About MORTIF

MORTIF (MORTon Indexer Fortran) is a pure Fortran 2003+ library to encode and decode multidimensional integer indexes into Morton's Z-order (also called Morton order or Morton code).

In mathematical analysis and computer science, the Z-order curve is a function that maps multidimensional data to one dimension while preserving locality of the data points. It was introduced in 1966 by G. M. Morton. The Z-value of a point in multiple dimensions is calculated by interleaving the binary representations of its coordinate values.

Morton's code (Z-order) is a scheme to map multi-dimensional arrays onto a linear one with a great deal of spatial locality.

MORTIF exposes four elemental Fortran procedures:

Procedure	Kind	Description
morton2D	function	Encode two 32-bit indexes → one 64-bit Morton code
demorton2D	subroutine	Decode a 64-bit Morton code → two 32-bit indexes
morton3D	function	Encode three 32-bit indexes → one 64-bit Morton code
demorton3D	subroutine	Decode a 64-bit Morton code → three 32-bit indexes

Being elemental, all four procedures work transparently on scalars and conformable arrays.

References

1. Morton, G. M. — A Computer Oriented Geodetic Data Base and a New Technique in File Sequencing, IBM technical report, 1966.
2. Stocco, L. J. and Schrack, G. — On Spatial Orders and Location Codes, IEEE Transactions on Computers, vol. 58, no. 3, March 2009.
3. Baert, J., Lagae, A. and Dutré, Ph. — Out-of-Core Construction of Sparse Voxel Octrees, SIGGRAPH/Eurographics High-Performance Graphics, 2013.

Authors

• Stefano Zaghi — @szaghi

Contributions are welcome — see the Contributing page.

Copyrights

MORTIF is distributed under a multi-licensing system:

Use case	License
FOSS projects	GPL v3
Closed source / commercial	BSD 2-Clause
Closed source / commercial	BSD 3-Clause
Closed source / commercial	MIT

Anyone interested in using, developing, or contributing to MORTIF is welcome — pick the license that best fits your needs.