Five Hilbert curve algorithms, implemented from original papers, with bug fixes. Type stable, tested exhastively, including a new continuous curve for domains with unequal side lengths.
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.
| Version | Date | Changes |
|---|---|---|
| 0.6.0 | 2025-12-28 | Created continuous curve for unequal side lengths |
| 0.5.0 | 2025-04-14 | Simple2D is 2x faster, added support for StaticArrays |
| 0.4.0 | 2023-12-29 | Removed Compact from interface, comprehensive test suite |
| 0.3.0 | 2021-03-01 | Made Simple2D type-stable, combinatorial testing |
| 0.2.0 | 2021-02-03 | Fixed bitshifting bug, improved GlobalGray type handling |
| 0.1.0 | 2020-12-17 | Initial release |
A video about using Hilbert curves:
