S2 Library deep dive. How does it work, features, usage, visualisations and more. Based on real life work experience @Google

1. S2
shorturl.at/DIUV4
@dmarcous

2. “flat two-dimensional projections (similar to an atlas) on a
three-dimensional sphere (similar to a globe).”
“While the Earth is not quite spherical, it is much closer to
being a sphere than it is to being flat!”
What

3. Or is it ?!
No, it isn’t.

5. ● Index geo data
○ [40.779717,-73.947738] is in cell : 89c258b
● Fast geo operations
○ Measuring distances
○ Computing centroids
○ Finding neighbours
● Aggregate geo data
○ {Cell : 89c258b, MAU : 10k}
● Awesome DS features (slides)
Why

6. How does it work?

7. ● Flexible (arbitrary shapes)
● Fast (geo ops, en/decoding)
● Granular (user’s choice)
● Evenly sized (as much as possible)
● Easy to use (cubes, straight lines)
● Shortest paths based (spherical geodesics)
Design Principles

8. Project a cube onto a sphere

9. Faces

10. Quadtree
Each node has 4 children

11. Cells

12. Granularity (S2 statistics)

13. Hilbert Space Filling Curve
● Map points in multidimensional space to a one-dimensional space
● spatially similar objects are given close numeric indices
● Fractal

14. Planetary View

15. Cell Enumeration

16. ● hierarchy (is cell x contained by cell y?)
● neighbour queries (return all adjacent cells on the same level)
O(1) Time & Space Complexity
O(1) is a constant number of ops, not dependant on N, but usually > 1.
That's still considered very fast for geo ops, especially neighbour queries.
Bit Operations

17. 1. Projecting six faces of a cube onto the unit sphere
2. Partitioning each cell into four children recursively using a quadtree
3. For all of the cells of a given level :
a. Enumerate cell Ids along a hilbert space filling curve
Building a S2 cell hierarchy

18. ● S2Builder
● S2ShapeIndex - Spatial Indexing
○ A.K.A “S2 Cover” / “Region Coverer”
○ Building a S2 cell hierarchy
Main Clases

19. Region Coverer

20. Hawaii = Collection of 22 Cells

21. Usage

22. Impl
google/s2geometry (cpp) - try installing on mac… I dare you...
sidewalklabs/s2sphere (Python)
dmarcous/S2Utilities (JVM) - functional

23. S2 Utilities

24. wicket - WKT
region-coverer - S2 Covers
Viz

25. ● Growth Prediction
○ Learning “how many # (users/sessions/events) will I have in the future” on a cell level.
○ Given a future date & cell, what will be the #amount?
● Reverse Geocoding
○ A wrapper of S2ShapeIndex
○ Inclusion queries over coordinates
○ Given (longitude,latitude) what city (polygon) does it belong to?
Use Cases

26. Alternatives
Geohash H3 (uber)