Overview
S2 is a library for spherical geometry that aims to have the same robustness,
flexibility, and performance as the best planar geometry libraries.
This is a library for manipulating geometric shapes. Unlike many geometry
libraries, S2 is primarily designed to work with spherical geometry, i.e.,
shapes drawn on a sphere rather than on a planar 2D map. (In fact, the name S2
is derived from the mathematical notation for the unit sphere S².) This makes
it especially suitable for working with geographic data.
More details about S2 in general are available on the S2 Geometry Website
s2geometry.io.
Scope
The library provides the following:

Representations of angles, intervals, latitudelongitude points, unit
vectors, and so on, and various operations on these types.

Geometric shapes over the unit sphere, such as spherical caps ("discs"),
latitudelongitude rectangles, polylines, and polygons. These are
collectively known as "regions".

A hierarchical decomposition of the sphere into regions called "cells". The
hierarchy starts with the six faces of a projected cube and recursively
subdivides them in a quadtreelike fashion.

Robust constructive operations (e.g., union) and boolean predicates (e.g.,
containment) for arbitrary collections of points, polylines, and polygons.

Fast inmemory indexing of collections of points, polylines, and polygons.

Algorithms for measuring distances and finding nearby objects.

Robust algorithms for snapping and simplifying geometry (with accuracy and
topology guarantees).

A collection of efficient yet exact mathematical predicates for testing
relationships among geometric objects.

Support for spatial indexing, including the ability to approximate regions
as collections of discrete "S2 cells". This feature makes it easy to build
large distributed spatial indexes.
On the other hand, the following are outside the scope of S2:
Robustness
What do we mean by "robust"?
In the S2 library, the core operations are designed to be 100% robust. This
means that each operation makes strict mathematical guarantees about its output,
and is implemented in such a way that it meets those guarantees for all possible
valid inputs. For example, if you compute the intersection of two polygons, not
only is the output guaranteed to be topologically correct (up to the creation of
degeneracies), but it is also guaranteed that the boundary of the output stays
within a userspecified tolerance of true, mathematically exact result.
Robustness is very important when building higherlevel algorithms, since
unexpected results from lowlevel operations can be very difficult to handle. S2
achieves this goal using a combination of techniques from computational
geometry, including conservative error bounds, exact geometric predicates,
and snap rounding.
The implementation attempts to be precise both in terms of mathematical
definitions (e.g. whether regions include their boundaries, and how degeneracies
are handled) and numerical accuracy (e.g. minimizing cancellation error).
Note that the intent of this library is to represent geometry as a mathematical
abstraction. For example, although the unit sphere is obviously a useful
approximation for the Earth's surface, functions that are specifically related
to geography are not part of the core library (e.g. easting/northing
conversions, ellipsoid approximations, geodetic vs. geocentric coordinates,
etc).
See http://godoc.org/github.com/golang/geo for specific package documentation.
For an analogous library in C++, see https://github.com/google/s2geometry, in
Java, see https://github.com/google/s2geometrylibraryjava, and Python, see
https://github.com/google/s2geometry/tree/master/src/python
Status of the Go Library
This library is principally a port of the
C++ S2 library, adapting to Go idioms
where it makes sense. We detail the progress of this port below relative to that
C++ library.
Full parity with C++.
Full parity with C++.
Full parity with C++.
Full parity with C++.
Approximately ~40% complete.
Complete These files have full parity with the C++ implementation.
 Cap
 Cell
 CellID
 CellUnion
 ContainsVertexQuery
 ConvexHullQuery
 CrossingEdgeQuery
 LatLng
 matrix3x3
 Metric
 PaddedCell
 Point
 PointCompression
 Region
 RegionCoverer
 RegionUnion
 s2edge_clipping
 s2edge_crosser
 s2edge_crossings
 s2edge_distances
 edgeVectorShape
 laxLoop
 laxPolyline
 s2projections  Helpers for projecting points between R2 and S2.
 s2rect_bounder
 s2stuv.go (s2coords.h in C++)  This file is a collection of helper and
conversion methods to and from STspace, UVspace, and XYZspace.
 s2wedge_relations
 ShapeIndex
 idSetLexicon,sequenceLexicon
Mostly Complete Files that have almost all of the features of the original
C++ code, and are reasonably complete enough to use in live code. Up to date
listing of the incomplete methods are documented at the end of each file.
 EdgeQuery/Closest/Furthest  missing Project, GetEdge
 ContainsPointQuery  missing visit edges
 laxPolygon
 Loop  Loop is mostly complete now. Missing Project, Distance, Union, etc.
 Polyline  Missing InitTo... methods, NearlyCoversPolyline
 Rect (AKA s2latlngrect in C++)  Missing Centroid, InteriorContains.
 s2_test.go (AKA s2testing and s2textformat in C++)  Missing Fractal test
shape generation. This file is a collection of testing helper methods.
 s2edge_distances  Missing Intersection
In Progress Files that have some work done, but are probably not complete
enough for general use in production code.
 CellIndex  A queryable index of CellIDs.
 Polygon  Polygons with multiple loops are supported. It fully implements
Shape and Region, but it's missing most other methods. (Area, Centroid,
Distance, Projection, Intersection, Union, Contains, Normalized, etc.)
 PolylineSimplifier  Initial work has begun on this.
 s2predicates.go  This file is a collection of helper methods used by other
parts of the library.
 s2shapeutil  Initial elements added. Missing VisitCrossings.
Not Started Yet. These files (and their associated unit tests) have
dependencies on most of the In Progress files before they can begin to be
started.
 BooleanOperation  used when assembling polygons and loops.
 Builder  This is a robust tool for creating the various Shape types from
collection of simpler S2 types.
 BuilderClosedSetNormalizer
 BuilderFindPolygonDegneracies
 BuilderGraph
 BuilderLayers
 BuilderSnapFunctions
 BuilderTesting
 Centroids
 ClosestPointQuery
 EdgeTesselator
 LoopMeasures
 PointIndex
 PointRegion
 PointUtil
 PolygonMeasures
 RegionIntersection
 RegionTermIndexer
 ShapeIndexRegion  Allows ShapeIndexes to be used as Regions for things like
Encode/Decode
Encoding and decoding of S2 types is fully implemented and interoperable with
C++ and Java.