Spatial algorithms and data structures (scipy.spatial)¶
Nearest-neighbor Queries¶
| KDTree(data[, leafsize]) | kd-tree for quick nearest-neighbor lookup |
| cKDTree | kd-tree for quick nearest-neighbor lookup |
| distance |
Delaunay Triangulation, Convex Hulls and Voronoi Diagrams¶
| Delaunay(points[, furthest_site, ...]) | Delaunay tesselation in N dimensions. |
| ConvexHull(points[, furthest_site, ...]) | Convex hulls in N dimensions. |
| Voronoi(points[, furthest_site, ...]) | Voronoi diagrams 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, ...) 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¶
| 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 p-th power of the L**p distance between two arrays. |