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Choosing a foundational 3D engine to build a 4D engine atop of

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So here's the deal : many many years ago, I saw screenshots of Miegakure, that very famous 4D puzzle-platforming game you probably all know about by now. The thing is, it never came out, not even a playable demo, except at big gaming events that I have no way to get to. As such, I decided a while ago that I had waited long enough and I decided to start working on my own mathematically accurate 4D rendering engine.

Without going too deep, the point of it is that 4D objects live in 4D space, and the so-called 4D camera just cuts a 3D slice of the 4D space and of every 4D object in it, which is then passed to your regular run-of-the-mill 3D engine to display. Doesn't sound like anything too hard then.

The big problem however comes from optimisation. In 3D engines, you expect your geometry to never change ever, allowing for a lot of cool stuff like GPU caching and the like, and is usually pretty vital for performance. However in a 4D engine, the thing that never changes is your 4D geometry, not the 3D geometry that results from the cutting (that in fact changes every frame). The more mathematically inclined will also think about spatial complexity, since in 4 dimensions you have "a lot more space" to put objects in (purposefully keeping it vague). Moreover, I don't want to go through the trouble of building an actual 3D engine, because a lot of existing engines do that a lot better, and I would probably waste all of my time and motivation working on 3D instead of 4D.

As a demonstration, my very first demo uses Three.js and is basically a 4D enigma : http://mattias.refeyton.fr/PAF/slicing . The goal is to get to the other side of the wall where the green cube is, knowing that the wall is too high to jump over and that you can't go around it. You can use ZQSD to move (French keyboard, sorry), and A and E to look "ana" and "kata", which are the 4D equivalent of left and right. You'll excuse the roughness of the whole thing, as it was done in 5 days for a school project (it was the perfect opportunity). This has only been tested on Firefox and Chrome.

Hence my question : what do I use as a foundation to work on this ? I'd like to use either C, C++ (for performance) or Haxe (for the multiple targets), if that gives any leads. Of course, doing it from scratch is a totally valid answer, as I would be able to include many 4D-only things (such as 4D lighting and other cool shit) that I'm having trouble seeing how I could implement them in an existing engine. Another thing to take in consideration is that there's probably going to be a 4D physics engine to come with it, and that I'm not sure how hard or easy making that work with an existing 3D engine would be.

Also I'm killing two birds with one stone by asking if anybody would be interested by a stream of this. I'm planning to eventually stream my work on this, which would include math on blank paper, and heavily mathematically-inclined discussion, not just coding (relatively little coding in fact).

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This isn't at all what I asked ; I'm not asking how to do 4D, because I already do that (and I already watched that a while ago anyway, even if it's not really the point). I'm not going to reiterate the question because it's all there already.

Edited by matrefeytontias

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