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""" |
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============================================================= |
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Spatial algorithms and data structures (:mod:`scipy.spatial`) |
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============================================================= |
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.. currentmodule:: scipy.spatial |
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.. toctree:: |
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:hidden: |
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spatial.distance |
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Spatial transformations |
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======================= |
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These are contained in the `scipy.spatial.transform` submodule. |
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Nearest-neighbor queries |
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======================== |
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.. autosummary:: |
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:toctree: generated/ |
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KDTree -- class for efficient nearest-neighbor queries |
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cKDTree -- class for efficient nearest-neighbor queries (faster implementation) |
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Rectangle |
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Distance metrics |
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================ |
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Distance metrics are contained in the :mod:`scipy.spatial.distance` submodule. |
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Delaunay triangulation, convex hulls, and Voronoi diagrams |
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========================================================== |
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.. autosummary:: |
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:toctree: generated/ |
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Delaunay -- compute Delaunay triangulation of input points |
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ConvexHull -- compute a convex hull for input points |
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Voronoi -- compute a Voronoi diagram hull from input points |
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SphericalVoronoi -- compute a Voronoi diagram from input points on the surface of a sphere |
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HalfspaceIntersection -- compute the intersection points of input halfspaces |
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Plotting helpers |
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================ |
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.. autosummary:: |
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:toctree: generated/ |
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delaunay_plot_2d -- plot 2-D triangulation |
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convex_hull_plot_2d -- plot 2-D convex hull |
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voronoi_plot_2d -- plot 2-D Voronoi diagram |
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.. seealso:: :ref:`Tutorial <qhulltutorial>` |
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Simplex representation |
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====================== |
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The simplices (triangles, tetrahedra, etc.) appearing in the Delaunay |
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tessellation (N-D simplices), convex hull facets, and Voronoi ridges |
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(N-1-D simplices) are represented in the following scheme:: |
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tess = Delaunay(points) |
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hull = ConvexHull(points) |
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voro = Voronoi(points) |
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# coordinates of the jth vertex of the ith simplex |
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tess.points[tess.simplices[i, j], :] # tessellation element |
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hull.points[hull.simplices[i, j], :] # convex hull facet |
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voro.vertices[voro.ridge_vertices[i, j], :] # ridge between Voronoi cells |
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For Delaunay triangulations and convex hulls, the neighborhood |
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structure of the simplices satisfies the condition: |
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``tess.neighbors[i,j]`` is the neighboring simplex of the ith |
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simplex, opposite to the ``j``-vertex. It is -1 in case of no neighbor. |
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Convex hull facets also define a hyperplane equation:: |
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(hull.equations[i,:-1] * coord).sum() + hull.equations[i,-1] == 0 |
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Similar hyperplane equations for the Delaunay triangulation correspond |
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to the convex hull facets on the corresponding N+1-D |
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paraboloid. |
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The Delaunay triangulation objects offer a method for locating the |
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simplex containing a given point, and barycentric coordinate |
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computations. |
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Functions |
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--------- |
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.. autosummary:: |
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:toctree: generated/ |
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tsearch |
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distance_matrix |
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minkowski_distance |
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minkowski_distance_p |
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procrustes |
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geometric_slerp |
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Warnings / Errors used in :mod:`scipy.spatial` |
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---------------------------------------------- |
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.. autosummary:: |
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:toctree: generated/ |
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QhullError |
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""" |
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from ._kdtree import * |
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from ._ckdtree import * |
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from ._qhull import * |
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from ._spherical_voronoi import SphericalVoronoi |
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from ._plotutils import * |
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from ._procrustes import procrustes |
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from ._geometric_slerp import geometric_slerp |
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from . import ckdtree, kdtree, qhull |
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__all__ = [s for s in dir() if not s.startswith('_')] |
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from . import distance, transform |
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__all__ += ['distance', 'transform'] |
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from scipy._lib._testutils import PytestTester |
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test = PytestTester(__name__) |
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del PytestTester |
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