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# 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.

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