February 25, 2009 at 01:444-dimensional games
In a topic about ten-dimensional space , in addition to ideas about substance use and all kinds of astral projections, ideas were expressed about a four-dimensional game in order to “see how it looks”.
This refers to 4 spatial dimensions.
Tricks with branching and overlay in time are in games like Chronotron and similar.
NB: Some of the games listed are found through the 4D page of Euclidean space , where there are many more delicious links on the topic.
Hypercube - "game" with the rotation of the tesseract. java-applet.
The game can be called conditionally. In fact, a variation of the controlled rotation of the tesseract and some other obscure bonuses for collisions.
If you don’t have stereo glasses, and the game falls out due to lack of memory (I’m eating a gig), there is a risk of staying cross-eyed :)
4D Maze is a four-dimensional labyrinth consisting of hypercubes. jar.
Absolutely honest four-dimensional labyrinth, with many settings for projections, perspectives, etc.
The maze is depicted as a stereo pair in a wireframe.
You can navigate in it by rotating along four axes, until a cluster of ugliness of the same color appears in front. Then you can go forward.
There seems to be no way out :)
4d building blocks . Puzzle with building shapes from objects.
Objects move along one of the axes.
It depicts a wireframe stereo projection in all sorts of options, including stereo glasses.
Magic Cube 4D . 4 dimensional rubik's cube.
It is depicted as segments spaced in 3d space.
The page has links to other implementations, including a 5-dimensional cube.
There are also links to its assembly algorithms and mathematical characteristics.
If your brain is ready - try to get into the table of records! :)
4D Mazeanother 4D maze. Download did not wait.
Adanaxis - 4D shooter in outer space.
A very and very solidly made space shooter, there are GPL and non-GPL versions, deb and rpm binaries. It's really nice to play.
All 10 spins are implemented. But, as the manual says, only four are needed for the game, and the rest is just a stick.
(The manual is lying! Without sliding immediately along the fourth axis (without turning), it’s very difficult to catch up with enemies - because, apparently, they move in 4D space freely.)
Control by default with the mouse, or key + mouse movement. Everything is arbitrarily reassigned.
Since space is not limited by anything, the geometry of space is not very clearly traced.
When rotating or moving in the fourth axis, four-dimensional objects appear and disappear, passing through a three-dimensional visible slice - exactly the same as it is shown in the videos, when the three-dimensional passes through “flatland”.
Everything is depicted as in an ordinary space shooter - 3d space with a perspective.
The main feature is that it is completely unrealistic to depict 4D space in projection onto a 2D screen.
If you use the Adanaxis approach - project in 3D, and then with its usual perspective projection in 2D, then the geometry of space can be traced not very clearly.
When displaying 4D space, it is simply necessary to generate a three-dimensional image.
The strabismus method is not very effective, because it is not applicable to large images, and small ones will not give the effect of "immersion" in space.
At one time, LCD glasses were in use, synchronizing the dimming of each "point" with the frame rate - they gave a stunning effect.But they work only with tube monitors and therefore have no popularity now. But they cost a lot :)
Recently, a link about the technology for correcting perspectives on the screen depending on the position of the head slipped on the hub. It seems to be a very simple and effective scheme. Although it is unclear whether it will go into production, how patented, and how difficult it is to do in home / garage conditions.
In the end, red-blue glasses remain, which, although they spoil the color rendition, are quite effective.
The transfer of a superdeep in the form of a wire model perspective also does not seem very successful, because it is difficult to navigate a pile of lines, even if they line up in clear spatial structures. And if you paint over with textures, then no space will be visible.
In this regard, it seems more effectivetranslucency method - display more hyper-deeper objects as “dissolving” in space , as was very effectively done in Adonaxis.
Another point is that to observe the topology of space, reference points are needed - fixed objects.
The most interesting option is the (fairly spacious) maze, where you can navigate through the walls, their lighting and textures.
However, from the experience of coursework in programming, many people know that in a labyrinth of identical cubes it is very easy to get lost in orientation even on simple forks.
In this regard, tunnels like Descent, which were intentionally made curves, are more adequate in this regard, which allows us not to lose orientation with respect to the “axis” of the tunnel during any turns in space.
As a simple scheme for implementation, I would take a model of a radial maze of the maze type - with passages between sectors of the 4D sphere.
The distortion configuration of the segment will provide an additional visual factor for determining the direction to the center of the sphere.
Rotations in 4-dimensional space are linear and their effect with spherical distortion cannot be confused. Probably :)
Another possible and proven option is flying over the landscape.
It is always visually clear where the "bottom" is, 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.
I haven’t been engaged in computer graphics for a hundred years, and I won’t write anything good in one sitting.
Although from a purely mathematical point of view, I do not see 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’ll take up this idea if no one realizes by that time.
The purpose of this post is to give an overview of existing 4D games and an occasion to discuss ideas for possible implementations.
Upd.
In the previous and this thread, I screwed up a bit about the number of possible rotations.
What is called turning “around the plane” is not an additional degree of freedom. Such a rotation is similar to 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, 6 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 spacecraft, and you can again take the mouse + three modifiers.
This refers to 4 spatial dimensions.
Tricks with branching and overlay in time are in games like Chronotron and similar.
Overview
NB: Some of the games listed are found through the 4D page of Euclidean space , where there are many more delicious links on the topic.
Hypercube - "game" with the rotation of the tesseract. java-applet.
The game can be called conditionally. In fact, a variation of the controlled rotation of the tesseract and some other obscure bonuses for collisions.
If you don’t have stereo glasses, and the game falls out due to lack of memory (I’m eating a gig), there is a risk of staying cross-eyed :)
4D Maze is a four-dimensional labyrinth consisting of hypercubes. jar.
Absolutely honest four-dimensional labyrinth, with many settings for projections, perspectives, etc.
The maze is depicted as a stereo pair in a wireframe.
You can navigate in it by rotating along four axes, until a cluster of ugliness of the same color appears in front. Then you can go forward.
There seems to be no way out :)
4d building blocks . Puzzle with building shapes from objects.
Objects move along one of the axes.
It depicts a wireframe stereo projection in all sorts of options, including stereo glasses.
Magic Cube 4D . 4 dimensional rubik's cube.
It is depicted as segments spaced in 3d space.
The page has links to other implementations, including a 5-dimensional cube.
There are also links to its assembly algorithms and mathematical characteristics.
If your brain is ready - try to get into the table of records! :)
4D Mazeanother 4D maze. Download did not wait.
Adanaxis - 4D shooter in outer space.
A very and very solidly made space shooter, there are GPL and non-GPL versions, deb and rpm binaries. It's really nice to play.
All 10 spins are implemented. But, as the manual says, only four are needed for the game, and the rest is just a stick.
(The manual is lying! Without sliding immediately along the fourth axis (without turning), it’s very difficult to catch up with enemies - because, apparently, they move in 4D space freely.)
Control by default with the mouse, or key + mouse movement. Everything is arbitrarily reassigned.
Since space is not limited by anything, the geometry of space is not very clearly traced.
When rotating or moving in the fourth axis, four-dimensional objects appear and disappear, passing through a three-dimensional visible slice - exactly the same as it is shown in the videos, when the three-dimensional passes through “flatland”.
Everything is depicted as in an ordinary space shooter - 3d space with a perspective.
Considerations
The main feature is that it is completely unrealistic to depict 4D space in projection onto a 2D screen.
If you use the Adanaxis approach - project in 3D, and then with its usual perspective projection in 2D, then the geometry of space can be traced not very clearly.
When displaying 4D space, it is simply necessary to generate a three-dimensional image.
The strabismus method is not very effective, because it is not applicable to large images, and small ones will not give the effect of "immersion" in space.
At one time, LCD glasses were in use, synchronizing the dimming of each "point" with the frame rate - they gave a stunning effect.
Recently, a link about the technology for correcting perspectives on the screen depending on the position of the head slipped on the hub. It seems to be a very simple and effective scheme. Although it is unclear whether it will go into production, how patented, and how difficult it is to do in home / garage conditions.
In the end, red-blue glasses remain, which, although they spoil the color rendition, are quite effective.
The transfer of a superdeep in the form of a wire model perspective also does not seem very successful, because it is difficult to navigate a pile of lines, even if they line up in clear spatial structures. And if you paint over with textures, then no space will be visible.
In this regard, it seems more effectivetranslucency method - display more hyper-deeper objects as “dissolving” in space , as was very effectively done in Adonaxis.
Another point is that to observe the topology of space, reference points are needed - fixed objects.
The most interesting option is the (fairly spacious) maze, where you can navigate through the walls, their lighting and textures.
However, from the experience of coursework in programming, many people know that in a labyrinth of identical cubes it is very easy to get lost in orientation even on simple forks.
In this regard, tunnels like Descent, which were intentionally made curves, are more adequate in this regard, which allows us not to lose orientation with respect to the “axis” of the tunnel during any turns in space.
As a simple scheme for implementation, I would take a model of a radial maze of the maze type - with passages between sectors of the 4D sphere.
The distortion configuration of the segment will provide an additional visual factor for determining the direction to the center of the sphere.
Rotations in 4-dimensional space are linear and their effect with spherical distortion cannot be confused. Probably :)
Another possible and proven option is flying over the landscape.
It is always visually clear where the "bottom" is, 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
I haven’t been engaged in computer graphics for a hundred years, and I won’t write anything good in one sitting.
Although from a purely mathematical point of view, I do not see 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’ll take up this idea if no one realizes by that time.
The purpose of this post is to give an overview of existing 4D games and an occasion to discuss ideas for possible implementations.
Upd.
In the previous and this thread, I screwed up a bit about the number of possible rotations.
What is called turning “around the plane” is not an additional degree of freedom. Such a rotation is similar to 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, 6 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 spacecraft, and you can again take the mouse + three modifiers.
