This video accompanies the paper Chris Yu, Henrik Schumacher, Keenan Crane "Repulsive Curves" ACM Transactions on Graphics (2021) For more information, see www.cs.cmu.edu/...
Yeah me too, I also wanted to ask: are these amazing visualizations, shown in the video, part of the software tools 🛠️ shared on github? Or can someone point me to the tools used to build such awesome visual effects?
How would you apply this untangling algorithm in real life? Any ideas? The demon knot earbuds example was funny, but I’m thinking more along the lines of proteins.
Yeah, this is a super interesting question: what sequence of Reidemeister moves is effectively made by the flow, especially versus other approaches you might use to simplify a knot diagram? There are a couple challenges here. First of all, Reidemeister moves are operations on a 2D knot diagram, whereas the flow operates directly on a 3D embedding of the curve. Of course, you can project from 3D into 2D, but each projection will yield a different set of moves. Is there a canonical projection? Some invariant (in terms of the dynamics of Reidemeister moves) among all projections? Etc. The other issue is detecting the moves, given a projection. This shouldn't be too hard to do (since in this case the geometry is just piecewise linear), basically a fun little exercise in computational geometry. :-)
@@keenancrane ahh. This is great. It hadnt occurred to me that the projections of the surface would also effect the Reidemeister move that it looked like. Thanks!
Кино
some of these curves are hard to look at, but i wouldn’t call them repulsive
They should have named it Repelling Curves.
I know right don't hurt their feelings
that multiagent path planning would look great in games
You could make a realistic looking brain with that.
Wow these are beautiful visualisations - and also, very clear and well explained.
So cool!!!
3:58 And I never expected this algorithm could be related to ramen :)
Amazing! Love the visualizations.
Yeah me too, I also wanted to ask: are these amazing visualizations, shown in the video, part of the software tools 🛠️ shared on github? Or can someone point me to the tools used to build such awesome visual effects?
جميل ومبدع
شكرا!
2:22 O_O Tape worms!
ウサギ一番ラーメン笑
fascinating
Good stuff, gonna be very helpful.
What a wonderful work. Congratulations to you and your team. We follow your works excitingly.
So many examples, looks great!
witchcraft!
This is really cool. Fantastic work!
Very cool work!
Very cool results!
this is great!
How would you apply this untangling algorithm in real life? Any ideas? The demon knot earbuds example was funny, but I’m thinking more along the lines of proteins.
the earbuds joke had me cracking up
This is amazing! Good job!!
This is super interesting. For unknotting is it clear how to understand r*meister moves that it uses? I find this really fascinating.
Also one of your fields looks like sprinkles and now I need a donut version.
Yeah, this is a super interesting question: what sequence of Reidemeister moves is effectively made by the flow, especially versus other approaches you might use to simplify a knot diagram?
There are a couple challenges here. First of all, Reidemeister moves are operations on a 2D knot diagram, whereas the flow operates directly on a 3D embedding of the curve. Of course, you can project from 3D into 2D, but each projection will yield a different set of moves. Is there a canonical projection? Some invariant (in terms of the dynamics of Reidemeister moves) among all projections? Etc.
The other issue is detecting the moves, given a projection. This shouldn't be too hard to do (since in this case the geometry is just piecewise linear), basically a fun little exercise in computational geometry. :-)
@@keenancrane ahh. This is great. It hadnt occurred to me that the projections of the surface would also effect the Reidemeister move that it looked like. Thanks!