125 lines
3.6 KiB
Python
125 lines
3.6 KiB
Python
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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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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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# Deprecated namespaces, to be removed in v2.0.0
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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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