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Comment by keenancrane | Hacker News Reader

If you liked repulsive curves, you may also enjoy repulsive surfaces:

https://www.cs.cmu.edu/~kmcrane/Projects/RepulsiveSurfaces/i...

Deep dive into repulsive geometry here: https://youtu.be/dtYGiCpzzbA

Hi Keenan. What do you use to generate your figures of surfaces with lines and other things drawn on them, e.g. figures 2-6 of the geodesic survey paper (http://www.cs.cmu.edu/~kmcrane/Projects/GeodesicSurvey/Geode...)? Lots of great pictures like that in the SIGGRAPH 2013 Course Notes too (https://www.cs.cmu.edu/~kmcrane/Projects/DDG/paper.pdf). I have made some similar figures with TikZ, but it's a lot of work and the results aren't as nice as I'd like.

Not the author so I don't know for sure, but it does list Polyscope in the main link.

https://github.com/nmwsharp/polyscope

He has a whole presentation about this: https://www.cs.cmu.edu/~kmcrane/Projects/Other/IllustratingG... . TLDR: it's a very manual process :) His lab is also working on Penrose, which is a domain specific language for mathematical diagrams: https://penrose.cs.cmu.edu/

Wow, my laborious-seeming TikZ workflow actually looks pretty simple in comparison! It's all in the one tool and the entire picture code is right there in the Latex source, easy to edit and version control. Shading on a surface is not something I've got nice yet, and lines becoming occluded is a manual effort, but I'm pretty sure I could produce something like the 6 hour figure on p24 in quite a bit less time than that.

Edges of surfaces caused by things like hills obscuring other parts of the same surface, or the surface curving back behind itself (many examples of both on p2 of this) are something I don't have a good way to do. I have done it by doing edge detection on an OpenGL depth buffer and vectorising the results, but that's hard to integrate with TikZ, and changing view angle means doing it all again. Shadows are another problem.

Nice talk! This seems like it could be an interesting tool model real phenomena. Have you considered if you can invert this to derive which constraints and energy function best match a particular sample? Say, take a video of cars entering and exiting a highway ramp, what constraints and energy functions best model the paths taken? This could be individual as well, for example a particular car may be driven "aggressively" according to humans, if you derived the constraints this way could you reliably predict humans' scoring?

Hi Keenan. Do you have advice for how a programmer can get started with implementing repulsive curves if they’re not familiar with the mathematics in the paper and video?

Oh, that's actually the one I was looking for. I should have thought to check your publications page first.

that talk made it really clear how tangent-point energy is easier to compute than mobius energy but not why it's a good proxy for it, it seems like a semihack

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