Spatial algorithms and data structures (scipy.spatial) — SciPy v1.15.3 Manual (original) (raw)
Spatial transformations#
These are contained in the scipy.spatial.transform submodule.
Nearest-neighbor queries#
| KDTree(data[, leafsize, compact_nodes, ...]) | kd-tree for quick nearest-neighbor lookup. |
|---|---|
| cKDTree(data[, leafsize, compact_nodes, ...]) | kd-tree for quick nearest-neighbor lookup |
| Rectangle(maxes, mins) | Hyperrectangle class. |
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. |
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| 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#
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. |
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| 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. |