Classe « Voronoi »

Informations générales

Héritage

builtins.object
    _QhullUser
        Voronoi

Définition

class Voronoi(_QhullUser):

help(Voronoi)

    Voronoi(points, furthest_site=False, incremental=False, qhull_options=None)

    Voronoi diagrams in N dimensions.

    .. versionadded:: 0.12.0

    Parameters
    ----------
    points : ndarray of floats, shape (npoints, ndim)
        Coordinates of points to construct a Voronoi diagram 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".)

    Attributes
    ----------
    points : ndarray of double, shape (npoints, ndim)
        Coordinates of input points.
    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.
        When qhull option "Qz" was specified, an empty sublist
        represents the Voronoi region for a point at infinity that
        was added internally.
    point_region : array 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.
        If qhull option "Qz" was specified, there will be one less
        element than the number of regions because an extra point
        at infinity is added internally to facilitate computation.
    furthest_site
        True if this was a furthest site triangulation and False if not.

        .. versionadded:: 1.4.0

    Raises
    ------
    QhullError
        Raised when Qhull encounters an error condition, such as
        geometrical degeneracy when options to resolve are not enabled.
    ValueError
        Raised if an incompatible array is given as input.

    Notes
    -----
    The Voronoi diagram is computed using the
    `Qhull library <http://www.qhull.org/>`__.

    Examples
    --------
    Voronoi diagram for a set of point:

    >>> import numpy as np
    >>> 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
    >>> fig = voronoi_plot_2d(vor)
    >>> plt.show()

    The Voronoi vertices:

    >>> vor.vertices
    array([[0.5, 0.5],
           [0.5, 1.5],
           [1.5, 0.5],
           [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], [0, 1, 3, 2], [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], [1, 3], [0, 2]]

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

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