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”.) 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()
```

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.

Previous topic

scipy.spatial.ConvexHull.close