130 lines
3.6 KiB
Python
130 lines
3.6 KiB
Python
|
"""
|
||
|
|
=============================================================
|
||
|
|
Spatial algorithms and data structures (:mod:`scipy.spatial`)
|
||
|
|
=============================================================
|
||
|
|
|
||
|
|
.. currentmodule:: scipy.spatial
|
||
|
|
|
||
|
|
.. toctree::
|
||
|
|
:hidden:
|
||
|
|
|
||
|
|
spatial.distance
|
||
|
|
|
||
|
|
Spatial transformations
|
||
|
|
=======================
|
||
|
|
|
||
|
|
These are contained in the `scipy.spatial.transform` submodule.
|
||
|
|
|
||
|
|
Nearest-neighbor queries
|
||
|
|
========================
|
||
|
|
.. autosummary::
|
||
|
|
:toctree: generated/
|
||
|
|
|
||
|
|
KDTree -- class for efficient nearest-neighbor queries
|
||
|
|
cKDTree -- class for efficient nearest-neighbor queries (faster implementation)
|
||
|
|
Rectangle
|
||
|
|
|
||
|
|
Distance metrics
|
||
|
|
================
|
||
|
|
|
||
|
|
Distance metrics are contained in the :mod:`scipy.spatial.distance` submodule.
|
||
|
|
|
||
|
|
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
|
||
|
|
HalfspaceIntersection -- compute the intersection points of input halfspaces
|
||
|
|
|
||
|
|
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, etc.) appearing in the Delaunay
|
||
|
|
tessellation (N-D simplices), convex hull facets, and Voronoi ridges
|
||
|
|
(N-1-D simplices) are represented in the following scheme::
|
||
|
|
|
||
|
|
tess = Delaunay(points)
|
||
|
|
hull = ConvexHull(points)
|
||
|
|
voro = Voronoi(points)
|
||
|
|
|
||
|
|
# coordinates of the jth vertex of the ith simplex
|
||
|
|
tess.points[tess.simplices[i, j], :] # tessellation 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 ith
|
||
|
|
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-D
|
||
|
|
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
|
||
|
|
geometric_slerp
|
||
|
|
|
||
|
|
Warnings / Errors used in :mod:`scipy.spatial`
|
||
|
|
----------------------------------------------
|
||
|
|
.. autosummary::
|
||
|
|
:toctree: generated/
|
||
|
|
|
||
|
|
QhullError
|
||
|
|
""" # noqa: E501
|
||
|
|
|
||
|
|
from ._kdtree import *
|
||
|
|
from ._ckdtree import *
|
||
|
|
from ._qhull import *
|
||
|
|
from ._spherical_voronoi import SphericalVoronoi
|
||
|
|
from ._plotutils import *
|
||
|
|
from ._procrustes import procrustes
|
||
|
|
from ._geometric_slerp import geometric_slerp
|
||
|
|
|
||
|
|
# Deprecated namespaces, to be removed in v2.0.0
|
||
|
|
from . import ckdtree, kdtree, qhull
|
||
|
|
|
||
|
|
__all__ = [s for s in dir() if not s.startswith('_')]
|
||
|
|
|
||
|
|
from . import distance, transform
|
||
|
|
|
||
|
|
__all__ += ['distance', 'transform']
|
||
|
|
|
||
|
|
from scipy._lib._testutils import PytestTester
|
||
|
|
test = PytestTester(__name__)
|
||
|
|
del PytestTester
|