Thank you for the kind words, and you're on point with "poetry using math".
I started 2-3 months ago or so doing this stuff, so don't be too intimidated to start. Especially with the two articles (Red Alp and this one), it should make it more accessible, hopefully :)
> Only critique is.. if you're sharing to teach, your compact/one line [460] char GLSL code is a poor delivery mechanism.
Understandable. Though, the demos are here to illustrate "what you can do with the trick I'm sharing". It's like, I'm teaching you how to do watercolor, and illustrate it with some paintings you won't be able to perform just with that knowledge. They're meant to inspire you to create. You're not looking at a tutorial, you're looking at art.
> And GLSL syntax looks a bit tedious to be honest, but I'd love to dive in.
With the vectorization everywhere, it's surprisingly convenient given how simple the syntax is. I personally just miss some sinpi/cospi/etc, and/or a PI and TAU constant.
Thank you! Do we have a guarantee that these subcurves are solvable with Newton's method? The approach with derivatives has this because we know there is one crossing, and also clipping them to the zero-derivatives makes sure there won't be multiple curve "pits".
What you described in your first message seemed similar to the approach used in the degree N root solving algorithm by Cem Yuksel; splitting the curve in simpler segments, then bisect into them. I'd be happy to explore what you suggested, but I'm not mathematically literate, so I'll be honest with you; what you're saying here is complete gibberish to me, and it's very hard to follow your point. It will take me weeks to figure out your suggestion and make a call as to whether it's actually simpler or more performant than what is proposed in the article.
I'm interested in the approach you're describing but it's hard to follow a comment in the margin. Is there a paper or an implementation example somewhere?
Finding the sign of the distance has been extremely challenging to me in many ways, so I'm very curious about the approach you're presenting. The snippet you shared has a "a³-bcd ≤ 0" formula which is all I get without more context. Can you elaborate on it or provide resources?
The winding number logic is usually super involved, especially when multiple sub-shapes start overlap and subtracting each other. Is this covered or orthogonal to what you are talking about?
Ah nice for noticing d!=0 is d>0. Not sure how I missed the multiplication to get rid of the vector form; I guess I was too obsessed with the x-x trick...
I added your changes to the Shadertoy version with your HN nickname. I'll integrate it to the original later.
Yeah. If you want implicit conversion, you need to specify a constructor like float(cond), but that would be longer than the ternary form. I thought about using a vec3() but vec3(...).x is still too long and using the vec3 directly doesn't look viable. Declaring a bool adds more characters as well. There is also step() giving the same number of chars: a=step(.001,h), but it's not more optimal: https://iquilezles.org/articles/gpuconditionals/
If you see a way to make it shorter, feel free to share :)
Ah, someone reported this to me today, but I must admit I have no idea how to address the issue. Currently the canvas animations are stopped when out of context, but yeah they have to be loaded.
Hey, thank you, that's a nice one. I added the change to the Shadertoy version with your credit. I will add a note/update on the blog and demo page later. Thanks again :)
Hehe, thanks. The thing is, it could hardly have been prerecorded animations :D
I don't know if you tried before, but compressing noise is particularly hard, so 16 videos would have been quite too much of bandwidth. The total size of the shaders is something around 70kB (not minimized) for endless lossless videos, and since I had to write them anyway if I were doing records of them, it was really a no-brainer to embed them to be honest.
> Have any of you ever gotten lost tweaking fade functions to get that perfect wave-like look?
You cannot use anything for the fade function, because you likely want the derivative (and potentially the second derivative) to be 0. See https://gist.github.com/KdotJPG/417d62708c76d53972f006cb906f... for making different ones. I personally never tried anything else than the hermite and the quintic.
I started 2-3 months ago or so doing this stuff, so don't be too intimidated to start. Especially with the two articles (Red Alp and this one), it should make it more accessible, hopefully :)