2D and 3D Voronoi tessellations: a python entry point for the voro++ library
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README.md

pyvoro

3D Voronoi tessellations: a python entry point for the voro++ library

Recently Added Features:

Released on PyPI - thanks to a contribution from @ansobolev, you can now install the project with pip - just type pip install pyvoro, with sudo if that's your thing.

support for numpy arrays - thanks to a contribution from @christopherpoole, you can now pass in a 2D (Nx3 or Nx2) numpy array.

2D helper, which translates the results of a 3D tesselation of points on the plane back into 2D vectors and cells (see below for an example.)

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.

Installation

Recommended - installation via pip:

pip install pyvoro

Installation from source is the same as for any other python module. Issuing

python setup.py install

will install pyvoro system-wide, while

python setup.py install --user

will install it only for the current user. Any other setup.py keywords can also be used, including

python setup.py develop

to install the package in 'development' mode. Alternatively, if you want all the dependencies pulled in automatically,
you can still use pip:

pip install -e .

-e option makes pip install package from source in development mode.

You can then use the code with:

import pyvoro
pyvoro.compute_voronoi( ... )
pyvoro.compute_2d_voronoi( ... )

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.)

Initially only non-radical tessellation, and computing all information (including cell adjacency). Other code paths may be added later.

2D tessellation

You can now 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.)

NOTES:

  • 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.
  • A checkout of voro++ itself is included in this project. moving setup.py and the pyvoro folder into a newer checkout of the voro++ source may well also work, but if any of the definitions used are changed then it will fail to compile. by all means open a support issue if you need this library to work with a newer version of voro++; better still fix it and send me a pull request :)