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Early preview of "The Continuity of Splines" (Patreon)

Published:
2022-09-20 21:53:32
Edited:
2022-09-20 22:10:44
Imported:
2024-07
Tags:

Content

Hey everyone!!

As some of you know, I've been working on a sequel to the bézier video for quite some time, and, it's finally, almost finished!

Note that the video is for you patreon supporters only, please do not share it!

I'd love to hear some feedback on things you feel is missing, or if something was particularly unclear to you! I won't be able to do things like add more splines, so I'm mostly looking for feedback on clarity, both in concepts, content and visuals

Some things to keep in mind for this early version:
• audio quality is pretty bad, this voiceover is temporary
• no music yet
• outro and credits missing
• some janky animation and voiceover timings

This video has been by far one of my biggest undertakings, hopefully it will have been worth the wait 💖

Oh, and, here's the script! if you want to comment on it or see my planned todo markers:

https://acegikmo.notion.site/Script-The-Continuity-of-Splines-ba5c295d20e54bb0a7e34320763188bf 

Thank you all again for your continued support! I very much appreciate it, it's what allows me to explore and share all these concept with the world ❤

// Freya

Files

[Patreon supporters only!] The Continuity of Splines (Draft)

please do not share this early access video! this is for patreon supporters only ❤

Comments

David Rector

Your earlier videos on Bezier curves helped me a lot when I was writing a spline editor so I could simulate arbitrarily shaped mechanical cams. Thanks for providing this great content.

Joseph Heck

Hi Freya! Love the new video, it's wonderful! Two pieces stood out that confused me. You jumped in to talking about control points early on, but I wasn't sure what was a control point and what wasn't at first. I've seen enough for it to make sense over time, but it was a bit of lingering confusion up front, so if there's a way to describe what you mean there, it might help a bit. The second was near the end, when you introduced the name of the Uniform Cubic B-Spline, and you made a mention of "how it applied to all the previous splines" - but I totally didn't get what you meant by it applied to the previous splines. Hope that helps as you're polishing. Love the work, thank you!

David Mclean

This video is absolutely wonderful. I’m a new subscriber so this is my first video. And I’ve never seen Math in such a Beautiful and logical way better. I’m up in bed at midnight wanting to see more.

Freyja Domville

I would suggest linking to the "Beauty of Beziér Curves" video for the first chapter (unless you're planning to have this supercede that). It might make the video faster to get into the point if you say "For more information on the basics, then please look at the video in the annotation, but here are a couple bits of extra information that might make them make even more sense". Similarly I think you'd benefit from referring to the previous discussion on equal distribution for the basics, but then saying "in the matrix form, the differentiation process can be simplified further and expresses continuity pretty nicely". Otherwise, seems good!

Freya Holmér
>>92037881

thank you! I should mention the bezier video, but I do want to make sure this video works on its own, so I think I'll keep those parts in anyway, what do you mean by "in the previous discuss on equal distribution"?

Freya Holmér
>>92021661

thanks for the feedback! yeah I have a note in my script about how I introduce the term control point without explaining it, I just use point and control point interchangeably, which is probably bad. I was considering adding an "anatomy of a spline" visual that shows all these terms in context. maybe I can do that at the start of the bezier spline section as for uniform cubic, I should make it more clear what I mean yeah. I do explain it later but it's probably more confusing than helpful to mention it earlier, so maybe I'll just omit that part!

Freyja Domville

"anyway, what do you mean by "in the previous discuss on equal distribution"?" I wasn't that awake when I wrote this, but this refers to the use of differentiation in the previous video. See: https://youtu.be/aVwxzDHniEw?t=1026 specifically for what I mean by this. Apologies for the confusion!

Winston

This is a work of art, just like the previous bezier video! I really had to laugh a bit at the first visualization of polynomial coefficients with all the vectors adding up, that really would be a bit hard to wrap your head around. The other way to think of them with the four vectors was very neat and made it much easier to think about them. Overall everything was explained very well. I liked how the chapters were smoothly leading into each other, you could even say they were continuous!

Daniel Klug

I thought it was very striking when you first went into 3d with the spline visualization. Awesome work! One thing that I wasn't sure about was what 'velocity' meant in terms of the curve. It wasn't clear to me what was causing that speed up/slow down while traversing the curve. I think that section could use a little more explanation.

s1mon

Lots of great stuff in here. Very happy to get to see this in advance of public release. I feel like some of the comments on lack of local control for Béziers are a bit overblown. For many high end (Class-A) surfacing people, everything is based on Béziers of degree 3, 5, and 7. (e.g. these are default choices in Alias). I routinely use much higher degrees in ID surfacing, precisely because the curves are C/Ginf internally. One thing you skip over is how deCasteljau allows you to increase the degree and have precisely the same curve, and how as this happens, the control polygon approaches the curve as the degree approaches infinity. This makes the non-endpoints of the control polygon less mysterious. Yes they only have so much influence, but if you aren't pathological in your placement of them, they serve their purpose. I do get a bit baffled by the idea that for a series of degree-3 Béziers, the tangents need to be mirrored to be C1. Isn't there some scale factor as well? Can't I take something where the second curve is C1 with mirrored tangents, and then split that second curve (using deCasteljau) and still have something which is C1? BTW, happy to see the cusp example with the asterisk on the C1->G1, C2->G2 etc discussion.

Freya Holmér
>>92076847

Thanks for the feedback! As for using béziers in surface modeling, the C infinity internally across a single segment applies to all splines, so that's at least not a bézier specific trait. I've limited the scope to this video to uniform cubics, apart from the bézier intro, and so I don't want to go too far into the higher degree ones, because I worry it might be confusing and feel like too much information for one video (and too much work for me to add after the fact!). This is why I don't talk about the continuity characteristics of higher degree bézier joins, or degree elevation As for mirrored tangents being required for C1 - it is required, but this is specifically for uniform cubic béziers! Curve splitting can be done perfectly continuously if you use non-uniform béziers, since you then have control over the speed, if I'm not mistaken. Non-uniform splines in general is another whole topic I didn't get into, but, perhaps in a future video! My initial idea was to work all the way from lerp to NURBS, but, the video was getting overwhelmingly large and difficult to finish as is, so, another day! anyway, glad you liked it otherwise!

Klystron

Came to say the video was fantastic, very informative. Thanks for your hard work! I think I spotted a VO error (but not sure as English is not my first language) - it’s the pronunciation of “oscillating”, the C should be silent, right?

Freya Holmér
>>92139610

ahah, I now have the opposite problem as in the bézier video. The word is "osculating", which is pronounced with a hard c, which is a different word than "oscillating" which does have a soft c, but I mispronounced it in the bézier video, and in this video it's correctly pronounced!

Klystron
>>92139610

Oh no 😂 but on the upside, you’re also teaching us English math terms!

Tom Finnigan
>>92076847

I think for Class-A surfacing high degree is nice because it gives you more direct control over the reflections and you can get higher-continuity blends. The lack of local control doesn't really matter since you're trying to create smooth, continuous surfaces. But there are lots of other situations where splines are used where you're creating more intricate curves, and it'd be annoying to not have local control, such as creating fonts, camera paths, or animation curves

Ruby Quail

as an Industrial designer who has spent far too much time crying over NURBS in rhino, this is wonderful!