scipy.spatial

Spatial algorithms and data structures (scipy.spatial)

• spatial.distance

• spatial.transform

Spatial transformations

These are contained in the scipy.spatial.transform submodule.

Nearest-neighbor queries

.. autosummary:: 
    :toctree:generated/
    KDTree      -- class for efficient nearest-neighbor queries
    cKDTree     -- class for efficient nearest-neighbor queries (faster implementation)
    Rectangle

Distance metrics

Distance metrics are contained in the scipy.spatial.distance submodule.

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

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

.. autosummary:: 
    :toctree:generated/
    tsearch
    distance_matrix
    minkowski_distance
    minkowski_distance_p
    procrustes
    geometric_slerp

Warnings / Errors used in scipy.spatial

.. autosummary:: 
    :toctree:generated/
    QhullError