What S2 does
The S2 system projects the Earth onto the six faces of a cube, then recursively subdivides each face into four. Cells are numbered along a Hilbert space filling curve, which gives every cell a single 64 bit id where nearby ids tend to mean nearby cells.
Why it beats a flat grid
- Low distortion. The cube projection keeps cell areas more uniform than a plain latitude and longitude grid, which warps badly near the poles.
- Multiple levels. A region can be covered by a small set of cells at mixed resolutions, large cells in the middle and small ones along the edges.
- One dimensional ids. Because the Hilbert curve preserves locality, range scans on the id approximate spatial ranges.
Covering a region
A region cover picks the fewest cells that fully contain a shape within level limits. That cover becomes a set of key ranges you can scan in an ordinary sorted index.
Key idea
S2 maps the sphere to cube faces and a Hilbert curve so spatial proximity becomes proximity of compact integer cell ids.