Freya Holmér patreon

New video: The Continuity of Splines

🕑 Added 2022-12-08 10:36:35 +0000 UTC

Comments

Doug

Thanks Freya, you are my hero.

Freya Holmér

So, cubic hermite splines are only C1 continuous, which means acceleration and jolt are discontinuous at control points. They do auto-calculate whatever acceleration and jolt is required to meet the constraints of the control points, but they don't work to minimize jolt none of the splines I covered are specifically designed to minimize jolt, which is a bit of a different question altogether. It might be the case that some of them do by accident, but to find an optimal path to minimize energy (or jolt) is something that's more in the realm of path planning and energy optimization, rather than pure splines. my guess would be that the B-spline does the best job at minimizing it, but even that one is still not continuous in jolt across control points, only in acceleration, unless you constrain the control points further with optimization algorithms

Doug

Freya, I hope you can clear up a confusion I have. At 40:24, when describing a Hermite spline, you say “It effectively auto-calculates the acceleration and jolt to make this curve”. At 42:44, still describing a Hermite spline, you say “In other words, while this spline doesn't meet the criteria for C2 continuity, it is always C1”. At 59:49, you give an example of a non-uniform single dimension over time Hermite spline. This non-uniform single dimension over time Hermite spline is exactly what I need to control each axis of a bridge crane in a factory setting (real life). However, it is critical that I account for Jerk. In the real world a crane experiencing Jerk is a bad thing. Your first statement makes me hopeful that Jerk will become non-existent, but your second statement makes me doubt that assumption. Can you please clarify or expand on this?

Freya Holmér

thank you! hope your head is still intact

Merijn Vogel

Watching your talk at the Dutch Game Day 2023. My head only exploded a few times 🤣. Very nice presentation!

Freya Holmér

thank you! and yes, the music was made by Jazz Mickle (https://queenjazz.bandcamp.com/), specifically for this video :) Except the bézier curve section track, which is the same as from the bézier video (although she made that one as well)