Repulsive Curves

If you liked repulsive curves, you may also enjoy repulsive surfaces:<p><a href="https:&#x2F;&#x2F;www.cs.cmu.edu&#x2F;~kmcrane&#x2F;Projects&#x2F;RepulsiveSurfaces&#x2F;index.html" rel="nofollow">https:&#x2F;&#x2F;www.cs.cmu.edu&#x2F;~kmcrane&#x2F;Projects&#x2F;RepulsiveSurfaces&#x2F;i...</a><p>Deep dive into repulsive geometry here: <a href="https:&#x2F;&#x2F;youtu.be&#x2F;dtYGiCpzzbA" rel="nofollow">https:&#x2F;&#x2F;youtu.be&#x2F;dtYGiCpzzbA</a>

This is immediately useful for a <i>huge</i> number of practical real-world applications.<p>Make sure to watch the short explanatory video (and turn the sound <i>on</i>) -- here&#x27;s the direct link:<p><a href="https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=-uXFYpVumh4" rel="nofollow">https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=-uXFYpVumh4</a><p>The short video is great. The paper looks great (based on a very quick skim; this is an area in which the authors have far more expertise than me). The high-level explanations are great. The web page is great -- informative and to-the-point. Really impressive work!<p>--<p>EDIT: The senior author is here at <a href="https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=31134139" rel="nofollow">https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=31134139</a> -- his comment should probably be above mine. Please upvote it.

The video has some really interesting &#x2F; creative examples. Using this for path planning by treating paths as curves through space-time was particularly impressive.

Keenan Crane&#x27;s [1] lab has been putting out some top notch research in recent years.<p>In particular, their work on discrete differential geometry [2] is really worth diving into (and Mr Crane is a <i>really</i> good pedagogue).<p>[1] <a href="https:&#x2F;&#x2F;www.cs.cmu.edu&#x2F;~kmcrane&#x2F;" rel="nofollow">https:&#x2F;&#x2F;www.cs.cmu.edu&#x2F;~kmcrane&#x2F;</a><p>[2] <a href="https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=mas-PUA3OvA&amp;list=PL9_jI1bdZmz0hIrNCMQW1YmZysAiIYSSS" rel="nofollow">https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=mas-PUA3OvA&amp;list=PL9_jI1bdZm...</a>

I can think immediately of applications:<p>- bio engineering -- predicting (?) or designing (?) molecules that are large chains to perform some particular function<p>- coverage path planning -- sort of a &quot;roomba&quot; problem -- find a continuous path, through a space, that covers the space<p>- 3-D printing -- find the extrusion path that maximally covers some area or areas with high strength with a minimum amount of material

Keenan Crane simply makes the most beautiful papers out there

FWIW, Nathan Dunfield&#x27;s hand drawings are typically very difficult to improve upon.<p>This is an impressive paper. Thank you for sharing!

One of the insights here is using the “tangent point energy” as part of the repulsion loss function. If anyone’s used, or knows of, a python implementation of this TPE function then please lmk!

The graph layout example is really compelling.

Wow, imagine this could be very useful for a variety of logistics&#x2F;routing applications (IE train routing, assembly line optimization, self-driving cars). Perhaps this kind of stuff is in play there already and this just helps make it easier to visualize?<p>Lovely visualizations as well. Really makes it tangible.

This could work well for PCB trace routing optimization too? Handling multiple layers might be bit difficult, but maybe not insurmountable?

Hold on, wasn&#x27;t there a similar paper last year wrt non-intersecting shape&#x2F;mesh optimization? (edit: I think it was a topology paper actually)<p>I found this: <a href="https:&#x2F;&#x2F;arxiv.org&#x2F;pdf&#x2F;2201.06256.pdf" rel="nofollow">https:&#x2F;&#x2F;arxiv.org&#x2F;pdf&#x2F;2201.06256.pdf</a> but I don&#x27;t think it&#x27;s what I&#x27;m thinking of.

Beautiful &amp; compelling presentation

The applications in particular are the piece I find most enjoyable about this publication. The robot path distance maximization, space-filling, and auto-earbud-untangler are pretty neat.

The mobile experience is unfortunately quite repulsive so I didn’t read the article :( But wanted to..