BijectiveHilbert

This Hilbert curve library encodes a multi-dimensional grid index into a single integer, such that nearby integers are nearby grid indices. See the Usage.

julia> using Pkg; Pkg.add("BijectiveHilbert")
julia> using BijectiveHilbert
julia> xy_coordinates = zeros(Int, 8, 8)
julia> for y in 1:size(xy_coordinates, 2)
           for x in 1:size(xy_coordinates, 1)
               z = encode_hilbert(Simple2D(Int), [x, y])
               xy_coordinates[x, y] = z
           end
       end
julia> xy_coordinates
8×8 Array{Int64,2}:
  1   2  15  16  17  20  21  22
  4   3  14  13  18  19  24  23
  5   8   9  12  31  30  25  26
  6   7  10  11  32  29  28  27
 59  58  55  54  33  36  37  38
 60  57  56  53  34  35  40  39
 61  62  51  52  47  46  41  42
 64  63  50  49  48  45  44  43
julia> X = zeros(Int, 2)
julia> decode_hilbert!(Simple2D(Int), X, xy_coordinates[5, 7])
julia> X == [5, 7]

This function, called a Hilbert curve, is used most often for geospatial work or database implementation but is equally appropriate for dealing with large TIFF files. It belongs to the class of space-filling, self-avoiding, simple, and self-similar (FASS) curves, which includes Peano curves, and Morton z-curves.

Included are several variations of the Hilbert curve. They are type-stable and thoroughly tested, including bug fixes to amend the published algorithms.

Simple2D encodes two-dimensional Cartesian indices. Fastest and easiest to use.
SpaceGray encodes multi-dimensional Cartesian indices that all have the same power-of-two extent. The fastest multi-dimensional version.
GlobalGray like SpaceGray but a different pattern.
FaceContinuous like SpaceGray and GlobalGray, but another pattern again.