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Yeah, that was a glitch I've fixed already lol

I interpret that formula intuitively, but this proof should suffice: *Step 1:* The function determines the chance that a circle with the radius r is within a circle with the radius R. F(r) = (πr²)/​(πR²)=r²/R² *Step 2:* ζ ∈ [0, 1] F(r) = ζ *Step 3:* r²/R² = ζ → r = R√ζ

I didn't want the video to be engulfed by math; instead, I wanted to make it intuitively clear. Think of it this way: picking a random ring (radius) and then picking a random point on the ring. What happens next is an intuitive solution to the points grouping around the center. If you want a remote explanation of this intuitive solution, it's a way to prevent values close to the boundaries of random(0, 1). For instance, sqrt(0.01) is 0.1, which makes the position noticably closer to the middle ring.

The second one's more consistent, but if the first one gets lucky and doesn't miss the circle, it'll be faster.

Yeah I thought of that too because of a video I watched a few days ago on that topic!

If rand here is a macro for random(0, 1), then I could see it giving a rather unnaturally higher average. Perhaps you have an idea on why that'd be helpful, no joking.

​@@rustwithoutrustsqrt(rand) and max(rand,rand) have the exact same probability distribution. i don't know if there's a reason to use one over the other in code, though.

@@alliesakat Because Noah Barger's music always improves whatever it touches

Yeeeeah! Big W to Noah Barger for the soundtrack.

@@lanata64 Yes, whether they overlap.

@@rustwithoutrust i wonder if it'd be faster to do some sort of continuous/'event based' CD, and then lower the tick rate.

@@lanata64 Well, if an object moves, it can always potentially collide, so this is the most natural approach to check for a collision on every position change.

@@rustwithoutrust well yeah, but i was wondering if a continuous cd method that doesn't use 'overlap-checking' in the same way might be faster if you can lower the tick rate (since the max tolerable movement per tick could be far higher)

which one?

@@rustwithoutrust yes

Hey, I'll take a look at it and maybe do a video.

@@rustwithoutrust The k-dimensional data structures, like space filling indexes, can do queries for things that are not points: Rectangles (a, b, c, d) and (e, f, g, h) intersect if (0, 0, a, b) <= (e, f, g, h) <= (c, d, inf, inf) The collision problem which is hard in 2D becomes a simple range query in 4D space

I think overcoming syntax mistakes takes making a couple of relatively big projects. What you could have even bigger problems with is the borrow checker, but most of the time fixing errors related to it includes changing the structure or the logic for it to be memory-safe; that also takes a couple of projects to overcome. But you aren't forced to use Rust, so if Go works for you, keep in mind it's garbage-collected, which is its disadvantage. The way I see it, if you need a company-level codebase that never segfaults and is easy to maintain for years, Rust is your option.

@@rustwithoutrust so what would you recommend ? I start with a rust book and build project after that :) ?

Yes, I recommend to read the official book and go through a few unofficial ones. But ultimately, you'll learn the most from building a project.

@@rustwithoutrust thank u so much !!

Thanks!

Glad you liked it!

the repo is in the description

real

That's cool. Thanks for sharing

this I understand. I did not get the quad tree. not the creators fault. im slow and not too bright.

that's C

hell yeah

do you think quadtrees are optimal for those 2d collision demonstrations?

​@@rustwithoutrust For 2D and 3D collision demos with almost similarly sized objects (for example particles), QuadTrees and Octrees are pretty solid and get the job done nicely 😊. They’re a good choice when everything’s about the same size, but for more complex physics, raycasting or different-sized objects, other approaches might work better 😉.

Hey, didn't expect to see you here! I wanted to thank you for your work on Kraft, it's been a pleasure to go through the source code and learn a thing or two! Why haven't you split up the source, since kraft.pas is a really long file? Are you aiming for having a unit-only physics engine?

@@BenjaminRosseaux Would there be a way to dynamically effect the radius of each object in the quad tree?

@@brickmasterhunt4561 Although it is possible to have objects with different radii in a Quadtree or Octree, this approach is not very optimal. The main issue is that objects would have to overlap into neighboring cells based on their new radius, complicating the structure. Additionally, neighboring cells would need to be constantly checked and updated based on the object's radius, increasing complexity and potentially leading to an O(n²) runtime in the worst case. This becomes particularly inefficient as the number of objects grows. Moreover, this approach introduces inefficiencies since Quadtrees and Octrees are designed more primarily for fixed bounding volumes, uniform element sizes, or otherwise purely static runtime lookups. Different radii and different object sizes (especially those larger than a Quadtree or Octree leaf cell) would negate the spatial partitioning benefits in the dynamic usage case. Alternatives like dynamic self-balancing AABB BVH/BIH trees or even loose Quadtrees/Octrees can handle varying object sizes and radii more efficiently.

thanks!

You can check out kul-sudo/quadtrees on GitHub for the implementation

good question

Excuse me, what? That is simply a lie without any base under it. Moreover, you can run it all yourself and see that difference.

@@rustwithoutrust I assumed the numbers on the corner of the screen are the particle counts. Is that not what they are?

It's said it's the processor time

@@ClokworkGremlin you should maybe watch the video you're commenting on? He literally says what the number is in the video.

@@rustwithoutrust Ah. I missed where that was mentioned at 1:30-1:31. How many points were in this test sample? I've found the overall gain varies wildly based on the density of points being tested. At 1,000 points, varying from 1 and 5 units in radius, across a 1,000x1,000 unit square, I have both a sparse grid-based system and a quadtree based system that run close to 20x as fast as the brute force solution. At 10,000 or more points under the same conditions, the brute force solution is no longer viable due to both time and memory constraints. Working on a bounds sorting solution now, to see how it compares. The dense grid works about the same as the sparse grid, but takes up considerably more memory.

blur

​@@rustwithoutrustvery avant-garde 🧐

@leeroyjenkins0 Yeah, have you seen the subtitles? I've been grinding French and decided it'd be good to make French subtitles. If that's what you mean.

@rustwithoutrust oh! 😂 No sorry I just picked an artsy word for fun Best of luck with that! It really is a crazy language..! I happen to speak it fluently, it's very understandable! Other than working on common idioms. Some notes as an aside "here's the point" would probably be "en résumé" in this context, and often point would be more "argument" than "point" even if it's usually understood, especially in Canada I'd guess. "Move into the cell" would be more "Dans" than "dedans" if you specify the object of "what is it moving into" you don't use the "de" as that's what "de" is referring to. "Utile pour des collisions" would be more "utile pour les collisions" mostly because you're talking about "collisions" as a concept. Small details like that. Also, for this type of video you'd probably address the audience as a plurality so sticking more towards "vous" (not necessarily as the polite form, just addressing all viewers at once), but that's nuanced by the target audience, including the fact that "tu" is more prevalent in french Canadian. That aside neat bite-sized video ^^ Cheers!

I'll probably make French subtitles for all my videos, because that could be good practice for me. Moreover, I'm soon starting to read a book in French that'll definitely boost me and give me more understanding of those little things!

ok, no need for an alarm clock

@@rustwithoutrust lol. Definitely face palmed when reflecting on my own novice attempts at collision detection. Great video. Subscribed.

thanks! yeah, most of those ways aren't that obvious initially

octrees or octonion trees?

Octtree is exactly the same but in 3d. Instead of 4 leaves in node you have 8.

relatable

You'd use octrees for that

The thing about Bound and Sweep is that it's only O(n) *after* the bounds have been sorted. Nearly all known sorting algorithms are O(nlogn), which quad trees are too, so while Bound and Sweep is a lot faster than a brute force approach (where you test every possible collision) would be, it's still slower than most spatial hashing algorithms, including the one featured in this video. I actually just spent some time implementing and testing in my collision test bench, and while it's competitive at <100 points, it falls off rapidly at 1000+.

@@ClokworkGremlin use O(n) sorting algorithm, like radix binary tree sort, you can add and remove items from the tree super fast without a new sort also, I just also tested that sorting algorithm in java against Arrays.sort, holds up until like millions of elements, because of system sort native optimizations.

@@ClokworkGremlin yes you can modify the axis sort tree just like with 2d quad tree and 3d octree.

@@ClokworkGremlin in other words, you can separate the axes for the limit values completely, ie separately check x, y and z axes limit intersections. and use linear time sort. ironically radix binary tree sort is 1D binary tree.

Yes, if the cells overlap by 2 object radiuses, then collisions can be easily handled between several cells.

@@rustwithoutrust 🌌🧠

When I did my test implementation, I made it so that cells aren't split in half, they're split based on the bounds of the objects within them, so almost all cells overlap, but if two objects might be colliding then they're guaranteed to both be in at least one cell.

it's like that with a lot of data structures, like spatial hash maps too.

you're right

that's C

@@rustwithoutrust Indeed. C wasn't what I had in mind from Rust Without Rust!

same, lmao

kekw

@@DanDeebster Why not? It's right in the name: *without* Rust!

I created map applications in my previous job. Having kilometres/miles of road polygons, buildings, forests, rivers, lakes, cables, lamp posts, side walks etc. a large region could consist of 5 gigabytes of vector data and having the quad trees in files with indexes to the vectors we could zoom anywhere on the map and draw the area in just 20ms. Large vectors would be clipped before drawing to optimise drawing speed. Also large polygons or lines would be stored on upper levels and these span multiple quads.

Even for uniformly distributed objects, splitting the test area reduces the total number of collision checks which need to be made, so it does help a lot. Where quad trees should be most helpful is when you have irregularly distributed objects, which allows some of the branches to just be ignored entirely.

kul-sudo/quadtrees on GitHub. Have it done with gravity.

real

it's actually all a scam

real

pos.x / cell width, pos.y / cell height is the hash function here for getting the cell by the position. But many seem to criticize me for this terminology.

​@@rustwithoutrust You're only listing inputs without explaining the concept you titled this video.