hilbert_curve_3d

hilbert_curve_3d, a MATLAB code which converts 3D Hilbert curve data between spatial coordinates of a lattice point (x,y,z) and the linear coordinate H which describes the ordering of that point on the curve.

Licensing:

The information on this web page is distributed under the MIT license.

Languages:

hilbert_curve_3d is available in a MATLAB version and an Octave version and a Python version.

Related Data and Programs:

hilbert_curve_3d_test

hilbert_curve, a MATLAB code which computes the sequence of discrete 2D Hilbert curves whose limit is a space-filling curve.

hilbert_curve_display, a MATLAB code which displays a 2D Hilbert curve of given order.

Reference:

1. Nick Berry,
   Hilbert curves,
   http://datagenetics.com/blog/march22013
2. Brian Hayes,
   Crinkly curves,
   American Scientist,
   Volume 101, Number 3, May-June 2013, pages 178-183.
3. David Walker,
   Algorithms for encoding and decoding 3D Hilbert Orderings,
   UTC Research Institute,
   University of Tennessee at Chattanooga, TN 37403,
   arXiv:2308.05673v2

Source Code:

• h_to_xyz.m, converts a 1D Hilbert coordinate H to a 3D Hilbert lattice coordinate.
• i4_log2.m, returns the integer part of the logarithm base 2 of an integer.
• rmin.m, the smallest power of 2 greater than integers x, y and z.
• xyz_to_h.m, converts a 3D Hilbert lattice coordinate to a 1D Hilbert coordinate H.