pyvoro2 0.4.2

Python bindings for Voro++ (3D Voronoi and Laguerre tessellations) with periodic and topology utilities.

pyvoro2

Documentation: https://IvanChernyshov.github.io/pyvoro2/

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pyvoro2 is a Python interface to the C++ library Voro++ for computing 3D tessellations around a set of points:

• Voronoi tessellations (standard, unweighted)
• power / Laguerre tessellations (weighted Voronoi, via per-site radii)

The focus is not only on computing polyhedra, but on making the results useful in scientific settings that are common in chemistry, materials science, and condensed matter physics — especially periodic boundary conditions and neighbor graphs.

pyvoro2 is designed to be honest and predictable:

• it vendors and wraps an upstream Voro++ snapshot (with a small numeric robustness patch for power/Laguerre diagrams);
• the core tessellation modes are standard Voronoi and power/Laguerre.

Quickstart

1) Standard Voronoi in a bounding box

For 3D visualization, install the optional dependency: pip install "pyvoro2[viz]".

import numpy as np
import pyvoro2 as pv
from pyvoro2.viz3d import view_tessellation

points = np.random.default_rng(0).uniform(-1.5, 1.5, size=(10, 3))
box = pv.Box(((-2, 2), (-2, 2), (-2, 2)))
cells = pv.compute(points, domain=box, mode='standard')

view_tessellation(
    cells,
    domain=box,
    show_vertices=False,
)

2) Power/Laguerre tessellation (weighted Voronoi)

radii = np.full(len(points), 1.2)

cells = pv.compute(
    points,
    domain=box,
    mode='power',
    radii=radii,
    include_empty=True,  # power diagrams can have zero-volume cells
)

3) Periodic crystal cell with neighbor image shifts

cell = pv.PeriodicCell(
    vectors=(
        (10.0, 0.0, 0.0),
        (2.0,  9.0, 0.0),
        (1.0,  0.5, 8.0),
    )
)

cells = pv.compute(points, domain=cell, return_face_shifts=True)

# Each face can include:
#   adjacent_cell  (neighbor id)
#   adjacent_shift (which periodic image produced the face)

Numerical safety notes

Voro++ uses a few fixed absolute tolerances internally (most importantly a hard near-duplicate check around ~1e-5 in container distance units). For very small or very large coordinate systems, this can lead to hard process termination or loss of accuracy.

pyvoro2 does not silently rescale your coordinates. If you work in unusual units, rescale explicitly before calling into the C++ layer.

As an additional safety net, you can ask pyvoro2 to run a fast Python-side near-duplicate pre-check before entering the C++ layer:

cells = pv.compute(points, domain=cell, duplicate_check='raise')

For stricter post-hoc checks, see:

• pyvoro2.validate_tessellation(..., level='strict')
• pyvoro2.validate_normalized_topology(..., level='strict')

Note: pyvoro2 vendors a Voro++ snapshot that includes the upstream numeric robustness fix for power/Laguerre mode (radical pruning). This avoids rare cross-platform edge cases where fully periodic power tessellations could yield a non-reciprocal face/neighbor graph under aggressive floating-point codegen.

Why use pyvoro2

Voro++ is fast and feature-rich, but it is a C++ library with a low-level API. pyvoro2 aims to be a scientific interface that stays close to Voro++ while adding practical pieces that are easy to get wrong:

• triclinic periodic cells (PeriodicCell) with robust coordinate mapping
• partially periodic orthorhombic cells (OrthorhombicCell) for slabs and wires
• optional per-face periodic image shifts (adjacent_shift) for building periodic graphs
• diagnostics and normalization utilities for reproducible topology work
• convenience operations beyond full tessellation:
  • locate(...) (owner lookup for arbitrary query points)
  • ghost_cells(...) (probe cell at a query point without inserting it)
  • inverse fitting utilities for fitting power weights from desired pairwise plane locations

Documentation overview

The documentation is written as a short scientific tutorial: it starts with the geometric ideas, then explains domains and operations, and only then dives into implementation-oriented details.

Section	What it contains
Concepts	What Voronoi and power/Laguerre tessellations are, and what you can expect from them.
Domains	Which containers exist (Box, OrthorhombicCell, PeriodicCell) and how to choose between them.
Operations	How to compute tessellations, assign query points, and compute probe (ghost) cells.
Topology and graphs	How to build a neighbor graph that respects periodic images, and how normalization helps.
Inverse fitting	Fit power/Laguerre radii from desired pairwise plane positions (with optional constraints/penalties).
Visualization	Optional py3Dmol helpers for debugging and exploratory analysis.
Examples (notebooks)	End-to-end examples that combine the pieces above.
API reference	The full reference (docstrings).

Installation

Most users should install a prebuilt wheel:

pip install pyvoro2

To build from source (requires a C++ compiler and Python development headers):

pip install -e .

Testing

pyvoro2 uses pytest. The default test suite is intended to be fast and deterministic:

pip install -e ".[test]"
pytest

Additional test groups are opt-in:

• Fuzz/property tests (randomized):

  pytest -m fuzz --fuzz-n 100
  

• Cross-check tests vs pyvoro (requires installing pyvoro first):

  pip install pyvoro
  pytest -m pyvoro --fuzz-n 100
  

• Slow tests (if any are added in the future):

  pytest -m slow
  

Tip: you can combine markers, e.g. pytest -m "fuzz and pyvoro" --fuzz-n 100.

Project status

pyvoro2 is currently in beta.

The core tessellation modes (standard and power/Laguerre) are stable, and a large part of the work in this repository focuses on tests and documentation. A future 1.0 release is planned once the inverse-fitting workflow is more mature and native 2D support is added.

AI-assisted development

Some parts of the implementation, tests, and documentation were developed with AI assistance (OpenAI ChatGPT). The maintainer reviews and integrates changes, and remains responsible for the resulting code and scientific claims.

Details are documented in the AI usage page.

License

• pyvoro2 is released under the MIT License.
• Voro++ is vendored and redistributed under its original license (see the project pages).

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This README is auto-generated from the MkDocs sources in docs/. To update it, edit the docs pages and re-run: python tools/gen_readme.py.