'A5' Discrete Global Grid System

Bindings for the "A5 geospatial index" < https://a5geo.org/>. 'A5' partitions the Earth's surface into pentagonal cells across 31 resolution levels using an equal-area projection onto a dodecahedron. Provides functions for indexing coordinates to cells, traversing the cell hierarchy, computing cell boundaries, and compacting/uncompacting cell sets. Powered by the 'A5' 'Rust' crate via 'extendr'.

a5R

a5R provides R bindings for the A5 pentagonal geospatial index, powered by the a5 Rust crate via extendr.

A5 partitions the Earth’s surface into pentagonal cells across 31 resolution levels. Cells are equal-area and encoded as 64-bit integers; at the finest resolution each covers about 30 mm².

a5R 1.0 uses the A5 1.0 cell index, which numbers cells differently from earlier versions. Convert ids stored by a5R 0.x with a5_migrate().

Installation

install.packages("a5R")

Or install the development version from GitHub:

# install.packages("pak")
pak::pak("belian-earth/a5R")

Building from source needs a Rust toolchain (cargo and rustc).

Quick example

library(a5R)

# Index a point to a cell
cell <- a5_lonlat_to_cell(-3.19, 55.95, resolution = 10)
cell
#> <a5_cell[1]>
#> [1] 63bb948000000000

# Get the boundary polygon
a5_cell_to_boundary(cell)
#> <wk_wkb[1] with CRS=OGC:CRS84>
#> [1] <POLYGON ((-3.175718 55.93546, -3.145905 55.97569, -3.151641 56.01921, -3.219413 56.00818, -3.226037 55.96443, -3.175718 55.93546...>

# Navigate the hierarchy
a5_cell_to_parent(cell)
#> <a5_cell[1]>
#> [1] 63bb960000000000
a5_cell_to_children(cell)
#> <a5_cell[4]>
#> [1] 63bb942000000000 63bb946000000000 63bb94a000000000 63bb94e000000000

Polygons become coverings, one per feature. Here North Carolina’s counties are filled with cells, coloured by their distance from Wake County’s centroid:

nc <- sf::read_sf(system.file("shape/nc.shp", package = "sf")) |>
  sf::st_transform(4326)
nc$a5 <- a5_polygon_to_cells(nc, resolution = 9, containment = "overlapping")

cells <- unique(a5_uncompact(nc$a5))
wake <- sf::st_coordinates(sf::st_centroid(nc$geometry[nc$NAME == "Wake"]))
centre <- a5_lonlat_to_cell(wake[, 1], wake[, 2], resolution = 9)
dist <- a5_cell_distance(centre, cells, units = "km")

plot(a5_cell_to_boundary(cells), col = hcl.colors(50)[cut(as.numeric(dist), 50)], border = "grey50", lwd = 0.5)
plot(nc$geometry, border = "white", lwd = 0.5, add = TRUE)

See vignette("a5R") for a full walkthrough of indexing, boundaries, hierarchy, traversal, and geometry-to-cell conversion.

Features

• Vectorised Rust core: all operations implemented in Rust and called from R via extendr. A benchmark suite mirroring the TypeScript, Python and Rust ports runs on every pull request and fails on regressions above 15%.
• vctrs + wk integration: cell indices use an a5_cell type with tibble support; geometries return as wk_wkb/wk_wkt vectors compatible with sf and terra.
• Coverings: polygons, disks and caps become a5_covering vectors, one compacted cell set per feature, that combine (a5_union(), a5_intersect(), a5_difference()), test (a5_contains()) and measure (a5_area()) without expanding to millions of cells. See vignette("coverings").
• Geometry indexing: a5_polygon_to_cells() and a5_line_string_to_cells() map polygons and great-circle lines to cells.
• Traversal: a5_grid_disk() and a5_spherical_cap() select neighbours by hop count or great-circle distance.
• Spatial hierarchy: a5_cell_to_supercell() and a5_cell_to_subcells() move between resolutions by location, so aggregation counts each fine cell inside the coarse cell it lies in.
• Arrow and Parquet: cells and coverings convert to Arrow uint64 columns and back exactly, with the A5 index recorded in the schema. See vignette("arrow-parquet").
• Multi-threading: opt-in parallel processing via rayon for vectorised operations. See vignette("multithreading").

Acknowledgements

A5 was created by Felix Palmer. This package is a thin R wrapper around his work and would not exist without it. The Query-farm team maintain the DuckDB A5 extension, which wraps the same Rust crate and provided a valuable reference for this project.