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

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pyvoro

======

3D Voronoi tessellations: a python entry point for the [voro++ library](http://math.lbl.gov/voro++/)

**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](https://pythonhosted.org/an_example_pypi_project/setuptools.html#using-setup-py) `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:

--------

```python

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:

```python

{ # (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:

```python

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:

```python

{ # 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 :)

======

3D Voronoi tessellations: a python entry point for the [voro++ library](http://math.lbl.gov/voro++/)

**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](https://pythonhosted.org/an_example_pypi_project/setuptools.html#using-setup-py) `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:

--------

```python

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:

```python

{ # (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:

```python

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:

```python

{ # 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 :)

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