Discontinuous curve with unequal dimensions and Compact

[fatteneder]

MWE

using BijectiveHilbert

xy = zeros(Int64, 4, 8)
alg = Compact(Int64, [4, 8])
CI = CartesianIndices(xy)
for cixy in CI
  ix, iy = Tuple(cixy)
  z = encode_hilbert(alg, [ix, iy])
  xy[ix,iy] = z
  display(decode_hilbert!(alg, [ix,iy], z))
end

display(xy)

The above yields

4×8 Matrix{Int64}:
  1   4   5   6  59  60  61  64
  2   3   8   7  58  57  62  63
 15  14   9  10  55  56  51  50
 16  13  12  11  54  53  52  49

It appears that the indexing is off and that the curve is not continuous.

Am I doing something wrong or is it just not possible to have it continuous?

[fatteneder]

Perhaps it is not really discontinuous because it wraps around through the boundary from 16->49.

[adolgert]

You found a bug! The goal of this algorithm is to give you continuous indices. It looks to me like the 6th bit, that gives the value 32, is extra on the right side. 49 - 32 = 17, so it would be next.

This is going to be difficult to debug because the original preprint had errors, the paper had errors, and the final code I used as a reference didn't have much testing, so who knows how it was? I just reread the main paper, and it will take some attention.

By the way, the best workaround for this is to use a regular Hilbert curve, record the indices, throw out the ones you don't want, and then sort them. It's an extra level of indirection, and it can be time consuming, but sometimes it's enough.

Meanwhile, I'll take a look again at the paper and code. And thank you!