Cloth

Brilliant !

If you aren't ready for it in 3d, do it in 2d.

There are a few algorithms like some cloth sims based on particle positions and springs, which can be coded easily, but that was misleading to me when trying to improve, I had to dig a lot more into physics and numerical analysis then mapping the problem to code, which can end up clunky and with a lot of magic numbers.

You didn't specifically ask about game development, but that domain is where the majority of graphics, mathematics, lighting, physics, etc, knowledge is distributed. And it can be difficult to find information solely about (e.g.) cloth simulation and other niche topics without it being coupled into game development resources.

I happened to read https://alextardif.com/LearningGraphics.html today, which might give you some pointers in various directions. https://learnopengl.com/ gets a consistently good rap, even today when there are newer APIs like Vulkan, Metal and DX12. Consider the API as 5% of the problem to solve though (less tbh, though Vulkan is proving even heavier than I was warned).

If you don't want to learn C/C++, I understand there's a large community around WebGL, so finding their subreddits and other forums could be a good starting point too.

However, again, the API and platform is really just a wrapper around the actual physics simulation (the impressive/novel part).

(Source: I'm a web dev/gradle/java developer who is once again building a game engine in their spare time after a previous attempt many years ago)

It's only a few lines of code, and it's still my "hello world" for any interactive programming system or gamedev library.

Make the ball respond to keyboard ... that's velocity! But it's too jerky, so we wanna smooth it out... that's acceleration! Make it fall, that's gravity! (Constant acceleration in one direction.) Ball keeps moving endlessly is weird, let's make it slow down a tiny bit each frame... hey look, that's friction!

The next year in school we learned the math for most of the same stuff (velocity, acceleration, gravity, friction) and it was pretty straightforward to me (even though I still suck at math) because I already had the "instantaneous" (frame by frame) model built up from making it in code, so I could sorta-kinda translate that to the continuous (formula-based) perspective.

I made a cloth thingy like this a few years ago after watching a video about it. The actual cloth sim code is like, 3 lines iirc.

It basically just jiggles the system a few times based on stuff being too close or too far away. So the idea is that the movement of one part transfers to all the others.

I'm a bit confused now since I saw some that have hard limits on the segment length (e.g. chain sims), whereas this one seems to be more stretchy (spring based?)

The neat thing about this stuff is that if you aren't going for physical accuracy (or efficiency), you can half-ass it by just guessing and fiddling with the code or the math. E.g. I still don't get how springs actually work, but my own terrible guess works well enough to be amusing!

[0] Whereas after repeated attempts over decades, web never really clicked for me. Well, it did when PHP was popular... I can still make stuff with PHP and vanilla JS, hahaha.

Web dev (and not just in java) is dominated by "component integration" concerns, containing lots of structure but little content. Computation is delegated to libraries, and the problems more about complexity of integration (at build time) scaled distributed systems (at runtime). In contrast, writing a simulation is computationally intensive, so most of the code is content. It's homogenous where web dev is heterogenous. The problems are entirely constrained by single process performance within a time budget determined by fps.

All that means is that you can focus on one runtime. I suggest the browser, since it solves the distribution problem. Ganja[1] is perhaps the ultimate "content, not structure" simulation project. It's very strange, and lies unmaintained because it's impenetrable. Yet it works. A bit more structured is D3 who's authors have written cutting edge visulation/layout algorithms for you, for example in support of force directed graphs[2]. A more friendly way to get started would be with some variant of Processing[3], which started as a Java thing and then got ported around, including to Python and JavaScript. A word of warning: something like cloth simulation is to a game engine what a single cell is to a mouse. Game engines are huge, in other words, and again you won't be writing simulations, lots of (internal) integrations.

1 - https://github.com/enkimute/ganja.js/blob/master/ganja.js

2 - https://github.com/d3/d3-force/tree/main/src

3 - https://processing.org/

In this case it’s basic “verlet” integration, which involves updating 2d vectors forming the grid based on their current and previous position, and constraining them to a certain distance from their immediate neighbours. Draw lines between them and you have a cloth. I first came across it because I was fascinated by physics simulation and it was one of the simplest things to implement. A lot of bang for your buck in terms of results. It gets far more complicated from there.

One thing they didn't emphasize is that cloth has a functional purpose as well. It obscures the shape of the enemy so that it's more difficult to distinguish its model. In a game with very precise hit boxes—arguably the most innovative aspect of FromSoft games—and melee combat being a core gameplay element, free-flowing cloth makes it difficult to gauge how close to the enemy you need to position your character in order to make contact, and how far away you should be to avoid getting hit. Adding this to unpredictable movement and attack patterns adds even more challenge and makes every encounter unique.

This is actually the same quality cloth has in real life as well. An enemy in a robe or cloak is much more intimidating and challenging.

I don't enjoy their games because of the gameplay loop, but they're really some of the best designed video games ever made.

It's very simple to implement a basic setup like this, and I agree that the results are super cool.

From what I understand it's not just floating point errors, but due to the nature of approximating continues function as simple discrete steps. Linked wikipedia article has a graph demonstrating that with large steps the error accumulates way before floating point precision is a concern.

There are different numeric integration techniques with different tradeoffs. Stuff like Eulers method, Verlet, Runge-Kutte. In some of them overall energy tends to accumulate in others it gets lost both of which is wrong. Some of the more complex ones tend to behave a bit better, but then you get into the problem whether gains from each individual step being more complex outweighs what you would get from running more iterations of simpler/faster algorithm.

It's not only the rounding error, it's also quantisation of time and other minor errors coming from the mathematical model itself.

If the error is on the damping side, you get the real life effect of motion eventually stopping due to energy dissipation. If it's on the acceleration side you get a runaway simulation.

https://arxiv.org/abs/2407.01361