The Continuity of Splines

Anytime béziers are mentioned on HN, I feel compelled to share these absolutely incredible videos from Freya Holmér ▶ this video (73 minutes) link (24 minutes)

For me, it's Bézier curves --- Freya Holmér has a wonderful video on them: ▶ this video and I've been trying to read through _METAFONT: The Program_ and link and I keep wondering if I shouldn't just try scripting Inkscape.... I want to do a couple of different things, and not sure if they all fit in one project or no: - implement a single line font in my current project: link - implement a way to convert arbitrary curves into smooth arcs (for DXFs or G2/G3 arcs for G-code) - work up an interactive version of METAFONT/METAPOST which allows both programming and drawing

If splines/beziers are of any interest to you, I could not recommend these videos from Freya Holmer enough. ▶ this video link

I didn't really understand Bézier splines until I watched this excellent video [0] from Freya Holmér. It talks about various kinds of splines, and the various equations behind them. Explains the importance of the derivatives of splines (as other comments here have pointed out). [0]: ▶ this video

the splines yt video ( ▶ this video ) is (IMHO) one of the best educational videos on a programming topic, full stop.

If this paper is interesting to you, you may also be interested in this amazingly well done video on the continuation of splines. It isn't exactly the same thing, and delves into some deeper concepts, but I've watched it like 3 times over the last year. ▶ this video

Oh lovely, can't wait to give this a watch. Freya dives deep, and gives wonderful talks. Her video "The Continuity of Splines"[0] is my favorite watch of the past year. [0] ▶ this video

Another upvote for Freya Holmér's amazing video "The Continuity of Splines". She covers the insightful "reflection test" around the 28:05 mark: ▶ this video and actual "curvature combs" at 32:26. Finally, she covers the continuity of curvature combs that B-Splines exhibit around the 54:00 mark: ▶ this video

> I just need to find the perfect GUI toolkit which allows Bézier Curve representations in a way which clicks and makes sense to me, and suits my next project. Not a proper answer, but here is a very good video on splines: ▶ this video

I've been reading through a PDF on my Kindle Scribe which I downloaded from the original site --- it's a great overview, and most importantly, includes citations and references to the various papers where folks shared their research/progress. These days of course, one would just get _The Essentials of CAGD_ and similar texts, or read: link or watch: ▶ this video Highly recommended for anyone who wants an understanding of how modern CAD software came about. For my part, I have found it invaluable in working on my current project as described at: link

Obligatory video on splines: ▶ this video From what I've read, Apple rounded corners are using G^2 or G^3 geometric continuity to generate smoother curves. It's hard to tell which smoothing function this library uses since it looks like it's based on PNG masking.

A wonderful example of this is: The Continuity of Splines ▶ this video and The Beauty of Bézier Curves link by Freya Holmér link While not animated, I find: _Euclid's Elements_ (Joyce's Java Version) very helpful link Since my current project has pretty much devolved to putting a UI on various trigonometric functions and allowing the user to program them, I'd be very glad of other resources in this space (currently working through Hilbert's _Geometry and the Imagination_ and the book which matches link and just finished the _Make:Geometry/Trigonometry/Calculus_ series, and have had recommended Curves and Surfaces for CAGD: A Practical Guide by Gerald Farin)