5 ms·

I love 4D graphics. Many years ago, in my freshman year of college, I wanted to create a 4d space game, and spent about a year grinding out an OpenGL rendering

I love 4D graphics. Many years ago, in my freshman year of college, I wanted to create a 4d space game, and spent about a year grinding out an OpenGL rendering engine. I taught myself the requisite mathematics and realized that my conception of hyperspace as operative in my game, was fundamentally wrong. So I moved on. Still have the code laying around, although I lost the Linux port I ginned up at one point. Really should polish it and release it. :)

beaumayns 6y ago
I'm curious, in what way was your conception wrong? Sounds like it could still be interesting.
- pnathan 6y ago
  my initial thought was that hyperspace would allow a _shortening_ of the distance traveled from point P0(x,y,z,q) to P1(x,y,z,q). Since I was _really_ into space combat games at the time... that would have been really cool! However, - and this is obvious when you work through it - when you use Euclidean distance (https://mathworld.wolfram.com/Distance.html https://mathworld.wolfram.com/Distance.html - see the General equation), the distance travelled increases, thus obviating a key part of my game, which was to "jump" through hyperspace to shorten the trip. I didn't care to rewrite math enough to make the game work out, and since I'd spent so much time learning math, graphics,and larger-scale program design, I was burnt out. It was a great experience. One day I might return to the notion, but it'll be around the hyper-dimensionality experience, not as a combat game. I don't like the slice mode of 4D games qua the OP, I far prefer projections from 4D as a way to understand the 4D realm.
joekunin 6y ago
I would love to know more about the kind of math involved in this.
- pnathan 6y ago
  The simplest answer is that I was aiming at doing a projection from 4D into 2D. 4 dimensions in Euclidean space have 6 planes. A 4D rotation thus has to have a ton more of sine/cosine calculations than a 2D one. Projections down from the 4th induce this as well. You have to project each point into the space you're visualizing. I didn't really get into camera / FOV calculations, I kept that fixed, don't remember much about those decisions. It was 2001 when I started the project, and I took a final swing around 2005 to get a final thing. Not sure of the state of the information today, but at that time, I was unable to find almost anything about the mathematics involved in the 4d->3d work. I was a freshman at a community college, literally printing off articles from Wolfram and interlibrary loaning books on graphics. I had to deduce from the principles of 3d->2d projection what it'd take to do a 4d->3d projection. I went on to take a minor in mathematics and retain a good deal of that information even now. Given an adequate graphing/windowing context with a PutLine/PutPoint in 3d or 2d, I could cook up a 4D library over a weekend of focus. I just don't know what to do with that library besides goofing off rotating a cube or whatever. N.b., one of the issues with doing something here is that you really need a 4D CAD tool. Think Blender, but 4D. Otherwise you're laboriously typing in `Point p = new Point(0,0,0,1); Point p2 = new Point(/ugh/);` or some such, maybe in a text file. Haven't looked into the area in, you know, 15 years. Maybe there's such a tool out there today.

beaumayns 6y ago

I'm curious, in what way was your conception wrong? Sounds like it could still be interesting.

pnathan 6y ago
my initial thought was that hyperspace would allow a _shortening_ of the distance traveled from point P0(x,y,z,q) to P1(x,y,z,q). Since I was _really_ into space combat games at the time... that would have been really cool! However, - and this is obvious when you work through it - when you use Euclidean distance (https://mathworld.wolfram.com/Distance.html https://mathworld.wolfram.com/Distance.html - see the General equation), the distance travelled increases, thus obviating a key part of my game, which was to "jump" through hyperspace to shorten the trip. I didn't care to rewrite math enough to make the game work out, and since I'd spent so much time learning math, graphics,and larger-scale program design, I was burnt out. It was a great experience. One day I might return to the notion, but it'll be around the hyper-dimensionality experience, not as a combat game. I don't like the slice mode of 4D games qua the OP, I far prefer projections from 4D as a way to understand the 4D realm.

joekunin 6y ago

I would love to know more about the kind of math involved in this.

pnathan 6y ago
The simplest answer is that I was aiming at doing a projection from 4D into 2D. 4 dimensions in Euclidean space have 6 planes. A 4D rotation thus has to have a ton more of sine/cosine calculations than a 2D one. Projections down from the 4th induce this as well. You have to project each point into the space you're visualizing. I didn't really get into camera / FOV calculations, I kept that fixed, don't remember much about those decisions. It was 2001 when I started the project, and I took a final swing around 2005 to get a final thing. Not sure of the state of the information today, but at that time, I was unable to find almost anything about the mathematics involved in the 4d->3d work. I was a freshman at a community college, literally printing off articles from Wolfram and interlibrary loaning books on graphics. I had to deduce from the principles of 3d->2d projection what it'd take to do a 4d->3d projection. I went on to take a minor in mathematics and retain a good deal of that information even now. Given an adequate graphing/windowing context with a PutLine/PutPoint in 3d or 2d, I could cook up a 4D library over a weekend of focus. I just don't know what to do with that library besides goofing off rotating a cube or whatever. N.b., one of the issues with doing something here is that you really need a 4D CAD tool. Think Blender, but 4D. Otherwise you're laboriously typing in `Point p = new Point(0,0,0,1); Point p2 = new Point(/ugh/);` or some such, maybe in a text file. Haven't looked into the area in, you know, 15 years. Maybe there's such a tool out there today.