The software 'SHBundle' offers several routines for the spherical-harmonic analysis and spherical-harmonic-synthesis in Matlab. It also enables the calculation of partial derivatives (e.g. gradients), the conversion between compex/real coefficients and functions and the X-number implementation for ultra-high degrees of expansion.

History of the software

The first routines were created by Nico Sneeuw since 1994 at the IAPG, TU München, and collected until 2000 to form the 1st version of the SHbundle. The software was updated 2002 and 2008 by Nico Sneeuw and Matthias Weigelt and others to versions 2 and 3, respectively. Version 4 contains the modifications and additional tools, written by Matthias Weigelt at the Institute of Geodesy of the University of Stuttgart (GIS) until 2012.
In 2013, the SHbundle v4 was modified and a few tools have been added to form SHbundle 2013. Tools, which are not related to spherical harmonics, were removed from this package and became part of other software bundles. The most important here is uberall which contains all helper functions used by SHbundle and other packages.
From this version onwards, we decided to make the software available to the public.

The SHbundle relies on a few functions of the bundle uberall. Additionally, you might find some useful functions for visualisation in the visBundle.


The latest version can be found at

It would be great if you could acknowledge our work in case you use the bundles for a publication.


The presented bundles are free software in the sense of the GNU General Public Licence:

Lizence and disclaimer: (

This package is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 3 of the License, or (at your option) any later version.
This package is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.
You should have received a copy of the GNU General Public License along with Octave; see the file COPYING. If not, see


Please feel free to make comments on the software, notify us about bugs or even provide useful enhancements via E-Mail


To the top of the page