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.mandmakemex2d.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:
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.