The phrase "UVW unwrap a tetrahedralized mesh" is unbelievably cursed.

"ok, now that Hyperbolica is finished I'll just do something easy like, idk, golf in 4D?"

several years from now: "now that I've created a time machine I can kickstart the creation of Unreal Engine's 4D project support, this is so I can make the grass texture on this mini-golf course look a little less flat"

"For every triangle you can see, there's probably at least 10x as many that you can't see."
Sounds like someone needs to invent 4D occlusion culling, lol.

"I don't really want another multi-year project like Hyperbolica, so this will probably be a relatively short and minimalist game that I just spend a couple months on and release." - CodeParade, July 2022

There is actually a nice way to extrude a shape made of triangles into a shape made of tetrahedra in a way which always guarantees the edges always line up.

The mathematical structure which accomplishes this is called a simplicial set. It's basically a way of organizing simplices and gluing data to form shapes.

The key ideas to how it works are
1) Having the edges of each triangle ordered so that the way they're glued to each other is compatible with that order
2) Keeping track of "degenerate" simplices. For instance, you can consider a line as a degenerate triangle where one edge has length 0. This of course wouldn't need to be rendered. It would just go into the algorithm for tetrahedralizing the prisms.

From here, the Cartesian product of the simplicial interval with the simplicial set which represents your surface will produce a simplicial set for the solid, and all the edges will naturally line up. I believe simplicial sets are implemented in Sage if you want to check it out.

I can already tell the speedruns for this game are going to be INSANE

Easy and 4d should not be in the same sentence

"They don't look like leaves." Bruh you are inventing 4D leaves, they can look like whatever you want 😂

Imagine time traveling back 20 years
to tell people a 4D golf game is real

Something tells me you're gonna be one of those programmers that falls ass backwards into creating an entirely new standard in generalized engine building that gets picked up by everyone.  Like the adoption of quaternions in game physics

Dude... you are really breaking new ground and discovering new frontiers here. Things that no one has ever done before.
Please keep making these, documenting all the problems you encountered making a 4D game.
I find these problems fascinating. These are problems you wouldn't even know existed unless you were trying to build a 4d game world. So cool.

5:04 HoxelDraw!

”for the same reason we can’t use a 2d tree in a 3d game” yeah right

This channel really has a longstanding tradition of glossing over/subtlety flexing/giving for granted really High level math skills and use it as tools for it's projects

I was wondering how this project went along, glad my expectations have been met and you've properly went insane
Keep going!

I don't understand why you can rotate through the 4th dimension (slices) while the golf ball is moving. While you're aiming this makes sense, as you're aiming through another dimension (and we have to slice through it so our little 3d brains can understand), but while the ball is moving it's like you're giving it additional momentum through the 4th dimension.

5:48 THE HORROR

I've been playing the game so much and I've been mesmerized by how it all just works so well and what it must have taken. I'm so glad you made this devlog.

I love how there's so much nonsensical random content on YouTube, but every so often, there's something so brilliant that represents the culmination of so much work, and I happen to be around to witness it!

you could totally make a really long version where you explain the problems in great detail and we would all watch it