MATLAB mex files to run Voro++ for calculating Laguerre diagrams/power diagrams in 2D and 3D periodic and non-periodic domains.

• Download and change directory to the top-level.
• In MATLAB, run the scripts makemex.m and makemex2d.m

See the MATLAB live scripts Examples2d.mlx and Examples3d.mlx or the corresponding PDF files Examples2d.pdf and Examples3d.pdf.

This code relies on Voro++ by Chris H. Rycroft:

• https://math.lbl.gov/voro++/
• https://github.com/chr1shr/voro

When using this code please consider citing the following paper:

• Chris H. Rycroft, "Voro++: A three-dimensional Voronoi cell library in C++", Chaos 19, 041111 (2009).

The folder voro_src is a snapshot of Voro++. We modified the files cell_2d.cc, cell_2d.hh, cell.cc and cell.hh to compute the second moments of the Laguerre cells.

See LICENCE.md

• The domain of the Laguerre tessellation must be a box (a rectangle in 2D or a cuboid in 3D). In particular, the code does not compute unbounded Laguerre tessellations or, e.g., Laguerre tessellations of polygonal domains.
• 3D code: If the Laguerre tessellation is non-periodic, then all the seeds must lie inside the bounding box, otherwise they are simply discarded. This limitation does not apply to the 3D periodic code or the 2D code.
• 3D code: The Laguerre tessellation must be either non-periodic or triply periodic (periodic in all 3 directions). This limitation does not apply to the 2D code, where you can choose the diagram to be periodic in the x- or y-directions (Laguerre tessellation of a flat cylinder), both directions (Laguerre tessellation of a flat torus) or neither direction.

We plan to address some of these limitations in a future update, as well as adding more sophisticated visualisation tools.

• Power Diagrams, MATLAB File Exchange: https://www.mathworks.com/matlabcentral/fileexchange/44385-power-diagrams
• Fast Bounded Power Diagram, MATLAB File Exchange: https://www.mathworks.com/matlabcentral/fileexchange/56633-fast-bounded-power-diagram
• Geogram: https://github.com/BrunoLevy/geogram

This repository was created by

• Steve Roper, University of Glasgow
• David Bourne, Heriot-Watt University and the Maxwell Institute for Mathematical Sciences

This code was used to create Laguerre tessellations for the following paper:

• Bourne, D.P., Kok, P.J.J., Roper, S.M. & Spanjer, W.D.T. (2020) Laguerre tessellations and polycrystalline microstructures: A fast algorithm for generating grains of given volumes, Philosophical Magazine, 100, 2677-2707. https://doi.org/10.1080/14786435.2020.1790053

Please consider citing this paper if you find our code useful.