scipy.spatial.Voronoi

class scipy.spatial.Voronoi(points, furthest_site=False, incremental=False, qhull_options=None)

Voronoi diagrams in N dimensions.

New in version 0.12.0.

Parameters :

points : ndarray of floats, shape (npoints, ndim)

Coordinates of points to construct a convex hull from

furthest_site : bool, optional

Whether to compute a furthest-site Voronoi diagram. Default: False

incremental : bool, optional

Allow adding new points incrementally. This takes up some additional resources.

qhull_options : str, optional

Additional options to pass to Qhull. See Qhull manual for details. (Default: “Qbb Qc Qz Qx” for ndim > 4 and “Qbb Qc Qz” otherwise. Incremental mode omits “Qz”.)

Raises :

QhullError :

Raised when Qhull encounters an error condition, such as geometrical degeneracy when options to resolve are not enabled.

Notes

The Voronoi diagram is computed using the Qhull libary [Qhull].

References

[Qhull]

(1, 2) http://www.qhull.org/

Examples

Voronoi diagram for a set of point:

>>> points = np.array([[0, 0], [0, 1], [0, 2], [1, 0], [1, 1], [1, 2],
...                    [2, 0], [2, 1], [2, 2]])
>>> from scipy.spatial import Voronoi, voronoi_plot_2d
>>> vor = Voronoi(points)

Plot it:

>>> import matplotlib.pyplot as plt
>>> voronoi_plot_2d(vor)
>>> plt.show()

(Source code)

The Voronoi vertices:

>>> vor.vertices
array([[ 0.5,  0.5],
       [ 1.5,  0.5],
       [ 0.5,  1.5],
       [ 1.5,  1.5]])

There is a single finite Voronoi region, and four finite Voronoi ridges:

>>> vor.regions
[[], [-1, 0], [-1, 1], [1, -1, 0], [3, -1, 2], [-1, 3], [-1, 2], [3, 2, 0, 1], [2, -1, 0], [3, -1, 1]]
>>> vor.ridge_vertices
[[-1, 0], [-1, 0], [-1, 1], [-1, 1], [0, 1], [-1, 3], [-1, 2], [2, 3], [-1, 3], [-1, 2], [0, 2], [1, 3]]

The ridges are perpendicular between lines drawn between the following input points:

>>> vor.ridge_points
array([[0, 1],
       [0, 3],
       [6, 3],
       [6, 7],
       [3, 4],
       [5, 8],
       [5, 2],
       [5, 4],
       [8, 7],
       [2, 1],
       [4, 1],
       [4, 7]], dtype=int32)

Attributes

points	(ndarray of double, shape (npoints, ndim)) Points used for constructing the Voronoi diagram.
vertices	(ndarray of double, shape (nvertices, ndim)) Coordinates of the Voronoi vertices.
ridge_points	(ndarray of ints, shape (nridges, 2)) Indices of the points between which each Voronoi ridge lies.
ridge_vertices	(list of list of ints, shape (nridges, *)) Indices of the Voronoi vertices forming each Voronoi ridge.
regions	(list of list of ints, shape (nregions, *)) Indices of the Voronoi vertices forming each Voronoi region. -1 indicates vertex outside the Voronoi diagram.
point_region	(list of ints, shape (npoints)) Index of the Voronoi region for each input point. If qhull option “Qc” was not specified, the list will contain -1 for points that are not associated with a Voronoi region.

Methods

add_points(points[, restart])	Process a set of additional new points.
close()	Finish incremental processing.