_MhdZddlTddlTddlTddlmZddlTddlmZddl m Z ddl m Z m Z mZdeDZddl mZmZed d gz Zd d lmZeeZ[d S)aC ============================================================= 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 ` 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 )*)SphericalVoronoi) procrustes)geometric_slerp)ckdtreekdtreeqhullc<g|]}|d|S)_) startswith).0ss V/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/scipy/spatial/__init__.py rys) 5 5 51<<#4#4 51 5 5 5)distance transformrr) PytestTesterN)__doc___kdtree_ckdtree_qhull_spherical_voronoir _plotutils _procrustesr_geometric_slerprrrr dir__all__rrscipy._lib._testutilsr__name__testrrr%skkZ000000######------%$$$$$$$$$ 5 5ccee 5 5 5!!!!!!!!J $$......|HLLr