pyvoro-rimoli
2D and 3D Voronoi and radical (Laguerre) tessellations in Python, with the current Voro++.
This is a maintained fork of pyvoro,
by way of pyvoro-mmalahe. The Python
interface is unchanged: the package is still imported as pyvoro, and code
written for pyvoro works as before. What changes is the bundled Voro++, which
was version 0.4.6 (2013) and is now the current upstream version.
Why this fork
Voro++ 0.4.6 has a bug in the radical tessellation: in some configurations a cell is returned uncut, and the cells overlap instead of partitioning the domain. Four discs of radius 0.1 at the quarter points of a unit square, for example, must give four cells of area 0.25:
import pyvoro
cells = pyvoro.compute_2d_voronoi(
[[0.25, 0.25], [0.75, 0.25], [0.25, 0.75], [0.75, 0.75]],
[[0.0, 1.0], [0.0, 1.0]], 0.5, radii=[0.1] * 4)
print([c['volume'] for c in cells])
# Voro++ 0.4.6: [1.0, 1.0, 1.0, 1.0]
# this fork: [0.25, 0.25, 0.25, 0.25]
The bug was fixed upstream in February 2026 (Voro++ commits 04fecfa and b0dac57), and this fork bundles Voro++ at commit b0dac57. The fork was made for MicroStructPy, whose microstructures are radical tessellations, but it can replace pyvoro in any project.
Installation
pip install pyvoro-rimoli
Wheels are provided for Linux (x86_64 and aarch64), macOS (Intel and Apple silicon) and Windows (x86_64), for Python 3.9 to 3.14. On other platforms, pip builds the package from source, which needs a C++ compiler.
pyvoro, pyvoro-mmalahe and pyvoro-rimoli all install the same pyvoro
module, so only one of them should be installed. To switch:
pip uninstall pyvoro pyvoro-mmalahe
pip install pyvoro-rimoli
To install from a clone of this repository and run the tests:
pip install . pytest
pytest tests
Usage
import pyvoro
pyvoro.compute_voronoi( ... )
pyvoro.compute_2d_voronoi( ... )
Features:
- Radical (weighted) option, which weights the Voronoi cell sizes according to a set of supplied radius values.
- Periodic boundary support. Note that each cell is returned in the frame of reference of its source point, so points can (and will) be outside the bounding box.
- 2D helper, which translates the results of a 3D tessellation of points on the plane back into 2D vectors and cells (see below for an example).
- Support for numpy arrays (thanks to a contribution from @christopherpoole): you can pass in a 2D (Nx3 or Nx2) numpy array.
Example
import pyvoro
pyvoro.compute_voronoi(
[[1.0, 2.0, 3.0], [4.0, 5.5, 6.0]], # point positions
[[0.0, 10.0], [0.0, 10.0], [0.0, 10.0]], # limits
2.0, # block size
radii=[1.3, 1.4] # particle radii -- optional, and keyword-compatible arg.
)
returning an array of voronoi cells in the form:
{ # (note, this cell is not calculated using the above example)
'volume': 6.07031902214448,
'faces': [
{'adjacent_cell': 1, 'vertices': [1, 5, 8, 3]},
{'adjacent_cell': -3, 'vertices': [1, 0, 2, 6, 5]},
{'adjacent_cell': -5, 'vertices': [1, 3, 9, 7, 0]},
{'adjacent_cell': 146, 'vertices': [2, 4, 11, 10, 6]},
{'adjacent_cell': -1, 'vertices': [2, 0, 7, 4]},
{'adjacent_cell': 9, 'vertices': [3, 8, 10, 11, 9]},
{'adjacent_cell': 11, 'vertices': [4, 7, 9, 11]},
{'adjacent_cell': 139, 'vertices': [5, 6, 10, 8]}
],
'adjacency': [
[1, 2, 7],
[5, 0, 3],
[4, 0, 6],
[8, 1, 9],
[11, 7, 2],
[6, 1, 8],
[2, 5, 10],
[9, 0, 4],
[5, 3, 10],
[11, 3, 7],
[6, 8, 11],
[10, 9, 4]
],
'original': [1.58347382116, 0.830481034382, 0.84264445125],
'vertices': [
[0.0, 0.0, 0.0],
[2.6952010660213537, 0.0, 0.0],
[0.0, 0.0, 1.3157105644765856],
[2.6796085747800173, 0.9893738662896467, 0.0],
[0.0, 1.1577688788929044, 0.9667194826924593],
[2.685575135451888, 0.0, 1.2139446383811037],
[1.5434724537773115, 0.0, 2.064891808748473],
[0.0, 1.2236852383897006, 0.0],
[2.6700186049990116, 1.0246853171897545, 1.1392273839598812],
[1.6298653128290692, 1.8592211309121414, 0.0],
[1.8470793965350985, 1.7199178301499591, 1.6938166537039874],
[1.7528279426840703, 1.7963648490662445, 1.625024494263244]
]
}
Note that this particle was the closest to the coord system origin - hence
(unimportantly) lots of vertex positions that are zero or roughly zero, and
(importantly) negative cell ids which correspond to the boundaries (of which
there are three at the corner of a box, specifically ids 1, 3 and 5, (the
x_i = 0 boundaries, represented with negative ids hence -1, -3 and -5 --
this is voro++'s conventional way of referring to boundary interfaces.)
2D tessellation
You can run a simpler function to get the 2D cells around your points, with all the details handled for you:
import pyvoro
cells = pyvoro.compute_2d_voronoi(
[[5.0, 7.0], [1.7, 3.2], ...], # point positions, 2D vectors this time.
[[0.0, 10.0], [0.0, 10.0]], # box size, again only 2D this time.
2.0, # block size; same as before.
radii=[1.2, 0.9, ...] # particle radii -- optional and keyword-compatible.
)
the output follows the same schema as the 3D for now, since this is not as annoying as having a whole new schema to handle. The adjacency is now a bit redundant since the cell is a polygon and the vertices are returned in the correct order. The cells look like a list of these:
{ # note that again, this is computed with a different example
'adjacency': [
[5, 1],
[0, 2],
[1, 3],
[2, 4],
[3, 5],
[4, 0]
],
'faces': [
{ 'adjacent_cell': 23, 'vertices': [0, 5]},
{ 'adjacent_cell': -2, 'vertices': [0, 1]},
{ 'adjacent_cell': 39, 'vertices': [2, 1]},
{ 'adjacent_cell': 25, 'vertices': [2, 3]},
{ 'adjacent_cell': 12, 'vertices': [4, 3]},
{ 'adjacent_cell': 9, 'vertices': [5, 4]}
],
'original': [8.168525781010283, 5.943711239620341],
'vertices': [
[10.0, 5.324580764844442],
[10.0, 6.442713105218478],
[9.088894888250326, 7.118847221681966],
[6.740750220282158, 6.444386346261051],
[6.675322891805883, 5.678806294642725],
[7.77400067532073, 5.02320427474993]
],
'volume': 5.102702932807149
}
(note that the edges will now be indexed -1 to -4, and the 'volume' key is in fact the area.)
Note on compilation: if a cython .pyx file is being compiled in C++ mode, all
cython-visible code must be compiled "as c++" - this will not be compatible
with any C functions declared extern "C" { ... }. In this library, the author
just used c++ functions for everything, in order to be able to utilise the c++
std::vector<T> classes to represent the (ridiculously non-specific) geometry
of a Voronoi cell.
Releasing
- Update the version in
pyproject.tomland the list of changes inCHANGELOG.md, commit, and push. The Wheels workflow builds and tests the wheels on every push. - On GitHub, publish a release with the tag
vX.Y.Z. The Wheels workflow builds and tests the wheels and the source distribution again, and uploads them to PyPI.
The upload uses PyPI's trusted publishing, so no token is stored in the repository. It needs a one-time setup by the owner of the PyPI account: in Your account > Publishing, add a pending publisher for a GitHub repository with
- PyPI project name:
pyvoro-rimoli - owner:
rimoli, repository name:pyvoro - workflow name:
wheels.yml - environment name:
pypi
The first release then creates the project on PyPI.
License
pyvoro is an extension of Voro++ and is released under the same modified BSD
license (see LICENSE). Voro++ Copyright (c) 2008, The Regents of the
University of California, through Lawrence Berkeley National Laboratory.
Credits
- Voro++: Chris H. Rycroft.
- pyvoro: Joe Jordan, with contributions from Andrey Sobolev, Christopher Poole and Wendell Smith.
- pyvoro-mmalahe (Python 3 packaging): Michael Malahe, with a contribution from Oromion.
- pyvoro-rimoli (current Voro++, wheels, tests): Julian Rimoli.
1 maintainer
Metadata
1 maintainer
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