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At:
  ): 
MESSAGE UNAVAILABLE DUE TO EXCEPTION: pybind11::detail::error_stringUnable to cast Python instance of type  to C++ type '?' (#define PYBIND11_DETAILED_ERROR_MESSAGES or compile in debug mode for details)Unexpected PYBIND11_BYTES_AS_STRING() failure.Unexpected PyByteArray_AsString() failure.Unable to cast Python  instance to C++ rvalue: instance has multiple references (#define PYBIND11_DETAILED_ERROR_MESSAGES or compile in debug mode for details)pybind11::detail::get_internals_pp_from_capsule() FAILEDInternal error: pybind11::detail::error_fetch_and_normalize::restore() called a second time. ORIGINAL ERROR: pybind11_function_record_capsuleCould not allocate string object!Caught an unknown exception!Caught an unknown nested exception!pybind11_static_propertymake_static_property_type(): error allocating type!make_static_property_type(): failure in PyType_Ready()!__module__pybind11_builtins__dict__pybind11_typemake_default_metaclass(): error allocating metaclass!make_default_metaclass(): failure in PyType_Ready()!%.200s.__init__() must be called when overriding __init____init____setstate__*, selfarg = , /Internal error while parsing type signature (1).__qualname__Internal error while parsing type signature (2)Cannot overload existing non-function object "" with a function of the same name__name__cpp_function::cpp_function(): Could not allocate function objectoverloading a method with both static and instance methods is not supported; #define PYBIND11_DETAILED_ERROR_MESSAGES or compile in debug mode for more details_pybind11_conduit_v1_(*args, **kwargs)
Overloaded function.

. cpp_function::cpp_function(): Could not allocate instance method objectvectorpybind11::__init__(self, ...) called with invalid or missing `self` argument(): incompatible constructorfunction arguments. The following argument types are supported:
    , 
Invoked with: <repr raised Error>; kwargs: {}=Unable to convert function return value to a Python type! The signature was
	pybind11::detail::get_type_info: type has multiple pybind11-registered basespybind11::detail::instance::get_value_and_holder: type is not a pybind11 base of the given instance (#define PYBIND11_DETAILED_ERROR_MESSAGES or compile in debug mode for type details)Could not allocate tuple object!Could not allocate dict object!loader_life_support: internal errorException escaped from default exception translator!formatUnable to convert call argument '' to Python object (#define PYBIND11_DETAILED_ERROR_MESSAGES or compile in debug mode for details)

Did you forget to `#include <pybind11/stl.h>`? Or <pybind11/complex.h>,
<pybind11/functional.h>, <pybind11/chrono.h>, etc. Some automatic
conversions are optional and require extra headers to be included
when compiling your pybind11 module.Could not allocate weak reference!pybind11_objectmake_object_base_type(): error allocating type!PyType_Ready failed in make_object_base_type(): instance allocation failed: new instance has no pybind11-registered base types: No constructor defined!pybind11_object_dealloc(): Tried to deallocate unregistered instance!FATAL: Internal consistency check failed: Invalid clear_patients() call.Internal error in module_::create_extension_module()Computing Delaunay triangulations.
xyverbose--

Compute a Delaunay triangulation.

Parameters
----------
x, y : 1d arrays
    The coordinates of the point set, which must consist of at least
    three unique points.
verbose : int
    Python's verbosity level.

Returns
-------
triangles, neighbors : int arrays, shape (ntri, 3)
    Indices of triangle vertices and indices of triangle neighbors.
versionversion()
--

Return the qhull version string.__doc__multiarray_ARRAY_APIFAILURE obtaining numpy _ARRAY_API pointer.pybind11 numpy support requires numpy >= 1.7.0numpy__version__numpy.libNumpyVersionmajornumpy._corenumpy.coreNumPy: shape ndim doesn't match strides ndimcannot create a pybind11::array_t from a nullptrarg(): cannot specify an unnamed argument after a kw_only() annotation or args() argumentx and y must be 1D arraysx and y must be 1D arrays of the same lengthx and y arrays must have a length of at least 3x and y arrays must consist of at least 3 unique points/dev/nullCould not open devnullqhull d Qt Qbb Qc QzError in qhull Delaunay triangulation calculation: {} (exitcode={}); use python verbose option (-v) to see original qhull error.input inconsistencysingular input dataprecision errorinsufficient memoryinternal errorarray is not writeableQhull could not free all allocated memoryqhull error: insufficient memory to copy %d points
qhull internal error (qh_determinate): only implemented for dimension >= 2
qh_detjoggle: joggle=%2.2g maxwidth=%2.2g
qh_detmaxoutside: MAXoutside %2.2g from qh.max_outside %2.2g, ONEmerge %2.2g, MINoutside %2.2g, DISTround %2.2g
_max-widthError-roundoffqh_detroundoff: increase qh.ANGLEround by option 'R%2.2g'
Angle-premerge-with-randomAngle-postmerge-with-randomCentrum-premerge-with-randomCentrum-postmerge-with-random_one-merge_near-insideqhull option error: the joggle for 'QJn', %.2g, is below roundoff for distance computations, %.2g
Visible-distanceU-max-coplanarWidth-outside_wide-facetqhull input warning: minimum visibility V%.2g is greater than 
minimum outside W%.2g.  Flipped facets are likely.
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_facetarea: f%d area %2.2g
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_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)
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.
_joggle-seedqh_joggleinput: joggle input by %4.4g with seed %d
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
input has same x coordinateqhull 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
%6.3g 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 internal error (qh_projectpoints): newdim %d should be %d after projection
qh_projectpoints: projected %d points from dim %d to dim %d
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
qh_sethalfspace: halfspace at offset %6.2g to point:  %6.2gqhull input error: feasible point is not clearly inside halfspace
feasible point: 
     halfspace: 
     at offset:  and distance: qh_sethalfspace_all: compute dual for halfspace intersection
qhull error: insufficient memory to compute dual of %d halfspaces
The halfspace was at index %d
qh_sharpnewfacets: %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 center:p%d dist %.2g, qh_distplane: from p%d to f%d
qh_findbest: point p%d starting at f%d isnewfacets? %d, unless %d exit if > %2.2g, testhorizon? %d, noupper? %d, Last qh_addpoint p%d, Last merge #%d, max_outside %2.2g
qh_findbest: neighbors of f%d, bestdist %2.2g f%d
qh_findbesthorizon: test neighbors of f%d bestdist %2.2g f%d ischeckmax? %d noupper? %d minsearch %2.2g is_5x? %d searchdist %2.2g
qh_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, Last merge #%d
qh_findbestnew: bestfacet f%d bestdist %2.2g for p%d f%d bestoutside? %d 
qh_backnormal: zero diagonal at column %d.
zero diagonal on back substitutionqh_gausselim: 0 pivot at column %d. (%2.2g < %2.2g)
Matrix:zero pivot for Gaussian eliminationqh_gausselem: resultqh_getangle: %4.4g
qhull 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_setfacetplane: facet f%d created.
  Last point added to hull was p%d.

Current summary is:
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: %2.2g 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_freebuffers: freeing up global memory buffers
qh_freebuffers: finished
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 internal error (qh_initflags): qh.NOerrexit was not cleared before calling qh_initflags().  It should be cleared after setjmp().  Exit qhull.
delaunayfacetsincidencemathematicanormalsoffFilepointssummaryvoronoiqhull input warning: no maximum cosine angle given for option 'An'.  A1.0 is coplanar
Angle-premerge-Angle-postmergeqhull input warning: no centrum radius given for option 'Cn'
Centrum-premerge-Centrum-postmergeqhull option error: expecting a positive number for maximum roundoff 'En'.  Got '%s'
qhull option warning: no maximum roundoff given for option 'En'
Distance-roundoffqhull option error: expecting 'Hn,n,n,...' for feasible point of halfspace intersection. Got '%s'
Halfspace-aboutHalfspaceqhull option warning: missing random perturbation for option 'Rn'
Random-perturbqhull option warning: missing visible distance for option 'Vn'
Visibleqhull option warning: missing coplanar distance for option 'Un'
U-coplanarqhull option error: expecting a positive number for outside width 'Wn'.  Got '%s'
qhull option warning: missing outside width for option 'Wn'
W-outsideFareaFArea-totalFcoplanarsFCentrumsFd-cdd-inFD-cdd-outFFacets-xridgeFinnerFIDsFmergesFMapleFneighborsFNeighbors-vertexFouterFOptionsFpoint-intersectFPoint-nearestFQhullFsummaryFSizeFtrianglesFVertex-averageFxtremesqhull option warning: unknown 'F' output option 'F%c', skip to next space
Gall-pointsGcentrumsGintersectionsGinnerGno-planesGouterGpointsGridgesGtransparentGverticesqhull option warning: missing dimension for option 'GDn'
qhull option warning: can only drop one dimension.  Previous 'GD%d' ignored
GDrop-dimqhull option warning: unknown 'G' geomview option 'G%c', skip to next space
Pdrop-facets-dim-lessPDrop-facets-dim-morePgood-facetsPGood-facet-neighborsPoutput-forcedPprecision-ignoreqhull option warning: missing facet count for keep area option 'PAn'
PArea-keepqhull option warning: missing facet area for option 'PFn'
PFacet-area-keepqhull option warning: missing merge count for option 'PMn'
PMerge-keepqhull option warning: unknown 'P' print option 'P%c', skip to next space
Qallow-shortQbBound-unit-boxQbbound-lastqh_initflags: project dimension %d
Qb-project-dimQbound-dim-lowQBound-dim-highQcoplanar-keepQfurthest-outsideQgood-facets-onlyQinterior-keepQmax-outside-onlyQrandom-outsideQsearch-initial-simplexQtriangulateQTestPointsqhull option warning: missing number of test points for option 'QTn'
QupperDelaunayQvertex-neighbors-convexQxact-mergeQz-infinity-pointQ0-no-premergeQ1-angle-mergeQ10-no-narrowQ11-trinormals QtriangulateQ12-allow-wideQ14-merge-pinched-verticesQ15-check-duplicatesqhull option warning: unknown 'Q' qhull option 'Q1%c', skip to next space
Q2-no-merge-independentQ3-no-merge-verticesqhull option warning: can not follow '1', '2', or '3' with a digit.  'Q%c%c' skipped
Q4-avoid-old-into-newQ5-no-check-outerQ6-no-concave-mergeQ7-no-breadth-firstQ8-no-near-insideQ9-pick-furthestqhull option warning: good point already defined for option 'QGn'.  Ignored
qhull option warning: missing good point id for option 'QGn'.  Ignored
QGood-if-dont-see-pointQGood-if-see-pointQJoggleqhull option warning: missing random seed for option 'QRn'
QRotate-idQRandom-seedqhull option warning: good vertex already defined for option 'QVn'.  Ignored
qhull option warning: no good point id given for option 'QVn'.  Ignored
QV-good-facets-not-pointQV-good-facets-pointQwarn-allowqhull option warning: unknown 'Q' qhull option 'Q%c', skip to next space
Tannotate-outputTcheck-frequentlyTflushTstatisticsTverifyTz-stdoutqhull option warning: output file undefined(stdout).  Option 'Tz' ignored.
qhull option warning: missing point id for cone for trace option 'TCn'
TCone-stopqhull option warning: missing frequency count for trace option 'TFn'
TFacet-logrqhull option error: cannot open 'TI' file "%s"
TInput-fileqhull option warning: qh.fout was not set by caller of qh_initflags.  Cannot use option 'TO' to redirect output.  Ignoring option 'TO'
wqhull option error: cannot open file "%s" for writing as option 'TO'.  It is already in use or read-only
TOutput-fileqhull option warning: missing count of added points for trace option 'TAn'
TA-stop-addTrace-pointqhull 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'
Trace-mergeqhull option warning: missing rerun count for trace option 'TRn'
TRerunqhull option warning: missing furthest point id for trace option 'TVn'
TV-stop-before-pointTV-stop-after-pointqhull option warning: missing max width for trace option 'TWn'
TWide-traceqhull 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
qhull option error: see previous warnings, use 'Qw' to override: '%s' (last offset %d)
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
_pre-mergeqhull 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
Qbbound-last-qj_zero-centrumqhull 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
Q3-no-merge-vertices-dim-highqh_initqhull_globals: trace last of TR%d runs at level %d
QRotate-randomqhull 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)
qh_initqhull_outputflags: %s
Pgoodqhull 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')
FvoronoiFverticesqhull 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.
Qcoplanarqhull option warning: drop dimension 'GD%d' is only available for 3-d/4-d Geomview
run-idqhull 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 internal error (qh_option): option (%d chars) has more than %d chars.  May overflow temporary buffer.  Option '%s'
  %s %2.2gqh_option: option would overflow qh.qhull_options. Truncated '%s'
qhull internal error (qh_produce_output): temporary sets not empty(%d)
    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 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
%6.16g 0
%d%d
no normal for facet f%d
qhull input error (qh_printafacet): option 'Fp' needs qh->feasible_point
%d %d %d %6.16g 
1 %d
%d
Vertices and facets:
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
LIST # %s | %s
4VECT %d %d 1
VECT %d %d 1
# 1 point per line
1 0 # 1 color for all
0 1 1 1  # color of points
4OFF %d %d 1
qhull warning: input sites of Delaunay regions (option 'i').  Use option 'p' or 'o' for Voronoi centers.  Disable warning with option 'Pp'
%s | %s
begin
    %d %d real
qhull warning: output is the Delaunay triangulation
PLOT(CURVES(
PLOT3D(POLYGONS(
{
%d
%d %d %d
%s | %s
begin
%d %d real
qhull internal error (qh_printbegin): can not use this format for dimension %d
 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
%8.4g %8.4g %8.4g 0
1 }}}
qhull warning: no facets printed
qhull internal error (qh_printend): number of ridges %d != number printed %d and at end %d
}
end
));
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 internal error (qh_printextremes_2d): loop in facet list.  facet %d nextfacet %d
VECT 1 2 1 2 1 # f%d
%8.4g %8.4g %8.4g
%8.4g %8.4g %8.4g
%8.4g %8.4g %8.4g 1.0
,[[%16.8f, %16.8f], [%16.8f, %16.8f]]
Line[{{%16.8f, %16.8f}, {%16.8f, %16.8f}}]
{ OFF %d 1 1 # f%d
%8.4g %d %8.4g %8.4g %8.4g 1.0 }
,
[[%16.8f, %16.8f, %16.8f]]Polygon[{{%16.8f, %16.8f, %16.8f}}]%sOFF 3 1 1 # f%d
# r%d between f%d f%d
3 0 1 2 %8.4g %8.4g %8.4g
OFF 3 1 1 # ridge between f%d f%d
# ridge between f%d f%d
 MERGEridge
 DUPLICATEridge
 NULLfacet
- f%d
    - flags: top bottom simplicial tricoplanar upperDelaunay visible newfacet tested notG seen seen2 isarea coplanarhorizon mergehorizon cycledone keepcentrum dupridge mergeridge1 mergeridge2 newmerge flipped notfurthest degenerate redundant    - area: %2.2g
    - replacement: f%d
    - shares same visible/horizon as f%d
    - owner of normal & centrum is facet f%d
    - was horizon to f%d
    - merges: %dmax
    - merges: %d
    - normal:     - offset: %10.7g
    - center:     - maxoutside: %10.7g
    - outside set(furthest p%d):
         - outside set:    - outside set:  %d points.  Furthest    - furthest distance= %2.2g
    - coplanar set(furthest p%d):
    - coplanar set:    - coplanar set:  %d points.      furthest distance= %2.2g
    - vertices:    - neighboring facets: MERGEridge DUPLICATEridge    - ridges (tentative ids): r%d    - ridges:
     - horizon ridge to visible facet
     - all ridges:qhull warning: CDD format is not available for centrums, halfspace
intersections, and OFF file format.
%d 1
%s | %s
0
2 10 %d %d %d %d %d %d %d %d %d %d
2 %6.16g %6.16g
VECT 1 %d 1 %d 1 OFF 3 1 1 # intersect f%d f%d
%8.4g %8.4g %8.4g # %8.4g %8.4g %8.4g %8.4g # p%d(coplanar facets)
projected p%d
3 0 1 2 %8.4g %8.4g %8.4g 1.0
VECT 1 2 1 2 1
 # p%d
VECT 1 1 1 1 1
%8.4g %8.4g %8.4g 1
 p%d:  %8.4g     - r%d nonconvex mergevertex mergevertex2 simplicialtop simplicialbot           vertices:           between f%d and f%d
{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
1
}}}
qhull internal error (qh_printvdiagram): unknown print format %d.
  NULLvertex
- p%d(v%d): %5.2g deleted delridge  neighbors: p%d(v%d)1 %d
{appearance {+edge -face} OFF %d %d 1 # Voronoi centers and cells
%d
%d %d 1
 0 # infinity not used
# %d f%d
 # p%d(v%d)
 # p%d is coplanar or isolated
%d %d %d %d %d %dqhull input error: halfspace intersection needs a feasible point.  Either prepend the input with 1 point or use 'Hn,n,n'.  See manual.
qhull error: insufficient memory for 'Hn,n,n'
qhull input warning: more coordinates for 'H%s' than dimension %d
qhull input error: filename expected, none found.
qhull input error: missing quote after filename -- %s
qh_qhull: all facets are clearly convex and no coplanar points.  Post-merging and check of maxout not needed.
First post-mergeFor testing vertex neighborsFor post-mergingqh_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: algorithm completed
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
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
_runqh_buildcone: created %d newfacets for p%d(v%d) new facet 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

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
coplanar horizonqh_findhorizon: point p%d is coplanar to horizon f%d, dist=%2.7g < qh->MINvisible(%2.7g)
horizonempty horizonqhull 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
qh_joggle_restart: qhull restart because of %s
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
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
DISTANTqh_partitioncoplanar: point p%d is coplanar with facet f%d (or inside) dist %2.2g
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)
nearly incident pointqh_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_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_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
 and at-infinity  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
 'good'  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 halfspaces: %d
  Number of non-redundant halfspaces: %d
similar and redundantsimilar  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 vertices: %d
coplanar and interiorinterior  Number of %s points: %d
  Number of facets: %d
  Number of 'good' facets: %d
  Number of%s non-simplicial facets: %d
  Number of triangulated facets: %d

Statistics for: %s | %s QR%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
  Input joggled by: %2.2g
  %s facet area:   %2.8g
ApproximateTotal  %s volume:       %2.8g
  Maximum distance of point above facet: %2.2g (%.1fx)
  Maximum distance of vertex below facet: %2.2gqhull 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->%dnonecoplanaranglecoplanarconcaveconcavecoplanartwistedflipdupridgesubridgeverticesdegenredundantmirrorcoplanarhorizonqh_premerge: premerge centrum %2.2g angle %4.4g for apex p%d newfacet_list f%d
reason
%s with 'C%.2g' and 'A%.2g'
qh_postmerge: postmerge.  test vneighbors? %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_all_vertexmerges: starting to merge %d vertex merges for apex p%d facet f%d
qh_appendmergeset: f%d is already redundant (%d) or f%d is already redundant (%d).  Ignore merge f%d and f%d type %d
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_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
qh_checkzero: skip convexity check until first pre-merge
qh_checkzero: testall %d, facets are %s
not concave, flipped, or dupridgeclearly convexqh_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_find_newvertex: find new vertex for v%d from r%d 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
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_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
qh_flippedmerges: begin
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_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)
qh_getmergeset: started.
qh_getmergeset: %d merges found
qh_getmergeset_initial: %d merges found
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_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
makeridges: appended r%d to ridges for f%d.  Next is ridges for neighbor 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_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_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
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_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_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
  same cycle: f%dMERGING CYCLEqhull internal error (qh_mergecycle): does not work for tricoplanar facets.  Use option 'Q11'
qh_mergecycle: end of trace facet
qh_mergecycle_all: merge new facets into coplanar horizon facets.  Bulk merge a cycle of facets with the same horizon facet
qhull internal error (qh_mergecycle_all): f%d without normal
qh_mergecycle_all: merged %d same cycles or facets into coplanar horizons and %d degenredundant facets
qh_mergecycle_facets: make newfacet new and samecycle deleted
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
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.
MERGINGqh_mergefacet: end of wide tracing
qh_mergefacet: check f%d and f%d for redundant and degenerate neighbors
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_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_del: deleted v%d when merging f%d into 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
TRACEqhull internal error (qh_mergevertices): facets did not share a ridge
qh_neighbor_intersections: %d vertices in neighbor intersection of v%d
qh_neighbor_vertices: %d non-subridge, vertex neighbors for v%d
qh_neighbor_vertices_facet: found %d vertex neighbors for v%d in f%d (simplicial? %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)
qh_reducevertices: reduce extra vertices, shared vertices, and redundant vertices
qh_reducevertices: renamed %d shared vertices and %d redundant vertices. Degen? %d
qh_redundant_vertex: check if v%d from a deleted ridge can be renamed
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_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_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_renamevertex: rename v%d to v%d in %d ridges with old f%d and neighbor f%d
qh_renamevertex: ignore duplicate check for r%d.  top f%d (size %d) will be degenerate after rename v%d to v%d
qh_renamevertex: ignore duplicate check for r%d.  bottom f%d (size %d) will be degenerate after rename v%d to v%d
qh_renamevertex: renaming v%d to v%d in several facets for qh_redundant_vertex or MRGsubridge
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_appendmerge: coplanar angle %4.4g between f%d and f%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_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_test_vneighbors: testing vertex neighbors for convexity
qh_test_vneighbors: found %d non-convex, vertex neighbors
MERGEDqh_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_vertexridges: found %d ridges for v%d
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_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.
good 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_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)
qhull precision error: point p%d is outside facet f%d, distance= %6.8g maxoutside= %6.8g nearest vertices %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_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)
non-convex initial simplexqhull 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)
concave ridgeqhull precision error: f%d is concave to f%d, since p%d(v%d) is %6.4g above f%d
coplanar ridgeqhull 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
vertices for fridges for foutsideset for fcoplanarset for fneighbors for fqhull 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
vertices for rqhull 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
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_checklists: check qh.%s_list f%d and qh.vertex_list v%d
newfacetvisibleqh_checklists: check %slist f%d and qh.vertex_list v%d
qh.facet_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
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
neighbors for vqhull 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.
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_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
qh_findfacet_all: p%d, noupper? %d, 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_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
qhull %s Statistics: %s | %s
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_initialhull: qh.interior_pointqh_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
initial simplex is flatQhull precision error: Initial simplex is flat (facet %d is coplanar with the interior point)
_narrow-hullqh_initialhull: simplex constructed
qh_makenewfacets: created %d new facets f%d..f%d from point p%d to horizon
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
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_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_prependfacet: prepend f%d before f%d
hash %d f%d v%d 
 neighbors: %dqh_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_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_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: 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
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_null: delete null facet f%d
qh_vertexneighbors: determining neighboring facets for each vertex
qh_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
flipped facetqh_delfacet: delete f%d
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
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
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
ridge with multiple neighborsqhull 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_matchvertices: matched by skip %d(v%d) and skip %d(v%d) same? %d
qh_newfacet: created facet f%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_removefacet: removed f%d from facet_list, newfacet_list, and visible_list
qh_removevertex: remove v%d from qh.vertex_list
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)
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:
%s set is null
%s set=%p maxsize=%d size=%d elems= %pqhull internal error (qh_setreplace): elem %p not found in set
qhull internal error (qh_setsize): current set size %d is greater than maximum size %d
set: qh_settemp: temp set %p of %d elements, depth %d
qhull internal error (qh_settempfree): set %p(size %d) was not last temporary allocated(depth %d, set %p, size %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_settruncate): size %d out of bounds for set:
qhull internal error (qh_setzero): index %d or size %d out of bounds for set:
precision statisticsave. 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 half ridges in outputconcave half ridges in outputflipped facetscoplanar horizon facets for new verticescoplanar points during partitioningdegenerate hyperplanes recomputed with gaussian eliminationnearly singular or axis-parallel hyperplaneszero divisors during back substitutezero divisors during gaussian eliminationdupridges with multiple neighborsdupridges with flip facet into good neighbordupridges with flip facet into good flip neighborsummary informationnumber of vertices in outputnumber of facets in outputnumber of non-simplicial facets in outputsimplicial facets that were non-simplicialaverage number of ridges per facetmaximum number of ridgesaverage number of neighbors per facetmaximum number of neighborsaverage number of vertices per facetmaximum number of verticesaverage number of neighbors per vertexcpu seconds for qhull after inputvertices created altogetherfacets created altogetherridges created altogetherfacets before post mergeaverage merges per facet (at most 511)  maximum merges for a facet (at most 511)average 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 ridgetotal area of facets  maximum facet area  minimum facet areabuild hull statisticspoints processedretries due to precision problems  max. random jogglemax. vertices at any one timeave. visible facets per iteration  ave. visible facets without an horizon neighbor  ave. facets deleted per iteration    maximumave. visible vertices per iterationave. horizon facets per iterationave. new or merged facets per iteration    maximum (includes initial simplex)average new facet balance  standard deviationaverage partition balance  countsearches of all points for initial simplexdeterminants for facet area  determinants not computed because vertex too lowdeterminants for initial hull or voronoi verticespoints ignored (!above max_outside)points ignored (pinched apex)points ignored (!above a good facet)points ignored (didn't create a good new facet)good facets founddistance tests for facet visibilitydistance tests to report minimum vertexpoints checked for facets' outer planes  ave. distance tests per checkresets of visit_id  resets of vertex_visit  max visit_id/2  max vertex_visit/2partitioning statistics (see previous for outer planes)total vertices deleted    maximum vertices deleted per iterationcalls to findbest ave. facets tested max. facets tested ave. coplanar searchcalls to findbestnew ave. clearly better calls due to qh_sharpnewfacetscalls to findhorizon 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 facetinside points  near inside points kept with a facet  inside points that were coplanar with a facetcalls to findbestlower  with search of vertex neighbors  with rare search of all facets  facets per search of all facetsdifference in max_outside at final checkdistance tests for initial partitionpartitions of a pointdistance tests for partitioningdistance tests for checking flipped facetsdistance tests for checking convexitydistance tests for checking good pointdistance tests for outputdistance tests for statisticstotal number of distance testspartitions of coplanar points or deleted vertices   distance tests for these partitionsdistance tests for computing furtheststatistics for matching ridgestotal lookups for matching ridges of new facetsaverage number of tests to match a ridgetotal lookups of subridges (duplicates and boundary)average number of tests per subridgeduplicated ridges in same merge cycleduplicated ridges with flipped facetsstatistics for determining mergesangles computed for ridge convexitybest merges used centrum instead of verticesdistance tests for best mergedistance tests for centrum convexitydistance tests for vertex convexitydistance tests for checking simplicial convexitycoplanar angles in getmergesetcoplanar centrums or vertices in getmergesetconcave ridges in getmergesetconcave-coplanar ridges in getmergesettwisted ridges in getmergesetstatistics for mergingmerge iterationsave. initial non-convex ridges per iteration  maximum  ave. additional non-convex ridges per iteration  maximum additional in one passinitial non-convex ridges for post merging  additional non-convex ridgesmax 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 mergedmerged a simplexsimplices merged into coplanar horizoncycles of facets merged into coplanar horizon  ave. facets per cycle  max. facetsnew facets merged into coplanar horizonnew facets merged into horizonnew facets mergedhorizon facets merged into new facetsvertices deleted by mergingvertices deleted by merging into coplanar horizonvertices deleted by degenerate facetmerges due to flipped facets in duplicated ridgemerges due to redundant neighbors  detected by qh_test_nonsimplicial_merge instead of qh_test_redundant_neighborsnon-convex vertex neighborsmerges due to angle coplanar facets  average merge distance  maximum merge distancemerges due to coplanar facetsmerges due to concave facetsmerges due to concave-coplanar facetscoplanar/concave merges due to avoiding old mergemerges due to degenerate facetsmerges due to removing flipped facetsmerges due to dupridgesmerges due to twisted facetsstatistics for vertex mergesmerge pinched vertices for a duplicate ridgemerge pinched vertices for a dupridgerenamed vertices shared by two facetsrenamed vertices in a pinched facetrenamed vertices shared by multiple facetsrename failures due to duplicated ridges  found new vertex in ridgedeleted ridges due to renamed verticesdropped neighbors due to renamed verticesmerge degenerate facets due to dropped neighbors  facets deleted because of no neighborsvertices removed from facets due to no ridges  deletedretry qh_addpoint after merge pinched vertex  tot. merge pinched vertex due to dupridge  max. merge pinched vertex for a qh_addpointvertex intersections for locating redundant verticesintersections failed to find a redundant vertexintersections found redundant vertices   ave. number found per vertex   max. found for a vertex  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 vertices and their neighbor setsfor input points, outside and coplanar sets, and qhTfor ridges and their vertex setsVoronoi ridge statisticsnon-simplicial Voronoi vertices for all ridges  ave. distance to ridge  max. distance to ridgebounded ridges  ave. distance of midpoint to ridge  max. distance of midpoint to ridgebounded ridges with ok normal  ave. angle to ridge  max. angle to ridgebounded ridges with near-zero normalTriangulation statistics ('Qt')non-simplicial facets triangulated  ave. new facets created (may be deleted)  max. new facets creatednull new facets deleted (duplicated vertex)mirrored pairs of new facets deleted (same vertices)degenerate new facets in output (same ridge)qhull internal error: qh_checklists failed on qh_collectstatistics

%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: %6.2e 

%s
 *0 cnt*%7.2g%7d%7.3g %s
qhull warning (qh_stddev): expecting num > 0.  Got num %d, tot %4.4g, tot2 %4.4g.  Returning 0.0
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.
[QH%.4d]QH%.4d qhullqh_new_qhull: initialize Qhull
qh_new_qhull: build new Qhull for %d %d-d points with %s

qhull error while handling previous error in qh_errexit.  Exit program
ERRONEOUS_maxoutside
While executing: %s | %s
Options selected for Qhull %s:
%s
Last point added to hull was p%d.  Last merge was #%d.
Qhull has finished constructing the hull.
Qhull has started post-merging.

At error exit:
at error exitqhull internal error (qh_errexit): either error while reporting error QH%d, or qh.NOerrexit not cleared after setjmp(). Exit program with error status %d
%s VERTEX:
%s RIDGE:
%s FACET:
%s OTHER FACET:
ERRONEOUS and NEIGHBORING FACETS to output
printfacetlist: vertices
printfacetlist: facetlist
printfacetlist: end

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:

center pointfacet p%d distance= %4.2g

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:
  %d:  %8.4g  %8.4g  difference= %4.4g

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.

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
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