Does it support 2D voronoi model？

[fuze68]

Dear prof Chris Rycroft：
I am a student who just entered the field. After reading relevant literature, I want to reproduce two-dimensional cell voronoi model with simulation software and carry out the related work of my scientific research paper on this basis. Can I start with this program?

[chr1shr]

There are two options for doing two-dimensional tessellations.

For the first option, you can set the third dimension to cover the range -0.5 < z <0.5, and then introduce all of the particles at z = 0. The projection of the Voronoi cells to the xy-plane will then perfectly match the 2D Voronoi tessellation, and you can interpret the various cell statistics accordingly (e.g. 3D cell volume = 2D cell area).

The second option is to look at the dev branch of the repository, which contains a dedicated two-dimensional implementation of the library. It has the essentially the same layout as the regular code, but with _2d extensions to the class names. There is a 2d directory with a number of two-dimensional examples.

The dedicated 2D library is a lot more efficient than the first option, since it only has to represent each Voronoi cell as an irregular polygon, instead of a polyhedron. But if you are dealing with small systems (e.g. fewer than 1000 particles) then the computation times will take fractions of a second so you probably won't notice a big difference between the two different options.

You can read more about the 2D computations (as well as multithreading support) in a paper by my former student Jiayin Lu:

• J. Lu, E. Lazar, and C. H. Rycroft, An extension to Voro++ for multithreaded computation of Voronoi cells, Comput. Phys. Commun. 291, 108832 (2023). doi:10.1016/j.cpc.2023.108832 arXiv:2209.11606

[testyoulive]

Dear prof Chris Rycroft：
May I ask if the Floyd function in the v-connect file is available? I couldn't find its use case, but I really need to evenly distribute those Voronoi units

[chr1shr]

I'm not familiar with the "Floyd function". Are you talking about Lloyd's algorithm for evenly distributing points?

The library doesn't have a standard Lloyd example. But this is discussed in detail as part of our computational meshing paper:

• J. Lu and C. H. Rycroft, TriMe++: Multithreaded triangular meshing in two dimensions, Comput. Phys. Commun. 308, 109442 (2025). doi:j.cpc.2024.109442

You can also see this discussed in lecture 3 of these summer school slides, and there is some basic code to do it in the associated GitHub repository.