Why are splines?
January 7, 2023 6:44 PM Subscribe
why are splines? well my god I have good news for you, here's why splines! Super high quality animation and narration makes it so clear, easily on a par with 3Blue1Brown. Freya Holmér has a series of explainers about video game graphics, creates cool math visualizations, and streams coding on twitch.
If you watched the whole video, stay for the credits, over which she discusses her year-long experience making the video, and it's surprisingly engaging in itself.
If you watched the whole video, stay for the credits, over which she discusses her year-long experience making the video, and it's surprisingly engaging in itself.
I'm endlessly fascinated with well-animated math videos, this is great, thank you!
Still working through it, but this post would be diminished without reticulating splines.
posted by curious nu at 7:04 PM on January 7, 2023 [21 favorites]
Still working through it, but this post would be diminished without reticulating splines.
posted by curious nu at 7:04 PM on January 7, 2023 [21 favorites]
This is a great explainer. I know 3D art, but I don't know math, so this breakdown is utterly fascinating for me.
I knew there must be a reason for all those arbitrary rules about curves and tangents, but it's really satisfying to see the math framework laid out so clearly. The graphics and animation help a lot, it's really hard for me to digest equations and abstract formulas as strings of letters and numbers.
Thanks for the post, hynogogue.
posted by ishmael at 7:14 PM on January 7, 2023 [1 favorite]
I knew there must be a reason for all those arbitrary rules about curves and tangents, but it's really satisfying to see the math framework laid out so clearly. The graphics and animation help a lot, it's really hard for me to digest equations and abstract formulas as strings of letters and numbers.
Thanks for the post, hynogogue.
posted by ishmael at 7:14 PM on January 7, 2023 [1 favorite]
Still working through it, but this post would be diminished without reticulating splines.
I feel so seen
posted by panama joe at 7:22 PM on January 7, 2023 [7 favorites]
I feel so seen
posted by panama joe at 7:22 PM on January 7, 2023 [7 favorites]
Are you trying to tell me that these splines are ticulating again?
posted by Etrigan at 7:52 PM on January 7, 2023 [8 favorites]
posted by Etrigan at 7:52 PM on January 7, 2023 [8 favorites]
Talking about splines on a Saturday night? Get a life, NURBS!
posted by credulous at 8:38 PM on January 7, 2023 [13 favorites]
posted by credulous at 8:38 PM on January 7, 2023 [13 favorites]
But nobody ever asks, how are splines?
posted by Greg_Ace at 9:16 PM on January 7, 2023 [9 favorites]
posted by Greg_Ace at 9:16 PM on January 7, 2023 [9 favorites]
Fascinating! Nelson, now I wonder if "get your ducks in a row" comes from the ducks/whales of the physical splines.
posted by CompanionCube at 12:24 AM on January 8, 2023 [8 favorites]
posted by CompanionCube at 12:24 AM on January 8, 2023 [8 favorites]
More videos need the line "yeets off to fucking wherever".
posted by vasi at 3:39 AM on January 8, 2023 [7 favorites]
posted by vasi at 3:39 AM on January 8, 2023 [7 favorites]
The math goes a bit past my knowledge comfort zone but because the visualizations are so good, I think I understood the bulk of what was being explained. Terrific work.
posted by gwint at 5:29 AM on January 8, 2023 [1 favorite]
posted by gwint at 5:29 AM on January 8, 2023 [1 favorite]
Oh my gosh, at 23:37, with CC on:
"Our beloved cubic bézier has betrayed us. :("
Emoji in the CC! I've never seen that. That's wonderful.
posted by curious nu at 9:30 AM on January 8, 2023 [3 favorites]
"Our beloved cubic bézier has betrayed us. :("
Emoji in the CC! I've never seen that. That's wonderful.
posted by curious nu at 9:30 AM on January 8, 2023 [3 favorites]
This video is amazingly good. I can't even imagine how much work must have gone into making all the animations.
Years ago I did physics simulation and control theory stuff where continuity mattered, and even needed to figure out how to fit C2 splines in quaternion space, so this is stuff that I vaguely sort-of knew bits of, but now it actually fits together and makes sense.
posted by automatronic at 9:51 AM on January 8, 2023 [1 favorite]
Years ago I did physics simulation and control theory stuff where continuity mattered, and even needed to figure out how to fit C2 splines in quaternion space, so this is stuff that I vaguely sort-of knew bits of, but now it actually fits together and makes sense.
posted by automatronic at 9:51 AM on January 8, 2023 [1 favorite]
B-spline was extremely cool to see. Immediately thought of (one of the) ways we we design roadway curves -- which makes sense, since continuous changes in velocity and acceleration are incredibly important!
MATH
posted by curious nu at 10:32 AM on January 8, 2023 [3 favorites]
MATH
posted by curious nu at 10:32 AM on January 8, 2023 [3 favorites]
Started this all jaded because I thought I knew everything about the topic, turns out that I was totally ignorant of several various types of splines and even if the fact that C and G continuity were different concepts! A+ would watch again.
posted by q*ben at 3:01 PM on January 8, 2023 [1 favorite]
posted by q*ben at 3:01 PM on January 8, 2023 [1 favorite]
Roadway curves are actually just circular arc segments of constant radius. The vertical profiles are parabolic segments. This ensures constant acceleration through the curves and when cresting hills. Cite: linked article and experience as a land surveyor laying out roads.
You’d think that a smoother transition would be better (eliminating “jerk”) but it’s actually really dangerous for drivers to have to deal with increasing or decreasing curvature while turning. However I would not be at all surprised if railroads use smoother transitions. I’d be surprised if they didn’t!
Anyway this is a really great video and some of her other videos touch on more elementary (and more advanced) topics. I was sure I’d seen this on the blue before but apparently not!
posted by sjswitzer at 4:51 PM on January 8, 2023
You’d think that a smoother transition would be better (eliminating “jerk”) but it’s actually really dangerous for drivers to have to deal with increasing or decreasing curvature while turning. However I would not be at all surprised if railroads use smoother transitions. I’d be surprised if they didn’t!
Anyway this is a really great video and some of her other videos touch on more elementary (and more advanced) topics. I was sure I’d seen this on the blue before but apparently not!
posted by sjswitzer at 4:51 PM on January 8, 2023
Roadway curves are actually just circular arc segments of constant radius. The vertical profiles are parabolic segments. This ensures constant acceleration through the curves and when cresting hills. Cite: linked article and experience as a land surveyor laying out roads.
It's interesting with horizontal offsets, though, yeah? Yes, circular arc segments, but - in many cases - controlled by a point outside of the curve, which was the whole thing with the B-splines. That diagram immediately made me think of a whooole lot of transportation problems I worked through as part of the PE. (I live in a very grid-y city and the only new roads we ever make are short 1-block connections, so it's theoretical for me in any case)
posted by curious nu at 5:50 PM on January 8, 2023
It's interesting with horizontal offsets, though, yeah? Yes, circular arc segments, but - in many cases - controlled by a point outside of the curve, which was the whole thing with the B-splines. That diagram immediately made me think of a whooole lot of transportation problems I worked through as part of the PE. (I live in a very grid-y city and the only new roads we ever make are short 1-block connections, so it's theoretical for me in any case)
posted by curious nu at 5:50 PM on January 8, 2023
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posted by Nelson at 6:56 PM on January 7, 2023 [26 favorites]