Supercells and subcells: parents and children by location

a5_cell_to_supercell() returns, for each cell, the cell at a coarser resolution that contains its centre. a5_cell_to_subcell() returns, for each cell, the cells at a finer resolution whose centres lie inside it, as an a5_covering. These are the location-based counterparts of a5_cell_to_parent() and a5_cell_to_children(), which follow the index and often cross into neighbouring cells (see a5_hierarchy).

Usage

a5_cell_to_supercell(cell, resolution = NULL)

a5_cell_to_subcell(cell, resolution = NULL)

Arguments

cell

An a5_cell vector.

resolution

Integer scalar target resolution, or NULL for one step: one resolution coarser for a5_cell_to_supercell(), one finer for a5_cell_to_subcell(). Subcells require a resolution at or finer than every cell's own.

Value

• a5_cell_to_supercell(): an a5_cell vector the same length as cell. NA where cell is NA, where resolution is finer than the cell, or for a resolution-0 cell with resolution = NULL. A cell at resolution is returned unchanged.

• a5_cell_to_subcell(): an a5_covering vector the same length as cell. NA where cell is NA.

Details

The two functions define an exact partition. Every fine cell has exactly one supercell at each coarser resolution, and the subcells of a coarse cell are exactly the fine cells whose supercell it is, so the subcells of cells that tile an area tile it too, with no cell counted twice. A centre on a shared edge goes to the cell a5_lonlat_to_cell() assigns it to. Aggregating fine values by supercell therefore attributes each value to the coarse cell it lies in.

Supercell

The result equals a5_lonlat_to_cell(a5_cell_to_lonlat(cell), resolution), computed without converting the centre to degrees. It takes well under half the time of a5_lonlat_to_cell(), but far longer than a5_cell_to_parent(), which is a bit operation.

Subcells

Counts vary from cell to cell and average 4^d for a resolution difference d, or 5 * 4^(d - 1) from resolution 0. The covering is compacted, so it stores far fewer cells than it stands for at large differences; use a5_uncompact() for the cells, and never draw the stored cells, which are index parents whose outlines extend beyond the coarse cell. Resolution 30 covers only part of the globe, so a cell whose subcells reach past it has all its subcells given at resolution 29.

See also

a5_hierarchy for parents and children by index, vignette("spatial-hierarchy").

Examples

cell <- a5_lonlat_to_cell(-3.19, 55.95, resolution = 18)
a5_cell_to_supercell(cell, resolution = 15)
#> <a5_cell[1]>
#> [1] 63bb93f8a0000000
a5_cell_to_parent(cell, resolution = 15) # may differ
#> <a5_cell[1]>
#> [1] 63bb93f8a0000000

coarse <- a5_lonlat_to_cell(-3.19, 55.95, resolution = 10)
sub <- a5_cell_to_subcell(coarse, resolution = 12)
sub
#> <a5_covering[1]>
#> [1] res 12: 14 cells (11 stored)
kids <- a5_uncompact(sub)
all(a5_cell_to_supercell(kids, resolution = 10) == coarse)
#> [1] TRUE