So many problems in life can be solved by using a lookup texture instead of real-time calculations

I'm really glad Miratope was of some use. When I started coding it almost 3 years ago I honestly had very little idea of what I was even doing. I haven't been actively working on it for a while now, but I believe it's currently in good hands.

I think the property you migh be refering to at 2:56 is called star-convexity.

At 2:47, the "vertex that can reach every other vertex," that's a property of star-shaped polygons/regions. Every star-shaped polygon has an internal region that can see the entire boundary of the polygon; this region is called the kernel of the polygon. In 2D, it's the intersection of all half-planes defined by the edges; it generalizes to any dimension.

Precomputed data in textures. Gotta love it.

The fact that you’ve wrapped your head around this stuff to not only think, but also code and optimize, in four dimensions is seriously so impressive. That optimization with the lookup texture was sick as hell

2:55 in my analysis class, we called a subset of a vector space with that property "star shaped".

"Hmmm yes, fascinating," I say as I stroke my chin thoughtfully, completely and utterly failing to comprehend anything that's being shown or said

Holy shit that optimization into a 64 bit table encoded to RGB values is FUCKING BRILLIANT!!! I adore your projects so much!!

3:01 it is called a Star Domain! In geometry, a set S in the Euclidean space R^n is called a star domain (or star-convex set, star-shaped set or radially convex set) if there exists an s0 in S such that for all p in S, the line segments from s0 to p lies in S. This definition is immediately generalizable to any real, or complex, vector space. (wikipedia)

I came in here thinking, "He's going to explain it!!! I can't wait to finally understand 4D world", I came out still confused but motivated. Idk how he casually just talks about 4d like it's nothing, but it made me motivated and happy to know that it is achievable to get to that level.

When i was doing 4d rendering, i did consider building meshes to render, but eventually i just thought back on your videos and the work of inigo quilez and raymarched it instead. super simple and ran decently well, mostly. though sending the primitives to the GPU was an interesting experience

Nice optimization with the lookup table! Getting more and more pumped to experience all this in its final form.

I don’t understand most of this but it makes me feel good that someone does 😂 keep up the good work!

love 4d stuff bruh

Watching these videos is a crashcourse to visualising a 4D world which i’ve wanted for some time now, sick coding on top of that and this is a nerds dream walkthrough, great work!

Man, I can't even remotely follow this anymore. You have a truly impressive sense of visualization. I'm not giving up or anything, I'll get it one day. But you're trying to toss the ball as gently as you can and It's still flying miles over my head. LOL

That lookup table should be the games icon/logo

Considering sending this to my computer graphics professor. It's really cool taking his class and then coming back to this video and actually _understanding_ what you're talking about. Feel like this is something he might find interesting. I didn't understand the brilliance of the lookup texture when I first saw this video, but that's actually really clever.

Oh, by the way: the property you’re looking for, beyond convex, is called **stellar convex**. Just learned about it in my topology class!

The moment I heard “we could get the cpu to slice it and then send it to the gpu” a very loud ‘blaring wrong buzzer’ sound went off in my head. Your solution for it was incredible though! Love ur stuff

That truly is such a beautiful optimization, and i feel second hand pride for it, cause I'm so excited about all things 4d gaming

I'm deeply fascinated by your projects! They always fiddle with mathematics in depth.

This is endlessly cool. Well done. Been watching your videos for years and always look forward to the next one - but I always appreciate why they take time. Never compromise your quality for clout.

2:58 It's called star convexity! (A set with that property is a star-convex set or just a star domain)

That was an amazing way to take Super Nintendo programming theory into the modern era. Tip of the hat to you sir.

You are a huge inspiration! Loved Hyperbolica, especially the farm level. The art gallery platforming was insane as well. Hyped for this!

I don't know if you read sci-fi but the chapter detailing how being in four dimensional space looks and behaves in Cixin Liu's "Death's End", the third novel in the Three Body Problem trilogy, it's just so coherent and believeable and I think you'd love it. Absolutely blew my mind. For instance, it explains via analogy how us looking at a two dimensional world with 2d creatures from above would see their bones organs and muscles, how when you're observing from above there is not concept of "inside" in 2d. The application one dim higher is that there is no "inside" of objects in 3d, looking at someone's hand you could see the bones and muscles as easily as the skin. looking at a rock means seeing every cross section at once, it is described as "one hundred million times the visual information you see in normal space". It explains how you had to move your body carefully, because it is impossible for 3d beings to locate their hands with four coordinates, there is always one dimension you can't quite figure out how to move in, and as such you can easily touch someone's bones instead of their hand, or poke their organs by mistake. It goes into so much detail and it's all so believable, with analogies and explanations letting you actually understand the foundations of this fabricated reality and letting you play around and figure out narratives that work with them. That trilogy is the best sci-fi I had ever read watched or experienced, possibly that I will ever experience. I highly recommend you go read that chapter, around the middle of the book. It doesn't spoil much of the plot. After that, just read the books. So good. Love your channel, cheers!

Your explination is great but my 3 dimensional brain can't comprehend the complexities of the 4th dimension. I admire your courage to pursue the 4th Dimension!

They say the creator of Roller Coaster Tycoon is the goat. Huge game by 1 developer, written completly in assembly, runs even on the lowest end pcs beautifully. CodeParade: Yeah rendering millions of tetraheadrons (I don't even know how to write this) in 4D should do the trick.

This is so insane. This man is pushing new territory for rendering, it's like if you made 3d meshes by writing the coordinates out in a list, except you can't even reference real life to think about the positions of those coordinates. And then he even optimised it for modern gpus.

I freakin love this channel. Please consider making longer and more detailed videos. 8min leaves me craving more!

That music is really good!!! Thanks for leaving the source!

Ngl, i know nothing about coding, and what i know about 4d space is thanks to you, and my brain is melting, but you have a relaxing voice and good pace with explaining, so even if i understand less than a fish understanding trigonometry, i enjoy your videos

The lookup table idea is so good it has me even more excited than most of the rest of the video

3:01 it's called a star shaped region! I had this in my analysis course.

You clever dog, you! Love listening about your dev adventures man! Thanks

How smart a mans gotta be to come up with his own 4d render optimizations

I love clever optimizations like textures. Love how this is turning out so far!

2:57 That's called the "star-convexity" of a polyhedron. If a polyhedron is star-convex, "there exists a point within the polyhedron (called the "star center") that can be connected to every point on the surface of the polyhedron by a line segment that is entirely contained within the polyhedron"

2:55 it should be a "star domain", see related description on Wikipedia.

Nice use of Rhino !🎉 for the visuals

If you encounter a problem in life that appears to have no solution, try throwing a lookup table at it. -Sun Tzu-

Singlehandedly making amazing mathematical fantasticals accessible like this and marble marcher AND giving great insight into their creation. Would love to see what would happen if you had the budget etc of a massive game dev company. Excluding all complications of multiple minds etc.

Code parade making his 5048498484937th video on 4d games/worlds

Fascinating to see how you've made the lookup table for this!

Really appreciate the technical details. It's rare to learn about both math and coding from one video!

first code parade video to officially lose me. great work man

Dude your solution to build the look up table is so fucking smart

Yay! I'm always glad to see you posting.

True 4d is all of the different views combined and more that we can’t comprehend

What would happen if you combine 4D and hyperbolic geometry?

Dude! You are on the frontier of 4D rendering and pushing it further! Amazing

Not sure if anyone else has mentioned it, but tetrahedral meshing is something done very commonly in fluid simulation codes, you may be able to use one of those software packages to make your tet meshes more robust and less skewed.

Alright. That's brilliant. I can't wait to play!

Excited to play this game.

This video has so much math and/or coding knowledge it hurts my brain to try to think about it.

Hopefully this will be a warmup for a 4D fractal marble marcher

Genius ideas you have got. Even though I didn't understand the last part about slicing, I hope at some point in the future I will understand it well.

Ain't afraid to admit that I need the assistance of Google to get through these videos. But you keep putting out great stuff so I'll keep at it

That lookup grid is a fantastic idea to save on processing power!

Incredible work, these ideas are great, can't wait for the game.

This is inspiring! I'd love to hear your thought process when it comes to designing a 4d level, like, conceptually, because I can't imagine how you'd even begin doing that.

Replacing logic with a data structure is one of my favorite things. When I made a Rubik's cube simulator/solver in Javascript with three.js, I had trouble knowing exactly which way to rotate a face to move a piece; like, which way should I rotate the right (R) face to move a piece from the top (U) to the front (F). Ended up manually typing a nested dictionary so that I could look up Move[R][U][F] to get R'. That was the most productive 10 minutes of typing in the whole project.

Superb video as always!

0:30 me when i see a honkin pair

Okay, i consider myself relatively acquainted with multidimensional spaces but you blew my brains out xD This is worthy of at least a few scientific papers!

I think this game concept is very, very unique! I've got the game wishlisted on Steam, and I can't wait to play it when it comes out!

2:36 my first thought was parametric equation spam with the third parameter going perpendicular to the other 2

I have been to a conferece recently, on cognitive linguistics and one of the talks had your game in the title. There are researchers that are interested in how players of impossible geometry games come up with words to describe locations and directions. They have a "VR gaming lab" in Berlin and play your games.

This is wild.

There are some really interesting symmetries in that texture you generated. Some combination of shift, rotational, and reflective symmetries, that it took me a few moments to realize are only apparent if you wrap both the edges.

Very impressing work ! 🙂

On 6:59 I remember making a lookup table for a ray tracing on shadertoy, also it calculated the bounding boxes too.

I saw 3d golf at game stop and thought of your game. I thought wow 3d golf that so last generation we have 4d golf now

(6:59) That actually looks like some very good pixel art of a plant.

I honestly can't wrap my head around the 4d concept of tetrahedras. But I'm stoked that someone else can, and that he's willing to try and explain it to us.

3:47 i need to fight my arch nemesis THE ROCK

A good lookup table solves so many problems.

How is someone this smart? This is like the top .000000001% of geniuses.

my favorite basic 4d shape so far is the semi-unholy union between a 3d cone and a 3d ellipsoid, because its tracing/marching math is VERY efficient (it is still only quadratic complexity) and it smoothly (parabola-tweening) unifies cone+ellipsoid(+sphere as special case ellipsoid); See [cone+Ellipsoid=Unicorn 4d - Shadertoy]

I understand the whole extrusion thing when making 3d objects 4d, but extrusion can only go son far. Like if you extrude a circle, you will get a cylinder, but not a sphere. I don't know if I just missied something or what, regardless, this remains an extremely impressive project.

2:55 The property is called star-shape (or I'm horribly mistaken). If I remember correctly, a shape is star-shape if there is a point (called the center point) such that every point in the shape is connected to the center point by a straight line (or a geodesic, for a non-Euclidean topology).

If you are a new developer looking at this and thinking "I'll never be able to code like that!" don't despair... I've been a software engineer for a few years now and this magic still baffles me and likely always will.

You are a true inspiration my guy

I think I would die working on this game. But I'm glad you're doing it.

Absolutely beautiful

Wow dude. That's amazing!

you are more than a magician. sir.

This was definitely an update where I didn't understand the maths. But glad to see it's going well!

The rendering is by far the most interesting thing so far

Imagine a shooter in this Engine WASD for the normal movement along the x and y axis Normal limited movement in the z axis Custom mouse binds for movement in the W axis (like q,e,scroll up,scroll down) what a absolute monster of a game to play

Only one person is actually playing 4D chess, and it's this man.

I love hearing about the crazy rending techniques. Can't wait for 4d windmill obstacles.

You probably already know this but 5:47 if you have deeply nested if-else functions, you can often abstract away a lot of that by logical inversion- this makes code much more readable (and sometimes faster since once a statement is deemed false what follows gets ignored through obligation). Plenty of articles out there about inverting if-else statements, should it be something you (or anyone else) want to explore. :)

“This 100% made sense”

My brain hurts. but i love it. Not a huge fan of golf, but i'm gonna get a copy just to indulge myself in the 4D aspect of that game.

I totally understand what you said

I do work with 3- and 4-manifolds, and love these videos. There's so much good concrete stuff to know beyond academic research programs!! Do you have any thoughts as to why your lookup table looked like that? I was surprised it wasn't symmetric in any way.

this is super impressive!