Institut für Theoretische Physik I
Universität Erlangen-Nürnberg
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UnivIS FAU Erlangen-Nürnberg

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3D Minkowski Tensor Package

This page is no longer maintained. Please visit for the current version.

Karambola is a program able to calculate the Minkowski Tensors of three-dimensional bodies and surfaces.

Minkowski Tensors can be calculated globally, or for subsets (called “labels”). The program takes its input in the form of triangulated surfaces. A more detailed description of the program is given in the included documentation, and in the papers referenced below.

Karambola is written in plain ISO C++ and only needs the GNU Scientific Library to compile. It is available as Free Software under the terms of the GNU General Public License, Version 3 or later.


The following articles describe the Minkowski Tensor Algorithms implemented by karambola:

The following articles describe analyses of physical systems based on these concepts.


Current version described in Minkowski Tensors of Anisotropic Spatial Structure (see reference above):

Source code (4.1 MB), New Journal of Phyics version