Spatial algorithms and data structures (scipy.spatial
)¶
Spatial transformations¶
These are contained in the scipy.spatial.transform
submodule.
Nearest-neighbor queries¶
|
kd-tree for quick nearest-neighbor lookup |
|
kd-tree for quick nearest-neighbor lookup |
|
Hyperrectangle class. |
Distance metrics are contained in the scipy.spatial.distance
submodule.
Delaunay triangulation, convex hulls, and Voronoi diagrams¶
|
Delaunay tessellation in N dimensions. |
|
Convex hulls in N dimensions. |
|
Voronoi diagrams in N dimensions. |
|
Voronoi diagrams on the surface of a sphere. |
|
Halfspace intersections in N dimensions. |
Plotting helpers¶
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Plot the given Delaunay triangulation in 2-D |
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Plot the given convex hull diagram in 2-D |
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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¶
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Find simplices containing the given points. |
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Compute the distance matrix. |
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Compute the L**p distance between two arrays. |
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Compute the pth power of the L**p distance between two arrays. |
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Procrustes analysis, a similarity test for two data sets. |
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Geometric spherical linear interpolation. |