This agrees with my experience on a project I’ve been working on this year, in particular related to porting the code. I’ve developed a strategy that I’m calling “Polyglot Mirroring” where the code is written in multiple languages at once, with LLMs handling the mirroring.

I actually made a Ask HN about it just today https://news.ycombinator.com/item?id=45091607 but for some reason the HN algorithm never even showed it on the Ask page :/

https://news.ycombinator.com/item?id=43971314 got some attention here, when I originally released the TypeScript version, so following up with the news that the library has now been entirely ported to Python.

Not only is this an implementation of the library in a language that is better suited to data science, but there are also many improvements to the underlying A5 grid since the original launch, in particular a true equal area projection, which even accounts for the ellipsoidal shape of the earth. https://a5geo.org/examples/area

To get started, take a look at https://a5geo.org/docs/quickstart/python

Yes, such indices (S2 & H3) are widely used for providing a index in databases, so geospatial features that are close by in the world and stored in nearby databases rows. https://cloud.google.com/bigquery/docs/grid-systems-spatial-...

Thanks. I always enjoy when geospatial topics show up on here. My background it geo, but unfortunately I have slowly drifted away. Geohash is about where I left off in the same general realm of concepts, so S2 / H3 are essentially new to me as well.

A5 cell boundaries are geodesics. One more difference that I thought of is that HEALPix is generally not aligned with the continents (makes sense as it is mostly used for astrophysics), whereas the hilbert curve used to index A5 is aligned with the continental land masses: https://a5geo.org/examples/globe

As a result, when A5 is used as a spatial index, it will generally not have jumps in the cell index values when querying nearby locations on land

If you're aggregating and comparing data across different locations for example: https://a5geo.org/examples/airbnb

The base platonic solid that Healpix is based on is the octahedron (https://en.wikipedia.org/wiki/Octahedron), which A5 uses the dodecahedron(https://en.wikipedia.org/wiki/Regular_dodecahedron).

The octahedron has a much higher angular defect (https://en.wikipedia.org/wiki/Angular_defect) than the dodecahedron, and thus when it is projected onto the sphere the cells are warped a lot. So while their areas may be the same, the shapes vary.

This article explains the geometric construction, and how it leads to the cells being a similar size and shape: https://a5geo.org/docs/technical/platonic-solids

Also from a data visualization point of view, the rectangular cells of Healpix (like S2) are arguably less pleasing to look at than hexagons/pentagons: https://h3geo.org/docs/comparisons/s2#visualization

Not sure I understand—healpix starts from the rhombic dodecahedron and then bisects the generalizations of the 12 squares each time. Where do octahedra come into play?

My mistake, you are correct. The base solid is indeed the rhombic dodecahedron. I believe the point about the angular defect is still valid though.

Bear in mind that this is a "Show HN", the library was released just a few weeks ago! Whereas the other libraries have been around for a decade+

The plan is certainly to release versions in other languages, if you would like to be involved, please get in touch. I agree the porting shouldn't be too difficult, as by design the library has just one simple dependency and the code should translate nicely to other C-style languages

For a visual explanation of how the system works, as well as interactive examples, check out the project website at https://a5geo.org/examples/

As a user, you generally don’t care about the math (and S2 is hardly simple either, as it warps the squares prior to projection). You just call the API and use the indices for spatial joins or computations.

The primary benefit is indeed the ability to treat cells as if they are equal areas. This is something people do currently with H3, but it introduces a bias. Contrary to popular belief, this is not only an issue near the poles or in the ocean.

The other difference is aesthetics, people generally find H3 more pleasing to look at than S2, which is why it gets used in visualization more. You can make the same argument for A5, although of course it is a matter of taste!

Finally, you are correct that H3 was originally developed at Uber for their specific use case, however it has since been used in many other contexts and I think it doesn’t hurt to have some alternatives as conceptually S2/H3/A5 are similar

Also check S2: http://s2geometry.io/, created at Google before H3, which uses squares and underpins the fast indexing in BigQuery amongst many other things