What if more people could easily create content like this?

Reminds me of this one, a lovely visualisation of how the math works:

yeah I’ve been dreaming of software that can make this easier! Basically a toolkit for giving more dynamic & computationally informed presentations

Holy…! This is mind-blowing. 🤯

• How was this video made?

🔨 Created in the Unity game engine

⭕ Using Shapes, my vector graphics plugin ❱ https://u3d.as/1W37

📈 Using Mathfs, my math library ❱ https://github.com/FreyaHolmer/Mathfs

...along with a bunch of hacky, partially broken, procedural animation tools I made specifically for this video

manim is a good first step in that direction but the context switch between code and animation is not very FoC-y https://3b1b.github.io/manim/

So let's say Freya wants to do a new video like this, a follow-up covering other curve types — hermite, catmul-rom, b-splines, etc. What does an FoC tool capable of creating animations with arbitrary curve formulations look like?

Honestly this seems pretty tailor made for flash.

ya live ‘coding’ animation stuff

@ibdknox — Not a bad thought. Perhaps, if you had more control over shape tweens — say, richer ways to add hints or control how the intermediate motion unfolded. Not to mention that if your source and dest shapes had different vertex counts, you'd get a big explosion of self-intersecting garbage because the vertex numbering was very... unstable. Shape tweens were so unreliable that we ended up doing all our fancy curve stuff using ActionScript and the canvas-like APIs. At which point, Unity + a decent vector shape library (like the one Freya made) is probably no worse than Flash in practice. But in theory.. yeah, something Flash-like with a little more forgiving / robust toolset could be a nice improvement over Unity. You're still in a compile->run workflow, but that's mostly orthogonal.

yeah, the compile -> run thing is just an implementation accident, it isn’t strictly needed. I think flash was very close to what you want for most of these kinds of things, it just needed a better implementation/libs (e.g. the vector issues you mention).

Though.. you're still beholden to the fact that the underlying vector lib will have a curve type that it uses — probably cubic bezier. If you want a different curve type... what's the better way to get that than "I just write my own geom algos and rasterizer"

a good graphics lib would make custom curves possible

To be more specific — I think the part I'm interested in is: how would you define a custom curve in an FoC way. As opposed to, how would you use a choice of existing curve algo (from a lib) in an FoC dynamic drawing tool.

I’ve never been motivated to make my own curve algo - my assumption is that you’d really just want to write equations. Is that what you’re thinking? Or is it that you want to visually describe the equations?

@Ivan Reese have you seen this? https://bivector.net/

I have not, but this looks extremely up my alley. The geom in Hest is mostly typical game stuff (ie cross product) with a tiny splash of Clifford, limited only by my lack of experience with the latter.

Oh! @Mariano Guerra I'm going to have to follow up on that! I have two videos I like to share to introduce people to Geometric Algebra: and . I probably found them posted here on FoC in the first place.

I cannot help but think that Inigo Quilez’s graphic animations (which are SDF bassed) and where you write the SDF as a function of time could be a good starting point for this kind of animation. Maybe compose multiple shadertoys via some sort of timeline representation?