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File: C:/Users/fred/anaconda3/Lib/site-packages/scipy/spatial/_qhull.cp312-win_amd64.pyd
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Wrappers for Qhull triangulation, plus some additional N-D geometry utilities

.. versionadded:: 0.9

: ASCIIAll dimensions preceding dimension %d must be indexed and not slicedAssertionErrorAttributeErrorBuffer view does not expose stridesCC:\b\abs_efv75hqhju\croot\scipy_1717521501389\work\scipy\spatial\_qhull.pyxCan only create a buffer that is contiguous in memory.Cannot assign to read-only memoryviewCannot compute for DelaunayCannot create writable memory view from read-only memoryviewCannot index with type 'Cannot transpose memoryview with indirect dimensionsConvexHullConvexHull.__init__ConvexHull._updateConvexHull.add_pointsConvexHull.points
    ConvexHull(points, incremental=False, qhull_options=None)

    Convex hulls in N dimensions.

    .. versionadded:: 0.12.0

    Parameters
    ----------
    points : ndarray of floats, shape (npoints, ndim)
        Coordinates of points to construct a convex hull from
    incremental : bool, optional
        Allow adding new points incrementally. This takes up some additional
        resources.
    qhull_options : str, optional
        Additional options to pass to Qhull. See Qhull manual
        for details. (Default: "Qx" for ndim > 4 and "" otherwise)
        Option "Qt" is always enabled.

    Attributes
    ----------
    points : ndarray of double, shape (npoints, ndim)
        Coordinates of input points.
    vertices : ndarray of ints, shape (nvertices,)
        Indices of points forming the vertices of the convex hull.
        For 2-D convex hulls, the vertices are in counterclockwise order.
        For other dimensions, they are in input order.
    simplices : ndarray of ints, shape (nfacet, ndim)
        Indices of points forming the simplical facets of the convex hull.
    neighbors : ndarray of ints, shape (nfacet, ndim)
        Indices of neighbor facets for each facet.
        The kth neighbor is opposite to the kth vertex.
        -1 denotes no neighbor.
    equations : ndarray of double, shape (nfacet, ndim+1)
        [normal, offset] forming the hyperplane equation of the facet
        (see `Qhull documentation <http://www.qhull.org/>`__  for more).
    coplanar : ndarray of int, shape (ncoplanar, 3)
        Indices of coplanar points and the corresponding indices of
        the nearest facets and nearest vertex indices.  Coplanar
        points are input points which were *not* included in the
        triangulation due to numerical precision issues.

        If option "Qc" is not specified, this list is not computed.
    good : ndarray of bool or None
        A one-dimensional Boolean array indicating which facets are
        good. Used with options that compute good facets, e.g. QGn
        and QG-n. Good facets are defined as those that are
        visible (n) or invisible (-n) from point n, where
        n is the nth point in 'points'. The 'good' attribute may be
        used as an index into 'simplices' to return the good (visible)
        facets: simplices[good]. A facet is visible from the outside
        of the hull only, and neither coplanarity nor degeneracy count
        as cases of visibility.

        If a "QGn" or "QG-n" option is not specified, None is returned.

        .. versionadded:: 1.3.0
    area : float
        Surface area of the convex hull when input dimension > 2.
        When input `points` are 2-dimensional, this is the perimeter of the convex hull.

        .. versionadded:: 0.17.0
    volume : float
        Volume of the convex hull when input dimension > 2.
        When input `points` are 2-dimensional, this is the area of the convex hull.

        .. versionadded:: 0.17.0

    Raises
    ------
    QhullError
        Raised when Qhull encounters an error condition, such as
        geometrical degeneracy when options to resolve are not enabled.
    ValueError
        Raised if an incompatible array is given as input.

    Notes
    -----
    The convex hull is computed using the
    `Qhull library <http://www.qhull.org/>`__.

    Examples
    --------

    Convex hull of a random set of points:

    >>> from scipy.spatial import ConvexHull, convex_hull_plot_2d
    >>> import numpy as np
    >>> rng = np.random.default_rng()
    >>> points = rng.random((30, 2))   # 30 random points in 2-D
    >>> hull = ConvexHull(points)

    Plot it:

    >>> import matplotlib.pyplot as plt
    >>> plt.plot(points[:,0], points[:,1], 'o')
    >>> for simplex in hull.simplices:
    ...     plt.plot(points[simplex, 0], points[simplex, 1], 'k-')

    We could also have directly used the vertices of the hull, which
    for 2-D are guaranteed to be in counterclockwise order:

    >>> plt.plot(points[hull.vertices,0], points[hull.vertices,1], 'r--', lw=2)
    >>> plt.plot(points[hull.vertices[0],0], points[hull.vertices[0],1], 'ro')
    >>> plt.show()

    Facets visible from a point:

    Create a square and add a point above the square.

    >>> generators = np.array([[0.2, 0.2],
    ...                        [0.2, 0.4],
    ...                        [0.4, 0.4],
    ...                        [0.4, 0.2],
    ...                        [0.3, 0.6]])

    Call ConvexHull with the QG option. QG4 means
    compute the portions of the hull not including
    point 4, indicating the facets that are visible
    from point 4.

    >>> hull = ConvexHull(points=generators,
    ...                   qhull_options='QG4')

    The "good" array indicates which facets are
    visible from point 4.

    >>> print(hull.simplices)
        [[1 0]
         [1 2]
         [3 0]
         [3 2]]
    >>> print(hull.good)
        [False  True False False]

    Now plot it, highlighting the visible facets.

    >>> fig = plt.figure()
    >>> ax = fig.add_subplot(1,1,1)
    >>> for visible_facet in hull.simplices[hull.good]:
    ...     ax.plot(hull.points[visible_facet, 0],
    ...             hull.points[visible_facet, 1],
    ...             color='violet',
    ...             lw=6)
    >>> convex_hull_plot_2d(hull, ax=ax)
        <Figure size 640x480 with 1 Axes> # may vary
    >>> plt.show()

    References
    ----------
    .. [Qhull] http://www.qhull.org/

    ConvexHull.verticesDelaunayDelaunay.__init__Delaunay._updateDelaunay.add_pointsDelaunay.convex_hullDelaunay.find_simplexDelaunay.lift_pointsDelaunay.plane_distanceDelaunay.points
    Delaunay(points, furthest_site=False, incremental=False, qhull_options=None)

    Delaunay tessellation in N dimensions.

    .. versionadded:: 0.9

    Parameters
    ----------
    points : ndarray of floats, shape (npoints, ndim)
        Coordinates of points to triangulate
    furthest_site : bool, optional
        Whether to compute a furthest-site Delaunay triangulation.
        Default: False

        .. versionadded:: 0.12.0
    incremental : bool, optional
        Allow adding new points incrementally. This takes up some additional
        resources.
    qhull_options : str, optional
        Additional options to pass to Qhull. See Qhull manual for
        details. Option "Qt" is always enabled.
        Default:"Qbb Qc Qz Qx Q12" for ndim > 4 and "Qbb Qc Qz Q12" otherwise.
        Incremental mode omits "Qz".

        .. versionadded:: 0.12.0

    Attributes
    ----------
    points : ndarray of double, shape (npoints, ndim)
        Coordinates of input points.
    simplices : ndarray of ints, shape (nsimplex, ndim+1)
        Indices of the points forming the simplices in the triangulation.
        For 2-D, the points are oriented counterclockwise.
    neighbors : ndarray of ints, shape (nsimplex, ndim+1)
        Indices of neighbor simplices for each simplex.
        The kth neighbor is opposite to the kth vertex.
        For simplices at the boundary, -1 denotes no neighbor.
    equations : ndarray of double, shape (nsimplex, ndim+2)
        [normal, offset] forming the hyperplane equation of the facet
        on the paraboloid
        (see `Qhull documentation <http://www.qhull.org/>`__ for more).
    paraboloid_scale, paraboloid_shift : float
        Scale and shift for the extra paraboloid dimension
        (see `Qhull documentation <http://www.qhull.org/>`__ for more).
    transform : ndarray of double, shape (nsimplex, ndim+1, ndim)
        Affine transform from ``x`` to the barycentric coordinates ``c``.
        This is defined by::

            T c = x - r

        At vertex ``j``, ``c_j = 1`` and the other coordinates zero.

        For simplex ``i``, ``transform[i,:ndim,:ndim]`` contains
        inverse of the matrix ``T``, and ``transform[i,ndim,:]``
        contains the vector ``r``.

        If the simplex is degenerate or nearly degenerate, its
        barycentric transform contains NaNs.
    vertex_to_simplex : ndarray of int, shape (npoints,)
        Lookup array, from a vertex, to some simplex which it is a part of.
        If qhull option "Qc" was not specified, the list will contain -1
        for points that are not vertices of the tessellation.
    convex_hull : ndarray of int, shape (nfaces, ndim)
        Vertices of facets forming the convex hull of the point set.
        The array contains the indices of the points belonging to
        the (N-1)-dimensional facets that form the convex hull
        of the triangulation.

        .. note::

           Computing convex hulls via the Delaunay triangulation is
           inefficient and subject to increased numerical instability.
           Use `ConvexHull` instead.
    coplanar : ndarray of int, shape (ncoplanar, 3)
        Indices of coplanar points and the corresponding indices of
        the nearest facet and the nearest vertex.  Coplanar
        points are input points which were *not* included in the
        triangulation due to numerical precision issues.

        If option "Qc" is not specified, this list is not computed.

        .. versionadded:: 0.12.0
    vertex_neighbor_vertices : tuple of two ndarrays of int; (indptr, indices)
        Neighboring vertices of vertices. The indices of neighboring
        vertices of vertex `k` are ``indices[indptr[k]:indptr[k+1]]``.
    furthest_site
        True if this was a furthest site triangulation and False if not.

        .. versionadded:: 1.4.0

    Raises
    ------
    QhullError
        Raised when Qhull encounters an error condition, such as
        geometrical degeneracy when options to resolve are not enabled.
    ValueError
        Raised if an incompatible array is given as input.

    Notes
    -----
    The tessellation is computed using the Qhull library
    `Qhull library <http://www.qhull.org/>`__.

    .. note::

       Unless you pass in the Qhull option "QJ", Qhull does not
       guarantee that each input point appears as a vertex in the
       Delaunay triangulation. Omitted points are listed in the
       `coplanar` attribute.

    Examples
    --------
    Triangulation of a set of points:

    >>> import numpy as np
    >>> points = np.array([[0, 0], [0, 1.1], [1, 0], [1, 1]])
    >>> from scipy.spatial import Delaunay
    >>> tri = Delaunay(points)

    We can plot it:

    >>> import matplotlib.pyplot as plt
    >>> plt.triplot(points[:,0], points[:,1], tri.simplices)
    >>> plt.plot(points[:,0], points[:,1], 'o')
    >>> plt.show()

    Point indices and coordinates for the two triangles forming the
    triangulation:

    >>> tri.simplices
    array([[2, 3, 0],                 # may vary
           [3, 1, 0]], dtype=int32)

    Note that depending on how rounding errors go, the simplices may
    be in a different order than above.

    >>> points[tri.simplices]
    array([[[ 1. ,  0. ],            # may vary
            [ 1. ,  1. ],
            [ 0. ,  0. ]],
           [[ 1. ,  1. ],
            [ 0. ,  1.1],
            [ 0. ,  0. ]]])

    Triangle 0 is the only neighbor of triangle 1, and it's opposite to
    vertex 1 of triangle 1:

    >>> tri.neighbors[1]
    array([-1,  0, -1], dtype=int32)
    >>> points[tri.simplices[1,1]]
    array([ 0. ,  1.1])

    We can find out which triangle points are in:

    >>> p = np.array([(0.1, 0.2), (1.5, 0.5), (0.5, 1.05)])
    >>> tri.find_simplex(p)
    array([ 1, -1, 1], dtype=int32)

    The returned integers in the array are the indices of the simplex the
    corresponding point is in. If -1 is returned, the point is in no simplex.
    Be aware that the shortcut in the following example only works correctly
    for valid points as invalid points result in -1 which is itself a valid
    index for the last simplex in the list.

    >>> p_valids = np.array([(0.1, 0.2), (0.5, 1.05)])
    >>> tri.simplices[tri.find_simplex(p_valids)]
    array([[3, 1, 0],                 # may vary
           [3, 1, 0]], dtype=int32)

    We can also compute barycentric coordinates in triangle 1 for
    these points:

    >>> b = tri.transform[1,:2].dot(np.transpose(p - tri.transform[1,2]))
    >>> np.c_[np.transpose(b), 1 - b.sum(axis=0)]
    array([[ 0.1       ,  0.09090909,  0.80909091],
           [ 1.5       , -0.90909091,  0.40909091],
           [ 0.5       ,  0.5       ,  0.        ]])

    The coordinates for the first point are all positive, meaning it
    is indeed inside the triangle. The third point is on an edge,
    hence its null third coordinate.

    Delaunay.transformDelaunay.vertex_neighbor_verticesDelaunay.vertex_to_simplexDimension %d is not directEllipsisEmpty shape tuple for cython.arrayFailed to allocate memory in setlist.init()Feasible point must be a (ndim-1,) arrayHHalfspaceIntersectionHalfspaceIntersection.__init__HalfspaceIntersection._updateHalfspaceIntersection.add_halfspacesHalfspaceIntersection.dual_vertices
    HalfspaceIntersection(halfspaces, interior_point, incremental=False, qhull_options=None)

    Halfspace intersections in N dimensions.

    .. versionadded:: 0.19.0

    Parameters
    ----------
    halfspaces : ndarray of floats, shape (nineq, ndim+1)
        Stacked Inequalities of the form Ax + b <= 0 in format [A; b]
    interior_point : ndarray of floats, shape (ndim,)
        Point clearly inside the region defined by halfspaces. Also called a feasible
        point, it can be obtained by linear programming.
    incremental : bool, optional
        Allow adding new halfspaces incrementally. This takes up some additional
        resources.
    qhull_options : str, optional
        Additional options to pass to Qhull. See Qhull manual
        for details. (Default: "Qx" for ndim > 4 and "" otherwise)
        Option "H" is always enabled.

    Attributes
    ----------
    halfspaces : ndarray of double, shape (nineq, ndim+1)
        Input halfspaces.
    interior_point :ndarray of floats, shape (ndim,)
        Input interior point.
    intersections : ndarray of double, shape (ninter, ndim)
        Intersections of all halfspaces.
    dual_points : ndarray of double, shape (nineq, ndim)
        Dual points of the input halfspaces.
    dual_facets : list of lists of ints
        Indices of points forming the (non necessarily simplicial) facets of
        the dual convex hull.
    dual_vertices : ndarray of ints, shape (nvertices,)
        Indices of halfspaces forming the vertices of the dual convex hull.
        For 2-D convex hulls, the vertices are in counterclockwise order.
        For other dimensions, they are in input order.
    dual_equations : ndarray of double, shape (nfacet, ndim+1)
        [normal, offset] forming the hyperplane equation of the dual facet
        (see `Qhull documentation <http://www.qhull.org/>`__  for more).
    dual_area : float
        Area of the dual convex hull
    dual_volume : float
        Volume of the dual convex hull

    Raises
    ------
    QhullError
        Raised when Qhull encounters an error condition, such as
        geometrical degeneracy when options to resolve are not enabled.
    ValueError
        Raised if an incompatible array is given as input.

    Notes
    -----
    The intersections are computed using the
    `Qhull library <http://www.qhull.org/>`__.
    This reproduces the "qhalf" functionality of Qhull.

    Examples
    --------

    Halfspace intersection of planes forming some polygon

    >>> from scipy.spatial import HalfspaceIntersection
    >>> import numpy as np
    >>> halfspaces = np.array([[-1, 0., 0.],
    ...                        [0., -1., 0.],
    ...                        [2., 1., -4.],
    ...                        [-0.5, 1., -2.]])
    >>> feasible_point = np.array([0.5, 0.5])
    >>> hs = HalfspaceIntersection(halfspaces, feasible_point)

    Plot halfspaces as filled regions and intersection points:

    >>> import matplotlib.pyplot as plt
    >>> fig = plt.figure()
    >>> ax = fig.add_subplot(1, 1, 1, aspect='equal')
    >>> xlim, ylim = (-1, 3), (-1, 3)
    >>> ax.set_xlim(xlim)
    >>> ax.set_ylim(ylim)
    >>> x = np.linspace(-1, 3, 100)
    >>> symbols = ['-', '+', 'x', '*']
    >>> signs = [0, 0, -1, -1]
    >>> fmt = {"color": None, "edgecolor": "b", "alpha": 0.5}
    >>> for h, sym, sign in zip(halfspaces, symbols, signs):
    ...     hlist = h.tolist()
    ...     fmt["hatch"] = sym
    ...     if h[1]== 0:
    ...         ax.axvline(-h[2]/h[0], label='{}x+{}y+{}=0'.format(*hlist))
    ...         xi = np.linspace(xlim[sign], -h[2]/h[0], 100)
    ...         ax.fill_between(xi, ylim[0], ylim[1], **fmt)
    ...     else:
    ...         ax.plot(x, (-h[2]-h[0]*x)/h[1], label='{}x+{}y+{}=0'.format(*hlist))
    ...         ax.fill_between(x, (-h[2]-h[0]*x)/h[1], ylim[sign], **fmt)
    >>> x, y = zip(*hs.intersections)
    >>> ax.plot(x, y, 'o', markersize=8)

    By default, qhull does not provide with a way to compute an interior point.
    This can easily be computed using linear programming. Considering halfspaces
    of the form :math:`Ax + b \leq 0`, solving the linear program:

    .. math::

        max \: y

        s.t. Ax + y ||A_i|| \leq -b

    With :math:`A_i` being the rows of A, i.e. the normals to each plane.

    Will yield a point x that is furthest inside the convex polyhedron. To
    be precise, it is the center of the largest hypersphere of radius y
    inscribed in the polyhedron. This point is called the Chebyshev center
    of the polyhedron (see [1]_ 4.3.1, pp148-149). The
    equations outputted by Qhull are always normalized.

    >>> from scipy.optimize import linprog
    >>> from matplotlib.patches import Circle
    >>> norm_vector = np.reshape(np.linalg.norm(halfspaces[:, :-1], axis=1),
    ...     (halfspaces.shape[0], 1))
    >>> c = np.zeros((halfspaces.shape[1],))
    >>> c[-1] = -1
    >>> A = np.hstack((halfspaces[:, :-1], norm_vector))
    >>> b = - halfspaces[:, -1:]
    >>> res = linprog(c, A_ub=A, b_ub=b, bounds=(None, None))
    >>> x = res.x[:-1]
    >>> y = res.x[-1]
    >>> circle = Circle(x, radius=y, alpha=0.3)
    >>> ax.add_patch(circle)
    >>> plt.legend(bbox_to_anchor=(1.6, 1.0))
    >>> plt.show()

    References
    ----------
    .. [Qhull] http://www.qhull.org/
    .. [1] S. Boyd, L. Vandenberghe, Convex Optimization, available
           at http://stanford.edu/~boyd/cvxbook/

    HalfspaceIntersection.halfspacesImportErrorIncompatible checksums (0x%x vs (0x82a3537, 0x6ae9995, 0xb068931) = (name))IndexErrorIndex out of bounds (axis %d)Indirect dimensions not supportedInput halfspaces cannot be a masked arrayInput interior point cannot be a masked arrayInput points array must have 2 dimensions.Input points cannot be a masked arrayInvalid mode, expected 'c' or 'fortran', got Invalid shape in axis MemoryError<MemoryView of %r at 0x%x><MemoryView of %r object>Need at least 2-D dataNo points givenOOut of bounds on buffer access (axis PickleErrorPoints cannot contain NaNQ11QBkQGQG_option_presentQJQbBQbbQbb Qc QzQbb Qc Qz Q12QbkQc_QhullQhullError_QhullUser_QhullUser.__del___QhullUser.__init___QhullUser._add_points_QhullUser._update_QhullUser.close_Qhull.__reduce_cython___Qhull.__setstate_cython___Qhull.add_points_Qhull.check_active_Qhull.close_Qhull.get_extremes_2d_Qhull.get_hull_facets_Qhull.get_hull_points_Qhull.get_paraboloid_shift_scale_Qhull.get_points_Qhull.get_simplex_facet_array_Qhull.get_voronoi_diagramQhull instance is closedQhull internal error: loop in facet listQhull options _Qhull.triangulate_Qhull.volume_areaQtQu QxQxQzRuntimeErrorSequenceStep may not be zero (axis %d)T
    Takes care of basic dealings with the Qhull objects
    TinvsTypeErrorUnable to convert item to objectValueErrorView.MemoryViewVoronoiVoronoi.__init__Voronoi._updateVoronoi.add_pointsVoronoi.points
    Voronoi(points, furthest_site=False, incremental=False, qhull_options=None)

    Voronoi diagrams in N dimensions.

    .. versionadded:: 0.12.0

    Parameters
    ----------
    points : ndarray of floats, shape (npoints, ndim)
        Coordinates of points to construct a Voronoi diagram from
    furthest_site : bool, optional
        Whether to compute a furthest-site Voronoi diagram. Default: False
    incremental : bool, optional
        Allow adding new points incrementally. This takes up some additional
        resources.
    qhull_options : str, optional
        Additional options to pass to Qhull. See Qhull manual
        for details. (Default: "Qbb Qc Qz Qx" for ndim > 4 and
        "Qbb Qc Qz" otherwise. Incremental mode omits "Qz".)

    Attributes
    ----------
    points : ndarray of double, shape (npoints, ndim)
        Coordinates of input points.
    vertices : ndarray of double, shape (nvertices, ndim)
        Coordinates of the Voronoi vertices.
    ridge_points : ndarray of ints, shape ``(nridges, 2)``
        Indices of the points between which each Voronoi ridge lies.
    ridge_vertices : list of list of ints, shape ``(nridges, *)``
        Indices of the Voronoi vertices forming each Voronoi ridge.
    regions : list of list of ints, shape ``(nregions, *)``
        Indices of the Voronoi vertices forming each Voronoi region.
        -1 indicates vertex outside the Voronoi diagram.
        When qhull option "Qz" was specified, an empty sublist
        represents the Voronoi region for a point at infinity that
        was added internally.
    point_region : array of ints, shape (npoints)
        Index of the Voronoi region for each input point.
        If qhull option "Qc" was not specified, the list will contain -1
        for points that are not associated with a Voronoi region.
        If qhull option "Qz" was specified, there will be one less
        element than the number of regions because an extra point
        at infinity is added internally to facilitate computation.
    furthest_site
        True if this was a furthest site triangulation and False if not.

        .. versionadded:: 1.4.0

    Raises
    ------
    QhullError
        Raised when Qhull encounters an error condition, such as
        geometrical degeneracy when options to resolve are not enabled.
    ValueError
        Raised if an incompatible array is given as input.

    Notes
    -----
    The Voronoi diagram is computed using the
    `Qhull library <http://www.qhull.org/>`__.

    Examples
    --------
    Voronoi diagram for a set of point:

    >>> import numpy as np
    >>> points = np.array([[0, 0], [0, 1], [0, 2], [1, 0], [1, 1], [1, 2],
    ...                    [2, 0], [2, 1], [2, 2]])
    >>> from scipy.spatial import Voronoi, voronoi_plot_2d
    >>> vor = Voronoi(points)

    Plot it:

    >>> import matplotlib.pyplot as plt
    >>> fig = voronoi_plot_2d(vor)
    >>> plt.show()

    The Voronoi vertices:

    >>> vor.vertices
    array([[0.5, 0.5],
           [0.5, 1.5],
           [1.5, 0.5],
           [1.5, 1.5]])

    There is a single finite Voronoi region, and four finite Voronoi
    ridges:

    >>> vor.regions
    [[], [-1, 0], [-1, 1], [1, -1, 0], [3, -1, 2], [-1, 3], [-1, 2], [0, 1, 3, 2], [2, -1, 0], [3, -1, 1]]
    >>> vor.ridge_vertices
    [[-1, 0], [-1, 0], [-1, 1], [-1, 1], [0, 1], [-1, 3], [-1, 2], [2, 3], [-1, 3], [-1, 2], [1, 3], [0, 2]]

    The ridges are perpendicular between lines drawn between the following
    input points:

    >>> vor.ridge_points
    array([[0, 3],
           [0, 1],
           [2, 5],
           [2, 1],
           [1, 4],
           [7, 8],
           [7, 6],
           [7, 4],
           [8, 5],
           [6, 3],
           [4, 5],
           [4, 3]], dtype=int32)

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    tsearch(tri, xi)

    Find simplices containing the given points. This function does the
    same thing as `Delaunay.find_simplex`.

    Parameters
    ----------
    tri : DelaunayInfo
        Delaunay triangulation
    xi : ndarray of double, shape (..., ndim)
        Points to locate

    Returns
    -------
    i : ndarray of int, same shape as `xi`
        Indices of simplices containing each point.
        Points outside the triangulation get the value -1.

    See Also
    --------
    Delaunay.find_simplex

    Notes
    -----
    .. versionadded:: 0.9

    Examples
    --------
    >>> import numpy as np
    >>> import matplotlib.pyplot as plt
    >>> from scipy.spatial import Delaunay, delaunay_plot_2d, tsearch
    >>> rng = np.random.default_rng()

    The Delaunay triangulation of a set of random points:

    >>> pts = rng.random((20, 2))
    >>> tri = Delaunay(pts)
    >>> _ = delaunay_plot_2d(tri)

    Find the simplices containing a given set of points:

    >>> loc = rng.uniform(0.2, 0.8, (5, 2))
    >>> s = tsearch(tri, loc)
    >>> plt.triplot(pts[:, 0], pts[:, 1], tri.simplices[s], 'b-', mask=s==-1)
    >>> plt.scatter(loc[:, 0], loc[:, 1], c='r', marker='x')
    >>> plt.show()

    unable to allocate array data.unable to allocate shape and strides.uniqueunpackupdate_updatevversion_infovertexvertexAvertexB_vertex_neighbor_verticesvertex_neighbor_vertices_vertex_to_simplexvertex_to_simplex vertices_verticesverticesvolumevolume_areavoronoi_verticesworkwrong dimensionality in xixx_shapexixi has different dimensionality than triangulationxi_shapezzeroszip00010203040506070809101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899
        Uninitialize this instance
        
        Return array of simplical facets currently in Qhull.

        Returns
        -------
        facets : array of int, shape (nfacets, ndim+1)
            Indices of coordinates of vertices forming the simplical facets
        neighbors : array of int, shape (nfacets, ndim)
            Indices of neighboring facets.  The kth neighbor is opposite
            the kth vertex, and the first neighbor is the horizon facet
            for the first vertex.

            Facets extending to infinity are denoted with index -1.
        equations : array of double, shape (nfacets, ndim+2)

        Returns all points currently contained in Qhull.
        It is equivalent to retrieving the input in most cases, except in
        halfspace mode, where the points are in fact the points of the dual
        hull.

        Returns
        -------
        points: array of double, shape (nrpoints, ndim)
            The array of points contained in Qhull.

        Returns the facets contained in the current Qhull.
        This function does not assume that the hull is simplicial,
        meaning that facets will have different number of vertices.
        It is thus less efficient but more general than get_simplex_facet_array.

        Returns
        -------
        facets: list of lists of ints
            The indices of the vertices forming each facet.
        
        Return the voronoi diagram currently in Qhull.

        Returns
        -------
        voronoi_vertices : array of double, shape (nvoronoi_vertices, ndim)
            Coordinates of the Voronoi vertices

        ridge_points : array of double, shape (nridges, 2)
            Voronoi ridges, as indices to the points array.

        ridge_vertices : list of lists, shape (nridges, *)
            Voronoi vertices for each Voronoi ridge, as indices to
            the Voronoi vertices array.
            Infinity is indicated by index ``-1``.

        regions : list of lists, shape (nregion, *)
            Voronoi vertices of all regions.

        point_region : array of int, shape (npoint,)
            Index of the Voronoi region for each input point.

        
        Compute the extremal points in a 2-D convex hull, i.e. the
        vertices of the convex hull, ordered counterclockwise.

        See qhull/io.c:qh_printextremes_2d

        
    Compute barycentric affine coordinate transformations for given
    simplices.

    Returns
    -------
    Tinvs : array, shape (nsimplex, ndim+1, ndim)
        Barycentric transforms for each simplex.

        Tinvs[i,:ndim,:ndim] contains inverse of the matrix ``T``,
        and Tinvs[i,ndim,:] contains the vector ``r_n`` (see below).

    Notes
    -----
    Barycentric transform from ``x`` to ``c`` is defined by::

        T c = x - r_n

    where the ``r_1, ..., r_n`` are the vertices of the simplex.
    The matrix ``T`` is defined by the condition::

        T e_j = r_j - r_n

    where ``e_j`` is the unit axis vector, e.g, ``e_2 = [0,1,0,0,...]``
    This implies that ``T_ij = (r_j - r_n)_i``.

    For the barycentric transforms, we need to compute the inverse
    matrix ``T^-1`` and store the vectors ``r_n`` for each vertex.
    These are stacked into the `Tinvs` returned.

    
        close()

        Finish incremental processing.

        Call this to free resources taken up by Qhull, when using the
        incremental mode. After calling this, adding more points is no
        longer possible.
        
        add_points(points, restart=False)

        Process a set of additional new points.

        Parameters
        ----------
        points : ndarray
            New points to add. The dimensionality should match that of the
            initial points.
        restart : bool, optional
            Whether to restart processing from scratch, rather than
            adding points incrementally.

        Raises
        ------
        QhullError
            Raised when Qhull encounters an error condition, such as
            geometrical degeneracy when options to resolve are not enabled.

        See Also
        --------
        close

        Notes
        -----
        You need to specify ``incremental=True`` when constructing the
        object to be able to add points incrementally. Incremental addition
        of points is also not possible after `close` has been called.

        
        Affine transform from ``x`` to the barycentric coordinates ``c``.

        :type: *ndarray of double, shape (nsimplex, ndim+1, ndim)*

        This is defined by::

            T c = x - r

        At vertex ``j``, ``c_j = 1`` and the other coordinates zero.

        For simplex ``i``, ``transform[i,:ndim,:ndim]`` contains
        inverse of the matrix ``T``, and ``transform[i,ndim,:]``
        contains the vector ``r``.

        
        Lookup array, from a vertex, to some simplex which it is a part of.

        :type: *ndarray of int, shape (npoints,)*
        
        Neighboring vertices of vertices.

        Tuple of two ndarrays of int: (indptr, indices). The indices of
        neighboring vertices of vertex `k` are
        ``indices[indptr[k]:indptr[k+1]]``.

        
        Vertices of facets forming the convex hull of the point set.

        :type: *ndarray of int, shape (nfaces, ndim)*

        The array contains the indices of the points
        belonging to the (N-1)-dimensional facets that form the convex
        hull of the triangulation.

        .. note::

           Computing convex hulls via the Delaunay triangulation is
           inefficient and subject to increased numerical instability.
           Use `ConvexHull` instead.

        
        find_simplex(self, xi, bruteforce=False, tol=None)

        Find the simplices containing the given points.

        Parameters
        ----------
        tri : DelaunayInfo
            Delaunay triangulation
        xi : ndarray of double, shape (..., ndim)
            Points to locate
        bruteforce : bool, optional
            Whether to only perform a brute-force search
        tol : float, optional
            Tolerance allowed in the inside-triangle check.
            Default is ``100*eps``.

        Returns
        -------
        i : ndarray of int, same shape as `xi`
            Indices of simplices containing each point.
            Points outside the triangulation get the value -1.

        Notes
        -----
        This uses an algorithm adapted from Qhull's ``qh_findbestfacet``,
        which makes use of the connection between a convex hull and a
        Delaunay triangulation. After finding the simplex closest to
        the point in N+1 dimensions, the algorithm falls back to
        directed search in N dimensions.

        
        plane_distance(self, xi)

        Compute hyperplane distances to the point `xi` from all simplices.

        
        lift_points(self, x)

        Lift points to the Qhull paraboloid.

        
    tsearch(tri, xi)

    Find simplices containing the given points. This function does the
    same thing as `Delaunay.find_simplex`.

    Parameters
    ----------
    tri : DelaunayInfo
        Delaunay triangulation
    xi : ndarray of double, shape (..., ndim)
        Points to locate

    Returns
    -------
    i : ndarray of int, same shape as `xi`
        Indices of simplices containing each point.
        Points outside the triangulation get the value -1.

    See Also
    --------
    Delaunay.find_simplex

    Notes
    -----
    .. versionadded:: 0.9

    Examples
    --------
    >>> import numpy as np
    >>> import matplotlib.pyplot as plt
    >>> from scipy.spatial import Delaunay, delaunay_plot_2d, tsearch
    >>> rng = np.random.default_rng()

    The Delaunay triangulation of a set of random points:

    >>> pts = rng.random((20, 2))
    >>> tri = Delaunay(pts)
    >>> _ = delaunay_plot_2d(tri)

    Find the simplices containing a given set of points:

    >>> loc = rng.uniform(0.2, 0.8, (5, 2))
    >>> s = tsearch(tri, loc)
    >>> plt.triplot(pts[:, 0], pts[:, 1], tri.simplices[s], 'b-', mask=s==-1)
    >>> plt.scatter(loc[:, 0], loc[:, 1], c='r', marker='x')
    >>> plt.show()

    
        add_halfspaces(halfspaces, restart=False)

        Process a set of additional new halfspaces.

        Parameters
        ----------
        halfspaces : ndarray
            New halfspaces to add. The dimensionality should match that of the
            initial halfspaces.
        restart : bool, optional
            Whether to restart processing from scratch, rather than
            adding halfspaces incrementally.

        Raises
        ------
        QhullError
            Raised when Qhull encounters an error condition, such as
            geometrical degeneracy when options to resolve are not enabled.

        See Also
        --------
        close

        Notes
        -----
        You need to specify ``incremental=True`` when constructing the
        object to be able to add halfspaces incrementally. Incremental addition
        of halfspaces is also not possible after `close` has been called.

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�����������������{%16.8f, %16.8f, %16.8f}Polygon[{distance tests for vertex convexitydistance tests for centrum convexitydistance tests for checking simplicial convexitydistance tests for checking convexityangles computed for ridge convexity and at-infinitydistance tests for facet visibilityView.MemoryView._err_no_memoryFsummaryView.MemoryView.memoryview_copyView.MemoryView.memoryview.copynumpyTcheck-frequentlyexactlyQgood-facets-onlyQmax-outside-onlyView.MemoryView._unellipsifyTverifyqh_rotatepoints: rotate points byndarraynumpy.import_arrayscipy.spatial._qhull._Qhull.get_simplex_facet_arrayscipy.spatial._qhull.arraydelaunayQupperDelaunay upperDelaunay_qhull.pyxQbBound-unit-box nonconvexQvertex-neighbors-convexclearly convex mergevertexFNeighbors-vertexintersections failed to find a redundant vertexaverage number of neighbors per vertex   ave. number found per vertexdistance tests to report minimum vertex  max. number of ridges per tested vertex  ave. number of ridges per tested vertexretry qh_addpoint after merge pinched vertex   max. found for a vertexscipy.spatial._qhull.Delaunay.vertex_to_simplex_find_simplexscipy.spatial._qhull.Delaunay.find_simplexQsearch-initial-simplexnon-convex initial simplexsearches of all points for initial simplexmerged a simplexView.MemoryView.pybuffer_indexmodule compiled against ABI version 0x%x but this version of numpy is 0x%xQ10-no-narrowQwarn-allowQbound-dim-low  determinants not computed because vertex too lowcalls to findbestnewQ4-avoid-old-into-newscipy.spatial._qhull.memoryviewView.MemoryView.array.get_memviewView.MemoryView.get_slice_from_memviewView.MemoryViewneighbors for vExpected a dimension of size %zu, got %zuTannotate-outputdistance tests for outputnumber of non-simplicial facets in outputnumber of facets in outputcoplanar half ridges in outputconcave half ridges in outputnumber of vertices in outputcpu seconds for qhull after inputTz-stdoutHalfspace-aboutFD-cdd-outQ7-no-breadth-firstat mostFPoint-nearest notfurthestQ9-pick-furthestdistance tests for computing furthest  Furthestcalls to findbestQbbound-lastat leastbroadcastQallow-short simplicialbot  countqh_detvnorm: Voronoi vertex or midpoint  max. merge pinched vertex for a qh_addpoint_lift_pointqh.interior_pointQz-infinity-pointQV-good-facets-not-pointQV-good-facets-pointTV-stop-after-pointTV-stop-before-pointQGood-if-dont-see-pointQGood-if-see-pointTrace-pointnearly incident pointcenter pointdistance tests for checking good pointpartitions of a pointnpy_intvalue too large to convert to intGtransparent%.200s() needs an argumentunbound method %.200S() needs an argumentView.MemoryView.memoryview.setitem_slice_assignmentlocal variable '%s' referenced before assignmentQ2-no-merge-independentsimilar and redundantqh_gausselem: resultat error exit  resets of vertex_visitscipy.spatial.setlist.initcoplanar angles in getmergesetconcave-coplanar ridges in getmergesetconcave ridges in getmergesettwisted ridges in getmergesetcoplanar centrums or vertices in getmergeset newfacet_wide-facetaverage number of neighbors per facetaverage number of ridges per facetaverage number of vertices per facet  repartitioned coplanar points above a corner facet  repartitioned coplanar points above a hidden facetvertices deleted by degenerate facet  repartitioned coplanar points above a twisted facetflipped facetrenamed vertices in a pinched facetmax. distance of a new vertex to a facetave. distance of a new vertex to a facetmax. distance of an output vertex to a facetmin. distance of an output vertex to a facet  near inside points kept with a facet  inside points that were coplanar with a faceta structscipy.spatial._qhull.Voronoi.ridge_dictfunc_dictsetting function's dictionary to a non-dictFpoint-intersectView.MemoryView.memoryview.convert_item_to_objectView.MemoryView._memoryviewslice.convert_item_to_objectView.MemoryView.memoryview.assign_item_from_objectView.MemoryView._memoryviewslice.assign_item_from_object__kwdefaults__ must be set to a dict object__annotations__ must be set to a dict object while calling a Python object__qualname__ must be set to a string object__name__ must be set to a string objectMissing type object%.200s.%.200s is not a type objectShared Cython type %.200s is not a type object_ARRAY_API is not PyCapsule object__defaults__ must be set to a tuple object%.200s.%.200s size changed, may indicate binary incompatibility. Expected %zd from C header, got %zd from PyObject%s.%s size changed, may indicate binary incompatibility. Expected %zd from C header, got %zd from PyObjectqh_initqhull_globals: disable qh.MERGEpinched for 2-d.  It has no effectinexactformatinitial simplex is flatintp_tdouble_ttotal number of distance testsscipy.spatial._qhull.Delaunay.lift_pointsscipy.spatial._qhull._Qhull.get_pointsscipy.spatial._qhull._Qhull.get_hull_pointsscipy.spatial._qhull._QhullUser._add_pointsscipy.spatial._qhull.Delaunay.add_pointsscipy.spatial._qhull._Qhull.add_pointsscipy.spatial._qhull.ConvexHull.add_pointsscipy.spatial._qhull.Voronoi.add_pointsGpointsscipy.spatial._qhull.Delaunay.pointsscipy.spatial._qhull.ConvexHull.pointsscipy.spatial._qhull.Voronoi.pointsGall-pointsangle tests for repartitioned coplanar pointsinside pointsQTestPointsView.MemoryView._err_extentsView.MemoryView.memoryview_copy_contents%.200s() takes no keyword argumentsfunc_defaultssuboffsetsfor ridges and their vertex setsfor facets and their normals, neighbor and vertex setsfor vertices and their neighbor sets calls due to qh_sharpnewfacetsscipy.spatial._qhull._Qhull.get_hull_facetsPgood-facetshorizon facets merged into new facetstotal lookups for matching ridges of new facetsmerges due to concave-coplanar facetsmerges due to coplanar facetsmerges due to angle coplanar facetsrenamed vertices shared by two facets  facets per search of all facets  with rare search of all facetstotal area of facetsmerges due to concave facetsmerges due to degenerate facetsrenamed vertices shared by multiple facetsmerges due to twisted facetsduplicated ridges with flipped facetsmerges due to removing flipped facetsdistance tests for checking flipped facets  max. facetsPdrop-facets-dim-less  maximum additional in one passdgetrs  detected by qh_test_nonsimplicial_merge instead of qh_test_redundant_neighborsFneighborsPGood-facet-neighborsnon-convex vertex neighborsFor testing vertex neighbors  with search of vertex neighborsmerges due to redundant neighborsa ridge with more than two neighbors  facets deleted because of no neighborsmaximum number of neighborsdupridges with multiple neighborsridge with multiple neighborsmerge degenerate facets due to dropped neighborsFcoplanarsrequired_optionsFOptions   distance tests for these partitionsGintersectionsmerge iterationssubmodule_search_locationsView.MemoryView.assert_direct_dimensionsbuiltinsGcentrumsFCentrumsscipy.spatial._qhull._get_barycentric_transformsretries due to precision problemschanges to cyfunction.__kwdefaults__ will not currently affect the values used in function callschanges to cyfunction.__defaults__ will not currently affect the values used in function callsnormalsfunc_globals%.200s() keywords must be stringsnbytes_barycentric_coordinatesQ15-check-duplicatesmetaclass conflict: the metaclass of a derived class must be a (non-strict) subclass of the metaclasses of all its basesnearly singular or axis-parallel hyperplanesGno-planespoints checked for facets' outer planesFxtremesFtrianglesFmergesstatistics for vertex mergesstatistics for determining mergesmerges due to dupridgesGridges  additional non-convex ridgesvertices removed from facets due to no ridgesaverage cosine (angle) of facet normals for all ridgesnon-simplicial Voronoi vertices for all ridgesstatistics for matching ridgesmaximum number of ridgesrename failures due to duplicated ridgesbounded ridgesBuffer exposes suboffsets but no stridesscipy.spatial._qhull.Delaunay.vertex_neighbor_verticesscipy.spatial._qhull.HalfspaceIntersection.dual_verticesGverticesFverticesscipy.spatial._qhull.ConvexHull.verticesQ3-no-merge-verticesQ14-merge-pinched-verticescoplanar horizon facets for new verticesvertex intersections for locating redundant verticesintersections found redundant verticesdeterminants for initial hull or voronoi verticesmaximum number of verticesbest merges used centrum instead of verticestwo new facets with the same verticespartitions of coplanar points or deleted verticesdropped neighbors due to renamed verticesdeleted ridges due to renamed verticescentrums frozen due to extra verticessimplicesscipy.spatial._qhull.HalfspaceIntersection.add_halfspacesscipy.spatial._qhull.HalfspaceIntersection.halfspacesTstatisticsdistance tests for statisticsprecision statisticsbuild hull statisticsVoronoi ridge statisticsFIDsSubscript deletion not supported by %.200sExpected %s, got %.200sUnable to initialize pickling for %.200sCannot convert %.200s to %.200s%.200s does not export expected C function %.200s
Statistics for: %s | %sBuffer dtype mismatch, expected %s%s%s but got %s  %sscipy.spatial._qhull._copy_docstrscipy.spatial.setlist.tocsrView.MemoryView._errmirror__pyx_fatalerrorcoplanar and interiordupridges with flip facet into good flip neighbor  ave. visible facets without an horizon neighbordupridges with flip facet into good neighborcalls to findbestlowerGouterFouterQ5-no-check-outer ave. clearly betterView.MemoryView.memoryview.get_item_pointera pointer_ARRAY_API is NULL pointerflatitercharacterView.MemoryView.array_cwrapperView.MemoryView.memoryview_cwrapperGinnerFinnerBig-endian buffer not supported on little-endian compilerfacets created altogetherridges created altogethervertices created altogetherunsignedintegercannot fit '%.200s' into an index-sized integerView.MemoryView._allocate_bufferloadernumber tricoplanarconcavecoplanaranglecoplanarQcoplanarU-max-coplanarU-coplanarsimilarView.MemoryView.memoryview.setitem_slice_assign_scalarvertices for rTCone-stop simplicialtop topView.MemoryView.copy_data_to_tempflipQinterior-keepQcoplanar-keepPMerge-keepPFacet-area-keepPArea-keep %pinteger division or modulo by zeroscipy.spatial._qhull._get_delaunay_infoTRerun_run new bestfacets during qh_findbesthorizon coplanarhorizon mergehorizoncalls to findhorizonempty horizonvertices deleted by merging into coplanar horizonnew facets merged into coplanar horizoncycles of facets merged into coplanar horizonsimplices merged into coplanar horizonnew facets merged into horizonreasonzero diagonal on back substitutionmode_optionraise: exception class must be a subclass of BaseExceptiondistance tests for initial partitionBad call flags for CyFunctionmin. denominator in hyperplane computationave. horizon facets per iterationave. visible facets per iterationave. new or merged facets per iteration  ave. additional non-convex ridges per iterationave. initial non-convex ridges per iterationave. visible vertices per iteration  ave. facets deleted per iteration    maximum vertices deleted per iterationset changed size during iterationdegenerate hyperplanes recomputed with gaussian eliminationzero divisors during gaussian eliminationzero pivot for Gaussian eliminationsummary information  standard deviationfloat divisionInternal class for passing memoryview slices to PythondgeconoriginFd-cdd-indegen seenView.MemoryView.memoryview.copy_fortranFATAL: module compiled as unknown endian keepcentrum_zero-centrumView.MemoryView.__pyx_unpickle_Enumscipy.spatial._qhull.Enum    maximumscipy.spatial._qhull.Delaunay.transform bottomCentrum-postmerge-with-randomAngle-postmerge-with-randomCentrum-premerge-with-randomAngle-premerge-with-randomQRotate-randomndimView.MemoryView._err_dimQb-project-dimGDrop-dimscipy.spatial._qhull._Qhull.get_voronoi_diagramscipy._lib.messagestreamMessageStreaminit scipy.spatial._qhullscipy.spatial._qhull.Delaunay.convex_hullscipy.spatial._qhull._QhullFQhull_narrow-hullNULL result without error in PyObject_CallFArea-totalTotalbounded ridges with near-zero normalbounded ridges with ok normalsimplicial facets that were non-simplicial simplicialinitial Delaunay cocircular or cospherical  ave. distance tests per checkdifference in max_outside at final checkneed more than %zd value%.1s to unpackscipy.linalg.cython_lapackQbbound-last-qjmemviewsliceobjscipy.spatial._qhull._visit_voronoiFvoronoistartswith_max-widthnumpy.core._multiarray_umathTflushQ3-no-merge-vertices-dim-highQBound-dim-highdoes not matchscipy.spatial._qhull.tsearch ave. coplanar searchTFacet-logvalue too large to convert to longbyte string is too longcomplexfloatingCannot handle repeated arrays in format stringunparsable format stringjoin() result is too long for a Python stringhasattr(): attribute name must be stringa stringdistance tests for partitioningcoplanar points during partitioningShared Cython type %.200s has the wrong size, try recompilingFor post-mergingvertices deleted by merginginitial non-convex ridges for post mergingstatistics for mergingView.MemoryView.memoryview.is_f_contigView.MemoryView.memoryview.is_c_contig %8.4g%7.3g%7.2g %6.2g %5.2g  Maximum distance of vertex below facet: %2.2g  Maximum distance of point above facet: %2.2gdgetrfError-roundoffDistance-roundoffcoplanarset for foutsideset for fneighbors for fridges for fvertices for fitemsizeFSizescipy.spatial._qhull._Qhull.check_activeconcaveinstance exception may not have a separate valuezero divisors during back substitutefurthest_sitePyObject_GetBuffer: view==NULL argument is obsoleteView.MemoryView.__pyx_unpickle_Enum__set_state degenerateinput has same x coordinateApproximateQ11-trinormals Qtriangulatescipy.spatial._qhull._Qhull.triangulatescipy.spatial._qhull.Delaunay._updatescipy.spatial._qhull._QhullUser._updatescipy.spatial._qhull.HalfspaceIntersection._updatescipy.spatial._qhull.ConvexHull._updatescipy.spatial._qhull.Voronoi._updatescipy.spatial._qhull._QhullUser.closescipy.spatial._qhull._Qhull.closebasefunc_closurePprecision-ignorePDrop-facets-dim-morebuffer dtypebase class '%.200s' is not a heap typeextension type '%.200s' has no __dict__ slot, but base type '%.200s' has: either add 'cdef dict __dict__' to the extension type or add '__slots__ = [...]' to the base typeinvalid vtable found for imported typeshapenone cycledoneArgument '%.200s' must not be None_is_coroutine_distplanecython_runtimeFATAL: module compiled as little endian, but detected different endianness at runtimemax. vertices at any one timefunc_name__mro_entries__ must return a tupleFMapleTOutput-fileTInput-fileoffFile_barycentric_coordinate_single  max. random joggleQJoggle  ave. facets per cycleduplicated ridges in same merge cyclenpy_doubleflexible visibleVisible'%.200s' object is not subscriptable'NoneType' object is not subscriptable'NoneType' object is not iterable'NoneType' is not iterable'%.200s' object is unsliceablescipy.spatial._qhull._Qhull.get_paraboloid_shift_scale newmergeCentrum-postmergeAngle-postmergeQ0-no-premergeFirst post-mergeQxact-mergeQ6-no-concave-merge_pre-merge_one-mergeQ1-angle-mergeTrace-mergefacets before post mergedistance tests for best mergecentrums frozen due to a wide mergecoplanar/concave merges due to avoiding old mergeFFacets-xridgenot concave, flipped, or dupridge  tot. merge pinched vertex due to dupridgemerge pinched vertices for a dupridge delridgeaverage number of tests per subridge DUPLICATEridge MERGEridgecoplanar ridge  max. distance of midpoint to ridge  ave. distance of midpoint to ridge  max. angle to ridge  ave. angle to ridge  max. distance to ridge  ave. distance to ridge  found new vertex in ridgeconcave ridgemerge pinched vertices for a duplicate ridgemerges due to flipped facets in duplicated ridge  maximum cosine of facet normals (flatest) across a ridge  minimum cosine of facet normals (sharpest) across a ridgeaverage number of tests to match a ridgeFVertex-averagefunc_codeQ12-allow-wide_maxoutside_is_point_fully_outsideQfurthest-outsideQrandom-outsideWidth-outsideW-outside_barycentric_inside_near-insideQ8-no-near-inside_find_simplex_bruteforceincidencescipy.spatial._qhull.Delaunay.plane_distanceVisible-distance  maximum merge distance  average merge distanceaverage new facet balanceaverage partition balancescipy.spatial._qhull._memoryviewsliceView.MemoryView.slice_memviewsliceView.MemoryView.memoryview_fromsliceView.MemoryView.transpose_memsliceView.MemoryView.memview_sliceView.MemoryView.memoryview.is_sliceView.MemoryView.memoryview_copy_from_sliceTWide-traceHalfspacesetlist.pxd__init__.cython-30.pxdPgood_cython_3_0_10.cython_function_or_methodCythonUnboundCMethodgood facets foundexpected bytes, NoneType foundappendresets of visit_idrun-idQRotate-idView.MemoryView.memoryview.setitem_indexedtwisted max. facets tested ave. facets testedtotal vertices deletedfunction's dictionary may not be deleted  deleted_find_simplex_directedBuffer dtype mismatch; next field is at offset %zd but %zd expectednon-simplicial facets triangulated  max. new facets createdpoints processedan integer is required flippedname '%U' is not definednew facets mergedtotal number of facets or cycles of facets mergedQRandom-seed_joggle-seedPoutput-forcedTA-stop-add%7dscipy.spatial._qhull._Qhull.get_extremes_2d     - r%d p%d f%d %d->%dcompile time Python version %d.%d of module '%.100s' %s runtime version %d.%dExpected a dimension of size %zu, got %dExpected %d dimensions, got %dExpected %d dimension(s), got %dqh_remove_mergetype: remove merge f%d f%d v%d v%d r%d r%d dist %2.2g type %d%d %d %dfunc_docufuncgenericscipy/spatial/_qhull.cp312-win_amd64.pyd.p/_qhull.cRandom-perturb isareascipy.spatial._qhull._Qhull.volume_areaFareadeterminants for facet area  maximum facet area  minimum facet areamathematicaqh.facet_View.MemoryView.array.__cinit__View.MemoryView.memoryview.__cinit__scipy.spatial._qhull.Delaunay.__init__scipy.spatial._qhull._QhullUser.__init__scipy.spatial._qhull.HalfspaceIntersection.__init__View.MemoryView.Enum.__init__scipy.spatial._qhull._Qhull.__init__scipy.spatial._qhull.ConvexHull.__init__scipy.spatial._qhull.Voronoi.__init__scipy.spatial._qhull._Qhull.options.__set__scipy.spatial._qhull._Qhull.mode_option.__set__View.MemoryView.array.memview.__get__View.MemoryView.memoryview.suboffsets.__get__View.MemoryView.memoryview.nbytes.__get__View.MemoryView.memoryview.strides.__get__View.MemoryView.memoryview.ndim.__get__scipy.spatial._qhull._Qhull.ndim.__get__View.MemoryView.memoryview.itemsize.__get__View.MemoryView.memoryview.size.__get__View.MemoryView.memoryview.base.__get__View.MemoryView.memoryview.shape.__get__View.MemoryView.memoryview.T.__get____dict____kwdefaults____defaults____annotations____builtins____globals____orig_bases__View.MemoryView.array.__getattr__View.MemoryView.memoryview.__str__View.MemoryView.memoryview.__repr__View.MemoryView.array.__getbuffer__View.MemoryView.memoryview.__getbuffer____loader__View.MemoryView.array.__setstate_cython__View.MemoryView.memoryview.__setstate_cython__View.MemoryView.Enum.__setstate_cython__scipy.spatial._qhull._Qhull.__setstate_cython__View.MemoryView._memoryviewslice.__setstate_cython__View.MemoryView.array.__reduce_cython__View.MemoryView.memoryview.__reduce_cython__View.MemoryView.Enum.__reduce_cython__scipy.spatial._qhull._Qhull.__reduce_cython__View.MemoryView._memoryviewslice.__reduce_cython__View.MemoryView.array.__setitem__View.MemoryView.memoryview.__setitem__View.MemoryView.array.__getitem__View.MemoryView.memoryview.__getitem__scipy.spatial._qhull._QhullUser.__del____pyx_capi____path____debug____closure____qualname____name____module____file____package____code____reduce__scipy.spatial._qhull._Qhull.__dealloc____doc__}][%16.8f, %16.8f, %16.8f][QH%.4d][for input points, outside and coplanar sets, and qhTDISTANTERRONEOUScannot import name %Scalling %R should have returned an instance of BaseException, not %RN_ARRAY_API notGMERGINGMERGING CYCLETRACEMERGED<cyfunction %U at %p><stringsource>%s set=%p maxsize=%d size=%d elems=Matrix:    - coplanar set:    - outside set:qh_printlists: max_outside %2.2g all facets:    - neighboring facets:  neighbors:
 neighbors:    - flags:     - all ridges:
  qh.visible_list f%d, newfacet_list f%d, facet_next f%d for qh_addpoint
  qh.newvertex_list v%d all vertices:    - vertices:           vertices:center:  same cycle:  freelists(bytes->count):    - ridges (tentative ids):qh_maxmin: found the max and min points (by dim):- p%d(v%d): mergevertex2 seen2 mergeridge2  max vertex_visit/2  max visit_id/2 mergeridge1_cython_3_0_10    - coplanar set:  %d points.    - outside set:  %d points.Interpreter change detected - this module can only be loaded into one interpreter per process.__int__ returned non-int (type %.200s).  The ability to return an instance of a strict subclass of int is deprecated, and may be removed in a future version of Python.
Qhull has finished constructing the hull.
Qhull has started post-merging.Module '_qhull' has already been imported. Re-initialisation is not supported.  Last point added to hull was p%d.  Last merge was #%d.Buffer not compatible with direct access in dimension %d.Python does not define a standard format string size for long double ('g')..
Early exit due to 'TAn', 'TVn', 'TCn', 'TRn', or precision error with 'QJn'.module compiled against API version 0x%x but this version of numpy is 0x%x . Check the section C-API incompatibility at the Troubleshooting ImportError section at https://numpy.org/devdocs/user/troubleshooting-importerror.html#c-api-incompatibility for indications on how to solve this problem .Centrum-premerge-Angle-premerge-qh_findbestnew: point p%d facet f%d. Stop? %d if dist > %2.2g,qh_findbest: point p%d starting at f%d isnewfacets? %d, unless %d exit if > %2.2g, Last qh_addpoint p%d, Last qh_addpoint p%d, qh.visit_id %d, vertex_visit %d, testhorizon? %d, noupper? %d, *0 cnt*total lookups of subridges (duplicates and boundary)null new facets deleted (duplicated vertex)points ignored (pinched apex)    maximum (includes initial simplex)int (__pyx_t_5scipy_7spatial_6_qhull_DelaunayInfo_t *, PyObject *, int, int, int)void (int, double *, double const *, double *, int)points ignored (didn't create a good new facet)points ignored (!above a good facet)memory usage statistics (in bytes)partitioning statistics (see previous for outer planes)mirrored pairs of new facets deleted (same vertices)C function %.200s.%.200s has wrong signature (expected %.500s, got %.500s)Argument '%.200s' has incorrect type (expected %.200s, got %.200s)__%.4s__ returned non-%.4s (type %.200s)Item size of buffer (%zu byte%s) does not match size of '%s' (%zu byte%s)Item size of buffer (%zd byte%s) does not match size of '%s' (%zd byte%s)precision problems (corrected unless 'Q0' or an error)%.200s() takes exactly one argument (%zd given)%.200s() takes no arguments (%zd given)%.200s() takes %.8s %zd positional argument%.1s (%zd given)nearly incident point (narrow hull)max distance of vertex or coplanar point above facet (w/roundoff)max distance of vertex below facet (or roundoff)int (__pyx_t_5scipy_7spatial_6_qhull_DelaunayInfo_t *, double *, double const *, double, double)int (__pyx_t_5scipy_7spatial_6_qhull_DelaunayInfo_t *, double *, double const *, int *, double, double)int (__pyx_t_5scipy_7spatial_6_qhull_DelaunayInfo_t *, double const *, double)int (int, double *, double const *, double *, double)degenerate new facets in output (same ridge)points ignored (!above max_outside)too many values to unpack (expected %zd)  ave. new facets created (may be deleted) p%d(v%d)%s (%s:%d)Buffer has wrong number of dimensions (expected %d, got %d)Out of bounds on buffer access (axis %d)Cannot copy memoryview slice with indirect dimensions (axis %d)Acquisition count is %d (line %d)average merges per facet (at most 511)  maximum merges for a facet (at most 511)void (int *, int *, __pyx_t_5scipy_6linalg_13cython_lapack_d *, int *, int *, int *)void (char *, int *, int *, __pyx_t_5scipy_6linalg_13cython_lapack_d *, int *, int *, __pyx_t_5scipy_6linalg_13cython_lapack_d *, int *, int *)void (char *, int *, __pyx_t_5scipy_6linalg_13cython_lapack_d *, int *, __pyx_t_5scipy_6linalg_13cython_lapack_d *, __pyx_t_5scipy_6linalg_13cython_lapack_d *, __pyx_t_5scipy_6linalg_13cython_lapack_d *, int *, int *)double (__pyx_t_5scipy_7spatial_6_qhull_DelaunayInfo_t *, int, double *)void (__pyx_t_5scipy_7spatial_6_qhull_DelaunayInfo_t *, double const *, double *)void (int, double *, double const *, double *)object of type 'NoneType' has no len()Triangulation statistics ('Qt')Does not understand character buffer dtype format string ('%c')'short''unsigned short''int''unsigned int''float''complex float''NoneType' object has no attribute '%.30s'multiple bases have vtable conflict: '%.200s' and '%.200s'Buffer dtype mismatch, expected '%s' but got %s in '%s.%s''char''unsigned char''signed char''bool''long''long long''unsigned long long''unsigned long''double''complex double''long double''complex long double' 'good'Expected a comma in format string, got '%c'Unexpected format string character: '%c'%s() got multiple values for keyword argument '%U'%s() got an unexpected keyword argument '%U'Buffer acquisition: Expected '{' after 'T'Unexpected end of format string, expected ')'Buffer acquisition failed on assignment; and then reacquiring the old buffer failed too!memviewslice is already initialized!{appearance {-normal -edge normscale 0} qh_voronoi_center: at infinity for qh_find_newvertex: find new vertex for v%d from qhull %6.16g %8.4g %6.3g qh_voronoi_center: det %2.2g factor %2.2g %6.2e good QH%.4d v%d r%d hash %d f%d %d %d %d qh_sethalfspace: halfspace at offset %6.2g to point: qhull input error: feasible point is not clearly inside halfspace
feasible point: 
     at offset:  %6.2g max. distance for merging two simplicial facets
 %6.2g max. roundoff error for arithmetic operations
 %6.2g min. denominator for division
  zero diagonal for Gauss:     - center: qh_initialhull: qh_setfacetplane: f%d offset %2.2g normal:     - normal: qh_distplane:  and distance: 
     halfspace:  p%d: 10 %d %d %d %d %d %d %d %d %d %d
2 0
2 VECT 1 %d 1 %d 1 OFF 3 1 1 # 1 point per line
1 0 p%d dist %.2g, %8.4g %8.4g %8.4g %8.4g # 
     1 }}}
%8.4g %8.4g %8.4g 1.0 }
{
qhull internal error (qh_merge_pinchedvertices): qh.visible_list (f%d), newfacet_list (f%d), or newvertex_list (v%d) not empty
qhull internal error (qh_checkfacet): degenerate facet f%d is not on qh.visible_list and qh.degen_mergeset is empty
qh_test_vneighbors: testing vertex neighbors for convexity
qhull error (qh_meminit): insufficient memory
qhull error (qh_memsetup): insufficient memory
qh_freeqhull: free global memory
qhull internal error: qh_checklists failed at qh_printsummary
qhull option error: cannot open file "%s" for writing as option 'TO'.  It is already in use or read-only
qh_projectinput: projected points to paraboloid for Delaunay
qh_check_maxout: determine actual minvertex
qh_rename_adjacentvertex: simplicial f%d contains old v%d and new v%d.  Will be marked degenerate by qh_renamevertex
qh_renamevertex: renaming v%d to v%d in oldfacet f%d for qh_rename_sharedvertex
  NULLvertex
qh_vertexneighbors: determining neighboring facets for each vertex
qhull internal error (qh_checkpolygon): vertex neighbors inconsistent (tot_vneighbors %d != tot_facetvertices %d).  Maybe duplicate or missing vertex
qh_createsimplex: created simplex
    - merges: %dmax
qhull input warning: exact merge ('Qx').  Verify may report that a point is outside of a facet.  See qh-optq.htm#Qx
qhull internal error (qh_memcheck): either qh->qhmem is overwritten or qh->qhmem is not initialized.  Call qh_meminit or qh_new_qhull before calling qh_mem routines.  ferr 0x%x, IsTracing %d, ALIGNmask 0x%x
qhull option error: no output specified for Geomview
qhull option warning: drop dimension 'GD%d' is only available for 3-d/4-d Geomview
qhull internal error: qh_checklists failed on reset of qh.vertex_visit %u
qhull internal error: qh_checklists failed on reset of qh.visit_id %u
ERRONEOUS and NEIGHBORING FACETS to output
qhull internal error (qh_addpoint): NULL facet.  Need to call qh_findbestfacet first
printfacetlist: facetlist
qh_removevertex: remove v%d from qh.vertex_list
qh_appendfacet: append f%d to facet_list
qhull internal error (qh_checkfacet): redundant facet f%d not on qh.visible_list
qhull internal error (qh_checkfacet): facet f%d is on qh.visible_list
qh_removefacet: removed f%d from facet_list, newfacet_list, and visible_list
qhull internal error (qh_checklists): new vertex list v%d is not on vertex list
qhull internal error (qh_buildhull): new vertex f%d in vertex list
qhull internal error (qh_buildhull): visible or new facet f%d in facet list
qh_furthestvertex: all vertices of f%d are in f%d.  Returning 0.0 for max and mindist
qhull input error (qh_printafacet): option 'Fp' needs qh->feasible_point
qhull internal error (qh_projectinput): HALFspace defined without qh.feasible_point
qh_maxmin: dim             min             max           width    nearzero  min-point  max-point
qhull internal error (qh_delvertex): vertex v%d was deleted but it was not partitioned as a coplanar point
qhull internal error (qh_merge_degenredunant): f%d is redundant but visible f%d has no replacement
qh_degen_redundant_facet: test facet f%d for degen/redundant

A wide merge error has occurred.  Qhull has produced a wide facet due to facet merges and vertex merges.
This usually occurs when the input is nearly degenerate and substantial merging has occurred.
See http://www.qhull.org/html/qh-impre.htm#limit

A Qhull topology error has occurred.  Qhull did not recover from facet merges and vertex merges.
This usually occurs when the input is nearly degenerate and substantial merging has occurred.
See http://www.qhull.org/html/qh-impre.htm#limit
qh_maybe_duplicateridge: will merge v%d into v%d (dist %2.2g) due to duplicate ridges r%d/r%d with the same vertices.  mergevertex set
qhull internal error (qh_setreplace): elem %p not found in set
qh_appendvertex: append v%d to qh.newvertex_list and set v.newfacet
qh_mergecycle_vneighbors: update vertex neighbors for newfacet
qh_mergecycle_ridges: add ridges to newfacet
qh_mergecycle_neighbors: delete shared neighbors from newfacet
qh_mergecycle_ridges: delete shared ridges from newfacet
qh_findgood_all: undo selection of qh.GOODclosest f%d since it would fail qh_inthresholds in qh_skipfacet
 NULLfacet
qh_check_bestdist: check that all points are within %2.2g of best facet
qh_merge_pinchedvertices: merge degenerate f%d into an adjacent facet
qh_mergecycle_all: merge new facets into coplanar horizon facets.  Bulk merge a cycle of facets with the same horizon facet
qhull internal error (qh_checkfacet): for facet f%d, neighbor f%d of ridge r%d not in facet
qh_triangulate: delete %d or more mirrored facets.  Mirrored facets have the same vertices due to a null facet
qh_triangulate: delete f%d.  All tricoplanar facets degenerate for non-simplicial facet
     - horizon ridge to visible facet
qh_mergecycle: end of trace facet
qhull option warning: joggle ('QJ') produces simplicial output (i.e., triangles in 2-D).  Unless merging is requested, option 'Qt' has no effect
qh_freeqhull: clear qhT except for qh.qhmem and qh.qhstat
0 1 1 1  # color of points
 %6.2g max. distance for near-inside points
qhull input error (qh_initqhull_globals): expecting between 1 and %d points.  Got %d %d-d points
qhull error: insufficient memory to copy %d points
qhull error: insufficient memory to project %d points
qhull internal error (qh_getcenter): not defined for %d points
qhull error: insufficient memory to joggle %d points
qh_settemppop: depth %d temp set %p of %d elements
qh_settemppush: depth %d temp set %p of %d elements
qh_freebuild: free global sets
qh_partitionall: partition all points into outside sets
qh_merge_pinchedvertices: merge one of %d pinched vertices before adding apex p%d.  Try to resolve duplicate ridges in newfacets
qh_attachnewfacets: attach horizon facets to new facets
qh_mergecycle_all: merged %d same cycles or facets into coplanar horizons and %d degenredundant facets
qh_merge_degenredundant: merge %d degenerate, redundant, and mirror facets
qhull internal error (qh_nearvertex): qh.VERTEXneighbors and facet->center required for tricoplanar facets
qh_findbestlower: all neighbors of facet %d are flipped or upper Delaunay.  Search all facets
qh_initialhull: initial orientation incorrect, qh.interior_point is %2.2g from f%d.  Reversing orientation of all facets
qh_initialhull: initial orientation incorrect, qh.interior_point is %2.2g from f%d.  Either axis-parallel facet or coplanar firstfacet f%d.  Force outside orientation of all facets
qh_triangulate: triangulate non-simplicial facets
qh_getpinchedmerges: dupridge (MRGdupridge) of coplanar horizon would produce a wide merge (%.0fx) due to pinched vertices v%d and v%d (dist %2.2g) for f%d and f%d.  qh_mergecycle_all will merge one or both facets
qhull internal error (qh_checkpolygon): actual number of facets is %d, cumulative facet count is %d - %d visible facets
qh_update_vertexneighbors: delete %d of %d vertex neighbors for v%d.  Removes to-be-deleted, visible facets
qh_check_maxout:  p%d(v%d) is qh.min_vertex %2.2g below facet f%d.  Point p%d for f%d is qh.max_outside %2.2g above f%d.  %d points are outside of not-good facets
qh_triangulate: delete visible facets -- non-simplicial, null, and mirrored facets
qh_findgood_all: %d good facets remain out of %d facets
printfacetlist: %d facets
qh_test_vneighbors: found %d non-convex, vertex neighbors
qhull internal error (qh_facetintersect): f%d or f%d not in other's neighbors
qh_triangulate_mirror: delete mirrored facets f%d and f%d and link their neighbors
qhull internal error (qh_forcedmerges): f%d and f%d had a dupridge but as f%d and f%d they are no longer neighbors
qh_merge_degenredundant: deleted v%d because f%d has no neighbors
qhull internal error (qh_findhorizon): visible facet f%d does not have neighbors
qh_mergefacet: check f%d and f%d for redundant and degenerate neighbors
qh_mergecycle_neighbors: update neighbors
qh_forcedmerges: dupridge f%d is degenerate with fewer than %d neighbors
qh_freebuffers: freeing up global memory buffers
qhull option error: Mathematica and Maple output is only available for 2-d and 3-d convex hulls and 2-d Delaunay triangulations
{appearance {+edge -face} OFF %d %d 1 # Voronoi centers and cells
qhull warning (qh_memsize): free list table has room for only %d sizes
qh_memsize: quick memory of %d bytes
qhull error (qh_memalloc): insufficient memory to allocate %d bytes
qh_mergecycle_ridges: found %d old ridges and %d new ones
qh_check_points: check all points below %2.2g of all facet planes
qh_addpoint: add p%d(v%d) %2.2g above f%d to hull of %d facets, %d merges, %d outside at %4.4g CPU secs.  Previous p%d(v%d) delta %4.4g CPU, %d facets, %d merges, %d hyperplanes, %d distplanes, %d retries
qh_mark_dupridges: found %d duplicated ridges (MRGdupridge) for qh_getpinchedmerges
qh_matchdupridge: make forced merge of dupridge for new f%d skip %d and f%d skip %d, maxdist %4.4g in qh_forcedmerges
qh_all_merges: drop merge of f%d (tested? %d) into f%d (tested? %d) mergetype %d, dist %2.2g, angle %4.4g.  Merge independent sets of coplanar merges
qhull internal error (qh_checkdelridge): expecting empty qh.vertex_mergeset in order to avoid calling qh_delridge_merge.  Got %d merges
qh_forcedmerges: merged %d facets, %d flipped facets, and %d degenredundant facets across dupridges
qh_forcedmerges: merge dupridges
qh_willdelete: move f%d to visible list, set its replacement as f%d, and clear f.neighbors and f.ridges
qh_attachnewfacets: delete interior ridges
qh_remove_extravertices: v%d deleted because it's lost all ridges
qh_remove_extravertices: v%d removed from f%d because it's lost all ridges
qhull internal error (qh_checkpolygon): expecting empty f.neighbors and f.ridges for visible facet f%d.  Got %d neighbors and %d ridges
qhull internal error (qh_checkfacet): f%d is 'newmerge' but it is not a newfacet on qh.newfacet_list f%d.  Missing call to qh_reducevertices
qh_checkfacet: vertex v%d in f%d intersect f%d but not in a ridge.  Repaired by qh_remove_extravertices in qh_reducevertices
qh_reducevertices: reduce extra vertices, shared vertices, and redundant vertices
qhull internal error (qh_appendmergeset): mirrored facets f%d and f%d do not have the same vertices
qhull internal error (qh_checkfacet): ridges r%d and r%d (f%d) have the same vertices
qh_triangulate: delete null facets from facetlist f%d.  A null facet has the same first (apex) and second vertices
qh_partitionvisible: partitioned %d points from outsidesets, %d points from coplanarsets, and %d deleted vertices
qhull internal error (qh_findbest_pinchedvertex): expecting subridge of qh.hull_dim-2 vertices for the intersection of new facets f%d and f%d minus their apex.  Got %d vertices
qhull internal error (qh_checkfacet): ridge between f%d and f%d has %d vertices
qh_buildhull: stop after adding %d vertices
qh_basevertices: found %d vertices
qh_deletevisible: delete %d visible facets and %d vertices
qhull internal error (qh_addpoint): infinite loop (%d retries) of merging pinched vertices due to dupridge for point p%d, facet f%d, and %d vertices
qh_remove_extravertices: test non-simplicial f%d for extra vertices
printfacetlist: vertices
qhull error: insufficient memory to compute dual of %d halfspaces
qh_findgood_all: f%d is closest(%2.2g) to split thresholds
qh_findgood: f%d is closest(%2.2g) to thresholds
qhull internal error: qh_checklists failed on qh_collectstatistics
qh_initqhull_globals: for %s | %s
qhull %s Statistics: %s | %s

While executing: %s | %s

Trace level T%d, IStracing %d, point TP%d, merge TM%d, dist TW%2.2g, qh.tracefacet_id %d, traceridge_id %d, tracevertex_id %d, last qh.RERUN %d, %s | %s
{appearance {linewidth 3} LIST # %s | %s
{appearance {+edge -evert linewidth 2} LIST # %s | %s
qh_new_qhull: build new Qhull for %d %d-d points with %s
qh_joggle_restart: qhull restart because of %s
qh_checkzero: testall %d, facets are %s
qh_initqhull_outputflags: %s
qhull input error: missing quote after filename -- %s
qhull error: filename is more than %d characters, %s

%s
qhull invoked by: %s | %s
  %s with options:
%s
Options selected for Qhull %s:
%s
qhull topology error (qh_matchdupridge): missing qh_DUPLICATEridge at f%d skip %d for new f%d skip %d hash %d ismatch %d.  Set by qh_matchneighbor
qhull internal error (qh_checkfacet): facet f%d still has a MERGEridge or DUPLICATEridge neighbor
qh_flippedmerges: merged %d flipped and %d degenredundant facets into a good neighbor
qh_maydropneighbor: test f%d for no ridges to a neighbor
qhull internal error (qh_voronoi_center):  need at least %d points to construct a Voronoi center
qh_degen_redundant_facet: f%d is flipped, will merge later
qhull input warning: no maximum cosine angle given for option 'An'.  A1.0 is coplanar
qh_findhorizon: %d horizon facets(good %d), %d visible(good %d), %d coplanar
qhull internal error (qh_memsize): qh_memsize called after qh_memsetup
qhull internal error (qh_matchnewfacets): %d neighbors did not match up
qhull error (qh_settemppush): can not push a NULL temp

If you need triangular output:
  - use option 'Qt' to triangulate the output
  - use option 'QJ' to joggle the input points and remove precision errors
  - use option 'Ft'.  It triangulates non-simplicial facets with added points.

If you must use 'Q0',
try one or more of the following options.  They can not guarantee an output.
  - use 'QbB' to scale the input to a cube.
  - use 'Po' to produce output and prevent partitioning for flipped facets
  - use 'V0' to set min. distance to visible facet as 0 instead of roundoff
  - use 'En' to specify a maximum roundoff error less than %2.2g.
  - options 'Qf', 'Qbb', and 'QR0' may also help
qhull internal error (qh_checkpolygon): unknown point %p for vertex v%d first_point %p
qhull internal error (qh_checkvertex): unknown point id %p
qh_mergevertex_neighbors: of f%d into f%d at furthest p%d f0= %p
qh_checkzero: qh_premerge is needed.  New facet f%d or its horizon f%d is non-simplicial, flipped, dupridge, or mergehorizon
qh_makenewfacets: created %d new facets f%d..f%d from point p%d to horizon
qhull option error: test vertex neighbors('Qv') needs a merge option
qh_buildhull: completed the hull construction
qh_sethalfspace_all: compute dual for halfspace intersection
qhull internal error (qh_projectpoints): newdim %d should be %d after projection
qh_setdelaunay: project %d points to paraboloid for Delaunay triangulation
qhull warning: output is the Delaunay triangulation
qhull internal error: qh_checklists failed in qh_checkpolygon
qh_flippedmerges: begin
qhull precision error: f%d is clearly not convex to f%d, since p%d(v%d) is %6.4g above or coplanar with f%d with qh.ZEROcentrum
 %6.2g radius of post-merge centrum
 %6.2g radius of pre-merge centrum
qhull internal error (qh_checkfacet): for simplicial facet f%d, #vertices %d + #neighbors %d != 2*qh->hull_dim
qhull internal error (qh_checkfacet): for facet f%d, #vertices %d or #neighbors %d < qh->hull_dim
qh_memcheck: check size of freelists on qh->qhmem
qh_memcheck: A segmentation fault indicates an overwrite of qh->qhmem

qhull error while handling previous error in qh_errexit.  Exit program
qhull internal error (qh_initqhull_globals): if qh.VORONOI is set, qh.DELAUNAY must be set.  Qhull constructs the Delaunay triangulation in order to compute the Voronoi diagram
%s set is null
qh_freebuild: free memory from qh_inithull and qh_buildhull
qh_outcoplanar: move outsideset to coplanarset for qh->NARROWhull
qhull internal error (qh_qhull): temporary sets not empty(%d) at end of Qhull
qh_new_qhull: initialize Qhull
computing area of each facet and volume of the convex hull
qh_buildhull: stop point or cone P%d in initial hull
qh_buildhull: start build hull
# 1 color for all
qh_initbuild: create sentinels for qh.facet_tail and qh.vertex_tail
Qhull precision warning (qh_check_maxout): f%d.maxoutside (%4.4g) is greater than computed qh.max_outside (%2.2g) + qh.DISTround (%2.2g).  It should be less than or equal
qhull internal error (qh_mergecycle_all): f%d without normal
qhull internal error (qh_checkfacet): facet f%d does not have a normal
qhull internal error (qh_findbest_pinchedvertex): expecting merge of adjacent, simplicial new facets.  f%d or f%d is not simplicial
qhull internal error (qh_replacefacetvertex): f%d is not simplicial
%s | %s
begin
    %d %d real
%s | %s
begin
%d %d real
qhull internal error (qh_settemppop): pop from empty temporary stack
qhull internal error: cannot call qh_findbestneighor for f%d while qh.CENTERtype is qh_ASvoronoi
qhull input error: %d attempts to construct a convex hull with joggled input.  Increase joggle above 'QJ%2.2g' or modify qh_JOGGLE... parameters in user_r.h
qhull exit due to qh_ERRdebug

A Qhull error has occurred.  Qhull should have corrected the above
precision error.  Please send the input and all of the output to
[email protected]
qh_mark_dupridges: found %d duplicated ridges (MRGdupridge) for qh_premerge.  Prepare facets for merging
qh_mergefacet: end of wide tracing
qhull precision error (qh_check_points): %d additional points outside facet f%d, maxdist= %6.8g
qhull precision error (qh_check_bestdist): point p%d is outside facet f%d, distance= %6.8g maxoutside= %6.8g
  %s facet area:   %2.8g
  %s volume:       %2.8g
    - offset: %10.7g
    - maxoutside: %10.7g
%6.16g %6.16g
3 0 1 2 %8.4g %8.4g %8.4g
%8.4g %8.4g %8.4g
%8.4g %8.4g %8.4g
qh_maxsimplex: selected point p%d for %d`th initial vertex, det=%4.4g, targetdet=%4.4g, mindet=%4.4g
qh_appendmergeset: dupridge will merge a non-flipped facet f%d into flipped f%d, dist %4.4g
qh_matchdupridge: make good forced merge of dupridge f%d skip %d into f%d skip %d, keep new f%d skip %d and f%d skip %d, dist %4.4g
qh_matchdupridge: keep dupridge f%d skip %d and f%d skip %d, dist %4.4g
qhull internal error (qh_appendmergeset): except for MRGdupridge, cannot merge a non-flipped facet f%d into flipped f%d, mergetype %d, dist %4.4g
qh_maxsimplex: searching all points for %d-th initial vertex, better than mindet %4.4g, targetdet %4.4g
qh_maxsimplex: searching all points for %d-th initial vertex, better than p%d det %2.2g and mindet %4.4g, targetdet %4.4g
qh_maxouter: max distance from facet to outer plane is %4.4g, qh.max_outside is %4.4g
qh_maxsimplex: searching all points ('Qs') for %d-th initial vertex, better than p%d det %4.4g, targetdet %4.4g, ratio %4.4g
qh_maxsimplex: searching all points for %d-th initial vertex, better than p%d det %4.4g and mindet %4.4g, ratio %4.4g
qhull precision error (qh_maxsimplex for voronoi_center): %d points with the same x coordinate %4.4g
qhull input error: input is less than %d-dimensional since all points have the same x coordinate %4.4g
qh_test_centrum_merge: coplanar f%d to f%d dist %4.4g, reverse dist %4.4g angle %4.4g
qh_all_merges: merge f%d and f%d type %d dist %2.2g angle %4.4g
  %d:  %8.4g  %8.4g  difference= %4.4g
qh_getangle: %4.4g
  CPU seconds to compute hull (after input): %2.4g
qhull precision error: facet f%d is flipped, distance= %6.12g
qhull precision error (qh_check_points): a coplanar point is %6.2g from convex hull.  The maximum value(qh.outside_err) is %6.2g
 distance= %4.2g
qh_detjoggle: joggle=%2.2g maxwidth=%2.2g
qh_findbestneighbor: f%d is best neighbor for f%d testcentrum? %d nonconvex? %d dist %2.2g min %2.2g max %2.2g
qhull precision error (qh_merge_twisted): twisted facet f%d with pinched vertices.  Could merge vertices, but too wide to merge into neighbor.   mindist %2.2g maxdist %2.2g vertexdist %2.2g neighbor f%d mindist %2.2g maxdist %2.2g
qhull precision error (qh_merge_twisted): twisted facet f%d does not contain pinched vertices.  Too wide to merge into neighbor.  mindist %2.2g maxdist %2.2g vertexdist %2.2g maxpinched %2.2g neighbor f%d mindist %2.2g maxdist %2.2g
qh_matchdupridge: try good dupridge f%d skip %d into new f%d skip %d at dist %2.2g otherdist %2.2g
qh_matchdupridge: try good dupridge flipped f%d skip %d into new f%d skip %d at dist %2.2g otherdist %2.2g
qh_matchdupridge: try good dupridge new f%d skip %d into f%d skip %d at dist %2.2g otherdist %2.2g
qh_matchdupridge: try good dupridge flipped new f%d skip %d into f%d skip %d at dist %2.2g otherdist %2.2g
qh_getpinchedmerges: try to merge pinched vertices for dupridges in new facets with apex p%d(v%d) max dupdist %2.2g
qh_findbesthorizon: test neighbors of f%d bestdist %2.2g f%d ischeckmax? %d noupper? %d minsearch %2.2g is_5x? %d searchdist %2.2g
qh_detvnorm: points %d %d midpoint dist %2.2g
qh_matchdupridge: try furthest dupridge f%d skip %d new f%d skip %d at dist %2.2g
qh_merge_degenredundant: facet f%d has %d neighbors, merge into f%d dist %2.2g
qh_partitionpoint: point p%d is inside all facets, closest to f%d dist %2.2g
qh_detvnorm: points %d %d Voronoi vertex %d dist %2.2g
qh_rename_adjacentvertex: merge #%d rename v%d (%d neighbors) to v%d (%d neighbors) dist %2.2g
qh_partitioncoplanar: point p%d is coplanar with facet f%d (or inside) dist %2.2g
qh_getpinchedmerges: will make the apex a coplanar point.  apex p%d(v%d) is the nearest vertex to v%d on dupridge.  Dist %2.2g
qhull precision error: point p%d is outside facet f%d, distance= %6.8g maxoutside= %6.8g nearest vertices %2.2g
Qhull internal error (qh_partitioncoplanar): infinite loop due to recursive call to qh_partitionpoint.  Repartition point p%d from f%d as a outside point dist %2.2g nearest vertices %2.2g
Qhull precision warning: repartition coplanar point p%d from f%d as an outside point above hidden facet f%d dist %2.2g nearest vertices %2.2g
Qhull precision warning: repartition coplanar point p%d from f%d as an outside point above twisted facet f%d dist %2.2g nearest vertices %2.2g
Qhull precision warning: in post-processing (qh_check_maxout) p%d(v%d) is %2.2g below f%d nearest vertices %2.2g
Qhull precision warning: in post-processing (qh_check_maxout) p%d for f%d is %2.2g above hidden facet f%d nearest vertices %2.2g
Qhull precision warning: in post-processing (qh_check_maxout) p%d for f%d is %2.2g above twisted facet f%d nearest vertices %2.2g
qh_check_maxout: p%d(v%d) is %.2g from f%d nearest vertices %2.2g
Qhull topology error (qh_partitioncoplanar): can not repartition coplanar point p%d from f%d as outside point above f%d.  It previously failed to form a cone of facets, dist %2.2g, nearest vertices %2.2g
qh_distround: %2.2g, maxabs %2.2g, maxsumabs %2.2g, maxdistsum %2.2g
qh_partitioncoplanar: repartition coplanar point p%d from f%d as an outside point above corner facet f%d dist %2.2g with angle %2.2g
qh_check_maxout: check and update qh.min_vertex %2.2g and qh.max_outside %2.2g
qh_mergefacet: #%d merge f%d into f%d for merge for mergetype %d (%s), mindist= %2.2g, maxdist= %2.2g, max_outside %2.2g
 Last merge #%d, max_outside %2.2g
qh_check_bestdist: max distance outside %2.2g
qh_check_points: max distance outside %2.2g
qh_addpoint: added p%d to convex hull with point balance %2.2g
qh_buildcone: created %d newfacets for p%d(v%d) new facet balance %2.2g
qh_detmaxoutside: MAXoutside %2.2g from qh.max_outside %2.2g, ONEmerge %2.2g, MINoutside %2.2g, DISTround %2.2g
qh_scalepoints: scaled %d'th coordinate [%2.2g, %2.2g] to [%.2g, %.2g] for %d points by %2.2g and shifted %2.2g
qh_facetarea: f%d area %2.2g
qh_getcentrum: for f%d, %d vertices dist= %2.2g
    - furthest distance= %2.2g
      furthest distance= %2.2g
  After %d retries, input joggled by: %2.2g
  Input joggled by: %2.2g
    - area: %2.2g
qh_checkzero: facet f%d and horizon f%d are not clearly convex.  v%d dist %.2g
qh_checkzero: facet f%d and f%d are not clearly convex.  v%d dist %.2g
qhull input error: 'Qb%d' or 'QB%d' inverts paraboloid since high bound %.2g < low bound %.2g
qh_markkeep: only keep %d largest and/or %d most merged facets and/or min area %.2g
qhull option error: the joggle for 'QJn', %.2g, is below roundoff for distance computations, %.2g
  Percentage of runs with precision errors: %4.1f
%7d calls to qh_setlarger
%7.2g     average copy size
qhull internal error (qh_maxsimplex): qh.MAXwidth required for qh_maxsimplex.  Used to estimate determinate
qhull topological error (qh_mark_dupridges): multiple dupridges for f%d and f%d, including reverse
qhull internal error (qh_detvnorm): too few points(%d) to compute separating plane
 %6.2g max. cosine for post-merge angle
 %6.2g max. cosine for pre-merge angle
qhull internal error (qh_infiniteloop): potential infinite loop detected.  If visible, f.replace. If newfacet, f.samecycle
qh_attachnewfacets: clear f.ridges and f.neighbors for visible facets, may become invalid before qh_deletevisible
qhull internal error (qh_maxsimplex): not enough points available
qhull option warning: negative point id for trace option 'TPn'.  Expecting 'TP-1' for tracing after qh_buildhull and qh_postmerge
qhull internal error (qh_checkdelridge): unexpected 'nonconvex' flag for ridge r%d in newfacet f%d.  Otherwise need to call qh_delridge_merge
qhull internal error (qh_checkdelridge): unexpected 'nonconvex' flag for ridge r%d in visible facet f%d.  Otherwise need to call qh_delridge_merge
qh_checkzero: skip convexity check until first pre-merge
qh_matchdupridge: duplicate ridge due to duplicate facets (f%d skip %d and f%d skip %d) previously reported as QH7084.  Maximize dupdist to force vertex merge
qh_degen_redundant_facet: f%d is contained in f%d.  merge
qh_test_redundant_neighbors: f%d is contained in f%d.  merge
qh_renamevertex: renaming v%d to v%d in several facets for qh_redundant_vertex or MRGsubridge
 DUPLICATEridge
qh_mark_dupridges: restore missing neighbors and ridges due to qh_MERGEridge
 MERGEridge
qhull internal error (qh_mergevertices): facets did not share a ridge
qh_memcheck: total size of freelists totfree is the same as qh->qhmem.totfree
qh_check_maxout: determine actual maxoutside
qhull option warning: additional output formats ('Fc',etc.) are not compatible with Geomview ('G').  Use option 'Po' to override
qhull option warning: missing space after option '%c'(%x), reserved for sub-options, ignoring '%c' options to next space
qhull option warning: unknown 'T' trace option 'T%c', skip to next space
qhull option warning: unknown 'Q' qhull option 'Q%c', skip to next space
qhull option warning: unknown 'P' print option 'P%c', skip to next space
qhull option warning: unknown 'G' geomview option 'G%c', skip to next space
qhull option warning: unknown 'F' output option 'F%c', skip to next space
qhull option warning: unknown 'Q' qhull option 'Q1%c', skip to next space
qh_getmergeset: %d merges found
qh_getmergeset_initial: %d merges found
qh_projectinput: updating lower and upper_bound
printfacetlist: end

input sites with last coordinate projected to a paraboloid
qh_initflags: option flags initialized
qhull warning: no facets printed
Qhull: algorithm completed
qh_all_merges: drop merge of f%d (del? %d) into f%d (del? %d) mergetype %d, dist %4.4g, angle %4.4g.  One or both facets is deleted
qh_rename_adjacentvertex: ignore rename.  Either v%d (%d) or v%d (%d) is deleted
qh_mergecycle_facets: make newfacet new and samecycle deleted
qh_merge_degenredundant: facet f%d has no neighbors.  Deleted
qh_initialhull: simplex constructed
 # p%d is coplanar or isolated
qh_newvertex: vertex p%d(v%d) created
 0 # infinity not used
qhull option warning: can only drop one dimension.  Previous 'GD%d' ignored
qhull option warning: no dimension given for Print option 'P%c' at: %s.  Ignored
qhull option warning: dimension %d for Qhull option 'Q%c' is >= %d.  Ignored
qhull option warning: dimension %d for Print option 'P%c' is >= %d.  Ignored
qhull option warning: value %2.4g for Print option 'P%c' is > +1 or < -1.  Ignored
qhull option warning: no good point id given for option 'QVn'.  Ignored
qhull option warning: good vertex already defined for option 'QVn'.  Ignored
qhull option warning: missing good point id for option 'QGn'.  Ignored
qhull option warning: good point already defined for option 'QGn'.  Ignored
qh_initialhull: ignore f%d flipped.  Test qh.interior_point (p-2) for clearly flipped
qhull option warning: can not follow '1', '2', or '3' with a digit.  'Q%c%c' skipped
qh_initbuild: initial hull created and points partitioned
qh_redundant_vertex: check if v%d from a deleted ridge can be renamed
qh_freebuffers: finished
qh_merge_nonconvex: avoid merging old facet f%d dist %2.2g.  Use f%d dist %2.2g instead
qhull precision warning (qh_getpinchedmerges): pinched vertices v%d and v%d (dist %2.2g, %.0fx) would produce a wide merge for f%d and f%d.  Will merge dupridge instead
qhull warning: 'Gnh' generates no output in 4-d
qhull warning: output for outer/inner planes and centrums not implemented in 4-d
qhull warning: output for vertices not implemented in 4-d
qhull option error: Geomview output is only available for 2-d, 3-d and 4-d
qh_order_vertexneighbors: order neighbors of v%d for 3-d
qhull option error: Geomview output for Voronoi diagrams only for 2-d
qhull warning: output for ridges and intersections not implemented in 2-d
           %3d % 14.8e % 14.8e % 14.8e  %4.4e  p%-9d p%-d
qhull internal error (qh_checklists): unknown or overwritten vertex v%d, either id >= qh.vertex_id (%d) or v.visitid %u > qh.visit_id %u.  vertexlist terminated at previous vertex v%d
qhull internal error (qh_checkpolygon): facet f%d occurs twice in neighbors of vertex v%d
qhull internal error (qh_replacefacetvertex): f%d already contains new v%d
qh_checklists: check %slist f%d and qh.vertex_list v%d
qh_checklists: check qh.%s_list f%d and qh.vertex_list v%d
qhull internal error (qh_checkpolygon): v%d is 'newfacet' but it is not on new vertex list v%d
qhull internal error (qh_checklists): expecting v%d.previous == v%d.  Got v%d
qhull internal error (qh_checklists): v%d already in vertexlist causing an infinite loop ... v%d > v%d ... > v%d > v%d.  Truncate vertexlist at v%d
qhull internal error (qh_checkfacet): vertices of f%d are not in descending id order at v%d
qhull internal error (qh_checkpolygon): missing vertex neighbors for v%d
qh_neighbor_vertices: %d non-subridge, vertex neighbors for v%d
qh_find_newvertex: vertices not in ridges for v%d
qh_vertexridges: found %d ridges for v%d
qhull internal error (qh_renameridgevertex): oldvertex v%d not found in r%d.  Cannot rename to v%d
qh_renamevertex: ignore duplicate check for r%d.  top f%d (size %d) will be degenerate after rename v%d to v%d
qh_renamevertex: ignore duplicate check for r%d.  bottom f%d (size %d) will be degenerate after rename v%d to v%d
qhull internal error (qh_checkvertex): neighbor f%d does not contain v%d
qh_triangulate: update neighbor lists for vertices from v%d
qh_update_vertexneighbors_cone: deleted %d visible vertexneighbors of v%d
qhull internal error (qh_checkpolygon): v%d is a vertex of facet f%d but f%d is not a neighbor of v%d
qh_neighbor_intersections: %d vertices in neighbor intersection of v%d
qh_renamevertex: rename vertices in non-simplicial neighbor f%d of v%d
qh_renameridgevertex: ridge r%d deleted.  It contained both v%d and v%d
qh_getpinchedmerges: will merge new facets to resolve dupridge between f%d and f%d with pinched v%d and v%d
qhull internal error (qh_replacefacetvertex): f%d does not contain old v%d
qh_renameridgevertex: swapped the top and bottom of ridge r%d
qhull internal error (qh_checkfacet): facet f%d has a duplicate ridge r%d
qh_newridge: created ridge r%d
qh_delridge_merge: drop merge of v%d into v%d (dist %2.2g r%d r%d) due to deleted, duplicated ridge r%d
qhull internal error (qh_mergecycle_ridges): bad ridge r%d
qh_next_vertexmerge: drop merge of v%d (del? %d) into v%d (del? %d) due to deleted vertex of r%d and r%d
qhull internal error (qh_appendvertexmerge): expecting two distinct ridges for MRGvertices.  Got r%d r%d
qh_merge_pinchedvertices: merge %d pinched vertices from dupridges in merged facets, apex p%d
qh_tracemerge: trace vertex deleted at furthest p%d
qh_maydropneighbor: facets f%d and f%d are no longer neighbors while adding furthest p%d
qhull internal error (qh_maydropneighbor): not valid for simplicial f%d while adding furthest p%d
qhull internal error (qh_maydropneighbor): not valid for simplicial neighbor f%d of f%d while adding furthest p%d
qh_tracemerge: trace facet and vertex after merge of f%d into f%d type %d (%s), furthest p%d
qh_setfacetplane: ====== vertex p%d(v%d) increases max_outside to %2.2g for new facet f%d last p%d
qh_partitioncoplanar: == p%d from f%d increases qh.max_outside to %2.2g of f%d last p%d
qhull internal error (qh_findbestnew): no new facets for point p%d
qh_mergecycle: ========= trace merge %d of samecycle %d into trace f%d, furthest is p%d
qh_mergefacet: ========= trace merge #%d for f%d into f%d for mergetype %d (%s), furthest is p%d
qh_mergefacet: ========= trace wide merge #%d(%2.2g) for f%d into f%d for mergetype %d (%s), last point was p%d

At %02d:%02d:%02d & %2.5g CPU secs, qhull has created %d facets and merged %d.
 The current hull contains %d facets and %d vertices.  Last point was p%d
qhull topology error (qh_checkfacet): vertex v%d in f%d intersect f%d but not in a ridge.  Last point was p%d
qh_check_dupridge: dupridge between f%d and f%d (vertex dist %2.2g), dist %2.2g, reverse dist %2.2g, ratio %2.2g while processing p%d
qhull internal error (qh_findbest_pinchedvertex): did not find best vertex for subridge of dupridge between f%d and f%d, while processing p%d
qh_normalize: norm=%2.2g too small during p%d
qh_test_nonsimplicial_merge: concave coplanar f%d v%d to f%d v%d, dist %4.4g and reverse dist %4.4g, angle %4.4g during p%d
qh_test_nonsimplicial_merge: coplanar f%d v%d to f%d v%d, dist %4.4g and reverse dist %4.4g, angle %4.4g during p%d
qh_test_nonsimplicial_merge: twisted concave f%d v%d to f%d v%d, dist %4.4g and reverse dist %4.4g, angle %4.4g during p%d
qh_test_nonsimplicial_merge: concave f%d v%d to f%d v%d, dist %4.4g and reverse dist %4.4g, angle %4.4g during p%d
qh_test_nonsimplicial_merge: concave centrum for f%d or f%d, dist %4.4g and reverse dist %4.4g, angle %4.4g during p%d
qh_test_centrum_merge: concave f%d to coplanar f%d, dist %4.4g and reverse dist %4.4g, angle %4.4g during p%d
qh_test_centrum_merge: concave f%d to f%d, dist %4.4g and reverse dist %4.4g, angle %4.4g during p%d
qh_checkflipped: facet f%d flipped, allerror? %d, distance= %6.12g during p%d
qh_flippedmerges: merge flipped f%d into f%d dist %2.2g during p%d
qhull precision error: f%d is coplanar to f%d, since p%d(v%d) is within %6.4g of f%d, during p%d
qh_find_newvertex: no vertex for renaming v%d (all duplicated ridges) during p%d
qh_setfacetplane: flipped orientation due to nearzero gauss and interior_point test.  During p%d
projected p%d
qhull internal error (qh_nearvertex): did not find bestvertex for f%d p%d
qh_nearvertex: v%d dist %2.2g for f%d p%d
qh_findbestlower: f%d dist %2.2g for f%d p%d
qhull input error: either QGn or QVn point is > p%d
 # p%d
qhull internal error (qh_checkpolygon): f%d has outside points before qh.facet_next f%d
qhull internal error (qh_checkfacet): f%d is 'dupridge' but it is not a newfacet on qh.newfacet_list f%d
qh_makenewplanes: make new hyperplanes for facets on qh.newfacet_list f%d
qh_premerge: premerge centrum %2.2g angle %4.4g for apex p%d newfacet_list f%d
qhull internal error (qh_checklists): qh.facet_next f%d for qh_addpoint is not on qh.facet_list f%d
qhull internal error (qh_checklists): qh.newfacet_list f%d is not on qh.facet_list f%d
qhull internal error (qh_checklists): qh.visible_list f%d is not on qh.facet_list f%d
qh_check_bestdist: check points below nearest facet.  Facet_list f%d
qhull internal error (qh_checkpolygon): f%d is 'visible' but it is not on qh.visible_list f%d
qhull internal error (qh_checkpolygon): f%d is 'newfacet' but it is not on qh.newfacet_list f%d or visible_list f%d
qh_findgood: found %d good facets with %d good horizon and qh.GOODclosest f%d
qhull internal error (qh_checklists): expecting f%d.previous == f%d.  Got f%d
qhull internal error (qh_attachnewfacets): could not find visible facet for horizon f%d of newfacet f%d
qhull internal error (qh_checklists): unknown or overwritten facet f%d, either id >= qh.facet_id (%d) or f.visitid %u > qh.visit_id %u.  Facetlist terminated at previous facet f%d
    - owner of normal & centrum is facet f%d
no normal for facet f%d
qhull warning (qh_check_points): missing normal for facet f%d
qh_mergesimplex: merged simplex f%d v%d into facet f%d
qh_mergesimplex: merge apex v%d of f%d into facet f%d
qh_mergesimplex: merge opposite v%d of f%d into facet f%d
qh_triangulate_link: relink neighbors f%d and f%d of null facet f%d
qh_triangulate_null: delete null facet f%d
qh_triangulate: all tricoplanar facets degenerate for last non-simplicial facet f%d
qhull internal error (qh_triangulate): tricoplanar facet f%d not owned by its visible, non-simplicial facet f%d
qhull internal error (qh_facet3vertex): only %d vertices for simplicial facet f%d
qh_buildtracing: start trace T%d for point TP%d above facet f%d
qh_triangulate_facet: triangulate facet f%d
qhull internal error (qh_partitioncoplanar): cannot partition coplanar p%d of f%d into visible facet f%d
qhull internal error (qh_partitionpoint): cannot partition p%d of f%d into visible facet f%d
qh_findgooddist: p%d is %2.2g above good facet f%d
qh_newfacet: created facet f%d
qh_maybe_duplicateridges: will merge v%d into v%d (dist %2.2g) due to duplicate ridges with the same vertices r%d/r%d in merged facet f%d
qh_all_vertexmerges: starting to merge %d vertex merges for apex p%d facet f%d
qh_findhorizon: find horizon for point p%d facet f%d
qhull internal error (qh_checkfacet): vertex v%d in r%d not in f%d intersect f%d
qhull internal error (qh_checklists): f%d already in facetlist causing an infinite loop ... f%d > f%d ... > f%d > f%d.  Truncate facetlist at f%d
qh_partitionvisible: partition %d deleted vertices as coplanar? %d points into new facets f%d
qh_partitionvisible: partition outside and coplanar points of visible and merged facets f%d into new facets f%d
    - shares same visible/horizon as f%d
qhull internal error (qh_findbestneighbor): no neighbors for f%d
qh_makeridges: make ridges for f%d
qhull internal error (qh_triangulate): ridges still defined for f%d
qhull internal error (qh_order_vertexneighbors): no neighbor of v%d for f%d
makeridges: appended r%d to ridges for f%d.  Next is ridges for neighbor f%d
qhull internal error (qh_checkfacet): facet f%d does not have a ridge for neighbor f%d
qhull internal error (qh_checkfacet): facet f%d has neighbor f%d, but f%d does not have neighbor f%d
qhull internal error (qh_checkfacet): facet f%d has a duplicate neighbor f%d
qh_renamevertex: rename v%d to v%d in %d ridges with old f%d and neighbor f%d
qhull internal error (qh_checkfacet): ridge r%d is nonconvex (%d), mergevertex (%d) or not tested (%d) for facet f%d, neighbor f%d
qh_mergevertex_neighbors: merge vertex neighborset for f%d into f%d
qh_mergevertex_del: deleted v%d when merging f%d into f%d
qh_mergesimplex: merge ridges and neighbors of f%d into f%d
qh_mergeridges: merge ridges of f%d into f%d
qh_mergefacet2d: merged v%d and neighbor f%d of f%d into f%d
qh_mergecycle_facets: merged facets from cycle f%d into f%d
qh_mergecycle_vneighbors: merged vertices from cycle f%d into f%d
qh_mergecycle_vneighbors: deleted v%d when merging cycle f%d into f%d
qhull topology error (qh_mergesimplex): f%d is a dupridge of f%d, cannot merge f%d into f%d
    - was horizon to f%d
from p%d to f%d
qh_mergecycle: merge #%d for facets from cycle f%d into coplanar horizon f%d
qh_makenew_nonsimplicial: created facet f%d from v%d and r%d of horizon f%d
qhull internal error (qh_rename_sharedvertex): v%d's neighbors not in f%d
qhull internal error (qh_checkfacet): deleted vertex v%d in f%d
qh_replacefacetvertex: replace v%d with v%d in f%d
qh_triangulate: identify degenerate tricoplanar facets from f%d
qhull internal error (qh_nextfurthest): null facet or infinite loop detected for qh.facet_next f%d facet_tail f%d
qhull internal error (qh_next_vertexmerge): expecting two vertices for vertex merge.  Got v%d v%d and optional f%d
qhull internal error (qh_matchnewfacets): expecting simplicial facets on qh.newfacet_list f%d for qh_matchneighbors, qh_matchneighbor, and qh_matchdupridge.  Got non-simplicial f%d
qhull internal error (qh_makenew_nonsimplicial): simplicial f%d sharing two ridges with f%d
qh_findbest: neighbors of f%d, bestdist %2.2g f%d
qhull internal error (qh_checkpolygon): facet f%d is a neighbor of vertex v%d but v%d is not a vertex of f%d
qh_furthestout: p%d is furthest outside point of f%d
qh_mergesimplex: update vertex neighbors of f%d
qh_test_degen_neighbors: test for degenerate neighbors of f%d
qh_freebuild: delete the previously-seen ridges of f%d
qhull precision error: f%d is concave to f%d.  Centrum of f%d is %6.4g above f%d
qhull precision error: f%d is coplanar or concave to f%d.  Centrum of f%d is %6.4g above f%d
qhull precision error: f%d is concave to f%d, since p%d(v%d) is %6.4g above f%d
qh_check_maxout: p%d is %.2g above f%d
qh_findgooddist: no good facet for p%d above f%d
qh_furthestvertex: v%d dist %2.2g is furthest (mindist %2.2g) of f%d above f%d
qhull precision error: initial simplex is not convex, since p%d(v%d) is %6.4g above opposite f%d
qh_delfacet: delete f%d
qh_prependfacet: prepend f%d before f%d
qh_update_vertexneighbors: will delete interior vertex p%d(v%d) of visible f%d
qh_update_vertexneighbors_cone: will delete interior vertex p%d(v%d) of visible f%d
qh_update_vertexneighbors: delete interior vertex p%d(v%d) of visible f%d
qhull internal error (qh_triangulate_link): neighbors f%d and f%d do not match for null facet or mirrored facets f%d and f%d
qh_triangulate_link: relink neighbors f%d and f%d of mirrored facets f%d and f%d
qh_mark_dupridges): dupridge due to duplicate vertices for subridges f%d and f%d
qh_maybe_duplicateridges: will merge v%d into v%d (dist %2.2g) due to opposite oriented ridges r%d/r%d for f%d and f%d
qhull topology warning (qh_matchneighbor): will merge vertices to undo new facets -- f%d and f%d have the same vertices (skip %d, skip %d) and same horizon ridges to f%d and f%d
qh_test_appendmerge: coplanar angle %4.4g between f%d and f%d
qh_getpinchedmerges: will merge pinched v%d into v%d to resolve dupridge between f%d and f%d
qh_findbest_pinchedvertex: best pinched p%d(v%d) and vertex p%d(v%d) are closest (%2.2g) for duplicate subridge between f%d and f%d
qh_renamevertex: renaming pinched v%d to v%d between f%d and f%d
qh_copynonconvex: moved nonconvex flag from r%d to r%d between f%d and f%d
qh_delridge_merge: delete ridge r%d between f%d and f%d
qh_findbest_ridgevertex: best pinched p%d(v%d) and vertex p%d(v%d) are closest (%2.2g) for duplicated ridge r%d (same vertices) between f%d and f%d
           between f%d and f%d
qh_mergeneighbors: merge neighbors of f%d and f%d
qh_merge_twisted: merge #%d for twisted f%d and f%d
qh_rename_sharedvertex: p%d(v%d) is shared by f%d(%d ridges) and f%d
qh_partitioncoplanar: partition coplanar point p%d starting with f%d dist? %2.2g, allnew? %d, gh.repart_facetid f%d
# intersect f%d f%d
OFF 3 1 1 # ridge between f%d f%d
# r%d between f%d f%d
3 %d %d %d %8.4g %8.4g %8.4g 1 #r%d f%d f%d
3 %d %d %d %8.4g %8.4g %8.4g 1 # f%d f%d
# %d f%d
    - replacement: f%d
- f%d
{INST geom { : centrum } transform { # f%d
VECT 1 2 1 2 1 # f%d
{ OFF %d 1 1 # f%d
OFF 3 1 1 # f%d
qh_all_merges: skip qh_reducevertices due to post-merging, no qh.VERTEXneighbors (%d), or hull_dim %d ==2 or >%d
qhull internal error (qh_matchdupridge): no MERGEridge match for dupridge new f%d skip %d at hash %d..%d
qhull internal error (qh_matchdupridge): no maximum or good match for dupridge new f%d skip %d at hash %d..%d
 Last merge #%d
The halfspace was at index %d
qh_findbesthorizon: p%d, newbest? %d, bestfacet f%d, bestdist %2.2g, numfacet %d, coplanarfacets %d, numdist %d
qhull internal error (qh_facet3vertex): ridges for facet %d don't match up.  got at least %d
qh_findbestfacet: f%d dist %2.2g isoutside %d totpart %d
qh_findfacet_all: p%d, noupper? %d, f%d, dist %2.2g, isoutside %d, totpart %d
qh_lib_check: Expecting qhullLibraryType QHULL_NON_REENTRANT(0), QHULL_QH_POINTER(1), or QHULL_REENTRANT(2).  Got %d
qh_matchneighbor: newfacet f%d skip %d hash %d hashcount %d
qh_matchdupridge: find dupridge matches for f%d skip %d hash %d hashcount %d
qh_meminitbuffers: memory initialized with alignment %d
qh_test_redundant_neighbors: test neighbors of f%d vertex_visit %d
qhull internal error (qh_printextremes_2d): loop in facet list.  facet %d nextfacet %d
qhull internal error (qh_detvridge3): neighbors of vertex p%d are not connected at facet %d
qhull internal error (qh_errexit): either error while reporting error QH%d, or qh.NOerrexit not cleared after setjmp(). Exit program with error status %d
qhull internal error (qh_checkpolygon): #vertices %d != #facets %d
qhull internal error (qh_deletevisible): qh->num_visible %d is not number of visible facets %d
    size in bytes: merge %d ridge %d vertex %d facet %d
         normal %d ridge vertices %d facet vertices or neighbors %d
qh_markvoronoi: isLower %d numcenters %d
qhull internal error (qh_checkpolygon): actual number of vertices is %d, cumulative vertex count is %d
qh_matchneighbor: f%d skip %d matched with new f%d skip %d
qh_facetintersect: f%d skip %d matches f%d skip %d
qh_matchdupridge: allow tricoplanar dupridge for new f%d skip %d and f%d skip %d
qh_detvnorm: points %d %d angle %2.2g nearzero %d
qh_initflags: project dimension %d
qhull internal error (qh_printbegin): can not use this format for dimension %d
qhull input warning: more coordinates for 'H%s' than dimension %d
qhull internal error (qh_detsimplex): #points %d < dimension %d
qh_initqhull_globals: initialize globals.  input_dim %d, numpoints %d, malloc? %d, projected %d to hull_dim %d
qhull internal error (qh_projectinput): dimension after projection %d != hull_dim %d
qh_projectpoints: projected %d points from dim %d to dim %d
qh_initqhull_globals: trace last of TR%d runs at level %d
qhull internal error (qh_memcheck): totfree %d not equal to freelist total %d
qh_settemp: temp set %p of %d elements, depth %d
qhull internal error (qh_lib_check): Cannot continue due to QH%d.  '%s' is not reentrant (e.g., qhull.so) or out-of-date.  Exit with %d
qh_matchneighbor: no match for f%d skip %d at hash %d
qh_matchneighbor: new f%d skip %d duplicates ridge for f%d skip %d matching f%d ismatch %d at hash %d
qh_matchnewfacets: maxdupdist %2.2g, new facets %d, unused hash entries %d, hashsize %d
qhull internal error (qh_setcheck): actual size %d of %s%d is greater than max size %d
qhull error (qh_memsetup): largest mem size %d is >= buffer size %d or initial buffer size %d
qhull internal error (qh_setsize): current set size %d is greater than maximum size %d
qhull internal error (qh_all_merges): expecting concave, coplanar, or twisted merge.  Got merge f%d f%d v%d mergetype %d
qhull internal error (qh_checkdelfacet): cannot delete f%d.  It is referenced by merge f%d f%d mergetype %d
qh_clearcenters: switched to center type %d
qh_merge_nonconvex: merge #%d for f%d and f%d type %d
qhull internal error (qh_merge_nonconvex): expecting mergetype MRGcoplanar..MRGconcavecoplanar.  Got merge f%d and f%d type %d
qh_appendmergeset: f%d is already redundant (%d) or f%d is already redundant (%d).  Ignore merge f%d and f%d type %d
qhull internal error (qh_getpinchedmerges): expecting MRGdupridge from qh_mark_dupridges.  Got merge f%d f%d type %d
qh_merge_pinchedvertices: merge f%d into f%d mergeType %d
qhull internal error (qh_printend): number of ridges %d != number printed %d and at end %d
qh_eachvoronoi: Voronoi ridge of %d vertices between sites %d and %d
qhull internal error (qh_checkvertex): expecting v%d.visitid <= qh.vertex_visit (%d).  Got visitid %d
qhull internal error (qh_checkfacet): expecting f%d.visitid <= qh.visit_id (%d).  Got visitid %d
qhull internal warning (point_add): unknown point %p id %d
qh_joggleinput: joggle input by %4.4g with seed %d
qh_mergecycle_neighbors: deleted %d neighbors and added %d
%d
%d %d %d
qh_partitioncoplanar: point p%d is more than near-inside facet f%d dist %2.2g allnew? %d
qh_partitioncoplanar: point p%d is inside facet f%d dist %2.2g allnew? %d
qh_resetlists: reset newvertex_list v%d, newfacet_list f%d, visible_list f%d, facet_list f%d next f%d vertex_list v%d -- NEWfacets? %d, NEWtentative? %d, stats? %d
qh_postmerge: postmerge.  test vneighbors? %d
qh_mark_dupridges: identify dupridges in facetlist f%d, allmerges? %d
qh_makenew_simplicial: create facet f%d top %d from v%d and horizon f%d skip %d top %d and visible f%d skip %d, flip? %d
qh_facetarea_simplex: area=%2.2g for point p%d, toporient %d, nearzero? %d
qh_detsimplex: det=%2.2g for point p%d, dim %d, nearzero? %d
qh_mergesimplex: move r%d with f%d to f%d, new neighbor? %d, maybe horizon? %d
qh_reducevertices: renamed %d shared vertices and %d redundant vertices. Degen? %d
qh_checkpolygon: check all facets from f%d, qh.NEWtentative? %d
qh_matchvertices: matched by skip %d(v%d) and skip %d(v%d) same? %d
qh_checkfacet: check f%d newmerge? %d
qh_all_merges: starting to merge %d facet and %d degenerate merges for new facets f%d, othermerge? %d
  Total number of nearly incident points: %d
  Number of nearly incident points: %d
  Number of %s points: %d
  Number of%s non-simplicial intersection points: %d
  Number of intersection points: %d
  Number of 'good' intersection points: %d
qh_sharpnewfacets: %d
  Number of%s non-simplicial facets: %d
  Number of facets: %d
  Number of triangulated facets: %d
  Number of merged facets: %d
  Number of 'good' facets: %d
  Number of%s Delaunay regions: %d
  Number of%s non-simplicial Delaunay regions: %d
    - merges: %d
  Number of%s Voronoi vertices: %d
  Number of%s non-simplicial Voronoi vertices: %d
  Number of vertices: %d
  Number of merged pinched vertices: %d
  Number of non-redundant halfspaces: %d
  Number of %s halfspaces: %d
  Number of halfspaces: %d
  Number of Voronoi regions%s: %d
  Number of input sites%s: %d
  Number of distance tests for qhull: %d
  Number of facets in hull: %d
  Number of distance tests for checking: %d
  Number of distance tests for merging: %d
  Total number of deleted points due to merging: %d
  Number of hyperplanes created: %d
  Number of points processed: %d
1 %d
qhull internal error (qh_memalloc): short totbuffer %d != totshort+totfree... %d
qhull internal error (qh_initstatistics): increase size of qhstat.id[].  qhstat.next %d should be <= sizeof(qh->qhstat.id) %d
%d
%d

precision constants:
 %6.2g max. abs. coordinate in the (transformed) input ('Qbd:n')
 %6.2g max. roundoff error for distance computation ('En')
 %6.2g max. roundoff error for angle computations
 %6.2g min. distance for outside points ('Wn')
 %6.2g min. distance for visible facets ('Vn')
 %6.2g max. distance for coplanar facets ('Un')
 %6.2g max. facet width for recomputing centrum and area
Line[{{%16.8f, %16.8f}, {%16.8f, %16.8f}}]
qhull input error: %d'th dimension's new bounds [%2.2g, %2.2g] too wide for
existing bounds [%2.2g, %2.2g]
qh_scalelast: scale last coordinate from [%2.2g, %2.2g] to [%2.2g, %2.2g]
qhull internal error: negative hashsize %d passed to qh_gethash [poly_r.c]
[[%16.8f, %16.8f], [%16.8f, %16.8f]]
qhull internal error (qh_memcheck): qh is 0.  It does not point to a qhT
{appearance {-edge -normal normscale 0} {
INST geom {define vsphere OFF
18 32 48

0 0 1
1 0 0
0 1 0
-1 0 0
0 -1 0
0 0 -1
0.707107 0 0.707107
0 -0.707107 0.707107
0.707107 -0.707107 0
-0.707107 0 0.707107
-0.707107 -0.707107 0
0 0.707107 0.707107
-0.707107 0.707107 0
0.707107 0.707107 0
0.707107 0 -0.707107
0 0.707107 -0.707107
-0.707107 0 -0.707107
0 -0.707107 -0.707107

3 0 6 11
3 0 7 6 
3 0 9 7 
3 0 11 9
3 1 6 8 
3 1 8 14
3 1 13 6
3 1 14 13
3 2 11 13
3 2 12 11
3 2 13 15
3 2 15 12
3 3 9 12
3 3 10 9
3 3 12 16
3 3 16 10
3 4 7 10
3 4 8 7
3 4 10 17
3 4 17 8
3 5 14 17
3 5 15 14
3 5 16 15
3 5 17 16
3 6 13 11
3 7 8 6
3 9 10 7
3 11 12 9
3 14 8 17
3 15 13 14
3 16 12 15
3 17 10 16
} transforms { TLIST
qhull internal error (qh_checklists): either qh.vertex_tail v%d is NULL, or its id is not 0, or its next is not NULL
qhull internal error (qh_checklists): either qh.facet_tail f%d is NULL, or its id is not 0, or its next is not NULL
qhull internal error (qh_appendvertexmerge): expecting temp set defined for qh.vertex_mergeset (0x%x).  Got NULL
qhull internal error (qh_appendmergeset): expecting temp set defined for qh.facet_mergeset (0x%x) and qh.degen_mergeset (0x%x).  Got NULL
qhull internal error (qh_willdelete): expecting qh.visible_list at before qh.newfacet_list f%d.   Got NULL
qhull internal error (qh_checklists): qh.visible_list f%d is after qh.newfacet_list f%d.  It should be at, before, or NULL
qhull configuration warning (qh_RANDOMmax in user_r.h): average of 1000 random integers (%.2g) is much different than expected (%.2g).  Is qh_RANDOMmax (%.2g) wrong?
qhull error (qh_memalloc): negative request size (%d).  Did int overflow due to high-D?
qhull error (qh_newhashtable): negative request (%d) or size (%d).  Did int overflow due to high-D?
));

At error exit:
qhull internal error (qh_setdelnth): nth %d is out-of-bounds for set:
qhull internal error (qh_setaddnth): nth %d is out-of-bounds for set:
qhull internal error (qh_setdelnthsorted): nth %d is out-of-bounds for set:
qhull internal error (qh_setnew_delnthsorted): nth %d is out-of-bounds for set:
qhull internal error (qh_setzero): index %d or size %d out of bounds for set:
qhull internal error (qh_settruncate): size %d out of bounds for set:

The input to qhull appears to be less than %d dimensional, or a
computation has overflowed.

Qhull could not construct a clearly convex simplex from points:
Vertices and facets:


Current summary is:
    - ridges:

The min and max coordinates for each dimension are:
%s VERTEX:
%s FACET:
%s OTHER FACET:
%s RIDGE:
    - coplanar set(furthest p%d):
    - outside set(furthest p%d):
qhull internal error (qh_errexit): exit code %d is greater than 255.  Invalid argument for exit().  Replaced with 255
qh_drop_mergevertex: unset mergevertex for r%d and r%d due to dropped vertex merge v%d to v%d.  Sets mergevertex2
qhull internal error (qh_checkfacet): for facet f%d, #ridges %d < #neighbors %d or(3-d) > #vertices %d or(2-d) not all 2
qhull internal error (qh_determinate): only implemented for dimension >= 2
qhull internal error (qh_facetarea_simplex): #points %d != dim %d -1
%8.4g %8.4g %8.4g 1
4VECT %d %d 1
4OFF %d %d 1
%d
%d %d 1
qhull error: dimension %d must be > 1
VECT 1 2 1 2 1
VECT 1 1 1 1 1
3 0 1 2 %8.4g %8.4g %8.4g 1.0
qhull internal error (qh_nextfurthest): num_outside %d is too low
by at least %d, or a random real %g >= 1.0
qhull warning (qh_stddev): expecting num > 0.  Got num %d, tot %4.4g, tot2 %4.4g.  Returning 0.0
%8.4g %8.4g %8.4g 0
%8.4g 0 0 0 # v%d
 0 %8.4g 0 0
0 0 %8.4g 0
qhull input error (qh_scalelast): can not scale last coordinate to [%4.4g, %4.4g].  Input is cocircular or cospherical.   Use option 'Qz' to add a point at infinity.
qhull error: 2^32 or more vertices.  vertexT.id field overflows.  Vertices would not be sorted correctly.
qhull input warning: minimum visibility V%.2g is greater than 
minimum outside W%.2g.  Flipped facets are likely.
qhull input error: point for QV%d is inside initial simplex.  It can not be made a vertex.
Qhull precision error: initial Delaunay input sites are cocircular or cospherical.  Use option 'Qz' for the Delaunay triangulation or Voronoi diagram of cocircular/cospherical points; it adds a point "at infinity".  Alternatively use option 'QJ' to joggle the input.  Use option 'Qs' to search all points for the initial simplex.

If the input should be full dimensional, you have several options that
may determine an initial simplex:
  - use 'QJ'  to joggle the input and make it full dimensional
  - use 'QbB' to scale the points to the unit cube
  - use 'QR0' to randomly rotate the input for different maximum points
  - use 'Qs'  to search all points for the initial simplex
  - use 'En'  to specify a maximum roundoff error less than %2.2g.
  - trace execution with 'T3' to see the determinant for each point.
qh_lib_check: Incorrect qhull library called.  Caller uses non-reentrant Qhull with a dynamic qhT via qh_QHpointer.  Qhull library is reentrant.
qh_lib_check: Incorrect qhull library called.  Caller uses non-reentrant Qhull with a static qhT.  Qhull library is reentrant.

qhull output completed.  Verifying that %d points are
below %2.2g of the nearest %sfacet.
qhull input warning: merging without checking outer planes('Q5' or 'Po').  Verify may report that a point is outside of a facet.
qhull input warning: no outer plane check ('Q5') or no processing of near-inside points ('Q8').  Verify may report that a point is outside of a facet.
qhull warning: CDD format is not available for centrums, halfspace
intersections, and OFF file format.

Testing all coplanar points.

%d points were well inside the hull.  If the hull contains
a lens-shaped component, these points were not verified.  Use
options 'Qci Tv' to verify all points.
Qhull precision error: initial Delaunay input sites are cocircular or cospherical.  Option 'Qs' searches all points.  Use option 'QJ' to joggle the input, otherwise cannot compute the upper Delaunay triangulation or upper Voronoi diagram of cocircular/cospherical points.
qh_matchnewfacets: match neighbors for new facets.
qh_all_merges: merged %d coplanar %d concave %d concavecoplanar %d twisted facets and %d degen or redundant facets.
qhull topology error (qh_findhorizon): empty horizon for p%d.  It was above all facets.

Precision problems were detected during construction of the convex hull.
This occurs because convex hull algorithms assume that calculations are
exact, but floating-point arithmetic has roundoff errors.

To correct for precision problems, do not use 'Q0'.  By default, Qhull
selects 'C-0' or 'Qx' and merges non-convex facets.  With option 'QJ',
Qhull joggles the input to prevent precision problems.  See "Imprecision
in Qhull" (qh-impre.htm).

If you use 'Q0', the output may include
coplanar ridges, concave ridges, and flipped facets.  In 4-d and higher,
Qhull may produce a ridge with four neighbors or two facets with the same 
vertices.  Qhull reports these events when they occur.  It stops when a
concave ridge, flipped facet, or duplicate facet occurs.
qhull warning: recomputing centrums for convexity test.  This may lead to false, precision errors.
qh_test_redundant_neighbors: f%d is degenerate with %d neighbors.

Output completed.  Verifying that all points are below outer planes of
all %sfacets.  Will make %2.0f distance computations.

Output completed.  Verifying that all points are below %2.2g of
all %sfacets.  Will make %2.0f distance computations.
When computing the Delaunay triangulation:
  - use 'Qz' to add a point at-infinity.  This reduces precision problems.
qhull input error (qh_joggleinput): the current joggle for 'QJn', %.2g, is too large for the width
of the input.  If possible, recompile Qhull with higher-precision reals.
qh_find_newvertex: found v%d for old v%d from %d vertices and %d ridges.
- Experimental option merge-pinched-vertices ('Q14') may avoid this error.  It merges nearly adjacent vertices.

At %d:%d:%d & %2.5g CPU secs, qhull has merged %d facets with max_outside %2.2g, min_vertex %2.2g.
  The hull contains %d facets and %d vertices.
- A bounding box for the input sites may alleviate this error.

A flipped facet occurs when its distance to the interior point is
greater than or equal to %2.2g, the maximum roundoff error.
qhull warning: more than 2^32 ridges.  Qhull results are OK.  Since the ridge ID wraps around to 0, two ridges may have the same identifier.
qhull internal error (qh_rename_adjacentvertex): expecting neighbor facets for v%d and v%d.  Got %d and %d neighbors resp.
    Option 'Qx' may avoid this problem.
qhull internal error (qh_initflags): qh.NOerrexit was not cleared before calling qh_initflags().  It should be cleared after setjmp().  Exit qhull.
qhull output warning: ignoring coplanar points, option 'Qc' was not set for the first run of qhull.
qhull input error: halfspace intersection needs a feasible point.  Either prepend the input with 1 point or use 'Hn,n,n'.  See manual.

If the input is lower dimensional:
  - use 'QJ' to joggle the input and make it full dimensional
  - use 'Qbk:0Bk:0' to delete coordinate k from the input.  You should
    pick the coordinate with the least range.  The hull will have the
    correct topology.
  - determine the flat containing the points, rotate the points
    into a coordinate plane, and delete the other coordinates.
  - add one or more points to make the input full dimensional.
qhull topology error: Only %d facets remain.  The input is too degenerate or the convexity constraints are too strong.
qhull precision warning: The initial hull is narrow.  Is the input lower
dimensional (e.g., a square in 3-d instead of a cube)?  Cosine of the minimum
angle is %.16f.  If so, Qhull may produce a wide facet.
Options 'Qs' (search all points), 'Qbb' (scale last coordinate), or
'QbB' (scale to unit box) may remove this warning.
See 'Limitations' in qh-impre.htm.  Use 'Pp' to skip this warning.
qhull warning: #vertices %d + #facets %d - #edges %d != 2.  A vertex appears twice in a edge list.  May occur during merging.
qhull input error: 'Qg QVn' (only good vertex) does not work with merging.
Use 'QJ' to joggle the input or 'Q0' to turn off merging.
qhull topology error (qh_partitionvisible): all new facets deleted as
       degenerate facets. Can not continue.
qhull topology error (qh_findbestnew): merging has formed and deleted a cone of new facets.  Can not continue.
qhull topology error (qh_matchneighbor): matchfacet f%d is in f%d neighbors but not vice versa.  Can not continue.

These points are the dual of the given halfspaces.  They indicate that
the intersection is degenerate.
qh_degen_redundant_facet: f%d is degenerate.
qh_maydropneighbors: f%d is degenerate.

These points either have a maximum or minimum x-coordinate, or
they maximize the determinant for k coordinates.  Trial points
are first selected from points that maximize a coordinate.

A Qhull internal error has occurred.  Please send the input and output to
[email protected]. If you can duplicate the error with logging ('T4z'), please
include the log file.
qhull input error: filename expected, none found.
qhull internal error (qh_memalloc): qhmem has not been initialized.
qh_getmergeset: started.
qhull internal error (qh_setcheck): %s%d(size %d max %d) is not null terminated.
qh_setfacetplane: facet f%d created.
qhull internal error (qh_buildhull): %d outside points were never processed.
qhull option warning: output file undefined(stdout).  Option 'Tz' ignored.
qhull warning: good vertex p%d does not match last good facet f%d.  Ignored.
qhull internal error (userprintf_r.c): fp is 0.  Wrong qh_fprintf was called.
qh_qhull: all facets are clearly convex and no coplanar points.  Post-merging and check of maxout not needed.
qh_sethyperplane_det: degenerate norm during p%d, use qh_sethyperplane_gauss instead.
qhull option warning: coplanars, vertices, and centrums output not available for 4-d output(ignored).  Could use 'GDn' instead.
qhull internal error (qh_partitionvisible): all new facets deleted or none defined.  Can not partition deleted v%d.
qh_sethyperplane_gauss: singular or axis parallel hyperplane at normalization during p%d.
qh_sethyperplane_gauss: nearly singular or axis parallel hyperplane during p%d.
qh_test_degen_neighbors: f%d is degenerate with %d neighbors.  Neighbor of f%d.

At %02d:%02d:%02d & %2.5g CPU secs, qhull has created %d facets and merged %d.
 The current hull contains %d facets and %d vertices.  There are %d
 outside points.  Next is point p%d(v%d), %2.2g above f%d.
qhull internal error (qh_printvdiagram): unknown print format %d.
qh_lib_check: Incorrect qhull library called.  Size of vertexT for caller is %d, but for qhull library is %d.
qh_lib_check: Incorrect qhull library called.  Size of setT for caller is %d, but for qhull library is %d.
qh_lib_check: Incorrect qhull library called.  Size of facetT for caller is %d, but for qhull library is %d.
qh_lib_check: Incorrect qhull library called.  Size of qhmemT for caller is %d, but for qhull library is %d.
qh_lib_check: Incorrect qhull library called.  Size of qhT for caller is %d, but for qhull library is %d.
qh_lib_check: Incorrect qhull library called.  Size of ridgeT for caller is %d, but for qhull library is %d.
qh_backnormal: zero diagonal at column %d.
qh_triangulate: and replace facet->f.triowner with tricoplanar facets that own center, normal, etc.
qhull input error: 'Qg' (ONLYgood) needs a good threshold('Pd0D0'), a good point(QGn or QG-n), or a good vertex with 'QJ' or 'Q0' (QVn).
qhull option error: option 'Fp' is only used for 
halfspace intersection('Hn,n,n').
qhull warning: point p%d is not a vertex('QV%d').
qhull warning: point p%d is a vertex for every facet('QV-%d').

Because of the high dimension, the min x-coordinate and max-coordinate
points are used if the determinant is non-zero.  Option 'Qs' will
do a better, though much slower, job.  Instead of 'Qs', you can change
the points by randomly rotating the input with 'QR0'.
,
qhull topology error (qh_next_vertexmerge): no nearly adjacent vertices to resolve dupridge.  Nearest v%d and v%d dist %2.2g (%.1fx)
qhull topology error (qh_next_vertexmerge): no nearly adjacent vertices to resolve duplicate ridges r%d and r%d.  Nearest v%d and v%d dist %2.2g (%.1fx)
qhull topology error (qh_next_vertexmerge): no nearly adjacent vertices to resolve opposite oriented ridges r%d and r%d in f%d and f%d.  Nearest v%d and v%d dist %2.2g (%.1fx)
qhull internal error (qh_initmergesets): expecting NULL mergesets.  Got qh.facet_mergeset (0x%x), qh.degen_mergeset (0x%x), qh.vertex_mergeset (0x%x)
qhull internal error (qh_freemergesets): expecting mergesets.  Got a NULL mergeset, qh.facet_mergeset (0x%x), qh.degen_mergeset (0x%x), qh.vertex_mergeset (0x%x)
qhull option warning: unknown option '%c'(%x)
qhull internal error (qh_checkfacet): facet f%d has deleted neighbor f%d (qh.visible_list)
qhull internal error (qh_degen_redundant_facet): facet f%d has deleted neighbor f%d (qh.visible_list)
qhull internal error (qh_test_redundant_neighbors): facet f%d has deleted neighbor f%d (qh.visible_list)
qhull internal error (qh_test_degen_neighbors): facet f%d has deleted neighbor f%d (qh.visible_list)
qhull internal error (qh_maydropneighbor): facet f%d has deleted neighbor f%d (qh.visible_list)
Qhull precision error: Initial simplex is flat (facet %d is coplanar with the interior point)
qhull topology error: facets f%d, f%d and f%d meet at a ridge with more than 2 neighbors.  Can not continue due to no qh.PREmerge and no 'Qx' (MERGEexact)
p%d(coplanar facets)
qhull error (qh_memalloc): insufficient memory to allocate short memory buffer (%d bytes)

memory statistics:
%7d quick allocations
%7d short allocations
%7d long allocations
%7d short frees
%7d long frees
%7d bytes of short memory in use
%7d bytes of short memory in freelists
%7d bytes of dropped short memory
%7d bytes of unused short memory (estimated)
%7d bytes of long memory allocated (max, except for input)
%7d bytes of long memory in use (in %d pieces)
%7d bytes of short memory buffers (minus links)
%7d bytes per short memory buffer (initially %d bytes)
qhull internal error (qh_freemergesets): expecting empty mergesets.  Got qh.facet_mergeset (%d merges), qh.degen_mergeset (%d merges), qh.vertex_mergeset (%d merges)
qhull internal error (qh_flippedmerges): facet_mergeset (%d merges) not at top of tempstack (%d merges)
qhull internal error (qh_mergefacet): either f%d and f%d are the same or one is a visible facet, mergetype %d (%s)
qh_appendvertexmerge: append merge v%d into v%d r%d r%d dist %2.2g type %d (%s)
qh_appendmergeset: f%d is already degenerate.  Ignore merge f%d type %d (MRGdegen)

To guarantee simplicial output:
  - use option 'Qt' to triangulate the output
  - use option 'QJ' to joggle the input points and remove precision errors
  - use option 'Ft' to triangulate the output by adding points
  - use exact arithmetic (see "Imprecision in Qhull", qh-impre.htm)
qh_getarea: computing area for each facet and its volume to qh.interior_point (dist*area/dim)
qh_partitionpoint: point p%d is outside facet f%d newfacet? %d, newoutside? %d (or narrowhull)
qh_freebuild: free temporary sets (qh_settempfree_all)
qhull configuration error (qh_RANDOMmax in user_r.h): random integer %d > qh_RANDOMmax (%.8g)
qh_findhorizon: point p%d is coplanar to horizon f%d, dist=%2.7g < qh->MINvisible(%2.7g)
qhull precision error: initial simplex is not convex, since p%d(v%d) is within roundoff of opposite facet f%d (dist %6.4g)
qhull input error (qh_scalelast): can not scale last coordinate to [%4.4g, %4.4g].  New bounds are too wide for compared to existing bounds [%4.4g, %4.4g] (width %4.4g)
qhull precision error (qh_check_bestdist): a coplanar point is %6.2g from convex hull.  The maximum value is qh.outside_err (%6.2g)
qh_gausselim: 0 pivot at column %d. (%2.2g < %2.2g)
qh_furthestnext: made f%d next facet(dist %.2g)

When computing the Delaunay triangulation of coordinates > 1.0,
  - use 'Qbb' to scale the last coordinate to [0,m] (max previous coordinate)
qhull option warning: 'TCn' (stopCone) ignored when used with 'QJn' (joggle)
qhull precision error (qh_mergefacet): wide merge for facet f%d into f%d for mergetype %d (%s).  maxdist %2.2g (%.1fx) mindist %2.2g (%.1fx) vertexdist %2.2g  Allow with 'Q12' (allow-wide)
qhull precision error (qh_mergefacet): wide merge for pinched facet f%d into f%d for mergetype %d (%s).  maxdist %2.2g (%.fx) mindist %2.2g (%.1fx) vertexdist %2.2g  Allow with 'Q12' (allow-wide)
Qhull precision error (qh_check_maxout): a facet or vertex merge produced a wide facet: v%d below f%d distance %2.2g (%.1fx). Trace with option 'TWn' to identify the merge.  Allow with 'Q12' (allow-wide)
Qhull precision error (qh_check_maxout): a facet merge, vertex merge, vertex, or coplanar point produced a wide facet %2.2g (%.1fx). Trace with option 'TWn' to identify the merge.   Allow with 'Q12' (allow-wide)
qhull precision error: f%d is flipped (interior point is outside)
qh_partitionpoint: point p%d is coplanar to facet f%d (dropped)
 # p%d(v%d)
qh_update_vertexneighbors: update v.neighbors for qh.newvertex_list (v%d) and qh.newfacet_list (f%d)
qh_update_vertexneighbors_cone: update v.neighbors for qh.newvertex_list (v%d) and qh.newfacet_list (f%d)
qh_update_vertexneighbors: delete interior vertices for qh.visible_list (f%d)
qh_update_vertexneighbors_cone: delete interior vertices for qh.visible_list (f%d)
qh_update_vertexneighbors: delete old vertices for qh.visible_list (f%d)
qh_update_vertexneighbors_cone: delete interior vertices, if any, for qh.visible_list (f%d)
qh_merge_degenredundant: merge redundant f%d into f%d (arg f%d)
qhull internal error (qh_produce_output): temporary sets not empty(%d)
qhull internal error (qh_produce_output2): temporary sets not empty(%d)
qhull internal error (point_add): point p%d is out of bounds(%d)
qhull internal error (qh_checkvertex): unknown vertex id v%d >= qh.vertex_id (%d)
qhull internal error (qh_checkfacet): unknown facet id f%d >= qh.facet_id (%d)
qh_mem %p n %8d free short: %d bytes (tot %d cnt %d)
qh_mem %p n %8d alloc short: %d bytes (tot %d cnt %d)
qh_mem %p n %8d alloc quick: %d bytes (tot %d cnt %d)
qh_mem %p n %8d free long: %d bytes (tot %d cnt %d)
qh_mem %p n %8d alloc long: %d bytes (tot %d cnt %d)
qhull option error: see previous warnings, use 'Qw' to override: '%s' (last offset %d)
qhull internal error (qh_forcedmerges): qh_settemppop (size %d) is not qh->facet_mergeset (size %d)
qh_appendmergeset: append merge f%d and f%d type %d (%s) dist %2.2g angle %4.4g to qh.facet_mergeset (size %d)
qh_appendmergeset: append merge f%d and f%d type %d (%s) to qh.degen_mergeset (size %d)
qhull internal error (qh_settempfree): set %p(size %d) was not last temporary allocated(depth %d, set %p, size %d)
qhull input error: not enough points(%d) to construct initial simplex (need %d)
qh_neighbor_vertices_facet: found %d vertex neighbors for v%d in f%d (simplicial? %d)
qh_rename_adjacentvertex: partition old p%d(v%d) as a coplanar point for furthest f%d dist %2.2g.  Maybe repartition later (QH0031)
qh_qhull: finished qh_buildhull and qh_postmerge, start tracing (TP-1)
qh_checkconvex: starting with f%d, also check that centrums of non-simplicial ridges are below their neighbors (dist<0.0)
qh_checkconvex: check that facets are not-flipped and for qh.ZEROcentrum that simplicial vertices are below their neighbor (dist<0.0)
qhull option error: option 'FC' is not available for Voronoi vertices('v')
qhull option error: use upper-Delaunay('Qu') or infinity-point('Qz') with Delaunay('d') or Voronoi('v')
qhull option error: can not use infinity-point('Qz') with upper-Delaunay('Qu')
qhull internal error (qh_appendmergeset): facet f%d or f%d is already a mirrored facet (i.e., 'redundant')
qh_checkconvex: check that facets are not-flipped and that simplicial vertices are convex by qh.DISTround ('En', 'Rn')
qhull option warning: 'Q0-no-premerge' ignored due to exact merge ('Qx') or pre-merge ('C-n' or 'A-n')
qhull option error: can not use merge-pinched-vertices ('Q14') with good-facets-only ('Qg')
qhull option error: can not use Delaunay('d') or Voronoi('v') with halfspace intersection('H')
qhull option error: option 'Ft' is not available for Voronoi vertices ('v') or halfspace intersection ('H')
PLOT3D(POLYGONS(
PLOT(CURVES(
qhull option warning: option 'Qbb' (scale-last-coordinate) is normally used with 'd' or 'v'
qhull internal error (qh_checkpolygon): f%d is on qh.newfacet_list f%d but it is not 'newfacet'
qhull option error: expecting 'Hn,n,n,...' for feasible point of halfspace intersection. Got '%s'
qhull option error: expecting a positive number for outside width 'Wn'.  Got '%s'
qhull option error: expecting a positive number for maximum roundoff 'En'.  Got '%s'
qhull internal error (qh_option): option (%d chars) has more than %d chars.  May overflow temporary buffer.  Option '%s'
qhull internal error (userprintf_r.c): fp and qh not defined for qh_fprintf '%s'
qh_option: option would overflow qh.qhull_options. Truncated '%s'
qhull warning: input sites of Delaunay regions (option 'i').  Use option 'p' or 'o' for Voronoi centers.  Disable warning with option 'Pp'
Qhull precision error (qh_check_maxout): large increase in qh.min_vertex during post-processing dist %2.2g (%.1fx).  See warning QH7083.  Allow with 'Q12' (allow-wide) and 'Pp'
Qhull precision error (qh_check_maxout): large increase in qh.max_outside during post-processing dist %2.2g (%.1fx).  See warning QH0032/QH0033.  Allow with 'Q12' (allow-wide) and 'Pp'
qhull option warning: missing max width for trace option 'TWn'
qhull option warning: missing outside width for option 'Wn'
qhull option warning: missing furthest point id for trace option 'TVn'
qhull option warning: missing visible distance for option 'Vn'
qhull option warning: missing coplanar distance for option 'Un'
qhull option warning: missing number of test points for option 'QTn'
qhull option warning: missing rerun count for trace option 'TRn'
qhull option warning: missing random seed for option 'QRn'
qhull option warning: missing random perturbation for option 'Rn'
qhull option warning: missing point id or -1 for trace option 'TPn'
qhull option warning: missing merge id for trace option 'TMn'
qhull option warning: missing merge count for option 'PMn'
qhull option warning: missing frequency count for trace option 'TFn'
qhull option warning: missing facet area for option 'PFn'
qhull option warning: no maximum roundoff given for option 'En'
qhull option error: transparent Delaunay('Gt') needs 3-d Delaunay('d') w/o 'GDn'
qhull option warning: missing dimension for option 'GDn'
qhull option warning: missing point id for cone for trace option 'TCn'
qhull input warning: no centrum radius given for option 'Cn'
qhull option warning: missing count of added points for trace option 'TAn'
qhull option warning: missing facet count for keep area option 'PAn'
qhull error: insufficient memory for 'Hn,n,n'
qh_detroundoff: increase qh.ANGLEround by option 'R%2.2g'
qh_distround: increase roundoff by random delta %2.2g for option 'R%2.2g'

%s with 'C%.2g' and 'A%.2g'
qhull internal error (qh_checkpolygon): f%d is on qh.visible_list f%d but it is not 'visible'
qhull option warning: no dimension given for Qhull option 'Q%c'
           last coordinate scaled to (%4.4g, %4.4g), width %4.4e for option 'Qbb'
qhull option warning: 'QJ' (joggle) will usually prevent coincident input sites for options 'Fc' and 'FP'
qhull option warning: qh.fout was not set by caller of qh_initflags.  Cannot use option 'TO' to redirect output.  Ignoring option 'TO'
qhull topology error (qh_check_dupridge): wide merge (%.1fx wider) due to dupridge between f%d and f%d (vertex dist %2.2g), merge dist %2.2g, while processing p%d
- Allow error with option 'Q12'
qhull internal error (qh_findhorizon): does not work for tricoplanar facets.  Use option 'Q11'
qhull internal error (qh_mergecycle): does not work for tricoplanar facets.  Use option 'Q11'
qhull internal error (qh_mergefacet): merge f%d into f%d for mergetype %d (%s) does not work for tricoplanar facets.  Use option 'Q11'
qhull option error: cannot open 'TI' file "%s"
qhull error (qh_new_qhull): start qhull_cmd argument with "qhull " or set to "qhull"
{INST geom { define centrum CQUAD  # f%d
-0.3 -0.3 0.0001     0 0 1 1
 0.3 -0.3 0.0001     0 0 1 1
 0.3  0.3 0.0001     0 0 1 1
-0.3  0.3 0.0001     0 0 1 1 } transform { 
qhull internal error (qh_checkfacet): facet f%d skip %d and neighbor f%d skip %d do not match 
%d %d %d %6.16g 
qh_findbestnew: bestfacet f%d bestdist %2.2g for p%d f%d bestoutside? %d 
qh_checkconvex: check that facets are not-flipped and that their centrums are convex by qh.DISTround ('En', 'Rn') 
 QR%d


The center point is coplanar with a facet, or a vertex is coplanar
with a neighboring facet.  The maximum round off error for
computing distances is %2.2g.  The center point, facets and distances
to the center point are as follows:


Furthest-site Voronoi vertices by the convex hull of %d points in %d-d:


Halfspace intersection by the convex hull of %d points in %d-d:


Furthest-site Delaunay triangulation by the convex hull of %d points in %d-d:


Delaunay triangulation by the convex hull of %d points in %d-d:


Voronoi diagram by the convex hull of %d points in %d-d:


Convex hull of %d points in %d-d:

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