Mapping Hilbert values to 3D points

Question

I have a set of Hilbert values (length from the start of the Hilbert curve to the given point).

What is the best way to convert these values to 3D points? Original Hilbert curve was not in 3D, so I guess I have to pick by myself the Hilbert curve rank I need. I do have total curve length though (that is, the maximum value in the set).

Perhaps there is an existing implementation? Some library that would allow me to work with Hilbert curve / values? Language does not matter much.

Answer 1

Not an answer about 3D conversion, but there is a nice algorithm and discussion of Hilbert values here Two-dimensional spatial hashing with space-filling curves

From MIT

4 algorithms for the n-dimensional Hilbert Space-Filling Curve

* A. R. Butz, "Alternative Algorithm for Hilbert's Space-Filling Curve",
  IEEE Trans. Comp., April, 1971, pp 424-426. [Butz 1971]

* S. W. Thomas, "hilbert.c" in the Utah Raster Toolkit circa 1993,
  http://web.mit.edu/afs/athena/contrib/urt/src/urt3.1/urt-3.1b.tar.gz

* D. Moore, Fast Hilbert Curves in C, without Recursion

* J.K.Lawder, Calculation of Mappings Between One and n-dimensional Values Using the Hilbert Space-filling Curve, [JL1_00]

Answer 2

I have written a 2D transformation of the hilbert curve. I will add a 3D transformation soon:

http://hilbert-curve.sourceforge.net