6 ms·
Evenly distributing points on a sphere
- ianai 8y agoCouldn’t this be used to model qubit states? Ie calculating function values on the resulting pairs.
- mrep 8y agoIf you are interested in spherical math, you should check out google's S2 library [0] which uses hilbert curves to classify areas on a sphere. Here is an overview of the cell hierarchy [1] [0]: http://s2geometry.io/ http://s2geometry.io/ [1]: http://s2geometry.io/devguide/s2cell_hierarchy http://s2geometry.io/devguide/s2cell_hierarchy
- deleted 8y ago[deleted]
- kjeetgill 8y agoFor anyone who was scratching thier head about how a plane filling curve gets mapped into a sphere; what S2 really does is project the sphere onto the six sides of a cube _and then_ fill each face with a Hilbert Curve index.
- mrep 8y agoLol and Holy shit! That totally explains why the s2 cell lengths vary based on where they are located in one of the six faces (aka, sides of a cube) of which the documentation does not explain clearly. I have spent many hours using this library and your comment has explained so much of what I was confused about it. Thank you
- kjeetgill 8y agoI'm glad I could help! I just picked up that fun fact from recently. You're going to get a kick out of: https://news.ycombinator.com/item?id=17765388 https://news.ycombinator.com/item?id=17765388
- extremelearning 8y agoAuthor here. So amazed to find that my blog post got featured on Hacker news. Happy to answer any questions that I can! :)
- gerdesj 8y agoI've seen the phylotaxis thing before but was unaware of the rather lovely Fibonacci Lattice. My maths is only Civ Eng grad level from >25 years ago but even I can appreciate this stuff. Your writing style is very approachable and well illustrated. Thank you.
- extremelearning 8y agoThanks for the kind words. I’m glad you found it interesting and useful. I think one of the advantages of writing blog posts rather than academic articles is that they are often more readable to a wider audience as the authors can be a little less formal in tone, expand on things (including copious illustrations), without worrying about space constraints.
- gerdesj 8y agoFor me, your style of writing provides a very decent balance. I'm not a scientist, nor engineer, mathematician or similar but I am a common (or garden) variety of nerd! Quite often I will plough through papers and some of the more challenging blog posts that are linked here. A post like yours is challenging but only for the right reasons. You avoid a too "chatty" and "pally" style and present facts concisely but with a bit of context - enough to point amateurs in the right direction.
- davik 8y agoHey I'm a math undergrad and this is a question I've been curious about before. Can you link me to some literature on this? Would this fall under discrete and computational geometry? I know there are some well known books in that area
- 8y ago
- nayuki 8y agoA somewhat related article recently on the HN front page - "Generating random points inside a sphere": https://karthikkaranth.me/blog/generating-random-points-in-a-sphere/ https://karthikkaranth.me/blog/generating-random-points-in-a... ; https://news.ycombinator.com/item?id=17688599 https://news.ycombinator.com/item?id=17688599
- aj7 8y agoIn 2D, this is the porno theater problem.