Classe « SphericalVoronoi »

Informations générales

Héritage

builtins.object
    SphericalVoronoi

Définition

class SphericalVoronoi(builtins.object):

help(SphericalVoronoi)

Voronoi diagrams on the surface of a sphere.

.. versionadded:: 0.18.0

Parameters
----------
points : ndarray of floats, shape (npoints, ndim)
    Coordinates of points from which to construct a spherical
    Voronoi diagram.
radius : float, optional
    Radius of the sphere (Default: 1)
center : ndarray of floats, shape (ndim,)
    Center of sphere (Default: origin)
threshold : float
    Threshold for detecting duplicate points and
    mismatches between points and sphere parameters.
    (Default: 1e-06)

Attributes
----------
points : double array of shape (npoints, ndim)
    the points in `ndim` dimensions to generate the Voronoi diagram from
radius : double
    radius of the sphere
center : double array of shape (ndim,)
    center of the sphere
vertices : double array of shape (nvertices, ndim)
    Voronoi vertices corresponding to points
regions : list of list of integers of shape (npoints, _ )
    the n-th entry is a list consisting of the indices
    of the vertices belonging to the n-th point in points

Methods
-------
calculate_areas
    Calculates the areas of the Voronoi regions. For 2D point sets, the
    regions are circular arcs. The sum of the areas is ``2 * pi * radius``.
    For 3D point sets, the regions are spherical polygons. The sum of the
    areas is ``4 * pi * radius**2``.

Raises
------
ValueError
    If there are duplicates in `points`.
    If the provided `radius` is not consistent with `points`.

Notes
-----
The spherical Voronoi diagram algorithm proceeds as follows. The Convex
Hull of the input points (generators) is calculated, and is equivalent to
their Delaunay triangulation on the surface of the sphere [Caroli]_.
The Convex Hull neighbour information is then used to
order the Voronoi region vertices around each generator. The latter
approach is substantially less sensitive to floating point issues than
angle-based methods of Voronoi region vertex sorting.

Empirical assessment of spherical Voronoi algorithm performance suggests
quadratic time complexity (loglinear is optimal, but algorithms are more
challenging to implement).

References
----------
.. [Caroli] Caroli et al. Robust and Efficient Delaunay triangulations of
            points on or close to a sphere. Research Report RR-7004, 2009.

.. [VanOosterom] Van Oosterom and Strackee. The solid angle of a plane
                 triangle. IEEE Transactions on Biomedical Engineering,
                 2, 1983, pp 125--126.

See Also
--------
Voronoi : Conventional Voronoi diagrams in N dimensions.

Examples
--------
Do some imports and take some points on a cube:

>>> import numpy as np
>>> import matplotlib.pyplot as plt
>>> from scipy.spatial import SphericalVoronoi, geometric_slerp
>>> from mpl_toolkits.mplot3d import proj3d
>>> # set input data
>>> points = np.array([[0, 0, 1], [0, 0, -1], [1, 0, 0],
...                    [0, 1, 0], [0, -1, 0], [-1, 0, 0], ])

Calculate the spherical Voronoi diagram:

>>> radius = 1
>>> center = np.array([0, 0, 0])
>>> sv = SphericalVoronoi(points, radius, center)

Generate plot:

>>> # sort vertices (optional, helpful for plotting)
>>> sv.sort_vertices_of_regions()
>>> t_vals = np.linspace(0, 1, 2000)
>>> fig = plt.figure()
>>> ax = fig.add_subplot(111, projection='3d')
>>> # plot the unit sphere for reference (optional)
>>> u = np.linspace(0, 2 * np.pi, 100)
>>> v = np.linspace(0, np.pi, 100)
>>> x = np.outer(np.cos(u), np.sin(v))
>>> y = np.outer(np.sin(u), np.sin(v))
>>> z = np.outer(np.ones(np.size(u)), np.cos(v))
>>> ax.plot_surface(x, y, z, color='y', alpha=0.1)
>>> # plot generator points
>>> ax.scatter(points[:, 0], points[:, 1], points[:, 2], c='b')
>>> # plot Voronoi vertices
>>> ax.scatter(sv.vertices[:, 0], sv.vertices[:, 1], sv.vertices[:, 2],
...                    c='g')
>>> # indicate Voronoi regions (as Euclidean polygons)
>>> for region in sv.regions:
...    n = len(region)
...    for i in range(n):
...        start = sv.vertices[region][i]
...        end = sv.vertices[region][(i + 1) % n]
...        result = geometric_slerp(start, end, t_vals)
...        ax.plot(result[..., 0],
...                result[..., 1],
...                result[..., 2],
...                c='k')
>>> ax.azim = 10
>>> ax.elev = 40
>>> _ = ax.set_xticks([])
>>> _ = ax.set_yticks([])
>>> _ = ax.set_zticks([])
>>> fig.set_size_inches(4, 4)
>>> plt.show()

Constructeur(s)

Signature du constructeur	Description
__init__(self, points, radius=1, center=None, threshold=1e-06)

Liste des opérateurs

Opérateurs hérités de la classe object

__eq__, __ge__, __gt__, __le__, __lt__, __ne__

Liste des méthodes

Toutes les méthodes Méthodes d'instance Méthodes statiques

Signature de la méthode	Description
calculate_areas(self)	Calculates the areas of the Voronoi regions. _{[extrait de calculate_areas.__doc__]}
sort_vertices_of_regions(self)	Sort indices of the vertices to be (counter-)clockwise ordered. _{[extrait de sort_vertices_of_regions.__doc__]}