from Hacker News

The Continuity of Splines [video]

by mcorcuera on 12/16/22, 1:33 PM with 41 comments

  • by s1mon on 12/17/22, 7:24 AM

    I’ve been following Freya’s work [0] for a while. She works in the game industry working with Unity, hosts a bunch of Discord channels, and live streams about game math and shaders. This video is relatively long, but it’s one year in the making. If you ever wanted to understand a bit more about Béziers vs B-Splines and G2 vs C2, this is great place to start.

    PS. I would also highly recommend these sources which have been covered before on HN:

    Curves and Surfaces by Bartosz Ciechanowski [1]

    A Primer on Bézier Curves by Pomax [2]

    [0] https://acegikmo.com/

    [1] https://ciechanow.ski/curves-and-surfaces/

    [2] https://pomax.github.io/bezierinfo/

  • by Yenrabbit on 12/17/22, 9:09 AM

    Truly a masterpiece of technical communication! Mind blowing to think about how much work went into this video.
  • by Garlef on 12/17/22, 2:16 PM

    If all of maths was taught this way, we'd be looking at a bright future (in terms of education).
  • by zengid on 12/17/22, 8:38 PM

    Is there any general rule that systems that have 'continuity' also having sensitivity to initial conditions? I can't help but think of chaos theory[0] when Freya describes the C2 continuous spline in the section on "Cascading Loss of Control" [1], and how it "yeets off to fucking wherever" (which is a great line).

    [0] https://en.wikipedia.org/wiki/Chaos_theory

    [1] https://www.youtube.com/watch?v=jvPPXbo87ds&t=1308s

  • by stkdump on 12/17/22, 10:24 AM

    I think the secret to get the C2 splines that pass through the control points right is to not just increase the degree but also add two more points, i.e. not 4 but 6 segments.
  • by acegikmo on 12/18/22, 2:37 PM

    I'm really happy yall like it!
  • by jimmySixDOF on 12/17/22, 10:04 AM

    Speaking about this taking her a year to produce, there was a new Unity release last week that effectively preempted her own work on a Spline tool for the asset store where her previous work is quite popular.
  • by dyml on 12/17/22, 8:47 PM

    I watched the entire video and I absolutely loved it. Great work, good explanation and very elegantly and beautifully done.
  • by adriancarrieres on 12/17/22, 8:14 AM

    Super cool video, it explains a lot of stuff in a nice visual way
  • by chasing on 12/17/22, 6:19 PM

    This video is fucking amazing.
  • by heywhatupboys on 12/17/22, 11:16 AM

    this is almost a 1:1 copy of the Bezier curve video posted some months ago. how is this video getting attention? Even has the same graphics...