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The ability to return an instance of a strict subclass of int is deprecated, and may be removed in a future version of Python.__int__ returned non-int (type %.200s)value too large to convert to intunbound method %.200S() needs an argument%.200s.%.200s is not a type object%.200s.%.200s size changed, may indicate binary incompatibility. Expected %zd from C header, got %zd from PyObjectAcquisition count is %d (line %d)%.200s() keywords must be strings%s() got multiple values for keyword argument '%U'Unexpected format string character: '%c'invalid vtable found for imported typejoin() result is too long for a Python stringCannot convert %.200s to %.200s__annotations__ must be set to a dict object__qualname__ must be set to a string object__name__ must be set to a string object__kwdefaults__ must be set to a dict objectchanges to cyfunction.__kwdefaults__ will not currently affect the values used in function calls__defaults__ must be set to a tuple objectchanges to cyfunction.__defaults__ will not currently affect the values used in function callsfunction's dictionary may not be deletedsetting function's dictionary to a non-dict while calling a Python objectNULL result without error in PyObject_Callinstance exception may not have a separate valuecalling %R should have returned an instance of BaseException, not %Rraise: exception class must be a subclass of BaseExceptionBuffer dtype mismatch, expected %s%s%s but got %sBuffer dtype mismatch, expected '%s' but got %s in '%s.%s'Expected a dimension of size %zu, got %zuExpected %d dimensions, got %dPython does not define a standard format string size for long double ('g')..Buffer dtype mismatch; next field is at offset %zd but %zd expectedBig-endian buffer not supported on little-endian compilerBuffer acquisition: Expected '{' after 'T'Cannot handle repeated arrays in format stringDoes not understand character buffer dtype format string ('%c')Expected a dimension of size %zu, got %dExpected a comma in format string, got '%c'Expected %d dimension(s), got %dUnexpected end of format string, expected ')'Buffer has wrong number of dimensions (expected %d, got %d)Item size of buffer (%zd byte%s) does not match size of '%s' (%zd byte%s)Item size of buffer (%zu byte%s) does not match size of '%s' (%zu byte%s)Buffer exposes suboffsets but no stridesC-contiguous buffer is not indirect in dimension %dBuffer and memoryview are not contiguous in the same dimension.Buffer is not indirectly contiguous in dimension %d.Buffer is not indirectly accessible in dimension %d.Buffer not compatible with direct access in dimension %d.memviewslice is already initialized!Argument '%.200s' has incorrect type (expected %.200s, got %.200s)cannot fit '%.200s' into an index-sized integerscipy.spatial._qhull._Qhull.mode_option.__set__scipy.spatial._qhull._Qhull.ndim.__get__%.200s() takes %.8s %zd positional argument%.1s (%zd given)scipy.spatial._qhull._QhullUser.closescipy.spatial._qhull._QhullUser.__del__scipy.spatial._qhull.Delaunay.pointsscipy.spatial._qhull.ConvexHull.pointsscipy.spatial._qhull.Voronoi.pointsscipy.spatial._qhull.HalfspaceIntersection.halfspacesscipy.spatial._qhull._Qhull.check_activescipy.spatial._qhull._Qhull.__setstate_cython__scipy.spatial._qhull.ConvexHull.add_pointsscipy.spatial._qhull.Voronoi.add_pointsscipy.spatial._qhull.Delaunay.add_points'%.200s' object is not subscriptablescipy.spatial._qhull._QhullUser._updatescipy.spatial._qhull._copy_docstr__mro_entries__ must return a tuplescipy.spatial._qhull._Qhull.get_hull_facetsscipy.spatial._qhull.HalfspaceIntersection.dual_verticesscipy.spatial._qhull.HalfspaceIntersection.add_halfspacesneed more than %zd value%.1s to unpackscipy.spatial._qhull.Voronoi._updatescipy.spatial._qhull.Delaunay.transformscipy.spatial._qhull.ConvexHull.verticesscipy.spatial._qhull.ConvexHull.__init__scipy.spatial._qhull._get_barycentric_transformsscipy.spatial._qhull._Qhull.__reduce_cython__Out of bounds on buffer access (axis %d)scipy.spatial._qhull.Delaunay.vertex_neighbor_verticesscipy.spatial._qhull._Qhull.get_hull_pointsscipy.spatial._qhull.Voronoi.__init__scipy.spatial._qhull.Delaunay.__init__scipy.spatial._qhull._Qhull.__init__Buffer acquisition failed on assignment; and then reacquiring the old buffer failed too!set changed size during iteration'NoneType' object has no attribute '%.30s'scipy.spatial._qhull._Qhull.get_paraboloid_shift_scale'%.200s' object is unsliceablescipy.spatial._qhull.Delaunay.lift_pointsscipy.spatial._qhull._get_delaunay_infoscipy.spatial._qhull._Qhull.volume_areascipy.spatial._qhull._Qhull.get_extremes_2dscipy.spatial._qhull.Voronoi.ridge_dictscipy.spatial._qhull._Qhull.__dealloc__scipy.spatial._qhull._Qhull.closescipy.spatial._qhull._visit_voronoi'NoneType' object is not subscriptablescipy.spatial._qhull._Qhull.add_pointsscipy.spatial._qhull._Qhull.get_voronoi_diagramscipy.spatial._qhull._Qhull.triangulatescipy.spatial._qhull._QhullUser._add_pointsscipy.spatial._qhull._QhullUser.__init__object of type 'NoneType' has no len()'NoneType' object is not iterablescipy.spatial._qhull._Qhull.get_pointsscipy.spatial._qhull.Delaunay._updatescipy.spatial._qhull.Delaunay.plane_distancescipy.spatial._qhull.HalfspaceIntersection._updatescipy.spatial._qhull.ConvexHull._updatescipy.spatial._qhull.Delaunay.convex_hullscipy.spatial._qhull.Delaunay.vertex_to_simplexscipy.spatial._qhull.Delaunay.find_simplexscipy.spatial._qhull.HalfspaceIntersection.__init__scipy.spatial._qhull._Qhull.get_simplex_facet_arrayscipy.spatial._qhull._Qhull.options.__set__Module '_qhull' has already been imported. Re-initialisation is not supported.compile time Python version %d.%d of module '%.100s' %s runtime version %d.%dint (__pyx_t_5scipy_7spatial_6_qhull_DelaunayInfo_t *, PyObject *, int, int, int)int (int, double *, double const *, double *, double)void (int, double *, double const *, double *, int)_barycentric_coordinate_singlevoid (int, double *, double const *, double *)void (__pyx_t_5scipy_7spatial_6_qhull_DelaunayInfo_t *, double const *, double *)double (__pyx_t_5scipy_7spatial_6_qhull_DelaunayInfo_t *, int, double *)int (__pyx_t_5scipy_7spatial_6_qhull_DelaunayInfo_t *, double const *, double)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)base 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 typemultiple bases have vtable conflict: '%.200s' and '%.200s'Unable to initialize pickling for %.200svoid (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 *)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 *)int (struct __pyx_array_obj *)struct __pyx_array_obj *(PyObject *, Py_ssize_t, char *, char const *, char *)PyObject *(PyObject *, int, int, __Pyx_TypeInfo const *)struct __pyx_memoryview_obj *(struct __pyx_memoryview_obj *, PyObject *)int (__Pyx_memviewslice *, Py_ssize_t, Py_ssize_t, Py_ssize_t, int, int, int *, Py_ssize_t, Py_ssize_t, Py_ssize_t, int, int, int, int)char *(Py_buffer *, char *, Py_ssize_t, Py_ssize_t)PyObject *(__Pyx_memviewslice, int, PyObject *(*)(char *), int (*)(char *, PyObject *), int)__Pyx_memviewslice *(struct __pyx_memoryview_obj *, __Pyx_memviewslice *)void (struct __pyx_memoryview_obj *, __Pyx_memviewslice *)PyObject *(struct __pyx_memoryview_obj *)PyObject *(struct __pyx_memoryview_obj *, __Pyx_memviewslice *)char (__Pyx_memviewslice *, int)Py_ssize_t (__Pyx_memviewslice *, int)Py_ssize_t (Py_ssize_t *, Py_ssize_t *, Py_ssize_t, int, char)void *(__Pyx_memviewslice *, __Pyx_memviewslice *, char, int)int (int, Py_ssize_t, Py_ssize_t)int (PyObject *, PyObject *, int)int (__Pyx_memviewslice, __Pyx_memviewslice, int, int, int)void (__Pyx_memviewslice *, int, int)void (__Pyx_memviewslice *, int, int, int)void (char *, Py_ssize_t *, Py_ssize_t *, int, int)void (__Pyx_memviewslice *, int, size_t, void *, int)void (char *, Py_ssize_t *, Py_ssize_t *, int, size_t, void *)_ARRAY_API is not PyCapsule objectmodule compiled against ABI version 0x%x but this version of numpy is 0x%xmodule was compiled against NumPy C-API version 0x%x (NumPy 1.23) but the running NumPy has C-API version 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.FATAL: module compiled as unknown endianFATAL: module compiled as little endian, but detected different endianness at runtime../../tmp/build-env-99e64tom/lib/python3.12/site-packages/numpy/__init__.cython-30.pxd_cython_3_1_6.cython_function_or_method_cython_3_1_6._common_types_metatype|\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\d\\\\\4@\\L\\X\\\\\\\\\\\\\\\\\\\\\p\bffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffnfffffffff&2>ffJfffffffffffffVfffzffffCCCCC]]C9MMM999999```````~``````````7Ar`=","""!!======OZ:Z%ZZYYYYususabcDccc[J8&r`p^L! )!  B P ! 4! c pB 2 P! #! @ c  B @B b jb X ~! { `y! w4! w c pwB pvi t fB eM! `e ! dc c6DB 0 !  ! <!3a / ,#! `"&a !]a tc QA >a ! __pyx_fatalerror00010203040506070809101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899 add_halfspaces(halfspaces, restart=False) Process a set of additional new halfspaces. Parameters ---------- halfspaces : ndarray of double, shape (n_new_ineq, ndim+1) New halfspaces to add. The dimensionality (ndim) should match that of the initial halfspaces. Like in the constructor, these are stacked inequalites of the form Ax + b <= 0 in format [A; b]. The original feasible point must also be feasible for these new inequalities. 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. 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() lift_points(self, x) Lift points to the Qhull paraboloid. plane_distance(self, xi) Compute hyperplane distances to the point `xi` from all simplices. find_simplex(self, xi, bruteforce=False, tol=None) Find the simplices containing the given points. Parameters ---------- 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. 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. 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]]``. Lookup array, from a vertex, to some simplex which it is a part of. :type: *ndarray of int, shape (npoints,)* 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``. 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. 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. 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. 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 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. 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. 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. 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) Uninitialize this instance 4A 2Saq *AQ%QhfBa 6s! *AQ >A t1   vV1Cs!! M avX_N!#1)1F'Q Qself._lock,self._qh cannot be converted to a Python object for picklingnumpy._core.umath failed to importnumpy._core.multiarray failed to importinvalid size for new points arrayfeasible point is not clearly inside halfspace: Qhull internal error: loop in facet listNote that Cython is deliberately stricter than PEP-484 and rejects subclasses of builtin types. If you need to pass subclasses then set the 'annotation_typing' directive to False.Input points array must have 2 dimensions.Input interior point cannot be a masked arrayInput halfspaces cannot be a masked arrayHalfspaceIntersection.halfspacesHalfspaceIntersection.dual_verticesHalfspaceIntersection.add_halfspacesFailed to allocate memory in setlist.init()Delaunay.vertex_neighbor_verticesA'q 2Saq *AQ 2Saq *AQ >JfARq *AQR),fBa b 2!3C61 >A A zq3a! M aa{'\(l!&d!)1F'QA N$05EQ O5 0 N$m5 A Tb$oURVVXX\\] 5c  U"2!  Q(!6 HD 6#Rq ITF!1A& M  Q t1j  2V1Er q AR}A AR( DARq  !5 DARq*AQ5jYb1jYb1 j!2QjYb1jYb1 j!2Q:RrHF!1q q,fARq9Aq7)3d$ar;d$arA]*ATwa!7)3d$ar;d$arA]*ATwa![D16A q q 9A 1  QA& M  Q Q t1a t1a D RvR{!DEaqU!1are1ATQ 1  QA \ LLLKt14A  5  gQe86A Ja vS%Q 4q  E ITl! 5c  U"2!  Q LJfAQ(!6AX M  Q  A   !64t2Q #1 at6a7Gt4qPRRS) !^2T t>d! a 2V1D Ba U!4qAV1 TQb 'V1+1Dd%q1Jat6q2Rt1 c!1QEaz$fF!yj!2Q 1rQ4q'qgQc!3a|3bJas$a!waqq ! rrT1 DARq &E5 1^1De1+1E1),U/DARq Q#!N![?$kAEaq,Bb%ZuIRq!%ZqF&"!3&7q(yZr"A%Qc):&&aU!=!5 1Ba!1DfAas%q$9E2Qb!#U&U!1!#U%waqQcuAuAEaz$fE$IU,b1%]!4vWG1AzN!1%&$*!$/q$'war:Rs#Ya$/q$A[ZqF!$A[V1E$A[ZqF&PQ)e1E 8;k>> 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() non-simplical facet encountered: incremental mode not enabled or already closed`halfspaces` should be provided as a 2D array are incompatible with incremental mode Wrappers for Qhull triangulation, plus some additional N-D geometry utilities .. versionadded:: 0.9 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 `__. 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) Takes care of basic dealings with the Qhull objects Raised when Qhull encounters an error condition, such as geometrical degeneracy when options to resolve are not enabled. R!  6qyaq&&vRq BfBjASvRq$aq  LQa U!1QiuEq )6EaqQbfAYay1 QiuAQira M& !  1 ! ! !1Cq9AWAU& uCqauAS '%qqWAQ611 uCqauASya$E$bARq5 uCqEat1AU!1Qira 1_Qhull.get_paraboloid_shift_scaleInput points cannot be a masked array 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 `__ 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 `__. 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/ Feasible point must be a (ndim-1,) array 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 `__ for more). paraboloid_scale, paraboloid_shift : float Scale and shift for the extra paraboloid dimension (see `Qhull documentation `__ 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 `__. .. 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. 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 `__ 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 `__. 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)
# may vary >>> plt.show() References ---------- .. [Qhull] http://www.qhull.org/ A M t51ATqqF!9AQ1DG183b83a*A"! t;gQJfA  QA M  Q t4q!#4t1BnAAR{"DARq#2TQb "A#1#1 %Q  QA( M  Q Q t1a t1a D Bd$a DA &+Zq Q  &E!AEaqQce7!1#^5A5 1BaaZqF&7!1ZuIRq!QgQaQ 81  QA KuKq HDaq Kt86! MXT%q MXT%qA BfAQfCs#QfBbfBa &Q %vQb$avQ %vT %vTqA 4*#Q 4q d! t1 A& Qa U!1Eat1A U!4q #9ARs#Yar$.d!1F)1Bd)STTVVW-.,-8aqAQat1A 4#3a &bbLb #5! #1D F$is! $a A t1 4qLQaU!4q")1Ja3ayAq 1t1A 2V2S4q *AQ 2Q RxrBfBa B 7!2Q!1!1F&3abbqD F"Aq  U!7!1Eat1q '4uAS5 !1F#Qs(!83cDA1P R{!1 rrCt1j2Q RxrBfBa B 7!2Q!1 4s! $b&81 !Dbb&vRqq!1F&3a 1Eawaq7qq!&$e1AQaEawaq}AQfA-6avRt5-.gU!as(!83a"/@ 4xs! ,aq 1 R|1AT9E F!4wnA#4wa)WA'v_A HAQJa6Aq  G;axq HAT4A 2Saq *AQ%QhfBa 6s! *AQ >A t1   vV1Cs!! M avX_4EQ%_L)1F'Q Q2! 2Saq *AQ%QhfBa >A A vV1Cs!! M avX_4EQ#1)1F'Q)D :V2Q *AQ R{!1$azd($6GrSXXY c 5A 81F!2T Zq "H *AQ LYd!A \ t1$$?q LLLKt14A LJfAQ N! "! )(!6A M  Q %Q!4vTQb TQb 4t1Ba 81  Qthread lock allocation failed_Qhull.get_simplex_facet_arrayHalfspaceIntersection._updateHalfspaceIntersection.__init__Cannot compute for Delaunaywrong dimensionality in xivertex_neighbor_verticesget_paraboloid_shift_scale_get_barycentric_transformsDelaunay.vertex_to_simplex_Qhull.get_voronoi_diagramPoints cannot contain NaN_vertex_neighbor_verticesscipy/spatial/_qhull.pyxmemory allocation failedQhull instance is closedget_simplex_facet_array_Qhull.__setstate_cython__Delaunay.plane_distanceA 4}Cq t1Cq1G4}G1(,At1A 3at#3a 4~Qa 2\$d'U$aQNeed at least 2-D data_Qhull.get_hull_points_Qhull.get_hull_facets_Qhull.get_extremes_2d_Qhull.__reduce_cython___QhullUser._add_pointsHalfspaceIntersectionDelaunay.find_simplexConvexHull.add_pointsscipy.spatial._qhullDelaunay.lift_pointsDelaunay.convex_hullvertex_to_simplexget_voronoi_diagramDelaunay.add_pointsConvexHull.verticesA$ 4|3a 9$a:>a:ridge_pointsridge_dictpoint_region_is_coroutine_initializingfind_simplexextremes_arrcheck_active_add_pointsRuntimeErrorvolume_areatriangulatetransformrcond_limit__mro_entries__mode_optionlower_boundlift_pointsincrementaldual_volumedual_pointsdual_facets_copy_docstrconvex_hullconcatenate_Qhull.closeMemoryErrorImportErrorA M  Qat1  Qvertices_verticesstartfacet_ridge_dict__pyx_vtable__point_ndimoption_sethalfspacesget_pointsfirst_violfacet_ndimcur_regionbruteforceatleast_2dasanyarrayadd_pointsValueErrorQhullErrorConvexHull_transformsimplices__reduce_ex____pyx_statenumpointsnumfacetsnextremesnextfacetneighborsncoplanarmin_bound__metaclass__max_boundisoutsideisenabledequationseps_broaddual_areaTypeError_QhullUserQbb Qc QzA 4xwa vQ  !A 4uCq ,aqxi_shape verticesupdate__setstate____set_name__refcheck__qualname__property_pointsnsimplexneighborisimplexinf_seen__getstate__extremesexitcodecoplanarbestdistadd_noteDelaunayx_shapevertexBvertexAtsearchtotlongrestartreshaperegions_qhullqhull__prepare__optionsnpointsnonzeronewaxisivertexfacetsidisablecurlong ;c  9Ks)1asarrayVoronoivolumevertex_updateuniquetolistresize__reduce__points pieces)option__module__latin1ipointid_mapfacetsencodeenabledoubled 3m1Acenterbad_hsastypezerosviolsstartsplitshapercondrangeqhull pointout_ordernumpynineqmsizeiworkisnanfinfofacetemptydtypedistscloseclear bytes (arrayanormTinvs_Qhullwork__test____spec__sizesetsselfnrhsndim__name____main__joinipivintpintc__init__infogood__func__filldistcopyaxisareaQxAt1ziptritoltmpsumsrcpopoutmsgminmaxmapldbldagetepsdstdot__doc____del__arrany__all__QbkQbbQbBQBkQ11A F!xinpmagc?Qz QxQuQtQcQJQGzxvpnmkjidcT +Q! LHC ?@@@@Y@qhull qhull error (qh_new_qhull): start qhull_cmd argument with "qhull " or set to "qhull" qh_new_qhull: initialize Qhull qh_new_qhull: build new Qhull for %d %d-d points with %s qhull error: insufficient memory for 'Hn,n,n' qh_projectpoints: projected %d points from dim %d to dim %d qhull internal error (qh_projectpoints): newdim %d should be %d after projection qhull error: insufficient memory to copy %d points qhull internal error (qh_determinate): only implemented for dimension >= 2 qh_detmaxoutside: MAXoutside %2.2g from qh.max_outside %2.2g, ONEmerge %2.2g, MINoutside %2.2g, DISTround %2.2g qhull internal error (qh_detsimplex): #points %d < dimension %d qh_detsimplex: det=%2.2g for point p%d, dim %d, nearzero? %d qh_distround: increase roundoff by random delta %2.2g for option 'R%2.2g' qh_distround: %2.2g, maxabs %2.2g, maxsumabs %2.2g, maxdistsum %2.2g qh_detjoggle: joggle=%2.2g maxwidth=%2.2g qh_detroundoff: increase qh.ANGLEround by option 'R%2.2g' qhull option error: the joggle for 'QJn', %.2g, is below roundoff for distance computations, %.2g qhull input warning: minimum visibility V%.2g is greater than minimum outside W%.2g. Flipped facets are likely. qhull internal error (qh_facetarea_simplex): #points %d != dim %d -1 qh_facetarea_simplex: area=%2.2g for point p%d, toporient %d, nearzero? %d qh_findgooddist: p%d is %2.2g above good facet f%d qh_findgooddist: no good facet for p%d above f%d qh_furthestnewvertex: v%d dist %2.2g is furthest new vertex for f%d qh_furthestvertex: all vertices of f%d are in f%d. Returning 0.0 for max and mindist qh_furthestvertex: v%d dist %2.2g is furthest (mindist %2.2g) of f%d above f%d computing area of each facet and volume of the convex hull qh_getarea: computing area for each facet and its volume to qh.interior_point (dist*area/dim) qh_maxmin: dim min max width nearzero min-point max-point %3d % 14.8e % 14.8e % 14.8e %4.4e p%-9d p%-d last coordinate scaled to (%4.4g, %4.4g), width %4.4e for option 'Qbb' qh_maxmin: found the max and min points (by dim):qh_maxouter: max distance from facet to outer plane is %4.4g, qh.max_outside is %4.4g qhull internal error (qh_maxsimplex): qh.MAXwidth required for qh_maxsimplex. Used to estimate determinate 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_maxsimplex: searching all points for %d-th initial vertex, better than mindet %4.4g, targetdet %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 qh_maxsimplex: searching all points for %d-th initial vertex, better than p%d det %2.2g and mindet %4.4g, targetdet %4.4g qhull internal error (qh_maxsimplex): not enough points available qh_maxsimplex: selected point p%d for %d`th initial vertex, det=%4.4g, targetdet=%4.4g, mindet=%4.4g qh_rotatepoints: rotate points byqh_scalelast: scale last coordinate from [%2.2g, %2.2g] to [%2.2g, %2.2g] 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 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 input error: 'Qb%d' or 'QB%d' inverts paraboloid since high bound %.2g < low bound %.2g qhull input error: %d'th dimension's new bounds [%2.2g, %2.2g] too wide for existing bounds [%2.2g, %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_setdelaunay: project %d points to paraboloid for Delaunay triangulation qhull error: insufficient memory to joggle %d points 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_joggleinput: joggle input by %4.4g with seed %d qhull internal error (qh_projectinput): dimension after projection %d != hull_dim %d qhull error: insufficient memory to project %d points qh_projectinput: updating lower and upper_bound qhull internal error (qh_projectinput): HALFspace defined without qh.feasible_point qh_projectinput: projected points to paraboloid for Delaunay qhull input error: feasible point is not clearly inside halfspace feasible point: qh_sethalfspace: halfspace at offset %6.2g to point: qh_sethalfspace_all: compute dual for halfspace intersection qhull error: insufficient memory to compute dual of %d halfspaces The halfspace was at index %d qhull internal error (qh_voronoi_center): need at least %d points to construct a Voronoi center qh_voronoi_center: at infinity for qh_voronoi_center: det %2.2g factor %2.2g _max-widthError-roundoffAngle-premerge-with-randomAngle-postmerge-with-randomCentrum-premerge-with-randomCentrum-postmerge-with-random_one-merge_near-insideVisible-distanceU-max-coplanarWidth-outside_wide-facetqh_facetarea: f%d area %2.2g p%dinput has same x coordinate%6.3g QJoggle_joggle-seed %6.2g%6.16g at offset: and distance: halfspace: qh_sharpnewfacets: %d p%d dist %.2g, center:ʡE3$ʡE3$$@)\(?<L=L@@@@<T@{Gz?MbP???A??ʡE3$qh_distplane: from p%d to f%d Last merge #%d Last qh_addpoint p%d,Matrix:qh_gausselem: resultqh_getangle: %4.4g Last merge was #%d. Current summary is: DISTANT%2.2g 0`Pqh_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_findbesthorizon: p%d, newbest? %d, bestfacet f%d, bestdist %2.2g, numfacet %d, coplanarfacets %d, numdist %d qhull topology error (qh_findbestnew): merging has formed and deleted a cone of new facets. Can not continue. qhull internal error (qh_findbestnew): no new facets for point p%d qh_findbestnew: point p%d facet f%d. Stop? %d if dist > %2.2g, Last qh_addpoint p%d, qh.visit_id %d, vertex_visit %d,qh_findbestnew: bestfacet f%d bestdist %2.2g for p%d f%d bestoutside? %d qh_findbest: point p%d starting at f%d isnewfacets? %d, unless %d exit if > %2.2g, testhorizon? %d, noupper? %d, Last merge #%d, max_outside %2.2g qh_findbest: neighbors of f%d, bestdist %2.2g f%d qh_backnormal: zero diagonal at column %d. zero diagonal on back substitutionqh_gausselim: 0 pivot at column %d. (%2.2g < %2.2g) zero pivot for Gaussian eliminationqhull internal error (qh_getcenter): not defined for %d points qh_getcentrum: for f%d, %d vertices dist= %2.2g qh_normalize: norm=%2.2g too small during p%d qh_sethyperplane_det: degenerate norm during p%d, use qh_sethyperplane_gauss instead. qh_sethyperplane_gauss: nearly singular or axis parallel hyperplane during p%d. qh_sethyperplane_gauss: singular or axis parallel hyperplane at normalization during p%d. qh_setfacetplane: facet f%d created. Last point added to hull was p%d.qh_setfacetplane: flipped orientation due to nearzero gauss and interior_point test. During p%d qh_setfacetplane: ====== vertex p%d(v%d) increases max_outside to %2.2g for new facet f%d last p%d qh_setfacetplane: f%d offset %2.2g normal: ;f?3Ey?;f?;f?3Ey?3Ey???qhull internal error (qh_option): option (%d chars) has more than %d chars. May overflow temporary buffer. Option '%s' qh_option: option would overflow qh.qhull_options. Truncated '%s' qhull internal error (qh_checkflags): hiddenflags must start and end with a space: "%s" qhull internal error (qh_checkflags): hiddenflags contains commas, newlines, or tabs: "%s" qhull option error: option %s is not used with this program. It may be used with qhull. qhull internal error (qh_clock): use qh_CLOCKtype 2 in user_r.h qh_freebuffers: freeing up global memory buffers qh_freebuild: free global sets qh_freebuild: free temporary sets (qh_settempfree_all) qh_freebuild: free memory from qh_inithull and qh_buildhull qh_freebuild: delete the previously-seen ridges of f%d qh_freeqhull: free global memory qh_freeqhull: clear qhT except for qh.qhmem and qh.qhstat qhull input error: more than %d characters in command line. qhull option error: transparent Delaunay('Gt') needs 3-d Delaunay('d') w/o 'GDn' qhull option error: option 'Fp' is only used for halfspace intersection('Hn,n,n'). qhull option error: option 'Ft' is not available for Voronoi vertices ('v') or halfspace intersection ('H') qhull option error: option 'FC' is not available for Voronoi vertices('v') qhull option warning: 'QJ' (joggle) will usually prevent coincident input sites for options 'Fc' and 'FP' qhull option error: Mathematica and Maple output is only available for 2-d and 3-d convex hulls and 2-d Delaunay triangulations qhull option error: Geomview output is only available for 2-d, 3-d and 4-d qhull option error: no output specified for Geomview qhull option error: Geomview output for Voronoi diagrams only for 2-d qhull option warning: coplanars, vertices, and centrums output not available for 4-d output(ignored). Could use 'GDn' instead. qhull output warning: ignoring coplanar points, option 'Qc' was not set for the first run of qhull. qhull option warning: drop dimension 'GD%d' is only available for 3-d/4-d Geomview qhull option warning: no dimension given for Print option 'P%c' at: %s. 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 dimension given for Qhull option 'Q%c' qhull option warning: dimension %d for Qhull option 'Q%c' is >= %d. Ignored qhull option error: see previous warnings, use 'Qw' to override: '%s' (last offset %d) qh_lib_check: Incorrect qhull library called. Caller uses non-reentrant Qhull with a static qhT. Qhull library is reentrant. 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: Expecting qhullLibraryType QHULL_NON_REENTRANT(0), QHULL_QH_POINTER(1), or QHULL_REENTRANT(2). Got %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 vertexT 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_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 setT 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. 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 qhull internal error (qh_initflags): qh.NOerrexit was not cleared before calling qh_initflags(). It should be cleared after setjmp(). Exit qhull. qhull input warning: no maximum cosine angle given for option 'An'. A1.0 is coplanar qhull input warning: no centrum radius given for option 'Cn' qhull option error: expecting a positive number for maximum roundoff 'En'. Got '%s' qhull option warning: no maximum roundoff given for option 'En' qhull option error: expecting 'Hn,n,n,...' for feasible point of halfspace intersection. Got '%s' qhull option warning: missing random perturbation for option 'Rn' qhull option warning: missing visible distance for option 'Vn' qhull option warning: missing coplanar distance for option 'Un' qhull option error: expecting a positive number for outside width 'Wn'. Got '%s' qhull option warning: missing outside width for option 'Wn' qhull option warning: unknown 'F' output option 'F%c', skip to next space qhull option warning: missing dimension for option 'GDn' qhull option warning: can only drop one dimension. Previous 'GD%d' ignored qhull option warning: unknown 'G' geomview option 'G%c', skip to next space qhull option warning: missing facet count for keep area option 'PAn' qhull option warning: missing facet area for option 'PFn' qhull option warning: missing merge count for option 'PMn' qhull option warning: unknown 'P' print option 'P%c', skip to next space qh_initflags: project dimension %d qhull option warning: missing number of test points for option 'QTn' qhull option warning: unknown 'Q' qhull option 'Q1%c', skip to next space qhull option warning: can not follow '1', '2', or '3' with a digit. 'Q%c%c' skipped qhull option warning: good point already defined for option 'QGn'. Ignored qhull option warning: missing good point id for option 'QGn'. Ignored qhull option warning: missing random seed for option 'QRn' qhull option warning: good vertex already defined for option 'QVn'. Ignored qhull option warning: no good point id given for option 'QVn'. Ignored qhull option warning: unknown 'Q' qhull option 'Q%c', skip to next space qhull option warning: output file undefined(stdout). Option 'Tz' ignored. qhull option warning: missing point id for cone for trace option 'TCn' qhull option warning: missing frequency count for trace option 'TFn' qhull option error: cannot open 'TI' file "%s" qhull option warning: qh.fout was not set by caller of qh_initflags. Cannot use option 'TO' to redirect output. Ignoring option 'TO' qhull option error: cannot open file "%s" for writing as option 'TO'. It is already in use or read-only qhull option warning: missing count of added points for trace option 'TAn' qhull option warning: negative point id for trace option 'TPn'. Expecting 'TP-1' for tracing after qh_buildhull and qh_postmerge 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 rerun count for trace option 'TRn' qhull option warning: missing furthest point id for trace option 'TVn' qhull option warning: missing max width for trace option 'TWn' qhull option warning: unknown 'T' trace option 'T%c', skip to next space qhull option warning: unknown option '%c'(%x) qhull option warning: missing space after option '%c'(%x), reserved for sub-options, ignoring '%c' options to next space qhull option warning: 'TCn' (stopCone) ignored when used with 'QJn' (joggle) qhull option warning: additional output formats ('Fc',etc.) are not compatible with Geomview ('G'). Use option 'Po' to override qh_initflags: option flags initialized qh_initqhull_globals: for %s | %s qhull input error (qh_initqhull_globals): expecting between 1 and %d points. Got %d %d-d points qhull option warning: 'Q0-no-premerge' ignored due to exact merge ('Qx') or pre-merge ('C-n' or 'A-n') qhull option warning: joggle ('QJ') produces simplicial output (i.e., triangles in 2-D). Unless merging is requested, option 'Qt' has no effect 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 qhull option error: can not use Delaunay('d') or Voronoi('v') with halfspace intersection('H') 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 option error: can not use merge-pinched-vertices ('Q14') with good-facets-only ('Qg') qh_initqhull_globals: disable qh.MERGEpinched for 2-d. It has no effectqhull option warning: option 'Qbb' (scale-last-coordinate) is normally used with 'd' or 'v' qhull option error: test vertex neighbors('Qv') needs a merge option qhull error: dimension %d must be > 1 qh_initqhull_globals: initialize globals. input_dim %d, numpoints %d, malloc? %d, projected %d to hull_dim %d qh_initqhull_globals: trace last of TR%d runs at level %d qhull configuration error (qh_RANDOMmax in user_r.h): random integer %d > qh_RANDOMmax (%.8g) 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 input error: not enough points(%d) to construct initial simplex (need %d) %s %2.2g, qh_freebuffers: finished qh_initqhull_outputflags: %s PgoodFvoronoiFverticesQcoplanardelaunayincidencemathematicanormalsoffFileAngle-premerge-Angle-postmergeCentrum-premerge-Centrum-postmergeDistance-roundoffHalfspace-aboutHalfspaceRandom-perturbVisibleU-coplanarW-outsideFareaFArea-totalFcoplanarsFCentrumsFd-cdd-inFD-cdd-outFFacets-xridgeFinnerFIDsFmergesFMapleFneighborsFNeighbors-vertexFouterFOptionsFpoint-intersectFPoint-nearestFQhullFsummaryFSizeFtrianglesFVertex-averageFxtremesGall-pointsGcentrumsGintersectionsGinnerGno-planesGouterGpointsGridgesGtransparentGverticesGDrop-dimPdrop-facets-dim-lessPDrop-facets-dim-morePgood-facetsPGood-facet-neighborsPoutput-forcedPprecision-ignorePArea-keepPFacet-area-keepPMerge-keepQallow-shortQbBound-unit-boxQbbound-lastQb-project-dimQbound-dim-lowQBound-dim-highQcoplanar-keepQfurthest-outsideQgood-facets-onlyQinterior-keepQmax-outside-onlyQrandom-outsideQsearch-initial-simplexQTestPointsQupperDelaunayQvertex-neighbors-convexQxact-mergeQz-infinity-pointQ0-no-premergeQ1-angle-mergeQ10-no-narrowQ11-trinormals QtriangulateQ12-allow-wideQ14-merge-pinched-verticesQ15-check-duplicatesQ2-no-merge-independentQ3-no-merge-verticesQ4-avoid-old-into-newQ5-no-check-outerQ6-no-concave-mergeQ7-no-breadth-firstQ8-no-near-insideQ9-pick-furthestQGood-if-dont-see-pointQGood-if-see-pointQRotate-idQRandom-seedQV-good-facets-not-pointQV-good-facets-pointQwarn-allowTannotate-outputTcheck-frequentlyTflushTstatisticsTverifyTz-stdoutTCone-stopTFacet-logTInput-fileTOutput-fileTA-stop-addTrace-pointTrace-mergeTRerunTV-stop-before-pointTV-stop-after-pointTWide-trace_pre-mergeQbbound-last-qj_zero-centrumQ3-no-merge-vertices-dim-highQRotate-randomrun-idjH0HHHHHHHHaHg,HHHHHHHHHHHHHHHPHHHDHHHH<```'``x```P`P`(`````````````g``@``````````````h```Is}S)aMCawM#^(vL'([4l+4b$De~DDDDDDDDDDDDDDDDDDDDDDDDDDDDTD*DDDDDDDD[D4D D9 cccqhull_r 8.0.2 (2020.2.r 2020/08/31)2020.2.r 2020/08/31433AYAA%d %d %d- f%d - flags: top bottom simplicial tricoplanar upperDelaunay visible newfacet notG seen seen2 isarea coplanarhorizon mergehorizon cycledone keepcentrum dupridge mergeridge1 mergeridge2 newmerge flipped notfurthest degenerate - area: %2.2g - replacement: f%d - was horizon to f%d - merges: %dmax - merges: %d - normal: %8.4g - offset: %10.7g - center: - maxoutside: %10.7g p%d: - outside set: Furthest - coplanar set: - vertices: - neighboring facets: p%d(v%d) MERGEridge DUPLICATEridge f%d%d %d %d )); VECT 1 2 1 2 1 # f%d %8.4g %8.4g %8.4g 1.0 { OFF %d 1 1 # f%d 0 %8.4g %8.4g %8.4g %8.4g 1.0 } [%16.8f, %16.8f, %16.8f]}]{%16.8f, %16.8f, %16.8f}, [Polygon[{ MERGEridge DUPLICATEridge NULLfacet %s | %s begin %d %d real %d %d - r%d nonconvex mergevertex mergevertex2 simplicialtop simplicialbot vertices: - ridges (tentative ids): - ridges: - all ridges: NULLvertex - p%d(v%d): %5.2g delridge neighbors: 1 %d 0 # infinity not used %d %d %d 1 # %d f%d # p%d(v%d) VECT 1 %d 1 %d 1 OFF 3 1 1 # intersect f%d f%d %8.4g %8.4g %8.4g %8.4g # p%d(coplanar facets) projected p%d OFF 3 1 1 # f%d # r%d between f%d f%d 3 0 1 2 %8.4g %8.4g %8.4g # ridge between f%d f%d VECT 1 2 1 2 1 # p%d VECT 1 1 1 1 1 %8.4g %8.4g %8.4g 1 no normal for facet f%d %d %d %d %6.16g %8.4g %8.4g %8.4g 0 1 }}} Vertices and facets: LIST # %s | %s 4VECT %d %d 1 # 1 point per line 1 # 1 color for all 0 1 1 1 # color of points 4OFF %d %d 1 %s | %s begin %d %d real PLOT(CURVES( PLOT3D(POLYGONS( { %d %d %d %d 0 2 %6.16g %6.16g beginBEGINENDThe halfspace was on line %d ./rbox D4 - shares same visible/horizon as f%d - owner of normal & centrum is facet f%d - outside set(furthest p%d): - outside set: %d points. - furthest distance= %2.2g - coplanar set(furthest p%d): - coplanar set: %d points. furthest distance= %2.2g qhull error: filename is more than %d characters, %s qhull internal error (qh_detvnorm): too few points(%d) to compute separating plane qh_detvnorm: Voronoi vertex or midpointqh_detvnorm: points %d %d midpoint dist %2.2g qh_detvnorm: points %d %d angle %2.2g nearzero %d qh_detvnorm: points %d %d Voronoi vertex %d dist %2.2g qhull internal error (qh_detvridge3): neighbors of vertex p%d are not connected at facet %d qh_eachvoronoi: Voronoi ridge of %d vertices between sites %d and %d qh_markkeep: only keep %d largest and/or %d most merged facets and/or min area %.2g qh_markvoronoi: isLower %d numcenters %d qh_order_vertexneighbors: order facet neighbors of v%d by 2-d (orientation), 3-d (adjacency), or n-d (f.visitid,id) qhull internal error (qh_order_vertexneighbors): call qh_vertexneighbors before calling qh_order_vertexneighbors qhull internal error (qh_order_vertexneighbors): no neighbor of v%d for f%d 3 %d %d %d %8.4g %8.4g %8.4g 1 # f%d f%d 3 %d %d %d %8.4g %8.4g %8.4g 1 #r%d f%d f%d qhull warning: no facets printed qhull internal error (qh_printend): number of ridges %d != number printed %d and at end %d qhull internal error (qh_printextremes_2d): loop in facet list. facet %d nextfacet %d %8.4g %8.4g %8.4g %8.4g %8.4g %8.4g [[%16.8f, %16.8f], [%16.8f, %16.8f]] Line[{{%16.8f, %16.8f}, {%16.8f, %16.8f}}] between f%d and f%d - horizon ridge to visible facet qhull internal error (qh_printvdiagram): unknown print format %d. {appearance {+edge -face} OFF %d %d 1 # Voronoi centers and cells # p%d is coplanar or isolated 3 0 1 2 %8.4g %8.4g %8.4g 1.0 OFF 3 1 1 # ridge between f%d f%d qhull input error (qh_printafacet): option 'Fp' needs qh->feasible_point {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 %8.4g 0 0 0 # v%d 0 %8.4g 0 0 0 0 %8.4g 0 {appearance {-normal -edge normscale 0} {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 { {INST geom { : centrum } transform { # f%d qhull warning: output for ridges and intersections not implemented in 2-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 warning: 'Gnh' generates no output in 4-d {appearance {linewidth 3} LIST # %s | %s {appearance {+edge -evert linewidth 2} LIST # %s | %s qhull warning: input sites of Delaunay regions (option 'i'). Use option 'p' or 'o' for Voronoi centers. Disable warning with option 'Pp' qhull warning: output is the Delaunay triangulation qhull internal error (qh_printbegin): can not use this format for dimension %d qhull warning: CDD format is not available for centrums, halfspace intersections, and OFF file format. Options selected for Qhull %s: %s 10 %d %d %d %d %d %d %d %d %d %d 2 size in bytes: merge %d ridge %d vertex %d facet %d normal %d ridge vertices %d facet vertices or neighbors %d qhull internal error (qh_produce_output2): temporary sets not empty(%d) qhull internal error (qh_produce_output): temporary sets not empty(%d) qhull input error: feasible point(dim 1 coords) is only valid for halfspace intersection qhull input warning: feasible point(dim 1 coords) overrides 'Hn,n,n' feasible point for halfspace intersection qhull error: insufficient memory for feasible point qhull input error: coordinates for feasible point do not finish out the line: %s qhull input error: only %d coordinates. Could not read %d-d feasible point. qhull input error: halfspace intersection needs a feasible point. Either prepend the input with 1 point or use 'Hn,n,n'. See manual. qhull input warning: more coordinates for 'H%s' than dimension %d qhull input error: short input file. Did not find dimension and number of points qhull input error: dimension %d (first or smaller number) should be at least 2 qhull input error: expecting between 1 and %d points. Got %d %d-d points qhull option error (qh_readpoints): can not use Delaunay('d') or Voronoi('v') with halfspace intersection('H') qhull input error: dimension %d (first number, includes offset) should be at least 3 for halfspaces qhull input error: dimension %d of feasible point is not one less than dimension %d for halfspaces qhull error: insufficient memory to read %d points qhull input warning: the input appears to be in cdd format. If so, use 'Fd' qhull input error: for cdd format, point at line %d does not start with '1' The input appears to be in cdd format. If so, you should use option 'Fd' qhull input error: line %d contained more than %d characters qhull warning: instead of %d points in %d-d, input contains %d points and %d extra coordinates. qhull error: instead of %d points in %d-d, input contains %d points and %d extra coordinates. Line %d is the first comment. Line %d is the first point. Line %d is the first short line. Line %d is the first long line. Continuing with %d points. Override with option 'Qa' (allow-short) This is the qhull test case. If any errors or core dumps occur, recompile qhull with 'make new'. If errors still occur, there is an incompatibility. You should try a different compiler. You can also change the choices in user_r.h. If you discover the source of the problem, please send mail to qhull_bug@qhull.org. Type 'qhull' for a short list of options. qh_readpoints: read in %d %d-dimensional points qhull input error: missing "begin" for cdd-formated input qhull input error: missing quote after filename -- %s qhull input error: filename expected, none found. >>L>>L>L>|>>>>>>>>> 8Ǎ`@pp hIDtD$dTdd44$Mb`?{Gz?????qh_joggle_restart: qhull restart because of %s 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 qh_buildtracing: start trace T%d for point TP%d above facet 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. 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 qhull internal error: qh_checklists failed on reset of qh.visit_id %u qhull internal error: qh_checklists failed on reset of qh.vertex_visit %u qh_findhorizon: find horizon for point p%d facet f%d qhull internal error (qh_findhorizon): does not work for tricoplanar facets. Use option 'Q11' qhull internal error (qh_findhorizon): visible facet f%d does not have neighbors qh_findhorizon: point p%d is coplanar to horizon f%d, dist=%2.7g < qh->MINvisible(%2.7g) qhull topology error (qh_findhorizon): empty horizon for p%d. It was above all facets. qh_findhorizon: %d horizon facets(good %d), %d visible(good %d), %d coplanar 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_nextfurthest): num_outside %d is too low by at least %d, or a random real %g >= 1.0 qhull internal error (qh_partitionpoint): cannot partition p%d of f%d into visible facet f%d nearly incident point (narrow hull)qh_partitionpoint: point p%d is outside facet f%d newfacet? %d, newoutside? %d (or narrowhull) qh_partitionpoint: point p%d is coplanar to facet f%d (dropped) qh_partitionpoint: point p%d is inside all facets, closest to f%d dist %2.2g qh_partitionall: partition all points into outside sets qh_partitioncoplanar: partition coplanar point p%d starting with f%d dist? %2.2g, allnew? %d, gh.repart_facetid f%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 qhull internal error (qh_partitioncoplanar): cannot partition coplanar p%d of f%d into visible facet f%d 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 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 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 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: repartition coplanar point p%d from f%d as an outside point above hidden facet f%d dist %2.2g nearest vertices %2.2g qh_partitioncoplanar: == p%d from f%d increases qh.max_outside to %2.2g of f%d last p%d qh_partitioncoplanar: point p%d is coplanar with facet f%d (or inside) dist %2.2g qh_buildcone: created %d newfacets for p%d(v%d) new facet balance %2.2g qh_partitionvisible: partition outside and coplanar points of visible and merged facets f%d into new facets f%d qhull topology error (qh_partitionvisible): all new facets deleted as degenerate facets. Can not continue. qh_partitionvisible: partition %d deleted vertices as coplanar? %d points into new facets f%d qhull internal error (qh_partitionvisible): all new facets deleted or none defined. Can not partition deleted v%d. qh_partitionvisible: partitioned %d points from outsidesets, %d points from coplanarsets, and %d deleted vertices qhull internal error (qh_addpoint): NULL facet. Need to call qh_findbestfacet first 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_addpoint: added p%d to convex hull with point balance %2.2g qh_buildhull: start build hull qhull internal error (qh_buildhull): visible or new facet f%d in facet list qhull internal error (qh_buildhull): new vertex f%d in vertex list qh_buildhull: stop point or cone P%d in initial hull qh_buildhull: stop after adding %d vertices qhull internal error (qh_buildhull): %d outside points were never processed. qh_buildhull: completed the hull construction 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 qh_qhull: all facets are clearly convex and no coplanar points. Post-merging and check of maxout not needed. qh_qhull: finished qh_buildhull and qh_postmerge, start tracing (TP-1) Testing all coplanar points. qhull internal error (qh_qhull): temporary sets not empty(%d) at end of Qhull qhull internal error: qh_checklists failed at qh_printsummary Early exit due to 'TAn', 'TVn', 'TCn', 'TRn', or precision error with 'QJn'. Furthest-site Voronoi vertices by the convex hull of %d points in %d-d: Voronoi diagram by the convex hull of %d points in %d-d: Number of Voronoi regions%s: %d Total number of deleted points due to merging: %d Number of nearly incident points: %d Total number of nearly incident points: %d Number of%s Voronoi vertices: %d Number of%s non-simplicial Voronoi vertices: %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: Number of input sites%s: %d Number of%s Delaunay regions: %d Number of%s non-simplicial Delaunay regions: %d Halfspace intersection by the convex hull of %d points in %d-d: Number of non-redundant halfspaces: %d Number of %s halfspaces: %d Number of intersection points: %d Number of 'good' intersection points: %d Number of%s non-simplicial intersection points: %d Convex hull of %d points in %d-d: Number of 'good' facets: %d Number of%s non-simplicial facets: %d Number of triangulated facets: %d Number of points processed: %d Number of hyperplanes created: %d Number of facets in hull: %d Number of distance tests for qhull: %d Number of distance tests for merging: %d Number of distance tests for checking: %d Number of merged facets: %d Number of merged pinched vertices: %d CPU seconds to compute hull (after input): %2.4g Percentage of runs with precision errors: %4.1f After %d retries, input joggled by: %2.2g Maximum distance of point above facet: %2.2g Maximum distance of vertex below facet: %2.2gERRONEOUScoplanar horizonempty horizonnearly incident point_runFirst post-mergeFor post-mergingFor testing vertex neighborsQhull: algorithm completed and at-infinity 'good'similar and redundantsimilarcoplanar and interiorApproximateTotal Number of halfspaces: %d Number of vertices: %d Number of %s points: %d Number of facets: %d Statistics for: %s | %s QR%d Input joggled by: %2.2g %s facet area: %2.8g %s volume: %2.8g (%.1fx) .AA0C>@@?qhull error (qh_memalloc): negative request size (%d). Did int overflow due to high-D? qh_mem %p n %8d alloc quick: %d bytes (tot %d cnt %d) qhull error (qh_memalloc): insufficient memory to allocate short memory buffer (%d bytes) qhull internal error (qh_memalloc): short totbuffer %d != totshort+totfree... %d qh_mem %p n %8d alloc short: %d bytes (tot %d cnt %d) qhull internal error (qh_memalloc): qhmem has not been initialized. qhull error (qh_memalloc): insufficient memory to allocate %d bytes qh_mem %p n %8d alloc long: %d bytes (tot %d cnt %d) qhull internal error (qh_memcheck): qh is 0. It does not point to a qhT 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 qh_memcheck: check size of freelists on qh->qhmem qh_memcheck: A segmentation fault indicates an overwrite of qh->qhmem qhull internal error (qh_memcheck): totfree %d not equal to freelist total %d qh_memcheck: total size of freelists totfree is the same as qh->qhmem.totfree qh_mem %p n %8d free short: %d bytes (tot %d cnt %d) qh_mem %p n %8d free long: %d bytes (tot %d cnt %d) qhull error (qh_meminit): insufficient memory qh_meminitbuffers: memory initialized with alignment %d qhull error (qh_memsetup): largest mem size %d is >= buffer size %d or initial buffer size %d qhull error (qh_memsetup): insufficient memory qhull internal error (qh_memsize): qh_memsize called after qh_memsetup qh_memsize: quick memory of %d bytes qhull warning (qh_memsize): free list table has room for only %d sizes 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) %7d calls to qh_setlarger %7.2g average copy size freelists(bytes->count): %d->%dmakeridges: appended r%d to ridges for f%d. Next is ridges for neighbor f%d qh_remove_extravertices: test non-simplicial f%d for extra vertices 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 qh_remove_mergetype: remove merge f%d f%d v%d v%d r%d r%d dist %2.2g type %dqh_appendmergeset: f%d is already redundant (%d) or f%d is already redundant (%d). Ignore merge f%d and f%d type %d qh_appendmergeset: f%d is already degenerate. Ignore merge f%d type %d (MRGdegen) 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_appendmergeset): except for MRGdupridge, cannot merge a non-flipped facet f%d into flipped f%d, mergetype %d, dist %4.4g qh_appendmergeset: dupridge will merge a non-flipped facet f%d into flipped f%d, dist %4.4g qhull internal error (qh_appendmergeset): facet f%d or f%d is already a mirrored facet (i.e., 'redundant') qhull internal error (qh_appendmergeset): mirrored facets f%d and f%d do not have the same vertices qh_appendmergeset: append merge f%d and f%d type %d (%s) to qh.degen_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) qhull internal error (qh_appendvertexmerge): expecting temp set defined for qh.vertex_mergeset (0x%x). Got NULL qhull internal error (qh_appendvertexmerge): expecting two distinct ridges for MRGvertices. Got r%d r%d qh_appendvertexmerge: append merge v%d into v%d r%d r%d dist %2.2g type %d (%s) qh_basevertices: found %d vertices 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 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' - Experimental option merge-pinched-vertices ('Q14') may avoid this error. It merges nearly adjacent vertices. - A bounding box for the input sites may alleviate this error. qhull internal error (qh_checkconnect): f%d is not attached to the new facets qhull internal error (qh_checkdelfacet): cannot delete f%d. It is referenced by merge f%d f%d mergetype %d qhull internal error (qh_checkdelridge): expecting empty qh.vertex_mergeset in order to avoid calling qh_delridge_merge. Got %d merges 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 not concave, flipped, or dupridgeqh_checkzero: skip convexity check until first pre-merge qh_checkzero: testall %d, facets are %s qh_checkzero: qh_premerge is needed. New facet f%d or its horizon f%d is non-simplicial, flipped, dupridge, or mergehorizon qh_checkzero: facet f%d and f%d are not clearly convex. v%d dist %.2g qh_checkzero: facet f%d and horizon f%d are not clearly convex. v%d dist %.2g qh_copynonconvex: moved nonconvex flag from r%d to r%d between f%d and f%d qh_degen_redundant_facet: test facet f%d for degen/redundant qh_degen_redundant_facet: f%d is flipped, will merge later qhull internal error (qh_degen_redundant_facet): facet f%d has deleted neighbor f%d (qh.visible_list) qh_degen_redundant_facet: f%d is contained in f%d. merge qh_degen_redundant_facet: f%d is degenerate. qh_delridge_merge: delete ridge r%d between f%d and f%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 qh_drop_mergevertex: unset mergevertex for r%d and r%d due to dropped vertex merge v%d to v%d. Sets mergevertex2 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 qhull internal error: cannot call qh_findbestneighor for f%d while qh.CENTERtype is qh_ASvoronoi qhull internal error (qh_findbestneighbor): no neighbors for f%d qh_findbestneighbor: f%d is best neighbor for f%d testcentrum? %d nonconvex? %d dist %2.2g min %2.2g max %2.2g 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 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_initmergesets): expecting NULL mergesets. Got qh.facet_mergeset (0x%x), qh.degen_mergeset (0x%x), qh.vertex_mergeset (0x%x) qh_makeridges: make ridges for f%d qh_mark_dupridges: identify dupridges in facetlist f%d, allmerges? %d qh_mark_dupridges): dupridge due to duplicate vertices for subridges f%d and f%d qh_mark_dupridges: found %d duplicated ridges (MRGdupridge) for qh_getpinchedmerges qh_mark_dupridges: found %d duplicated ridges (MRGdupridge) for qh_premerge. Prepare facets for merging qh_mark_dupridges: restore missing neighbors and ridges due to qh_MERGEridge qhull topological error (qh_mark_dupridges): multiple dupridges for f%d and f%d, including reverse 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 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 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_maydropneighbor: test f%d for no ridges to a neighbor qhull internal error (qh_maydropneighbor): not valid for simplicial f%d while adding furthest p%d qhull internal error (qh_maydropneighbor): facet f%d has deleted neighbor f%d (qh.visible_list) 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 neighbor f%d of f%d while adding furthest p%d qh_maydropneighbors: f%d is degenerate. qh_mergecycle_facets: make newfacet new and samecycle deleted qh_willdelete: move f%d to visible list, set its replacement as f%d, and clear f.neighbors and f.ridges qhull internal error (qh_willdelete): expecting qh.visible_list at before qh.newfacet_list f%d. Got NULL qh_mergecycle_facets: merged facets from cycle f%d into f%d qh_mergecycle_neighbors: delete shared neighbors from newfacet qh_mergecycle_neighbors: update neighbors qh_mergecycle_neighbors: deleted %d neighbors and added %d qh_mergecycle_ridges: delete shared ridges from newfacet qh_mergecycle_ridges: add ridges to newfacet qhull internal error (qh_mergecycle_ridges): bad ridge r%d qh_mergecycle_ridges: found %d old ridges and %d new ones qh_mergecycle_vneighbors: update vertex neighbors for newfacet qh_mergecycle_vneighbors: deleted v%d when merging cycle f%d into f%d qh_mergecycle_vneighbors: merged vertices from cycle f%d into f%d qh_mergefacet2d: merged v%d and neighbor f%d of f%d into f%d qh_mergeneighbors: merge neighbors of f%d and f%d qh_mergeridges: merge ridges of f%d into 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_mergesimplex: update vertex neighbors of 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 qhull topology error (qh_mergesimplex): f%d is a dupridge of f%d, cannot merge f%d into f%d qh_mergesimplex: move r%d with f%d to f%d, new neighbor? %d, maybe horizon? %d qh_mergesimplex: merged simplex f%d v%d into facet f%d qh_mergevertex_neighbors: merge vertex neighborset for f%d into f%d qh_mergevertex_neighbors: of f%d into f%d at furthest p%d f0= %p qhull internal error (qh_mergevertices): facets did not share a ridge qh_neighbor_intersections: %d vertices in neighbor intersection of v%d qh_neighbor_vertices_facet: found %d vertex neighbors for v%d in f%d (simplicial? %d) qh_neighbor_vertices: %d non-subridge, vertex neighbors for v%d 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_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_findbest_pinchedvertex): did not find best vertex for subridge of dupridge between f%d and f%d, while processing p%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_getpinchedmerges: try to merge pinched vertices for dupridges in new facets with apex p%d(v%d) max dupdist %2.2g qhull internal error (qh_getpinchedmerges): expecting MRGdupridge from qh_mark_dupridges. Got merge f%d f%d type %d 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 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 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 qh_getpinchedmerges: will merge new facets to resolve dupridge between f%d and f%d with pinched v%d and v%d qh_getpinchedmerges: will merge pinched v%d into v%d to resolve dupridge between f%d and f%d qhull internal error (qh_next_vertexmerge): expecting two vertices for vertex merge. Got v%d v%d and optional f%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 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 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 dupridge. Nearest v%d and v%d dist %2.2g (%.1fx) qhull internal error (qh_opposite_horizonfacet): expecting merge of simplicial facets, at least one of which is mergehorizon. Either simplicial or mergehorizon is wrong qhull internal error (qh_opposite_horizonfacet): merge facet f%d not connected to mergehorizon f%d qhull internal error (qh_renameridgevertex): oldvertex v%d not found in r%d. Cannot rename to v%d qh_renameridgevertex: ridge r%d deleted. It contained both v%d and v%d qh_renameridgevertex: swapped the top and bottom of ridge r%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_test_centrum_merge: coplanar f%d to f%d dist %4.4g, reverse dist %4.4g angle %4.4g qh_test_degen_neighbors: test for degenerate neighbors of f%d qhull internal error (qh_test_degen_neighbors): facet f%d has deleted neighbor f%d (qh.visible_list) qh_test_degen_neighbors: f%d is degenerate with %d neighbors. Neighbor of f%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_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 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: 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: 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_appendmerge: coplanar angle %4.4g between f%d and f%d qh_getmergeset: %d merges found qh_getmergeset_initial: %d merges found qh_test_redundant_neighbors: test neighbors of f%d vertex_visit %d qh_test_redundant_neighbors: f%d is degenerate with %d neighbors. qhull internal error (qh_test_redundant_neighbors): facet f%d has deleted neighbor f%d (qh.visible_list) qh_test_redundant_neighbors: f%d is contained in f%d. merge qh_renamevertex: rename v%d to v%d in %d ridges with old f%d and neighbor f%d qh_renamevertex: renaming v%d to v%d in several facets for qh_redundant_vertex or MRGsubridge 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 qh_renamevertex: rename vertices in non-simplicial neighbor f%d of v%d qh_renamevertex: renaming v%d to v%d in oldfacet f%d for qh_rename_sharedvertex qh_renamevertex: renaming pinched v%d to v%d between f%d and f%d qh_test_vneighbors: testing vertex neighbors for convexity qh_test_vneighbors: found %d non-convex, vertex neighbors qh_tracemerge: trace facet and vertex after merge of f%d into f%d type %d (%s), furthest p%d qh_tracemerge: trace vertex deleted at furthest p%d 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. qh_mergecycle: merge #%d for facets from cycle f%d into coplanar horizon f%d qh_mergecycle: ========= trace merge %d of samecycle %d into trace f%d, furthest is p%d qhull internal error (qh_mergecycle): does not work for tricoplanar facets. Use option 'Q11' qh_mergecycle: end of trace facet qh_vertexridges: found %d ridges for v%d qh_find_newvertex: find new vertex for v%d from qh_find_newvertex: vertices not in ridges for v%d qh_find_newvertex: found v%d for old v%d from %d vertices and %d ridges. qh_find_newvertex: no vertex for renaming v%d (all duplicated ridges) during p%d qh_redundant_vertex: check if v%d from a deleted ridge can be renamed qh_rename_adjacentvertex: merge #%d rename v%d (%d neighbors) to v%d (%d neighbors) dist %2.2g qh_rename_adjacentvertex: ignore rename. Either v%d (%d) or v%d (%d) is deleted qhull internal error (qh_rename_adjacentvertex): expecting neighbor facets for v%d and v%d. Got %d and %d neighbors resp. qh_rename_adjacentvertex: simplicial f%d contains old v%d and new v%d. Will be marked degenerate by qh_renamevertex qh_rename_adjacentvertex: partition old p%d(v%d) as a coplanar point for furthest f%d dist %2.2g. Maybe repartition later (QH0031) qhull internal error (qh_rename_sharedvertex): v%d's neighbors not in f%d qh_rename_sharedvertex: p%d(v%d) is shared by f%d(%d ridges) and f%d qhull internal error (qh_mergefacet): merge f%d into f%d for mergetype %d (%s) does not work for tricoplanar facets. Use option 'Q11' qh_mergefacet: ========= trace wide merge #%d(%2.2g) for f%d into f%d for mergetype %d (%s), last point was p%d qh_mergefacet: ========= trace merge #%d for f%d into f%d for mergetype %d (%s), furthest is p%d 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 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 internal error (qh_mergefacet): either f%d and f%d are the same or one is a visible facet, mergetype %d (%s) qhull topology error: Only %d facets remain. The input is too degenerate or the convexity constraints are too strong. Option 'Qx' may avoid this problem. qh_mergefacet: end of wide tracing qh_mergefacet: check f%d and f%d for redundant and degenerate neighbors qhull internal error (qh_merge_nonconvex): expecting mergetype MRGcoplanar..MRGconcavecoplanar. Got merge f%d and f%d type %d qh_merge_nonconvex: merge #%d for f%d and f%d type %d qh_merge_nonconvex: avoid merging old facet f%d dist %2.2g. Use f%d dist %2.2g instead qh_merge_twisted: merge #%d for twisted f%d and f%d 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 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 qh_merge_degenredundant: merge %d degenerate, redundant, and mirror facets qhull internal error (qh_merge_degenredunant): f%d is redundant but visible f%d has no replacement qh_merge_degenredundant: merge redundant f%d into f%d (arg f%d) qh_merge_degenredundant: facet f%d has no neighbors. Deleted qh_merge_degenredundant: deleted v%d because f%d has no neighbors qh_merge_degenredundant: facet f%d has %d neighbors, merge into f%d dist %2.2g qhull internal error (qh_flippedmerges): facet_mergeset (%d merges) not at top of tempstack (%d merges) qh_flippedmerges: merge flipped f%d into f%d dist %2.2g during p%d qh_flippedmerges: merged %d flipped and %d degenredundant facets into a good neighbor qh_forcedmerges: merge dupridges qhull internal error (qh_forcedmerges): qh_settemppop (size %d) is not qh->facet_mergeset (size %d) 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_forcedmerges: dupridge f%d is degenerate with fewer than %d neighbors qh_forcedmerges: merged %d facets, %d flipped facets, and %d degenredundant facets across dupridges qhull internal error (qh_merge_pinchedvertices): qh.visible_list (f%d), newfacet_list (f%d), or newvertex_list (v%d) not empty qh_merge_pinchedvertices: merge one of %d pinched vertices before adding apex p%d. Try to resolve duplicate ridges in newfacets qh_merge_pinchedvertices: merge %d pinched vertices from dupridges in merged facets, apex p%d qh_merge_pinchedvertices: merge degenerate f%d into an adjacent facet qh_merge_pinchedvertices: merge f%d into f%d mergeType %d qh_reducevertices: reduce extra vertices, shared vertices, and redundant vertices qh_reducevertices: renamed %d shared vertices and %d redundant vertices. Degen? %d qh_all_merges: starting to merge %d facet and %d degenerate merges for new facets f%d, othermerge? %d 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_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 qh_all_merges: merge f%d and f%d type %d dist %2.2g angle %4.4g qhull internal error (qh_all_merges): expecting concave, coplanar, or twisted merge. Got merge f%d f%d v%d mergetype %d qh_all_merges: skip qh_reducevertices due to post-merging, no qh.VERTEXneighbors (%d), or hull_dim %d ==2 or >%d qh_all_merges: merged %d coplanar %d concave %d concavecoplanar %d twisted facets and %d degen or redundant facets. qh_postmerge: postmerge. test vneighbors? %d qh_all_vertexmerges: starting to merge %d vertex merges for apex p%d facet f%d 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_mergecycle_all): f%d without normal qh_mergecycle_all: merged %d same cycles or facets into coplanar horizons and %d degenredundant facets qh_premerge: premerge centrum %2.2g angle %4.4g for apex p%d newfacet_list f%d clearly convexTRACEqh_getmergeset: started. MERGED same cycle:MERGING CYCLEv%d r%d MERGINGqh_flippedmerges: begin reason %s with 'C%.2g' and 'A%.2g' noneanglecoplanarconcaveconcavecoplanartwistedflipsubridgedegenmirror4@?I@qhull precision error: facet f%d is flipped, distance= %6.12g A flipped facet occurs when its distance to the interior point is greater than or equal to %2.2g, the maximum roundoff error. qh_vertexneighbors: determining neighboring facets for each vertex qhull precision error: point p%d is outside facet f%d, distance= %6.8g maxoutside= %6.8g nearest vertices %2.2g qh_checkconvex: check that facets are not-flipped and for qh.ZEROcentrum that simplicial vertices are below their neighbor (dist<0.0) qh_checkconvex: check that facets are not-flipped and that simplicial vertices are convex by qh.DISTround ('En', 'Rn') qh_checkconvex: check that facets are not-flipped and that their centrums are convex by qh.DISTround ('En', 'Rn') qhull precision error: f%d is flipped (interior point is outside) qhull precision error: initial simplex is not convex, since p%d(v%d) is %6.4g above opposite f%d 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 precision error: f%d is concave to f%d, since p%d(v%d) is %6.4g above f%d 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 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_checkconvex: starting with f%d, also check that centrums of non-simplicial ridges are below their neighbors (dist<0.0) qhull warning: recomputing centrums for convexity test. This may lead to false, precision errors. 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 qh_checkfacet: check f%d newmerge? %d qhull internal error (qh_checkfacet): unknown facet id f%d >= qh.facet_id (%d) qhull internal error (qh_checkfacet): expecting f%d.visitid <= qh.visit_id (%d). Got visitid %d qhull internal error (qh_checkfacet): facet f%d is on qh.visible_list qhull internal error (qh_checkfacet): redundant facet f%d not on qh.visible_list qhull internal error (qh_checkfacet): degenerate facet f%d is not on qh.visible_list and qh.degen_mergeset is empty qhull internal error (qh_checkfacet): facet f%d does not have a normal qhull internal error (qh_checkfacet): f%d is 'dupridge' but it is not a newfacet on qh.newfacet_list f%d 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 qhull internal error (qh_checkfacet): deleted vertex v%d in f%d qhull internal error (qh_checkfacet): vertices of f%d are not in descending id order at v%d 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 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_checkfacet): facet f%d still has a MERGEridge or DUPLICATEridge neighbor qhull internal error (qh_checkfacet): facet f%d has deleted neighbor f%d (qh.visible_list) 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 qhull internal error (qh_checkfacet): facet f%d has a duplicate ridge r%d qhull internal error (qh_checkfacet): ridge between f%d and f%d has %d vertices qhull internal error (qh_checkfacet): for facet f%d, neighbor f%d of ridge r%d not in facet qhull internal error (qh_checkfacet): ridge r%d is nonconvex (%d), mergevertex (%d) or not tested (%d) for facet f%d, 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): vertex v%d in r%d not in f%d intersect f%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_checkfacet: vertex v%d in f%d intersect f%d but not in a ridge. Repaired by qh_remove_extravertices in qh_reducevertices qhull internal error (qh_checkfacet): facet f%d skip %d and neighbor f%d skip %d do not match qhull internal error (qh_checkfacet): ridges r%d and r%d (f%d) have the same vertices qh_checklists: check qh.%s_list f%d and qh.vertex_list v%d qh_checklists: check %slist f%d and qh.vertex_list v%d 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_checklists): f%d already in facetlist causing an infinite loop ... f%d > f%d ... > f%d > f%d. Truncate facetlist at 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 qhull internal error (qh_checklists): expecting f%d.previous == f%d. Got f%d 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 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 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): 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_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_checklists): expecting v%d.previous == v%d. Got v%d qhull internal error (qh_checklists): new vertex list v%d is not on vertex list qhull internal error (qh_checkvertex): unknown point id %p qhull internal error (qh_checkvertex): unknown vertex id v%d >= qh.vertex_id (%d) qhull internal error (qh_checkvertex): expecting v%d.visitid <= qh.vertex_visit (%d). Got visitid %d qhull internal error (qh_checkvertex): neighbor f%d does not contain v%d qh_clearcenters: switched to center type %d qh_createsimplex: created simplex qhull internal error (qh_delvertex): vertex v%d was deleted but it was not partitioned as a coplanar point qhull internal error (qh_facet3vertex): only %d vertices for simplicial facet f%d qhull internal error (qh_facet3vertex): ridges for facet %d don't match up. got at least %d qh_findfacet_all: p%d, noupper? %d, f%d, dist %2.2g, isoutside %d, totpart %d qh_findbestfacet: f%d dist %2.2g isoutside %d totpart %d qh_findgood: f%d is closest(%2.2g) to thresholds qh_findgood: found %d good facets with %d good horizon and qh.GOODclosest f%d qhull warning: good vertex p%d does not match last good facet f%d. Ignored. qhull warning: point p%d is not a vertex('QV%d'). qhull warning: point p%d is a vertex for every facet('QV-%d'). qh_findgood_all: f%d is closest(%2.2g) to split thresholds qh_findgood_all: undo selection of qh.GOODclosest f%d since it would fail qh_inthresholds in qh_skipfacet qh_findgood_all: %d good facets remain out of %d facets qh_prependfacet: prepend f%d before f%d qh_furthestnext: made f%d next facet(dist %.2g) qh_furthestout: p%d is furthest outside point of f%d qhull internal error (qh_infiniteloop): potential infinite loop detected. If visible, f.replace. If newfacet, f.samecycle qh_matchdupridge: find dupridge matches for f%d skip %d hash %d hashcount %d 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 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 qh_matchdupridge: allow tricoplanar dupridge for new f%d skip %d and f%d skip %d 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: make forced merge of dupridge for new f%d skip %d and f%d skip %d, maxdist %4.4g in qh_forcedmerges 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 flipped new f%d skip %d into f%d skip %d at dist %2.2g otherdist %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 new f%d skip %d into f%d skip %d at dist %2.2g otherdist %2.2g qh_matchdupridge: try furthest dupridge f%d skip %d new f%d skip %d at dist %2.2g 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 qh_matchdupridge: keep dupridge f%d skip %d and f%d skip %d, dist %4.4g qhull internal error (qh_nearvertex): qh.VERTEXneighbors and facet->center required for tricoplanar facets 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: all neighbors of facet %d are flipped or upper Delaunay. Search all facets qh_findbestlower: f%d dist %2.2g for f%d p%d qhull error (qh_newhashtable): negative request (%d) or size (%d). Did int overflow due to high-D? qhull error: 2^32 or more vertices. vertexT.id field overflows. Vertices would not be sorted correctly. qh_newvertex: vertex p%d(v%d) created qh_makenewfacets: created %d new facets f%d..f%d from point p%d to horizon qhull internal error (qh_opposite_vertex): opposite vertex in facet f%d to neighbor f%d is not defined. Either is facet is not simplicial or neighbor not found qh_outcoplanar: move outsideset to coplanarset for qh->NARROWhull qhull internal warning (point_add): unknown point %p id %d qhull internal error (point_add): point p%d is out of bounds(%d) qh_check_bestdist: check points below nearest facet. Facet_list f%d qh_check_bestdist: check that all points are within %2.2g of best facet qhull output completed. Verifying that %d points are below %2.2g of the nearest %sfacet. qhull precision error (qh_check_bestdist): point p%d is outside facet f%d, distance= %6.8g maxoutside= %6.8g %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 (qh_check_bestdist): a coplanar point is %6.2g from convex hull. The maximum value is qh.outside_err (%6.2g) qh_check_bestdist: max distance outside %2.2g qh_check_points: check all points below %2.2g of all facet planes 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: exact merge ('Qx'). Verify may report that a point is outside of a facet. See qh-optq.htm#Qx 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. 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. qhull warning (qh_check_points): missing normal for facet f%d qhull precision error (qh_check_points): %d additional points outside facet f%d, maxdist= %6.8g qhull precision error (qh_check_points): a coplanar point is %6.2g from convex hull. The maximum value(qh.outside_err) is %6.2g qh_check_points: max distance outside %2.2g qh_check_maxout: check and update qh.min_vertex %2.2g and qh.max_outside %2.2g qh_check_maxout: determine actual minvertex Qhull precision warning: in post-processing (qh_check_maxout) p%d(v%d) is %2.2g below f%d nearest vertices %2.2g qh_check_maxout: p%d(v%d) is %.2g from f%d nearest vertices %2.2g qh_check_maxout: determine actual maxoutside 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 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 qh_check_maxout: p%d is %.2g above f%d 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 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 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 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 (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): 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) qh_printlists: max_outside %2.2g all facets: qh.visible_list f%d, newfacet_list f%d, facet_next f%d for qh_addpoint qh.newvertex_list v%d all vertices:qh_checkpolygon: check all facets from f%d, qh.NEWtentative? %d qhull internal error: qh_checklists failed in qh_checkpolygon qhull internal error (qh_checkpolygon): f%d is 'newfacet' but it is not on qh.newfacet_list f%d or visible_list f%d qhull internal error (qh_checkpolygon): f%d is on qh.newfacet_list f%d but it is not 'newfacet' 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 on qh.visible_list f%d but it is not 'visible' qhull internal error (qh_checkpolygon): f%d has outside points before qh.facet_next f%d 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_checkpolygon): v%d is 'newfacet' but it is not on new vertex list v%d qhull internal error (qh_checkpolygon): unknown point %p for vertex v%d first_point %p qhull internal error (qh_checkpolygon): actual number of facets is %d, cumulative facet count is %d - %d visible facets qhull internal error (qh_checkpolygon): missing vertex neighbors for v%d qhull internal error (qh_checkpolygon): vertex neighbors inconsistent (tot_vneighbors %d != tot_facetvertices %d). Maybe duplicate or missing vertex qhull internal error (qh_checkpolygon): facet f%d occurs twice in neighbors of vertex v%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 qhull internal error (qh_checkpolygon): v%d is a vertex of facet f%d but f%d is not a neighbor of v%d qhull internal error (qh_checkpolygon): actual number of vertices is %d, cumulative vertex count is %d qhull internal error (qh_checkpolygon): #vertices %d != #facets %d qhull warning: #vertices %d + #facets %d - #edges %d != 2. A vertex appears twice in a edge list. May occur during merging. qh_replacefacetvertex: replace v%d with v%d in f%d qhull internal error (qh_replacefacetvertex): f%d is not simplicial qhull internal error (qh_replacefacetvertex): f%d already contains new v%d qhull internal error (qh_replacefacetvertex): f%d does not contain old v%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_initialhull: ignore f%d flipped. Test qh.interior_point (p-2) for clearly flipped 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 initial Delaunay cocircular or cosphericalQhull 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. 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. input sites with last coordinate projected to a paraboloid Qhull precision error: Initial simplex is flat (facet %d is coplanar with the interior point) qh_initialhull: simplex constructed qhull input error: either QGn or QVn point is > p%d qh_initbuild: create sentinels for qh.facet_tail and qh.vertex_tail 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 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 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 input error: point for QV%d is inside initial simplex. It can not be made a vertex. qh_initbuild: initial hull created and points partitioned qh_triangulate_facet: triangulate facet f%d qh_triangulate_link: relink neighbors f%d and f%d of null facet f%d qh_triangulate_link: relink neighbors f%d and f%d of mirrored facets f%d and 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_mirror: delete mirrored facets f%d and f%d and link their neighbors qh_triangulate: triangulate non-simplicial facets qh_triangulate: delete null facets from facetlist f%d. A null facet has the same first (apex) and second vertices qhull internal error (qh_triangulate): ridges still defined for f%d qh_triangulate_null: delete null facet f%d qh_triangulate: delete %d or more mirrored facets. Mirrored facets have the same vertices due to a null facet qh_triangulate: update neighbor lists for vertices from v%d qh_triangulate: identify degenerate tricoplanar facets from f%d qh_triangulate: and replace facet->f.triowner with tricoplanar facets that own center, normal, etc. qh_triangulate: delete visible facets -- non-simplicial, null, and mirrored facets qh_triangulate: delete f%d. All tricoplanar facets degenerate for non-simplicial facet qhull internal error (qh_triangulate): tricoplanar facet f%d not owned by its visible, non-simplicial facet f%d qh_triangulate: all tricoplanar facets degenerate for last non-simplicial facet f%d flipped facetnon-convex initial simplexconcave ridgecoplanar ridgevertices for fridges for foutsideset for fcoplanarset for fneighbors for fvertices for rqh.facet_good hash %d f%d neighbors:neighbors for vqh_initialhull: qh.interior_pointinitial simplex is flat_narrow-hullqhull %s Statistics: %s | %s _Gqh_appendfacet: append f%d to facet_list qh_appendvertex: append v%d to qh.newvertex_list and set v.newfacet qh_attachnewfacets: delete interior ridges qh_attachnewfacets: attach horizon facets to new facets qhull internal error (qh_attachnewfacets): could not find visible facet for horizon f%d of newfacet f%d qh_attachnewfacets: clear f.ridges and f.neighbors for visible facets, may become invalid before qh_deletevisible qh_checkflipped: facet f%d flipped, allerror? %d, distance= %6.12g during p%d qh_removefacet: removed f%d from facet_list, newfacet_list, and visible_list qh_deletevisible: delete %d visible facets and %d vertices qhull internal error (qh_deletevisible): qh->num_visible %d is not number of visible facets %d qhull internal error (qh_facetintersect): f%d or f%d not in other's neighbors qh_facetintersect: f%d skip %d matches f%d skip %d qhull internal error: negative hashsize %d passed to qh_gethash [poly_r.c] qh_makenewplanes: make new hyperplanes for facets on qh.newfacet_list f%d qh_matchvertices: matched by skip %d(v%d) and skip %d(v%d) same? %d qh_matchneighbor: newfacet f%d skip %d hash %d hashcount %d two new facets with the same verticesqhull 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_matchneighbor: f%d skip %d matched with new f%d skip %d a ridge with more than two neighborsqhull 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) qhull topology error (qh_matchneighbor): matchfacet f%d is in f%d neighbors but not vice versa. Can not continue. qh_matchneighbor: new f%d skip %d duplicates ridge for f%d skip %d matching f%d ismatch %d at hash %d qh_matchneighbor: no match for f%d skip %d at hash %d qh_matchnewfacets: match neighbors for new facets. 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_matchnewfacets): %d neighbors did not match up qh_matchnewfacets: maxdupdist %2.2g, new facets %d, unused hash entries %d, hashsize %d qh_newfacet: created facet f%d qh_removevertex: remove v%d from qh.vertex_list qhull internal error (qh_makenew_nonsimplicial): simplicial f%d sharing two ridges with f%d qh_makenew_nonsimplicial: created facet f%d from v%d and r%d of horizon f%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 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. qh_newridge: created ridge r%d qh_update_vertexneighbors: update v.neighbors for qh.newvertex_list (v%d) and qh.newfacet_list (f%d) qh_update_vertexneighbors: delete %d of %d vertex neighbors for v%d. Removes to-be-deleted, visible facets qh_update_vertexneighbors: delete interior vertices for qh.visible_list (f%d) qh_update_vertexneighbors: delete interior vertex p%d(v%d) of visible f%d qh_update_vertexneighbors: delete old vertices for qh.visible_list (f%d) qh_update_vertexneighbors: will delete interior vertex p%d(v%d) of visible f%d qh_update_vertexneighbors_cone: update v.neighbors for qh.newvertex_list (v%d) and qh.newfacet_list (f%d) qh_update_vertexneighbors_cone: deleted %d visible vertexneighbors of v%d qh_update_vertexneighbors_cone: delete interior vertices, if any, for qh.visible_list (f%d) qh_update_vertexneighbors_cone: will delete interior vertex p%d(v%d) of visible f%d qh_update_vertexneighbors_cone: delete interior vertices for qh.visible_list (f%d) qh_delfacet: delete f%d ridge with multiple neighbors L%s set is null %p%s set=%p maxsize=%d size=%d elems=qhull internal error (qh_setaddnth): nth %d is out-of-bounds for set: qhull internal error (qh_setcheck): actual size %d of %s%d is greater than max size %d qhull internal error (qh_setcheck): %s%d(size %d max %d) is not null terminated. qhull internal error (qh_setdelnth): 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_settruncate): size %d out of bounds for set: qhull internal error (qh_setsize): current set size %d is greater than maximum size %d qhull internal error (qh_setreplace): elem %p not found in set qh_settemp: temp set %p of %d elements, depth %d qhull internal error (qh_settemppop): pop from empty temporary stack qh_settemppop: depth %d temp set %p of %d elements qhull error (qh_settemppush): can not push a NULL temp qh_settemppush: depth %d temp set %p of %d elements qhull internal error (qh_settempfree): set %p(size %d) was not last temporary allocated(depth %d, set %p, size %d) qhull internal error (qh_setzero): index %d or size %d out of bounds for set: (PQQPQDPQ4QTQP.EXE.exe *0 cnt*%7.2g%7d%7.3gprecision statisticsconcave half ridges in outputflipped facetssummary informationnumber of vertices in outputmaximum number of ridgesmaximum number of neighborsmaximum number of verticesfacets created altogetherridges created altogethervertices created altogetherfacets before post mergenumber of facets in outputtotal area of facets maximum facet area minimum facet area maximumbuild hull statisticspoints processed max. random jogglemax. vertices at any one timeaverage new facet balance standard deviation countaverage partition balancedeterminants for facet areapoints ignored (pinched apex)good facets found max. facets tested ave. facets tested ave. clearly betterresets of visit_id max visit_id/2 resets of vertex_visit max vertex_visit/2total vertices deletedcalls to findbest ave. coplanar searchcalls to findhorizoncalls to findbestnewcalls to findbestlowerinside pointsdistance tests for outputdistance tests for statisticspartitions of a pointdistance tests for best mergeconcave ridges in getmergesettwisted ridges in getmergesetstatistics for mergingmerge iterationsvertices deleted by merging max. facets ave. facets per cyclenew facets mergedmerged a simplexnon-convex vertex neighbors average merge distance maximum merge distancemerges due to coplanar facetsmerges due to concave facetsmerges due to dupridgesmerges due to twisted facetsstatistics for vertex merges found new vertex in ridge deleted max. found for a vertex ave. angle to ridge max. angle to ridge ave. distance to ridge max. distance to ridgebounded ridgesbounded ridges with ok normalVoronoi ridge statistics max. new facets created%6.2e ave. distance of a new vertex to a facetmax. distance of a new vertex to a facetmax. distance of an output vertex to a facetmin. distance of an output vertex to a facetmin. denominator in hyperplane computationprecision problems (corrected unless 'Q0' or an error)coplanar horizon facets for new verticescoplanar points during partitioningcoplanar half ridges in outputnearly singular or axis-parallel hyperplaneszero divisors during back substitutezero divisors during gaussian eliminationdegenerate hyperplanes recomputed with gaussian eliminationdupridges with multiple neighborsdupridges with flip facet into good neighbordupridges with flip facet into good flip neighbornumber of non-simplicial facets in outputsimplicial facets that were non-simplicialaverage number of neighbors per vertexcpu seconds for qhull after input maximum merges for a facet (at most 511)average merges per facet (at most 511)average number of neighbors per facetaverage number of ridges per facetaverage number of vertices per facetaverage cosine (angle) of facet normals for all ridges maximum cosine of facet normals (flatest) across a ridge minimum cosine of facet normals (sharpest) across a ridgeretries due to precision problemsave. visible facets per iteration ave. visible facets without an horizon neighbor ave. facets deleted per iterationave. visible vertices per iterationave. new or merged facets per iteration maximum (includes initial simplex)searches of all points for initial simplex determinants not computed because vertex too lowdeterminants for initial hull or voronoi verticespoints ignored (!above max_outside)points ignored (!above a good facet)points ignored (didn't create a good new facet)distance tests for facet visibilitydistance tests to report minimum vertexpoints checked for facets' outer planesave. horizon facets per iteration ave. distance tests per checkpartitioning statistics (see previous for outer planes) maximum vertices deleted per iteration calls due to qh_sharpnewfacets new bestfacets during qh_findbesthorizonangle tests for repartitioned coplanar points repartitioned coplanar points above a corner facet repartitioned coplanar points above a hidden facet repartitioned coplanar points above a twisted facet inside points that were coplanar with a facet with rare search of all facets facets per search of all facets with search of vertex neighborsdifference in max_outside at final checkdistance tests for partitioningdistance tests for initial partition near inside points kept with a facetdistance tests for checking flipped facetsdistance tests for checking convexitydistance tests for checking good pointtotal number of distance testspartitions of coplanar points or deleted vertices distance tests for these partitionsdistance tests for computing furthesttotal lookups for matching ridges of new facetstotal lookups of subridges (duplicates and boundary)average number of tests per subridgeaverage number of tests to match a ridgeduplicated ridges in same merge cycleduplicated ridges with flipped facetsstatistics for matching ridgesstatistics for determining mergesangles computed for ridge convexitybest merges used centrum instead of verticesdistance tests for centrum convexitydistance tests for checking simplicial convexitycoplanar angles in getmergesetcoplanar centrums or vertices in getmergesetconcave-coplanar ridges in getmergesetdistance tests for vertex convexitymax distance of vertex or coplanar point above facet (w/roundoff)max distance of vertex below facet (or roundoff)centrums frozen due to a wide mergecentrums frozen due to extra verticestotal number of facets or cycles of facets mergedsimplices merged into coplanar horizoncycles of facets merged into coplanar horizonvertices deleted by merging into coplanar horizonvertices deleted by degenerate facetmerges due to flipped facets in duplicated ridgehorizon facets merged into new facetsave. initial non-convex ridges per iterationinitial non-convex ridges for post mergingnew facets merged into coplanar horizonnew facets merged into horizon ave. additional non-convex ridges per iteration maximum additional in one pass additional non-convex ridgesmerges due to redundant neighbors detected by qh_test_nonsimplicial_merge instead of qh_test_redundant_neighborsmerges due to angle coplanar facetsmerges due to concave-coplanar facetscoplanar/concave merges due to avoiding old mergemerges due to degenerate facetsmerges due to removing flipped facetsmerge pinched vertices for a duplicate ridgemerge pinched vertices for a dupridgerenamed vertices shared by two facetsrenamed vertices shared by multiple facetsrenamed vertices in a pinched facetrename failures due to duplicated ridgesmerge degenerate facets due to dropped neighborsdropped neighbors due to renamed vertices facets deleted because of no neighborsdeleted ridges due to renamed verticesvertices removed from facets due to no ridges tot. merge pinched vertex due to dupridgeretry qh_addpoint after merge pinched vertex max. merge pinched vertex for a qh_addpoint ave. number found per vertexintersections found redundant verticesintersections failed to find a redundant vertexvertex intersections for locating redundant vertices ave. number of ridges per tested vertex max. number of ridges per tested vertexmemory usage statistics (in bytes)for facets and their normals, neighbor and vertex setsfor input points, outside and coplanar sets, and qhTfor ridges and their vertex setsfor vertices and their neighbor setsnon-simplicial Voronoi vertices for all ridgesbounded ridges with near-zero normal ave. distance of midpoint to ridge max. distance of midpoint to ridgeTriangulation statistics ('Qt')non-simplicial facets triangulated ave. new facets created (may be deleted)degenerate new facets in output (same ridge)mirrored pairs of new facets deleted (same vertices)null new facets deleted (duplicated vertex)qhull internal error: qh_checklists failed on qh_collectstatistics qhull internal error (qh_initstatistics): increase size of qhstat.id[]. qhstat.next %d should be <= sizeof(qh->qhstat.id) %d qhull warning (qh_stddev): expecting num > 0. Got num %d, tot %4.4g, tot2 %4.4g. Returning 0.0 %s qhull invoked by: %s | %s %s with options: %s 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 %6.2g max. distance for near-inside points %6.2g max. cosine for pre-merge angle %6.2g radius of pre-merge centrum %6.2g max. cosine for post-merge angle %6.2g radius of post-merge centrum %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: BC) W&(Awtyz*Ixnו78i?D56Z\[]cedfg__cc'uگ9:;<>EjmklSOF@$%Gv؊-!#" /H^4NM3KLZZkj-%s VERTEX: %s RIDGE: %s FACET: %s OTHER FACET: printfacetlist: vertices printfacetlist: facetlist printfacetlist: %d facets printfacetlist: end center point distance= %4.2g _maxoutside While executing: %s | %s At error exit: at error exitERRONEOUS and NEIGHBORING FACETS to output A Qhull error has occurred. Qhull should have corrected the above precision error. Please send the input and all of the output to qhull_bug@qhull.org 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. When computing the Delaunay triangulation of coordinates > 1.0, - use 'Qbb' to scale the last coordinate to [0,m] (max previous coordinate) When computing the Delaunay triangulation: - use 'Qz' to add a point at-infinity. This reduces precision problems. 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 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) A Qhull internal error has occurred. Please send the input and output to qhull_bug@qhull.org. If you can duplicate the error with logging ('T4z'), please include the log file. 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. 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: 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: These points are the dual of the given halfspaces. They indicate that the intersection 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. 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'. The min and max coordinates for each dimension are: 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. 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. %d: %8.4g %8.4g difference= %4.4g qhull error while handling previous error in qh_errexit. Exit program Last point added to hull was p%d. Qhull has finished constructing the hull. Qhull has started post-merging.qhull exit due to qh_ERRdebug 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 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 qhull internal error (qh_errexit): exit code %d is greater than 255. Invalid argument for exit(). Replaced with 255 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 @QH%.4d qhull internal error (userprintf_r.c): fp and qh not defined for qh_fprintf '%s' qhull internal error (userprintf_r.c): fp is 0. Wrong qh_fprintf was called. 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