" as an example, which is defied by this game: we can draw a straight line, have two other non-parallel lines intersect with it at different points, and yet manage to have them not intersect with each other by guiding one of them through a portal. It actually more closely resembles hyperbolic geometry under the right circumstances (i.e. at least one portal is present closer to the given line R than to point P).

Zeno Rogue3 years ago(+1)(-1)

Where did you get this from? The Wikipedia page you cite clearly disagrees with you:

His influence has led to the current usage of the term "non-Euclidean geometry" to mean either "hyperbolic" or "elliptic" geometry.

It does not say that "replacing the parallel postulate" is an example (it says this is what you do, and there are also kinematic geometries) and also "replacing the parallel postulate" means that you keep all the other postulates. If other postulates are not honoured either, it is in no way closer to hyperbolic geometry.

And I am still using non-Euclidean geometry wider than the Wikipedia line above, to mean "a geometry which is not Euclidean" like you want, i.e., including three-dimensional geometries like Solv and Nil. They are geometries i.e. they stretch the space, while portals do not stretch the space, they change the topology, not the geometry. For example, all triangles will still have angles which sum to 180 degrees, while in hyperbolic geometry, all have less.

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