ó ʽ÷Xc@`sÒdZddlmZmZmZddlTddlTddlTddlm Z ddl Tddl m Z ge ƒD]Zejdƒste^qtZedg7Zdd lmZdd lmZeƒjZd S( s× ============================================================= 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 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, ...) 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 i(tdivisiontprint_functiontabsolute_importi(t*(tSphericalVoronoi(t procrustest_tdistance(R(tTesterN(t__doc__t __future__RRRtkdtreetckdtreetqhullt_spherical_voronoiRt _plotutilst _procrustesRtdirtst startswitht__all__tRt numpy.testingRttest(((s5/tmp/pip-build-7oUkmx/scipy/scipy/spatial/__init__.pytYs    +