Lerp smoothing is broken

Freya Holmér explains why naive linear interpolation smoothing fails with variable frame rates and how to implement frame-rate independent exponential decay.

a journey through decay and delta time (I had to learn differential equations for this oh boy) Slides: patreon.com/posts/105228270 for my patreon supporters 💞 The slides are much nicer in person!! like, the AV team on site had me lower the refresh rate on my laptop because we couldn't get it to work otherwise, and on top of that, video compression on youtube is now ruining everything as usual ;-; Anyway, first, a big thanks to the organizers at Guadalindie for inviting me and letting me publish the recording! Second - I've been working on a blog post about lerp smoothing in the background, this talk is like a distilled version of half of that yet-to-be-published blog, so keep an eye out for that if you want to dig deeper! There's a whole side of this topic involving approximations to lerp smoothing, but it kind of exploded into a whole thing, which would take up another hour on top of what I already covered, so I couldn't fit it in! Lastly - if you want to stay in touch and in the know whenever I release new videos, blog posts or unity plugins, be sure to sign up to my mailing list! ✉️ Mailing list ❱ acegikmo.substack.com/ Recorded at Guadalindie 2024, May 3rd Timestamps: 00:00 Start 00:20 How to lerp smooth 02:07 The problem of framerate dependence 03:49 Linear motion 10:55 What is lerp? 12:32 The non-linear behavior of lerp smoothing 18:40 Finding continuity 20:23 Unraveling recursion 28:51 Going framerate independent 40:00 Half-Life 47:21 Summary 49:37 tldr (the useful part you want to copy/paste) 51:00 Q: How important is experimenting with math? 54:30 Bonus slide: Differential calculus 55:33 Bonus slide: Spring physics 56:39 Outro 💖 Patreon ❱ patreon.com/acegikmo 🐦 Twitter ❱ twitter.com/FreyaHolmer 📺 Twitch ❱ twitch.tv/acegikmo 💬 Discord ❱ discord.gg/v5VWuga 🌸 Instagram ❱ instagram.com/freya_holmer