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- """
- =============================================================
- Spatial algorithms and data structures (:mod:`scipy.spatial`)
- =============================================================
- .. currentmodule:: scipy.spatial
- .. toctree::
- :hidden:
- spatial.distance
- spatial.transform
- 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 * # type: ignore[import-not-found]
- 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
|
