ux

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 :)

> Thanks for putting this together.

I'm glad it reaches an audience :)

> 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.

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.

Thanks, I'll look into this. BTW, your 2nd shadertoy link is off (maybe it's private? Edit: seems you fixed it, thanks)

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.

Thanks!

Is this tutorial kind of abandoned? There are many teased chapters that never seem to have materialized somehow.

This is not equivalent; the `a` in `c.r+=w*a` is different, you need the original untouched w. The mountain looses its crack with your version.

But! You can save 1 char by replacing w with a:

    g -= a*=w,
    c += a*d*9.+...
    a = min(...),
    c.r += w*a*a*.2,

So thank you for the idea!