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H  JH  JH  JHF   ?   &  " "`2 a\#&#l`h" #gh@@Y#&#㿘@V''& D\ј`" $`aD**  "`' " "2  a\ l`h" gh@@Yf8!/"a\ l`h" gh@@Y? &      `D?`$``  ` "D`?`2`@UH@`Too many output arguments.qhull Not enough points.qhull internal warning (main): did not free %d bytes of long memory (%d pieces) qhull qh_new_qhull: build new Qhull for %d %d-d points with %s qh_freebuffers: freeing up global memory buffers qh_freebuffers: finished qh_freebuild: free memory from qh_inithull and qh_buildhull qh_freeqhull: free global memory .EXE.exe qh_initflags: project dimension %d wqh_initqhull_globals: for %s | %s qh_initqhull_globals: initialize globals. dim %d numpoints %d malloc? %d projected %d to hull_dim %d qhull %s %d %2.2g qh_detjoggle: joggle=%2.2g maxwidth=%2.2g qh_detsimplex: det=%2.2g for point p%d, dim %d, nearzero? %d qh_distround: %2.2g maxabs %2.2g maxsumabs %2.2g maxdistsum %2.2g qh_facetarea: f%d area %2.2g 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_getarea: computing volume and area for each facet qh_joggleinput: joggle input by %2.2g with seed %d qh_maxouter: max distance from facet to outer plane is %2.2g max_outside is %2.2g qh_maxsimplex: searching all points for %d-th initial vertex. qh_maxsimplex: searching all points for %d-th initial vertex, better than p%d det %2.2g qh_maxsimplex: selected point p%d for %d`th initial vertex, det=%2.2g qh_projectinput: updating lower and upper_bound qh_projectinput: projected points to paraboloid for Delaunay qh_projectpoints: projected %d points from dim %d to dim %d qh_scalelast: scale last coordinate from [%2.2g, %2.2g] to [0,%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_all: compute dual for halfspace intersection 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 qh_check_bestdist: max distance outside %2.2g qh_check_maxout: check and update maxoutside for each facet. qh_check_maxout: determine actual maxoutside and minvertex qh_check_maxout: maxoutside %2.2g, min_vertex %2.2g, outside of not good %d qh_check_points: check all points below %2.2g of all facet planes qh_check_points: max distance outside %2.2g qh_checkconvex: check all ridges are convex qhull precision error: f%d may be coplanar to f%d, since p%d (v%d) is within %6.4g during p%d qh_checkpolygon: check all facets from f%d qh_clearcenters: switched to center type %d qh_createsimplex: created simplex qh_findbestfacet: f%d dist %2.2g isoutside %d totpart %d qh_findfacet_all: 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 qh_findgood_all: f%d is closest (%2.2g) to thresholds 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 qh_initbuild: initial hull created and points partitioned qh_initialhull: initial orientation incorrect. Correct all facets qh_makenewfacets: created %d new facets from point p%d to horizon qh_matchduplicates: find duplicate matches for f%d skip %d hash %d hashcount %d qh_matchduplicates: duplicate f%d skip %d matched with new f%d skip %d merge qh_matchduplicates: duplicate f%d skip %d new f%d skip %d at dist %2.2g, max is now f%d f%d qh_matchduplicates: duplicate f%d skip %d matched with new f%d skip %d keep qh_newvertex: vertex p%d (v%d) created qh_outcoplanar: move outsideset to coplanarset for qh NARROWhull qh_prependfacet: prepend f%d before f%d qh_vertexneighbors: determing neighboring facets for each vertex qh_detvnorm: too few points (%d) to compute separating plane qh_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 qh_detvridge3: neigbors 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 neighbors of v%d for 3-d qhull internal error (qh_order_vertexneighbors): no neighbor of v%d for f%d %6.16g 0 %d %d %d %d no normal for facet f%d %6.16g %6.16g %6.16g %d %d qhull input error (qh_printafacet): option 'Fp' needs qh feasible_point %6.16g %d %d %d %6.16g %d %d %d %d %d %d qhull warning: output for ridges and intersections not implemented in 2-d qhull warning: output for outer/inner planes and centrums not implemented in 4-d qhull warning: output for vertices not implemented in 4-d qhull warning: 'Gnh' generates no output in 4-d {appearance {linewidth 3} LIST # %s | %s {appearance {+edge -evert linewidth 2} LIST # %s | %s LIST # %s | %s 4VECT %d %d 1 VECT %d %d 1 1 # 1 point per line 1 0 # 1 color for all 0 1 1 1 # color of points 4OFF %d %d 1 %d qhull warning: writing Delaunay. Use 'p' or 'o' for Voronoi centers %d %d %s | %s begin %d %d real %d %d qhull warning: output is the Delaunay triangulation { %d %d %d %d %d %d %d %d %d %d %d %d %d %s | %s begin %d %d real %d %d %d qhull internal error (qh_printbegin): can not use this format for dimension %d out of boundqhull warning: no facets printed qhull internal error (qh_printend): number of ridges %d != number printed %d and at end %d } end } 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 %d %d %d qh_printextremes_2d: loop in facet list. facet %d nextfacet %d %d %d %d %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 ,Line[{{%16.8f, %16.8f}, {%16.8f, %16.8f}}] { OFF %d 1 1 # f%d 0 %8.4g %d %d %8.4g %8.4g %8.4g 1.0 } , Polygon[{, {%16.8f, %16.8f, %16.8f}}]%d %d OFF 3 1 1 # f%d # r%d between f%d f%d %8.4g 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 %8.4g 3 0 1 2 %8.4g %8.4g %8.4g %d %d %d %d %d %d %d MERGEridge DUPLICATEridge NULLfacet - f%d - flags: top bottom simplicial upperDelaunay visible new tested notG seen coplanar mergehorizon keepcentrum dupridge mergeridge1 mergeridge2 newmerge flipped notfurthest degenerate redundant - area: %2.2g - replacement: f%d - shares same visible/horizon as f%d - was horizon to f%d - merges: %d - offset: %10.7g - maxoutside: %10.7g - outside set (furthest p%d): - outside set: %d points. - furthest distance= %2.2g - coplanar set (furthest p%d): - coplanar set: %d points. furthest distance= %2.2g - neighboring facets: MERGE DUP f%d - ridges (ids may be garbage): r%d - ridges: - all ridges: r%d 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@geom.umn.edu 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 'QJ' to joggle the input points and remove precision errors - or use option 'Ft' instead of 'Q0'. 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 '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) 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: facet 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. This is a Delaunay triangulation and the input is co-circular or co-spherical: - use 'Qz' to add a point "at infinity" (i.e., above the paraboloid) - or use 'QJ' to joggle the input and avoid co-circular data 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 %8.4g %8.4g %8.4g 1.0 3 0 1 2 %8.4g %8.4g %8.4g 1.0 VECT 1 2 1 2 1 %8.4g # p%d VECT 1 1 1 1 1 %8.4g # p%d %8.4g %8.4g %8.4g 1 p%d: %8.4g%6.16g %8.4g # p%d %s | %s begin %d %d real %d %d 1 end - r%d tested nonconvex 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 }}} qh_printvdiagram: unknown print format %d. %d NULLvertex - p%d (v%d): %5.2g deleted ridgedeleted neighbors: f%d p%d (v%d) %d %d %d 1 %d 0 %d %d %d %6.16g %6.16g %d %d %d %d qhull input error: feasible point (dim 1 coords) is only valid for halfspace intersection qhull input warning: feasible point (dim 1 coords) overrides 'Hn,n,n' feasible point for halfspace intersection qhull error: insufficient memory for feasible point qhull input error: coordinates for feasible point do not finish out the line: %s qhull input error: only %d coordinates. Could not read %d-d feasible point. qhull input error: halfspace intersection needs a feasible point. Either prepend the input with 1 point or use 'Hn,n,n'. See manual. qhull error: insufficient memory for 'Hn,n,n' qhull input warning: more coordinates for 'H%s' than dimension %d qh_premerge: premerge centrum %2.2g angle %2.2g for apex v%d facetlist f%d qh_postmerge: postmerge. test vneighbors? %d qh_all_merges: starting to merge facets beginning from f%d qh_all_merges: merged %d coplanar facets %d concave facets and %d degen or redundant facets. qh_basevertices: found %d vertices qh_checkzero: skip convexity check until first pre-merge qh_checkzero: facets are %s qh_checkzero: facet f%d needs pre-merging qh_checkzero: facet f%d and f%d are not clearly convex. v%d dist %.2g qh_copynonconvex: moved nonconvex flag from r%d to r%d qh_degen_redundant_facet: test facet f%d for degen/redundant qh_degen_redundant_facet: f%d is contained in f%d. merge qh_degen_redundant_neighbors: f%d is degenerate. qh_degen_redundant_neighbors: test neighbors of f%d with delfacet f%d qh_degen_redundant_neighbors: f%d is degenerate with %d neighbors. qh_degen_redundant_neighbors: f%d is contained in f%d. merge qh_degen_redundant_neighbors: f%d is degenerate with %d neighbors. Neighbor of f%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 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 qh_flippedmerges: merge flipped f%d into f%d dist %2.2g during p%d qh_flippedmerges: merged %d flipped facets into a good neighbor qh_forcedmerges: begin qh_forcedmerges: duplicate ridge between f%d and f%d, dist %2.2g and reverse dist %2.2g during p%d qh_forcedmerges: merged %d facets and %d flipped facets across duplicated ridges qh_getmergeset: started. qh_getmergeset: %d merges found qh_getmergeset_initial: %d merges found qh_makeridges: make ridges for f%d qh_mark_dupridges: identify duplicate ridges qh_mark_dupridges: found %d duplicated ridges qh_maydropneighbor: test f%d for no ridges to a neighbor qh_maydropneighbor: facets f%d and f%d are no longer neighbors during p%d qh_maydropneighbors: f%d is degenerate. qh_maydropneighbors: f%d is degenerate. qh_merge_degenredundant: facet f%d is contained in f%d, will merge 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 qh_merge_nonconvex: merge #%d for f%d and f%d type %d qh_merge_nonconvex: avoid merging old facet f%d dist %2.2g. Use f%d dist %2.2g instead qh_mergecycle: merge #%d for facets from cycle f%d into coplanar horizon f%d qh_mergecycle_all: begin qh_mergecycle_all: merged %d same cycles or facets into coplanar horizons 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 qh_mergecycle_ridges: found %d old ridges and %d new ones qh_mergecycle_vneighbors: update vertex neighbors for newfacet qh_mergecycle_vneighbors: deleted v%d when merging cycle f%d into f%d qh_mergecycle_vneighbors: merged vertices from cycle f%d into f%d qh_mergefacet2d: merged v%d and neighbor f%d of f%d into f%d qh_mergeneighbors: merge neighbors of f%d and f%d qh_mergeridges: merge ridges of f%d and f%d qh_mergesimplex: merge apex 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 qh_mergesimplex: merged simplex f%d apex v%d into facet f%d qh_mergevertex_del: deleted v%d when merging f%d into f%d qh_mergevertex_neighbors: merge vertex neighbors of f%d and f%d qh_neighbor_intersections: %d vertices in neighbor intersection of v%d qh_reducevertices: renamed %d shared vertices and %d redundant vertices. Degen? %d qh_redundant_vertex: check if v%d can be renamed qh_remove_extravertices: test 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_rename_sharedvertex: p%d (v%d) is shared by f%d (%d ridges) and f%d qh_renameridgevertex: ridge r%d deleted. It contained both v%d and v%d qh_renameridgevertex: swapped the top and bottom of ridge r%d qh_test_appendmerge: coplanar angle %4.4g between f%d and f%d qh_test_appendmerge: concave f%d to f%d dist %4.4g and reverse dist %4.4g angle %4.4g during p%d qh_test_appendmerge: coplanar f%d to f%d dist %4.4g, reverse dist %4.4g angle %4.4g qh_test_vneighbors: testing vertex neighbors for convexity qh_test_vneighbors: found %d non-convex, vertex neighbors qh_vertexridges: found %d ridges for v%d qh_qhull: all facets are clearly convex and no coplanar points. Post-merging and check of maxout not needed. qh_qhull: algorithm completed qh_addpoint: added p%d new facets %d new balance %2.2g point balance %2.2g qh_buildhull: start build hull qh_buildhull: stop point or cone P%d in initial hull qh_buildhull: completed the hull construction qh_findhorizon: find horizon for point p%d facet f%d qh_findhorizon: point p%d is coplanar to horizon f%d, dist=%2.7g < qh MINvisible (%2.7g) qh_findhorizon: %d horizon facets (good %d), %d visible (good %d), %d coplanar qh_partitionall: partition all points into outside sets qh_partitioncoplanar: point p%d is coplanar with facet f%d (or inside) dist %2.2g qh_partitionpoint: point p%d is outside facet f%d qh_partitionpoint: point p%d is inside all facets, closest to f%d dist %2.2g qh_partitionvisible: partitioned %d points from outsidesets and %d points from coplanarsets qh_precision: qhull restart because of %s qh_appendfacet: append f%d to facet_list qh_appendvertex: append v%d to vertex_list qh_attachnewfacets: delete interior ridges qh_attachnewfacets: attach horizon facets to new facets qh_checkflipped: facet f%d is flipped, distance= %6.12g during p%d qh_delfacet: delete f%d qh_deletevisible: delete %d visible facets and %d vertices qh_facetintersect: f%d skip %d matches f%d skip %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 qh_matchneighbor: f%d skip %d matched with new f%d skip %d 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. qh_matchvertices: matched by skip %d (v%d) and skip %d (v%d) same? %d qh_newfacet: created facet f%d qh_newridge: created ridge r%d qh_removefacet: remove f%d from facet_list qh_removevertex: remove v%d from vertex_list qh_updatevertices: delete interior vertices and update vertex->neighbors qh_updatevertices: delete vertex p%d (v%d) in f%d qh_updatevertices: delete vertex p%d (v%d) in f%d qh_backnormal: zero diagonal at column %d. qh_findbest: neighbors of f%d, bestdist %2.2g cutoff %2.2g searchdist %2.2g qh_findbest: horizon facet f%d qh_getangle: %2.2g qh_getcentrum: for f%d, %d vertices dist= %2.2g qh_normalize: norm=%2.2g too small during p%d qh_setfacetplane: flipped orientation after testing interior_point during p%d qh_sethyperplane_det: degenerate norm during p%d. 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. MATLAB R12 native?????00<0H0T0`0l0x00000000000000 0,080D0P0\0h0t0000000000000~0{0x(0u40r@0oL0lX0id0fp0c$  o. 1 Q3-no-merge-vertices-dim-highQRandom-seedQRotate-randomqhull configuration error (qh_RANDOMmax in user.h): random integer %d > qh_RANDOMmax (%.8g) qhull configuration warning (qh_RANDOMmax in user.h): average of 1000 randoms %.2g much less than expected (%.2g). Is qh_RANDOMmax wrong? qhull internal error (qh_initqhull_globals): qh_HASHfactor %d must be at least 1.1. Qhull uses linear hash probing qhull input error: not enough points (%d) to construct initial simplex (need %d) qhull input error: transparent Delaunay ('Gt') needs 3-d Delaunay ('d') w/o 'GDn' qhull input error: option 'Fp' is only used for halfspace intersection ('Hn,n,n'). qhull input error: option 'Ft' is not available for Voronoi vertices or halfspace intersection qhull input error: option 'Fc' is not available for Voronoi vertices ('v') FvoronoiFverticesqhull input warning: options 'Fc', 'FP', and 'Gp' need option 'Qc' or 'Qi' to record coplanar/inside points qhull input error: Mathematica output is only available for 2-d and 3-d convex hulls and Delaunay triangulations qhull input error: Geomview output is only available for 2-d, 3-d and 4-d qhull input error: no output specified for Geomview qhull input error: Geomview output for Voronoi diagrams only for 2-d qhull input warning: coplanars, vertices, and centrums output not available for 4-d output (ignored). Could use 'GDn' instead. qhull input warning: drop dimension 'GD%d' is only available for 3-d/4-d Geomview qhull warning: no dimension given for Print option '%c' at: %s. Ignored qhull warning: dimension %d for Print option '%c' is >= %d. Ignored qhull warning: value %2.4g for Print option %c is > +1 or < -1. Ignored qhull warning: no dimension given for Qhull option %c. Ignored qhull warning: dimension %d for Qhull option %c is >= %d. Ignored precision statisticsave. distance of a new vertex to a facet (not 0s)max. 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 problemscoplanar 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 eliminationridges with multiple neighborssummary informationnumber of vertices in outputnumber of facets in outputnumber of ridges in outputaverage 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 vertexmaximum number of neighborscpu 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 angle (cosine) for all ridges maximum angle (cosine) of a ridge minimum angle (cosine) of 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 iteration maximum ave. vertices deleted per iteration maximum vertices deletedave. horizon facets per iterationave. new or merged facets per iteration maximum (includes initial simplex)average new facet balance standard deviationaverage partition balance standard deviation number of trialssearches of all points for initial simplexdeterminants computed (area & initial hull)determinants not computed because vertex too lowpoints ignored (not above max_outside)points ignored (not 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 checkpartitioning statisticsinside points inside points kept with a facet inside points that were coplanar with a facetdifference 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 checking simplicial convexitycoplanar angles in getmergesetcoplanar centrums in getmergesetconcave 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 merged 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 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 neighborsnon-convex vertex neighborsmerges due to angle coplanar facets average merge distance maximum merge distancemerges due to coplanar facets average merge distance maximum merge distancemerges due to concave facets average merge distance maximum merge distancecoplanar/concave merges due to avoiding old merge average merge distance maximum merge distancemerges due to degenerate facets average merge distance maximum merge distancemerges due to removing flipped facets average merge distance maximum merge distancemerges due to duplicated ridges average merge distance maximum merge distancerenamed vertex statisticsrenamed vertices shared by two facetsrenamed vertices in a pinched facetrenamed vertices shared by multiple facetsrename failures due to duplicated ridges duplicate ridges detecteddeleted ridges due to renamed verticesdropped neighbors due to renamed verticesdegenerate facets due to dropped neighbors facets deleted because of no neighborsvertices removed from facets due to no ridges deletedvertex 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 and outside and coplanar setsfor 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 normal ave. angle to ridge max. angle to ridge %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 divisions zero diagonal for Gauss: %6.2e %s *0 cnt*%7.2g%7.2g%7d%7.3g %s qhull error: insufficient memory to copy %d points qhull internal error (qh_determinate): only implemented for dimension >= 2 _max-widthError-roundoffAngle-premerge-with-randomAngle-postmerge-with-randomCentrum-premerge-with-randomCentrum-postmerge-with-random_one-merge_near-insideqhull error: the joggle for 'QJn', %.2g, is below roundoff for distance computations, %.2g Visible-distanceU-coplanar-distanceWidth-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 qhull internal error (qh_facetarea_simplex): #points %d != dim %d -1 computing area of each facet and volume of the convex hull qhull error: insufficient memory to joggle %d points QJoggleQJoggleqhull error: the current joggle for 'QJn', %.2g, is too large for the width of the input. If possible, recompile Qhull with higher-precision reals. _joggle-seedqhull error: floating point constants in user.h are wrong REALepsilon %g REALmin %g REALmax %g -REALmax %g qh_maxmin: found the max and min points (by dim):input has same x coordinateqhull precision error (qh_maxsimplex for voronoi_center): %d points with the same x coordinate. qhull input error: input is less than %d-dimensional since it has the same x coordinate qhull internal error (qh_maxsimplex): not enough points available %s %6.3g %s p%d %d qhull internal error (qh_projectinput): dimension after projection %d != hull_dim %d qhull error: insufficient memory to project %d points qhull internal error (qh_projectpoints): newdim %d should be %d after projection qh_rotatepoints: rotate points byqhull input error: last coordinate's new bounds [0, %2.2g] too wide for existing bounds [%2.2g, %2.2g] with width %2.2g 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_sethalfspace: halfspace at offset %6.2g to point: %6.2g qhull input error: feasible point is not clearly inside halfspace feasible point: %6.16g halfspace: %6.16g at offset: %6.16g and distance: %6.16g qhull error: insufficient memory to compute dual of %d halfspaces The halfspace was at index %d qhull internal error (qh_voronoi_center): need at least %d points to construct a Voronoi center qh_voronoi_center: at infinity for qh_voronoi_center: det %2.2g factor %2.2g center:pointsp%d dist %.2g, qhull output completed. Verifying that %d points are below %2.2g of the nearest %sfacet. good qhull precision error: 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 (qh.outside_err) is %6.2g qh_check_maxout: p%d (v%d) is %.2g from f%d qh_check_maxout: p%d is %.2g above f%d qhull precision error: point p%d is outside facet f%d, distance= %6.8g maxoutside= %6.8g qhull input warning: merging without checking outer planes ('Q5'). Verify may report that a point is outside of a facet. qhull input warning: exact merge ('Qx'), 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. good Output completed. Verifying that all points are below %2.2g of all %sfacets. Will make %2.0f distance computations. good qhull precision error (qh_check_points): a coplanar point is %6.2g from convex hull. The maximum value (qh.outside_err) is %6.2g flipped facetqhull precision error: f%d is flipped (interior point is outside) coplanar or concave ridgeqhull precision error: initial simplex is not convex. Distance=%.2g concave ridgeqhull precision error: f%d is concave to f%d, since p%d (v%d) is %6.4g above coplanar ridgeqhull precision error: f%d is clearly not convex to f%d, since p%d (v%d) is %6.4g above coplanar ridgeconcave ridgeqhull precision error: f%d is concave to f%d. Centrum of f%d is %6.4g above f%d coplanar ridgeqhull precision error: f%d is coplanar or concave to f%d. Centrum of f%d is %6.4g above f%d qhull internal error (qh_checkfacet): facet f%d is on the visible_list qhull internal error (qh_checkfacet): facet f%d does not have a normal vertices for fridges for foutsideset for fcoplanarset for fneighbors for fqhull internal error (qh_checkfacet): deleted vertex v%d in f%d ERRONEOUSqhull 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 MERGE or DUP neighbor 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): 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 precision error (qh_checkfacet): vertex v%d in f%d intersect f%d but not in a ridge. This is ok under merging. Last point was p%d ERRONEOUSqhull internal error (qh_checkfacet): facet f%d skip %d and neighbor f%d skip %d do not match qh_checkfacet: ridges r%d and r%d have the same vertices ERRONEOUSqhull precision error: facet f%d is flipped, distance= %6.12g ERRONEOUS A flipped facet occurs when its distance to the interior point is greater than %2.2g, the maximum roundoff error. qhull internal error (qh_checkpolygon): f%d has outside set before qh facet_next qhull internal error (qh_checkpolygon): visible list f%d no longer on facet list 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 neighbors for vqhull internal error (qh_checkpolygon): vertex neighbors inconsistent. Totvneighbors %d, totvertices %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 internal error (qh_checkpolygon): #vertices %d + #facets %d - #edges %d != 2 qhull internal error (qh_checkvertex): unknown point id %p qhull internal error (qh_checkvertex): unknown vertex id %d qhull internal error (qh_checkvertex): neighbor f%d does not contain v%d ERRONEOUSqhull 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_findbestfacet: all facets are flipped or upper Delaunay qhull warning: good vertex p%d does not match last good facet f%d. Ignored. qhull internal error (qh_infiniteloop): potential infinite loop detected qhull input error: either QGn or QVn point is > p%d Trace level %d for %s | %s Options selected for qhull %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. initial facet is coplanar with interior pointqhull precision error: initial facet %d is coplanar with the interior point _narrow-hullqhull precision warning: The initial hull is narrow (the cosine of the minimum angle is %.9g). A coplanar point may lead to a wide facet. Options 'Qs' (search for best initial hull), 'QbB' (scale to unit box), or 'Qbb' (scale last coordinate) may remove this warning. Use 'Pp' to ignore this warning. See 'Limitations' in qh-impre.htm. qh_initialhull: simplex constructed, interior point: %6.4g qhull internal error (qh_matchduplicates): missing dupridge at f%d skip %d for new f%d skip %d hash %d qhull internal error (qh_matchduplicates): no MERGEridge match for duplicate f%d skip %d at hash %d qhull internal error (qh_matchduplicates): no maximum match at duplicate f%d skip %d at hash %d ridge with multiple neighborsDUPLICATED/MATCHqhull input error: more than %d vertices. Id field overflows and two vertices may have the same identifier. Vertices not sorted correctly. qhull internal warning (point_add): unknown point %p id %d qhull internal errror (point_add): point p%d is out of bounds (%d) hash %d f%d v%d neighbors: %d qh_printlists: facets: %d new facets %d visible facets %d next facet for addpoint %d vertices (new %d): %d qh_detvnorm: Voronoi vertex or midpointVertices and facets: - normal: - outside set: Furthest - coplanar set: Furthest - vertices:center point vertices:reason %s with 'C%.2g' and 'A%.2g' qhull error: f%d is not attached to the new facets not concave, flipped, or duplicate ridgedclearly convexqh_find_newvertex: find new vertex for v%d from v%d r%d qhull internal error (qh_findbestneighbor): no neighbors for f%d qhull internal error (qh_forcedmerges): f%d and f%d had a duplicate ridge but as f%d and f%d they are no longer neighbors qhull internal error (qh_merge_degenredunant): f%d redundant but f%d has no replacement qh_mergecycle: ========= trace merge %d of samecycle %d into trace f%d, furthest is p%d same cycle: f%d MERGING CYCLEqh_mergecycle: end of trace facet qh_mergecycle_all: f%d without normal qhull internal error (qh_mergecycle_ridges): bad ridge r%d qh_mergefacet: ========= trace wide merge #%d (%2.2g) for f%d into f%d, last point was p%d qh_mergefacet: ========= trace merge #%d involving f%d, furthest is p%d qh_mergefacet: #%d merge f%d into f%d, mindist= %2.2g, maxdist= %2.2g qhull internal error (qh_mergefacet): either f%d and f%d are the same or one is a visible facet qhull precision error: Only %d facets remain. Can not merge another pair. The convexity constraints may be too strong. Reduce the magnitude of 'Cn' or increase the magnitude of 'An'. For example, try 'C-0.001' instead of 'C-0.1' or 'A-0.999' instead of 'A-0.9'. Option 'Qx' may avoid this problem. MERGINGqh_mergefacet: end of wide tracing qh_mergevertex_neighbors: of f%d and f%d at furthest p%d f0= %p TRACETRACEqhull internal error (qh_mergevertices): facets did not share a ridge qhull internal error (qh_rename_sharedvertex): v%d's neighbors not in f%d ERRONEOUSqh_renamevertex: renamed v%d to v%d in several facets qh_renamevertex: renamed v%d to v%d in oldfacet f%d qh_renamevertex: renamed pinched v%d to v%d between f%d and f%d MERGEDqh_tracemerge: trace facet and vertex after merge of f%d and f%d, furthest p%d TRACEqh_tracemerge: trace vertex deleted at furthest p%d At %d:%d:%d & %2.5g CPU secs, qhull has merged %d facets. The hull contains %d facets and %d vertices. First post-mergeFor testing vertex neighborsFor post-merging Testing all coplanar points. qhull internal error (qh_qhull): temporary sets not empty (%d) qh_addpoint: NULL facet. Use qh_findbestfacet qhull precision error: %d attempts to construct a convex hull with joggled input. Increase joggle above 'QJ%2.2g' or modify qh_JOGGLE... parameters in user.h _runqhull 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 ERRONEOUSqhull internal error (qh_buildhull): %d outside points were never processed. 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 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) to hull of %d facets (%2.2g above f%d) and %d outside at %4.4g CPU secs. Previous was p%d. ERRONEOUSvisiblevisiblecoplanar horizonhorizonempty horizonqhull precision error (qh_findhorizon): empty horizon Point p%d was above all facets. qhull internal error (qh_nextfurthest): num_outside %d incorrect or random %2.2g >= 1.0 qh_partitioncoplanar: ====== p%d increases max_outside to %2.2g of f%d last p%d DISTANTnearly incident point (narrow hull)nearly incident point At a premature exit due to 'TVn', 'TCn', or precision error. 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 Number of nearly incident points: %d Total number of nearly incident points: %d Number of Voronoi vertices: %d Number of facets in hull: %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 and at-infinity Number of nearly incident points: %d Total number of nearly incident points: %d Number of Delaunay facets: %d Number of facets in hull: %d Halfspace intersection by the convex hull of %d points in %d-d: Number of nonredundant halfspaces: %d similar and redundantredundantsimilar Number of %s halfspaces: %d Number of intersection points: %d Number of 'good' intersections: %d Convex hull of %d points in %d-d: Number of vertices: %d coplanar and interiorinteriorcoplanar Number of %s points: %d Number of facets: %d Number of 'good' facets: %d Statistics for: %s | %s QR%d Number of points processed: %d Number of hyperplanes created: %d Number of distance tests for qhull: %d Number of merged facets: %d Number of distance tests for merging: %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 ApproximateTotal Maximum distance of %spoint above facet: %2.2gmerged (%.1fx) Maximum distance of %svertex below facet: %2.2gmerged (%.1fx) qhull error (qh_memalloc): insufficient memory qhull internal error (qh_memalloc): qhmem has not been initialized. qhull error (qh_memalloc): insufficient memory qh_memalloc long: %d bytes at %p qh_memfree long: %d bytes at %p qhull internal error (qh_meminit): sizeof(void*) < sizeof(int). qset.c will not work qhull internal error (qh_meminit): memory alignment %d is not a power of 2 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 error (qh_memsize): called after qhmem_setup qhull warning (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 long memory allocated (except for input) %7d bytes of long memory in use (in %d pieces) %7d bytes per memory buffer (initially %d bytes) %7d calls to qh_setlarger %7.2g average copy size freelists (bytes->count): %d->%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. ERRONEOUSqhull internal error (qh_setaddnth): nth %d is out-of-bounds for set: qhull internal error (qh_setaddnth): nth %d is out-of-bounds for set: qhull internal error (qh_setaddnth): nth %d is out-of-bounds for set: %s set is null %s set=%p maxsize=%d size=%d elems= %p qhull 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 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: qhull internal error (qh_attachnewfacets): couldn't find visible facet for horizon f%d of newfacet f%d flipped facetqhull 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 others neighbors qhull internal error (qh_makenew_nonsimplicial): simplicial f%d sharing two ridges with f%d two facets with the same verticesqhull precision error: Vertex sets are the same for f%d and f%d. Can not force output. a ridge with more than two neighborsqhull precision error: facets f%d, f%d and f%d meet at a ridge with more than 2 neighbors. Can not continue. qhull internal error (qh_matchnewfacets): %d neighbors did not match up qh_matchnewfacets: %d new facets, %d unused hash entries . hashsize %d qhull warning: more than %d ridges. Id field overflows and two ridges may have the same identifier. Otherwise output ok. zero diagonal on back substitutionqh_distplane: %6.16g from p%d to f%d qhull internal error (qh_findbest): unknown combination of arguments qh_findbest: point p%d starting at f%d bestoutside? %d newfacets %d ischeckmax %d ispartition %d isfindfacet %d testhorizon %d Last point added to hull was p%d. Last merge was #%d. qh_findbest: point p%d starting at f%d bestoutside? %d newfacets %d qh_findbest: all neighbors of facet %d are flipped or upper Delaunay. Please report this error to qhull_bug@geom.umn.edu with the input and all of the output. qhull precision error (qh_findbestnew): merging has formed and deleted an independent cycle of 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 if dist > %2.2g Last point added to hull was p%d. Last merge was #%d. qh_gausselim: 0 pivot at column %d. (%2.2g < %2.2g) Matrix:zero pivot for Gaussian eliminationqh_gausselem: resultqhull internal error (qh_getcenter): not defined for %d points qh_setfacetplane: facet f%d created. Last point added to hull was p%d. Last merge was #%d. 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