We do something similar for some limited geospatial search using elastic search. We make a set of h3 indexes for each of the hundreds of millions of gps recordings on our service, and store them in elastic search. Geospatial queries become full text search queries, where a point is on the line if the set of h3 indexes contains the point. You can do queries on how many cells overlap, which lets you match geospatial tracks on the same paths, and with ES coverage queries, you can tune how much overlap you want.

Instead of using integers IDs for the hexes, we created an encoded version of the ID that has the property that removing a character gets you the containing parent of the cell. This means we can do basic containment queries by querying with a low resolution hex (short string) as a prefix query. If a gps track goes through this larger parent cell, the track will have hexes with the same prefix. You don’t get perfect control of distances because hexes have varying diameters (or rather the approximation, since they aren’t circles they are hexes), but in practice and at scale for a product that doesn’t require high precision, it’s very effective.

I think at the end of this year we’ll have about 6tb of these hex sets in a four node 8 process ES cluster. Performance is pretty good. Also acts as our full text search. Half the time we want a geo search we also want keyword / filtering / etc on the metadata of these trips.

Pretty fun system to build, and the concept works with a wide variety of data stores. Felt like a total hack job but it has stood the test of time.

Thanks uber, h3 is a great library!

• jillesvangurp

  today at 6:27 AM

  Elastisearch and Opensearch have a built in geo_shape type that is a bit more optimal for queries like this.

  Before that existed (pre 1.0 actually), I did something similar with geohashes, which are similar to h3 but based on simple string encoded quad trees. I indexed all the street segments in openstreetmap with that (~800 million at the time) and implemented a simple reverse geocoder. Worked shockingly well.

  The geo_shape type uses a bkd tree in binary format. It's heavily optimized for this type of intersects/overlaps queries at scale. Basically does the same thing but using a lot less disk space and memory. It's similar to what you would find in proper GIS databases. Elasticsearch/opensearch also support h3 and geohash grid aggregations on top of geo_shape or geo_point types.

  I'm guessing the author is using something like postgresql which of course has similar geospatial indexing support via post gis.

• ajfriend

  today at 5:56 AM

  Very cool! And the prefix queries you mention are what I was trying to get at in another comment, but you explained it better :)

There is a lot of literature on join operations using discrete global grid systems (DGGS). H3 is a widely used DGGS optimized for visualization.

If joins are a critical performance-sensitive operation, the most important property of a DGGS is congruency. H3 is not congruent it was optimized for visualization, where congruency doesn’t matter, rather than analytical computation. For example, the article talks about deduplication, which is not even necessary with a congruent DGGS. You can do joins with H3 but it is not recommended as a general rule unless the data is small such that you can afford to brute-force it to some extent.

H3 is great for doing point geometry aggregates. It shines at that. Not so much geospatial joins though. DGGS optimized for analytic computation (and joins by implication) exist, they just aren’t optimal for trivial visualization.

• ajfriend

  today at 5:44 AM

  I agree that the lack of congruency in H3 hexagons can cause weird overlaps and gaps if you plot mixed resolutions naively, but there are some workarounds that work pretty well in practice. For example, if you have mixed resolutions from compacted H3 cells but a single “logical” target resolution underneath, you can plot the coarser cells not with their native geometry, but using the outline of their children. When you do that, there are no gaps. (Totally unrelated but fun: that shape is a fractal sometimes called a "flowsnake" or a "Gosper Island" (https://en.wikipedia.org/wiki/Gosper_curve), which predates H3 by decades.)

  That said, this feels like an issue with rendering geometry rather than with the index itself. I’m curious to hear more about why you think the lack of congruency affects H3’s performance for spatial joins. Under the hood, it’s still a parent–child hierarchy very similar to S2’s — H3 children are topological rather than geometric children (even though they still mostly overlap).

  • jandrewrogers

    today at 6:47 AM

    In a highly optimized system, spatial joins are often bandwidth bound.

    Congruency allows for much more efficient join schedules and maximizes selectivity. This minimizes data motion, which is particularly important as data becomes large. Congruent shards also tend to be more computationally efficient generally, which does add up.

    The other important aspect not raised here, is that congruent DGGS have much more scalable performance when using them to build online indexes during ingestion. This follows from them being much more concurrency friendly.

• 0xfaded

  today at 5:02 AM

  S2 has this property https://s2geometry.io

  • jandrewrogers

    today at 5:20 AM

    Yes, S2 is a congruent DGGS. Unfortunately, it kind of straddles the analytics and visualization property space, being not particularly good at either. It made some design choices, like being projective, that limit its generality as an analytic DGGS. In fairness, its objectives were considerably more limited when it was created. The potential use cases have changed since then.

    • mdasen

      today at 5:41 AM

      Is there a congruent DGGS that you would recommend?

      • jandrewrogers

        today at 6:22 AM

        None that are well-documented publicly. There are a multitude of DGGS, often obscure, and they are often designed to satisfy specific applications. Most don’t have a public specification but they are easy to design.

        If the objective is to overfit for high-performance scalable analytics, including congruency, the most capable DGGS designs are constructed by embedding a 2-spheroid in a synthetic Euclidean 3-space. The metric for the synthetic 3-space is usually defined to be both binary and as a whole multiple of meters. The main objection is that it is not an “equal area” DGGS, so not good for a pretty graphic, but it is trivially projected into it as needed so it doesn’t matter that much. The main knobs you might care about is the spatial resolution and how far the 3-space extends e.g. it is common to include low-earth orbit in the addressable space.

        I was working with a few countries on standardizing one such design but we never got it over the line. There is quite a bit of literature on this, but few people read it and most of it is focused on visualization rather than analytic applications.

I don't like what scrolling this site does to my browser history.

• nmstoker

  today at 5:26 AM

  Yes, noticed that too. Blocked me getting back to HN. Bad behaviour from the site.

Wouldn’t having a spatial index give you most of the performance gains talked about here without needing H3?