Designing a 4D World: The Technology behind Miegakure [Hide&Reveal]

The world we are building in Miegakure is a world in which there are four spatial dimensions instead of three. In this game, the fourth dimension is not time but a fourth dimension of space that works just like the first three dimensions we are familiar with. If you count time, this game is 5D! In this video we will talk a little bit about the unique technology we developed for the game. So, at first games were only 2D and took place solely along two directions. Then computers became powerful enough to render 3D graphics and this allowed for full 3D movement. Of course, the graphics we see, while they are computed in 3D, are actually displayed on a 2D screen. They are projected down from 3D to 2D, in a way that mimics how our eyes perceive the third dimension. But it doesn't stop there. If in a 2D game every object's position is represented in the computer using two numbers, and if in a 3D game every object's position is represented using three numbers, what if each position was represented using four numbers? In other words, what if there was another direction you could move along, in addition to the first three? Trying to answer this question is what that led us to develop this game. As far as we know, our universe has exactly three spatial dimensions — so it's difficult for us to picture what a four-dimensional world would look like. But a computer, on the other hand, does not care; it's just working with numbers as usual. So we had to come up with a way to display this calculated 4D world so that our three-dimensional brains could comprehend it. The way we chose is a method that has been popularized in the novella Flatland. This novella talks about a 2D square that can only see a 2D cross section of a 3D world. For the square, the third dimension is invisible and mysterious; the square has no concept of it because it is stuck seeing a 2D world. If a 3D object visits the 2D plane it appears to be deforming. In Miegakure, a similar process happens, but in one higher dimension: instead of taking a 2D slice of 3D objects, we are taking a 3D slice of 4D objects. It's hard to imagine, but luckily we don't have to – a computer can just display it for us! But how to build a 4D world and the objects that populate it, especially without being able to fully see them? In a 3D game, objects are usually made out of triangles. The surface of a 3D object is 2D, and triangles are the simplest 2D shape. To generalize this concept we add a dimension: the surface of a 4D object is 3D. So what is the simplest 3D shape? It's a pyramid-like shape called the tetrahedron. So to build the surface of any 4D object we want we can use the tetrahedron as a building block, and that's what this game does. What happens is that, instead of projecting the tetrahedra on the screen like we are doing now, we slice them using the 3D plane that represents what the player can see. That gives us a bunch of triangles, which we then draw the same way we would for a regular 3D game. What you see is the 2D projection of a 3D slice of a 4D object. But how do we even create 4D objects? We can't easily visually manipulate them using a 4D equivalent of Maya, but what we can do is generate them procedurally. So let's take a simple example. To build 4D crystals, we use a method similar to how we would build a 3D crystal procedurally, but instead of starting with a 2D hexagon and extruding it up, we start with a 3D dodecahedron and extrude it into the fourth dimension. I picked the dodecahedron because it often gives hexagons when you slice it. Surprisingly in this scene, every crystal is the exact same shape, only facing different directions and slightly longer or shorter. And yet they all look so different because you only see a slice of each of them. This is particularly interesting because of the known connections between high dimensional space and certain crystal structures. I can move a little bit in the fourth dimension and the scene will look slightly different, and again slightly different. There are technically an infinite number of unique slices one could take. Here is another, more complex example. The surface of this 4D shape called the 120-cell is made out of 120 dodecahedra. In this case I cut a hole inside each dodecahedron to make them hollow. While you could ignore all of this when playing the game, to me it feels even more beautiful when you know more about what is happening. So I wanted to share some of the things you may not realize when you finally get to play Miegakure.

Channel: Miegakure

Views: 1,151,357

Rating: 4.9411974 out of 5

Keywords: Hypercube, Tetrahedron, Tetrahedral Mesh, 4D, Math, Mathematics, Science, Fourth Dimension, Game, Technology, Making Of, 4D Game, 4th Dimension, Innovative, 600 Cell, Crystal, Penrose, Four-dimensional Space, Marc ten Bosch, Tesseract, Flatland, Education, 120-Cell, 4D Crystal, Explanation, Crystals, Mesh, 4D Mesh, fourth dimension

Id: vZp0ETdD37E

Length: 4min 28sec (268 seconds)

Published: Tue Mar 08 2016

Reddit Comments

[u/myexguessesmyuser]

The worst part of this is that after watching it you’ll want to play it and then you’ll realize it’s been in development for 8+ years with no release date in sight. :(

[u/[deleted]]

As someone currently writing his own custom 3D renderer designed for procedurally generated and manipulable objects, this is fascinating

Doesn't mean it doesn't make my head hurt trying to visualize 4D space though >_<

[u/AlwaysGeeky]

This looks amazing and the visualization/effect of shifting in the 4d plane is really impressive, but honestly, aside from the beauty of this, I don't see how it fits into the gameplay of your world... also I wouldn't assume many players to actually understand what is happening and really get the Math behind this.

As you mentioned in your video it is really hard for most "non-math" people to comprehend a 4D spacial system and almost impossible for people to understand what they are seeing when it is projected from 4D -> 3D -> 2D (screen). So if you have anything in the game which relies on the player understanding 4D or puzzles which are solved or involve anything specifically with the 4D science behind this, be prepared for players to be frustrated and not know what is going on. Personally whenever I work with people and anything involving 4D, I find it much easier to explain and people get it much quicker when they are actually working in 3D, like for example in VR... have you considered anything VR related for your game, or exploring getting Meigakure working on Occulus or Vive?

Either way, I look forward to seeing more of this and playing it in the future.

[u/Pella86]

I made a small implementationnin python of a 4D Snake.

https://youtu.be/8IUnqm8j4BE

There is also a C++ OpenGL version and i put the links to steve hollasch master thesis ans urticator 4d maze.

I will soon enough port the python game to blender

[u/seoulhunter169]

It hurts my brain. I want more!

[u/caramel_corn]

When is this game coming out? It's been in development forever. How does one go about findings a project this long without a release?

[u/alejandro712]

I'm really excited to stop hearing about this game and actually play it. At this point there has probably been more content created about the game than there ever will be content in the game, no matter how grandiose it is. It's been talked about for like a decade now.

[u/yannickl88]

my head hurts >.<

EDIT Cool game though, looks awesome!

[u/glupingane]

The game 4D Toys is out on SteamVR if anyone wants to play with this. If I recall correctly it's from the same maker. It's awesome