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"""
=============================================================
Spatial algorithms and data structures (:mod:`scipy.spatial`)
=============================================================
.. currentmodule:: scipy.spatial
Nearest-neighbor Queries
========================
.. autosummary::
:toctree: generated/
KDTree -- class for efficient nearest-neighbor queries
cKDTree -- class for efficient nearest-neighbor queries (faster impl.)
distance -- module containing many different distance measures
Rectangle
Delaunay Triangulation, Convex Hulls and Voronoi Diagrams
=========================================================
.. autosummary::
:toctree: generated/
Delaunay -- compute Delaunay triangulation of input points
ConvexHull -- compute a convex hull for input points
Voronoi -- compute a Voronoi diagram hull from input points
SphericalVoronoi -- compute a Voronoi diagram from input points on the surface of a sphere
Plotting Helpers
================
.. autosummary::
:toctree: generated/
delaunay_plot_2d -- plot 2-D triangulation
convex_hull_plot_2d -- plot 2-D convex hull
voronoi_plot_2d -- plot 2-D voronoi diagram
.. seealso:: :ref:`Tutorial <qhulltutorial>`
Simplex representation
======================
The simplices (triangles, tetrahedra, ...) appearing in the Delaunay
tesselation (N-dim simplices), convex hull facets, and Voronoi ridges
(N-1 dim simplices) are represented in the following scheme::
tess = Delaunay(points)
hull = ConvexHull(points)
voro = Voronoi(points)
# coordinates of the j-th vertex of the i-th simplex
tess.points[tess.simplices[i, j], :] # tesselation element
hull.points[hull.simplices[i, j], :] # convex hull facet
voro.vertices[voro.ridge_vertices[i, j], :] # ridge between Voronoi cells
For Delaunay triangulations and convex hulls, the neighborhood
structure of the simplices satisfies the condition:
``tess.neighbors[i,j]`` is the neighboring simplex of the i-th
simplex, opposite to the j-vertex. It is -1 in case of no
neighbor.
Convex hull facets also define a hyperplane equation::
(hull.equations[i,:-1] * coord).sum() + hull.equations[i,-1] == 0
Similar hyperplane equations for the Delaunay triangulation correspond
to the convex hull facets on the corresponding N+1 dimensional
paraboloid.
The Delaunay triangulation objects offer a method for locating the
simplex containing a given point, and barycentric coordinate
computations.
Functions
---------
.. autosummary::
:toctree: generated/
tsearch
distance_matrix
minkowski_distance
minkowski_distance_p
procrustes
"""
from __future__ import division, print_function, absolute_import
from .kdtree import *
from .ckdtree import *
from .qhull import *
from ._spherical_voronoi import SphericalVoronoi
from ._plotutils import *
from ._procrustes import procrustes
__all__ = [s for s in dir() if not s.startswith('_')]
__all__ += ['distance']
from . import distance
from numpy.testing import Tester
test = Tester().test
bench = Tester().bench
|
