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Spherical Voronoi Diagram

114 points by marysminefnuf

by mkl

0 subcomment

For me in Firefox Android, rotating the globe scrolls the page at the same time, so it's pretty hard to use.
SciPy can calculate spherical Voronoi diagrams, and MatPlotLib can display them with map projections. I haven't tried to display them as a rotatable globe, but years ago I did it in 2D for volcanos: https://news.ycombinator.com/item?id=21301942, https://imgur.com/closest-volcano-lsxjRXP (argh, Imgur has gotten really aggressive with autoplaying unrelated videos - at least they're silent).

by hermitcrab

1 subcomments

I remember seeing something similar to https://www.jasondavies.com/maps/voronoi/capitals/. But the areas were weighted by the populations of the capitals. You ended up with something quite close to real political maps IIRC.

by markstos

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Voroni is useful for spatial analysis when you want to assign points to a nearest /something/ like airplane positions to the nearest airport.
I used for intersection crash analysis to make sure each crash was assigned to at most intersection. I combined this with a radius around each intersection so crashes too far away were also not attributed to an intersection.
More here: https://mark.stosberg.com/intersection-crash-analysis-with-q...

by srean

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The first thing I noticed was the spherical Dodadecahedron and if you turn on Delaunay triangulation button, then it's dual the Icosahedron, my favourite, the relationship is entirely platonic.
It would be fun to do Turtle graphics with geodesic motions on the sphere. If one adds Loxodromic motions, even better.
The geodesic turtle on the globe would be a good way to play with other platonic solids.

by zokier

1 subcomments

Reminds me of this little map I created some time ago: https://ibb.co/TPVMCR3
My intent was to simplify the shapes of state borders as much as possible while retaining the topological (?) relationship between states. But there is no fancy math behind my map, it's just hand-drawn mess.

by kayo_20211030

3 subcomments

Thanks and very fun. The graphic "The United States of Voronoi" is another reminder of why the mercator projection is so counter-intuitive at times.

by wood_spirit

2 subcomments

Beautiful :)
The idea that springs to my mind is to do Delaunay and Voronoi using spherical geometry. I think the article uses flat Euclidean geometry but if we tweak the fifth axiom we could do spherical or hyperbolic?

by archontes

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