Spatial algorithms and data structures (scipy.spatial)#
Spatial transformations#
These are contained in the scipy.spatial.transform submodule.
Nearest-neighbor queries#
Distance metrics#
Distance metrics are contained in the scipy.spatial.distance submodule.
Delaunay triangulation, convex hulls, and Voronoi diagrams#
Delaunay(points[, furthest_site, ...])
Delaunay tessellation in N dimensions.
ConvexHull(points[, incremental, qhull_options])
Convex hulls in N dimensions.
Voronoi(points[, furthest_site, ...])
Voronoi diagrams in N dimensions.
SphericalVoronoi(points[, radius, center, ...])
Voronoi diagrams on the surface of a sphere.
HalfspaceIntersection(halfspaces, interior_point)
Halfspace intersections in N dimensions.
Plotting helpers#
delaunay_plot_2d(tri[, ax])
Plot the given Delaunay triangulation in 2-D
convex_hull_plot_2d(hull[, ax])
Plot the given convex hull diagram in 2-D
voronoi_plot_2d(vor[, ax])
Plot the given Voronoi diagram in 2-D
See also
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#
tsearch(tri, xi)
Find simplices containing the given points.
distance_matrix(x, y[, p, threshold])
Compute the distance matrix.
minkowski_distance(x, y[, p])
Compute the L**p distance between two arrays.
minkowski_distance_p(x, y[, p])
Compute the pth power of the L**p distance between two arrays.
procrustes(data1, data2)
Procrustes analysis, a similarity test for two data sets.
geometric_slerp(start, end, t[, tol])
Geometric spherical linear interpolation.
Warnings / Errors used in scipy.spatial #
Raised when Qhull encounters an error condition, such as geometrical degeneracy when options to resolve are not enabled.