s2

Update

S2/regioncoverer.go
S2/cellid.go
S2/cellunion.go

Overview

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.) This makes it especially suitable for working with geographic data.

The library consists of:

• Basic representations of angles, intervals, latitude-longitude points, unit 3D vectors, and conversions among them.

• Various shapes over the unit sphere, such as spherical caps ("discs"), latitude-longitude rectangles, polylines, and polygons. These are collectively known as "regions".

• Support for spatial indexing of collections of geometry, and algorithms for testing containment, finding nearby objects, finding intersections, etc.

• 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 quadtree-like fashion.

• The ability to approximate arbitrary regions as a collection of cells. This is useful for building inverted indexes that allow queries over arbitrarily shaped regions.

The implementations attempt to be precise both in terms of mathematical definitions (e.g. whether regions include their boundaries, representations of empty and full regions) and numerical accuracy (e.g. avoiding 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://code.google.com/archive/p/s2-geometry-library/, and in Java, see https://github.com/google/s2-geometry-library-java

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.

Note: The C++ code on code.google.com is an out-of-date snapshot of the Google-internal version, and isn't the basis of this Go library. When the C++ library is re-released, we will update this document.

ℝ¹ - One-dimensional Cartesian coordinates

Full parity with C++.

ℝ² - Two-dimensional Cartesian coordinates

Full parity with C++.

ℝ³ - Three-dimensional Cartesian coordinates

Full parity with C++.

S¹ - Circular Geometry

Complete

• ChordAngle

Mostly complete

• Angle - Missing Arithmetic methods, Trigonometric methods, Conversion to/from s2.Point, s2.LatLng, convenience methods from E5/E6/E7
• Interval - Missing ClampPoint, Complement, ComplementCenter, HaussdorfDistance

S² - Spherical Geometry

Approximately ~40% complete.

Complete These files have full parity with the C++ implementation.

• Cap
• Cell
• CellID
• LatLng
• matrix3x3
• Metric
• PaddedCell
• Point
• Region
• s2edge_clipping
• s2edge_crosser
• s2edge_crossings
• s2rect_bounder
• s2stuv.go (s2coords.h in C++) - This file is a collection of helper and conversion methods to and from ST-space, UV-space, and XYZ-space.
• s2wedge_relations
• ShapeIndex

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.

• CellUnion - Missing Union, Intersection, etc.
• Loop - Loop is mostly complete now. Missing Projection, Distance, Contains, Intersects, Union, etc.
• Polyline - Missing Projection, Intersects, Interpolate, etc.
• Rect (AKA s2latlngrect in C++) - Missing Centroid, Distance, InteriorContains.
• RegionCoverer - Missing FloodFill and SimpleCovering.
• 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, ClosestPair.

In Progress Files that have some work done, but are probably not complete enough for general use in production code.

• 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.

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.

• BoundaryOperation
• Builder - This is a robust tool for creating the various Shape types from collection of simpler S2 types.
• BuilderGraph
• BuilderLayers
• BuilderSnapFunctions
• ClosestEdgeQuery
• ClosestPointQuery
• ConvexHullQuery
• ContainsPointQuery - ShapeContainsPoint and FindContainingShapes
• CrossingEdgeQuery
• EdgeTesselator
• PointCompression
• PointIndex
• PolygonBuilder
• RegionIntersection
• RegionUnion
• Projections
• shapeutil
• lexicon
• priorityqueuesequence

Encode/Decode

Encoding of S2 Go types is committed and is interoperable with C++ and Java. Decoding for Loops, Polygons, Polylines, and Rects is now completed. The remaining types will be worked on in the future.