Voronoi Module¶

class
freud.voronoi.
Voronoi
(box, buff=0.1)[source]¶ Compute the Voronoi tessellation of a 2D or 3D system using qhull. This uses
scipy.spatial.Voronoi
, accounting for periodic boundary conditions.Module author: Benjamin Schultz <baschult@umich.edu>
Module author: Yina Geng <yinageng@umich.edu>
Module author: Mayank Agrawal <amayank@umich.edu>
Module author: Bradley Dice <bdice@bradleydice.com>
Since qhull does not support periodic boundary conditions natively, we expand the box to include a portion of the particles’ periodic images. The buffer width is given by the parameter
buff
. The computation of Voronoi tessellations and neighbors is only guaranteed to be correct ifbuff >= L/2
whereL
is the longest side of the simulation box. For dense systems with particles filling the entire simulation volume, a smaller value forbuff
is acceptable.
compute
(positions, box=None, buff=None)[source]¶ Compute Voronoi diagram.
Parameters:  box (
freud.box.Box
) – simulation box  buff (float) – buffer width
 box (

computeNeighbors
(positions, box=None, buff=None, exclude_ii=True)[source]¶ Compute the neighbors of each particle based on the Voronoi tessellation. One can include neighbors from multiple Voronoi shells by specifying
numShells
ingetNeighbors()
. An example of computing neighbors from the first two Voronoi shells for a 2D mesh is shown below.Retrieve the results with
getNeighbors()
.Example:
from freud import box, voronoi import numpy as np vor = voronoi.Voronoi(box.Box(5, 5, is2D=True)) pos = np.array([[0, 0, 0], [0, 1, 0], [0, 2, 0], [1, 0, 0], [1, 1, 0], [1, 2, 0], [2, 0, 0], [2, 1, 0], [2, 2, 0]], dtype=np.float32) first_shell = vor.computeNeighbors(pos).getNeighbors(1) second_shell = vor.computeNeighbors(pos).getNeighbors(2) print('First shell:', first_shell) print('Second shell:', second_shell)
Note
Input positions must be a 3D array. For 2D, set the z value to 0.

computeVolumes
()[source]¶ Computes volumes (areas in 2D) of Voronoi cells.
New in version 0.8.
Must call
compute()
before this method.Retrieve the results with
getVolumes()
.

getNeighborList
()[source]¶ Returns a neighbor list object.
In the neighbor list, each neighbor pair has a weight value.
In 2D systems, the bond weight is the “ridge length” of the Voronoi boundary line between the neighboring particles.
In 3D systems, the bond weight is the “ridge area” of the Voronoi boundary polygon between the neighboring particles.
Returns: Neighbor list Return type: NeighborList

getNeighbors
(numShells)[source]¶ Get
numShells
of neighbors for each particleMust call
computeNeighbors()
before this method.Parameters: numShells (int) – number of neighbor shells

getVolumes
()[source]¶ Returns an array of volumes (areas in 2D) corresponding to Voronoi cells.
New in version 0.8.
Must call
computeVolumes()
before this method.If the buffer width is too small, then some polytopes may not be closed (they may have a boundary at infinity), and these polytopes’ volumes/areas are excluded from the list.
The length of the list returned by this method should be the same as the array of positions used in the
compute()
method, if all the polytopes are closed. Otherwise try using a larger buffer width.Returns: numpy.ndarray
containing Voronoi polytope volumes/areas.Return type: numpy.ndarray
, shape= \(\left(N_{cells} \right)\), dtype=numpy.float32

getVoronoiPolytopes
()[source]¶ Returns a list of polytope vertices corresponding to Voronoi cells.
If the buffer width is too small, then some polytopes may not be closed (they may have a boundary at infinity), and these polytopes’ vertices are excluded from the list.
The length of the list returned by this method should be the same as the array of positions used in the
compute()
method, if all the polytopes are closed. Otherwise try using a larger buffer width.Returns: List of numpy.ndarray
containing Voronoi polytope verticesReturn type: list

setBox
(box)[source]¶ Reset the simulation box.
Parameters: box ( freud.box.Box
) – simulation box
