# Getting started with a5R

    library(a5R)

## Index a point

Map a longitude/latitude coordinate to a cell at a given resolution (0–30). Higher resolutions produce smaller cells.

    cell <- a5_lonlat_to_cell(-3.19, 55.95, resolution = 10)
    cell
    #> <a5_cell[1]>
    #> [1] 6344be8000000000

Convert back to the cell centre point:

    a5_cell_to_lonlat(cell)
    #> <wk_xy[1] with CRS=OGC:CRS84>
    #> [1] (-3.183746 55.9806)

## Cell boundaries

Get the boundary polygon for one or more cells:

    boundary <- a5_cell_to_boundary(cell)
    boundary
    #> <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...>

    plot(boundary, col = "#206ead20", border = "#206ead", asp = 1)

Boundaries are returned as `wk_wkb` vectors by default (set `format = "wkt"` for WKT). Both integrate directly with sf, terra, and other spatial tooling via the wk package.

## Hierarchy and compaction

A5 is a hierarchical grid: every cell has a parent at a coarser resolution and 4 children at the next finer resolution.

    parent <- a5_cell_to_parent(cell)
    parent
    #> <a5_cell[1]>
    #> [1] 6344be0000000000

    children <- a5_cell_to_children(cell)
    children
    #> <a5_cell[4]>
    #> [1] 6344be2000000000 6344be6000000000 6344bea000000000 6344bee000000000

We can visualise the relationship: the parent (dark outline) contains our cell (blue fill), which in turn contains its 4 children (orange):

    plot(NULL, xlim = c(-3.23, -3),  ylim = c(55.98, 55.99),
           xlab = "", ylab = "", asp = 1
           )
    plot(a5_cell_to_boundary(a5_cell_to_children(cell)),
         col = "#ad6e2020", border = "#ad6e20", add = TRUE)
    plot(a5_cell_to_boundary(cell), col = "#206ead40", border = "#206ead",
         lwd = 2, add = TRUE)
    plot(a5_cell_to_boundary(parent), border = "#333333", lwd = 2, add = TRUE)

Cell area decreases geometrically: each level is roughly 4x smaller.

    a5_cell_area(0:5)
    #> Units: [m^2]
    #> [1] 4.250547e+13 8.501094e+12 2.125273e+12 5.313184e+11 1.328296e+11
    #> [6] 3.320740e+10

### Compact and uncompact

When a complete set of siblings is present, `a5_compact()` merges them back into their shared parent. This is the inverse of `a5_cell_to_children()` and is useful for reducing the size of large cell sets without losing coverage.

    children
    #> <a5_cell[4]>
    #> [1] 6344be2000000000 6344be6000000000 6344bea000000000 6344bee000000000
    a5_compact(children)
    #> <a5_cell[1]>
    #> [1] 6344be8000000000

    # round-trips back to the original
    a5_uncompact(a5_compact(children), resolution = 11)
    #> <a5_cell[4]>
    #> [1] 6344be2000000000 6344be6000000000 6344bea000000000 6344bee000000000

Many a5R functions return compacted output automatically. For example, `a5_grid_disk()` and `a5_spherical_cap()` compact their results; use `a5_uncompact()` when you need a uniform-resolution grid (see Traversal below).

## Traversal

Find neighbouring cells by hop count with `a5_grid_disk()`, or by great-circle distance with `a5_spherical_cap()`:

    disk <- a5_grid_disk(cell, k = 10)
    cap <- a5_spherical_cap(cell, radius = 50000)

    plot(a5_cell_to_boundary(cap), col = "#6ead2020", border = "#6ead20", asp = 1)

    plot(a5_cell_to_boundary(disk), col = "#206ead20", border = "#206ead", asp = 1)

Both functions return a compacted cell vector: sibling groups are merged into coarser parent cells to save space. To recover a uniform grid at the original resolution, pass the result through `a5_uncompact()`:

    disk_grid <- a5_uncompact(disk, resolution = a5_get_resolution(cell))

    plot(a5_cell_to_boundary(disk_grid), col = "#206ead20", border = "#206ead", asp = 1)

## Converting geometries to a5 cells

`a5_polygon_to_cells()` returns the cells whose centres lie inside a polygon. It accepts any geometry that wk can handle (a `wk::rct()` bounding box, a WKT or WKB polygon, an `sf` / `sfc` feature) and also terra `SpatVector` polygons.

    cells <- a5_polygon_to_cells(wk::rct(-3.3, 55.9, -3.1, 56.0), resolution = 12)
    length(cells)
    #> [1] 36

    plot(a5_cell_to_boundary(cells), col = "#206ead20", border = "#206ead", asp = 1)

The returned vector is sorted and compacted: whenever four sibling cells all sit inside the polygon, they are merged into their parent so the result uses fewer slots without losing coverage. Call `a5_uncompact()` to expand back to a uniform grid at the target resolution:

    cells_uncom <- a5_uncompact(cells, 12)
    length(cells_uncom)
    #> [1] 69

    plot(a5_cell_to_boundary(cells_uncom), col = "#206ead20", border = "#206ead", asp = 1)

Multi-part inputs are handled natively: a `MULTIPOLYGON` or an `sfc` of multiple polygons returns the union of cells across all parts, and a `POLYGON` with holes returns the outer ring’s cells with the hole cells properly subtracted.

    library(sf)
    #> Linking to GEOS 3.12.2, GDAL 3.13.0, PROJ 9.4.1; sf_use_s2() is TRUE
    demo(nc, ask = FALSE, echo = FALSE)
    nca5 <- a5_polygon_to_cells(nc, resolution = 9) |>
      a5_uncompact(9)
    plot(a5_cell_to_boundary(nca5), col = "#03030320", border = "#6d20adff", asp = 1)

## Tracing a line

`a5_linestring_to_cells()` returns the cells whose pentagons are crossed by a great-circle polyline. Output is in discovery order along the path. Consecutive waypoints are connected by great-circle arcs, so antimeridian-crossing routes work transparently.

Multi-part inputs (`MULTILINESTRING` or an `sfc` of several linestrings) are handled natively: per-feature outputs are concatenated in feature order with first-seen deduplication.

To show what cell-by-cell tracing looks like, we can write a short phrase as a `MULTILINESTRING` (one stroke per letter) and ask A5 to fill in the cells:

    a5R_strokes <- wk::wkt(
      "MULTILINESTRING (
        (1.8 52.5, 1.2 52.8, 0.6 52.5, 0.4 52, 0.6 51.5, 1.2 51.2, 1.8 51.5, 2 52, 1.8 52.5, 2 51.2),
        (5 53, 3.5 53, 3.5 52.2, 4 52.2, 4.7 52, 5 51.6, 4.7 51.2, 4 51, 3.5 51.1),
        (6.5 51, 6.5 53, 7.5 53, 8 52.8, 8.2 52.5, 8 52.2, 7.5 52, 6.5 52, 8.2 51)
      )"
    )

    cells <- a5_linestring_to_cells(a5R_strokes, resolution = 9)
    length(cells)
    #> [1] 182

    plot(a5_cell_to_boundary(cells),
         col = "#206ead80", border = "#37af6d", asp = 1)

Each stroke is one continuous linestring; the function walks the great-circle path, expanding cell neighbours along the way, and returns the union across all strokes.