4D games

In the topic of the ten-dimensional space , in addition to ideas about the use of substances and all astral projections, ideas about a four-dimensional game were expressed in order to "see how it looks."
It means 4 spatial dimensions.
Focuses with branching and overlapping in time are in games like Chronotron and similar.

Overview

NB: Some of the games listed are found through the 4D Euclidean space page, where there are still many tasty related links.

Hypercube is a “game” with tesseract rotation. java-applet.
The game can be called conditional. In fact, a variation of the controlled rotation of the tesseract and some other unobtrusive bonuses for collisions.
If you do not have stereo glasses, and the game will fall due to lack of memory (I eat gig), there is a risk to remain cross-eyed :)

4D Maze is a four-dimensional maze consisting of hypercubes. jar
A completely honest four-dimensional maze, with many settings for the projections, perspectives and so forth.
The labyrinth is depicted as a stereo pair in wireframe.
You can navigate in it by rotating on four axes, until in front there will be a cluster of ugliness of the same color. Then you can go forward.
There is no way out, it seems :)
')
4d building blocks . Puzzle with the construction of figures from objects.
Objects move along one of the axes.
Depicts wireframe stereo projection in various options, including stereo.

Magic Cube 4D . 4th dimensional Rubik's cube.
It is depicted in the form of segments spaced apart in 3d space.
The page has links to other implementations, including the 5-dimensional cube.
Also there are links to its assembly algorithms and mathematical characteristics.
If your brain is ready - try to get into the table of records! :)

4D Maze is another 4D maze. boot did not wait.

Adanaxis is a 4D space shooter.
A very solidly made space shooter, there are GPL and non-GPL versions, deb and rpm binaries. It's really nice to play.
Implemented all 10 rotations. But, as the manual says, only four are needed for the game, and the rest are just poked.
(The manual is lying! Without slipping immediately along the fourth axis (without turns), it is very difficult to catch up with the enemies - because they seem to move freely in 4D space.)
Control by default, or the key + mouse movement. Everything is arbitrarily reassigned.
Since space is not limited by anything, the geometry of space is not very clearly visible.
When rotating or moving in the fourth axis, 4-dimensional objects appear and disappear, passing through a three-dimensional visible slice - exactly the way it is depicted in video clips when the three-dimensional passes through “flatland”.
Everything is depicted as in an ordinary space shooter - 3d space with perspective.

Considerations.

The main feature is that depicting 4D space in a projection on a 2D screen is completely unrealistic.
If we use the Adanaxis approach - to project in 3D, and then its usual perspective projection in 2D, then the geometry of space is not very clearly traced.
When displaying 4D space, it is simply necessary to generate a three-dimensional image.
The method of strabismus is not very effective, because it does not apply to large images, and small ones will not give the effect of “immersion” in space.
At one time, LCD glasses were in progress, synchronizing the darkening of each “point” with the frame rate — they gave a stunning effect. But they work only with pipe monitors and therefore are not popular right now. But they are expensive :)
Recently, a link about perspective correction technology on the screen, depending on the position of the head, jumped on the screen. It seems to be a very simple and effective scheme. Although it is not clear whether it will be launched into production, how patented it is, and how difficult it is to do in home / garage conditions.
In the end, there are red-blue glasses, which, although they spoil the color rendition, are quite effective.

The transfer of hyper-depths in the form of the perspective of a wire model also does not seem very successful, because it is difficult to navigate in the pile of lines, even if they are arranged in distinct spatial structures. And if you paint all the textures, then you will not see any space.
In this respect, the “translucency” method seems to be more effective - displaying more hyper-deep objects “dissolving” in space , as was done very effectively in Adonaxis.

Another point is that in order to observe the topology of space, reference points are needed - fixed objects.
The most interesting option seems to be the (rather spacious) maze where you can navigate the walls, their lighting and textures.
However, from the experience of coursework in programming, many people know that in a maze of identical cubes it is very easy to get off the orientation even at simple forks.
In this respect, tunnels like Descent, which were intentionally made curves, are more adequate, which made it possible not to lose orientation with respect to the “axis” of the tunnel during any reversals in space.

As a simple scheme for implementation, I would take a maze radial maze model - with aisles between sectors of the 4D sphere.
The segment distortion configuration will provide an additional visual factor for determining the direction to the center of the sphere.
Turns in 4-dimensional space are linear and their effect with spherical distortion is not confused. Maybe :)

Another possible and proven option is flying over the landscape.
It is always visually clear where the "bottom", and if you still hang a couple of suns - then the "north."
But the need to have north and bottom in all dimensions can greatly spoil the very idea of ​​demonstrating 4D space.

Disclaimer

For a hundred years I have not been doing computer graphics, and in one sitting I will not write anything worthwhile.
Although from a purely mathematical point of view, I don’t see any difficulties here. The same Euclidean space and matrix transformations. Only a perspective projection is not built on a plane but in three-dimensional space. And the 3D scene itself is rendered in a slightly modified way. Under the glasses, for example.
Perhaps, someday I will take up this idea, if no one by the time is implementing it.
The purpose of this post is to give an overview of existing 4D games and a reason to discuss ideas for possible implementations.

Upd.
In the previous and in this thread, I slightly screwed up about the number of possible rotations.
What is called a turn "around the plane" is not an additional degree of freedom. Such a rotation is similar to a rotation on a plane around a point - the center of rotation - the axis itself is perpendicular to this plane and does not lie in it.
Thus, 4 rotations are possible in 4D space: around ordinary, one-dimensional axes, perpendicular to the planes: xy, xz, xw, yz, yw, zw.
Each of the axes 0x 0y 0z and 0w is perpendicular to two of the planes.
This is significantly less than expected, the number of fingers needed to control the space ship, and you can again take the mouse + three modifiers.