S2 Sees the World Differently

Posted by Christi Kroll.

Humans have long been fascinated with translating the world around them into visual representation. Maps not only serve to direct us, they give us a sense of our own place in our surroundings; an understanding of the world and its bounds. In early days, maps were regional, supplemented with the sketches and recollections of travelers. As knowledge of the world and the scale of maps expanded, the challenge of representing a three-dimensional Earth on a two-dimensional plane, known as map projection, became apparent.

S2 Cells

Representation of the S2 Map Projection. Image Credit: S2Geometry

A major breakthrough in navigation was a cylindrical map projection published in the sixteenth century by Gerardus Mercator known as the Mercator Projection. This projection standardized maps for centuries due to its representation of north and south as up and down, respectively, while maintaining appropriate local borders, directions, and shapes.

Mercator Projection Map

Carta do Mundo de Mercator (1569), Public Domain

The most prevalent modern map projection system used today is the Universal Transverse Mercator System, which divides the Earth into 60 narrow zones of equal width (6° longitude) to minimize distortion. Latitude bands intersect these zones to create grid zones, which are referenced in coordinates. The key problem with this map projection is that the shape of the Earth is not a plane, which means that bits and pieces of the projection are stretched and distorted to fit a two-dimensional grid. Some of the grid zones are different sizes, and distortion increases as the boundaries of the grid zones are approached, which means that the grid pieces do not fit seamlessly together.

UTM Zones on Globe

The Earth divided by UTM zones. Notice that the segments decrease in width as they approach the pole. Image Credit: GISGeography

Conversely, S2, created by Google, is a map projection that maps points on the earth onto a mathematical sphere, then projects the sphere surface onto the six sides of a cube1. Each face of the cube is halved along each side, producing four quadrants, called “cells”, which are then each further subdivided into four more cells, and so on. 2. This organizes the projection of the Earth’s surface into discrete S2 cells- every cm2 on earth can be represented with a 64-bit integer3,4. This approach is more precise, reducing the distortion close to the poles of the Earth.

S2 Cells

A flattened representation of the six cube faces before projected to the sphere. Image credit:S2Geometry

Simply put, precision in the map projection system leads to precision in map representation. Our goal is to build the authoritative whole-Earth digital twin, rather than a digital twin built atop a two-dimensional atlas. Choosing S2 allows us to represent the Earth’s geography more accurately and seamlessly across the globe.

References:

  1. "S2 Projections": https://proj.org/operations/projections/s2.html
  2. "S2 Geometry — The New Boss in Location Tracking.": https://medium.com/@davalpargal/s2-geometry-the-new-boss-in-location-tracking-3fed12ca8323
  3. "Geometry on the Sphere: Google's S2 Library": https://docs.google.com/presentation/d/1Hl4KapfAENAOf4gv-pSngKwvS_jwNVHRPZTTDzXXn6Q/view#slide=id.i0
  4. "Google’s S2, geometry on the sphere, cells and Hilbert curve": https://blog.christianperone.com/2015/08/googles-s2-geometry-on-the-sphere-cells-and-hilbert-curve/