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X P߿< 0%P߰߳'0qhull internal warning (main): did not free %d bytes of long memory (%d pieces) size in bytes: hashentry %d merge %d ridge %d vertex %d facet %d normal %d ridge vertices %d facet vertices or neighbors %d qhull internal error (qh_produce_output): temporary sets not empty (%d) 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 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 4488x8no normal for facet f%d qhull input error (qh_printafacet): option 'Fp' needs qh feasible_point %d %d %d %6.16g p@D``$8@@|@@@8Vertices 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 # 1 color for all 0 1 1 1 # color of points 4OFF %d %d 1 qhull warning: writing Delaunay. Use 'p' or 'o' for Voronoi centers %s | %s begin %d %d real qhull warning: output is the Delaunay triangulation %d %d %d %d %s | %s begin %d %d real qhull internal error (qh_printbegin): can not use this format for dimension %d {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 qhull warning: no facets printed qhull internal error (qh_printend): number of ridges %d != number printed %d and at end %d 3 %d %d %d %8.4g %8.4g %8.4g 1 # f%d f%d 3 %d %d %d %8.4g %8.4g %8.4g 1 #r%d f%d f%d 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 Line[{{%16.8f, %16.8f}, {%16.8f, %16.8f}}] { OFF %d 1 1 # f%d %8.4g %8.4g %8.4g 1.0 } Polygon[{{%16.8f, %16.8f, %16.8f}OFF 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 - flags: simplicial upperDelaunay visible 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 - 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: - ridges (ids may be garbage): - ridges: - all ridges:qhull warning: CDD format is not available for centrums, halfspace intersections, and OFF file format. Options selected for qhull %s: %s %s | %s 7 %d %d %d %d %d %d %d 2 %6.16g %6.16g 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: center point 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 3 0 1 2 %8.4g %8.4g %8.4g 1.0 VECT 1 2 1 2 1 VECT 1 1 1 1 1 %8.4g %8.4g %8.4g 1 - r%d nonconvex 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 qh_printvdiagram: unknown print format %d. NULLvertex - p%d (v%d): deleted ridgedeleted neighbors: p%d (v%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: 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: missing "begin" for cdd-formated input qhull input error: short input file. Did not find dimension and number of points qhull input error: dimension %d (first number) should be at least 2 qhull input error: dimension %d (first number, includes offset) should be at least 3 for halfspaces qhull input error: dimension %d of feasible point is not one less than dimension %d for halfspaces qhull error: insufficient memory to read %d points qhull input warning: the input appears to be in cdd format. If so, use 'Fd' qhull input error: for cdd format, point at line %d does not start with '1' The halfspace was on line %d The input appears to be in cdd format. If so, you should use option 'Fd' qhull input error: line %d contained more than %d characters qhull warning: instead of %d %d-dimensional points, input contains %d points and %d extra coordinates. Line %d is the first point, line %d is the first (if any) comment, line %d is the first short line, and line %d is the first long line. Continue with %d points. ./rbox D4 This is the qhull test case. If any errors or core dumps occur, recompile qhull with 'make new'. If errors still occur, there is an incompatibility. You should try a different compiler. You can also change the choices in user.h. If you discover the source of the problem, please send mail to qhull_bug@geom.umn.edu. Type 'qhull' for a short list of options. qh_readpoints: read in %d %d-dimensional points 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 qhull 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 _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 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 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 computing area of each facet and volume of the convex hull qh_getarea: computing volume and area for each facet qhull error: insufficient memory to joggle %d points qhull 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-seedqh_joggleinput: joggle input by %2.2g with seed %d qh_maxmin: found the max and min points (by dim):qh_maxouter: max distance from facet to outer plane is %2.2g max_outside is %2.2g 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 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 qhull internal error (qh_maxsimplex): not enough points available qh_maxsimplex: selected point p%d for %d`th initial vertex, det=%2.2g 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 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 [0,%2.2g] qhull 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_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: qhull 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 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 p%d dist %.2g, 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 qhull internal error (qh_attachnewfacets): couldn't find visible facet for horizon f%d of newfacet f%d qh_checkflipped: facet f%d is flipped, 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 others neighbors qh_facetintersect: f%d skip %d matches f%d skip %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 facets with the same verticesqhull precision error: Vertex sets are the same for f%d and f%d. Can not force output. qh_matchneighbor: f%d skip %d matched with new f%d skip %d 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. 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): %d neighbors did not match up qh_matchnewfacets: %d new facets, %d unused hash entries . 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 %d ridges. Id field overflows and two ridges may have the same identifier. Otherwise output ok. 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_check_bestdist: check points below nearest facet. Facet_list f%d qh_check_bestdist: check that all points are within %2.2g of best facet qhull output completed. Verifying that %d points are below %2.2g of the nearest %sfacet. qhull precision error: 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_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: p%d (v%d) is %.2g from f%d qh_check_maxout: p%d is %.2g above f%d 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 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. Output completed. Verifying that all points are below %2.2g of all %sfacets. Will make %2.0f distance computations. 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 all ridges are convex 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 qhull precision error: f%d may be coplanar to f%d, since p%d (v%d) is within %6.4g during p%d qhull precision error: f%d is concave to f%d. Centrum of f%d is %6.4g above f%d qhull precision error: f%d is coplanar or concave to f%d. Centrum of f%d is %6.4g above f%d qhull 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 qhull 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 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 %2.2g, the maximum roundoff error. qh_checkpolygon: check all facets from f%d 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 qh_clearcenters: switched to center type %d qh_createsimplex: created simplex 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_findbestfacet: all facets are flipped or upper Delaunay 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 qhull warning: good vertex p%d does not match last good facet f%d. Ignored. 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 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. qh_initbuild: initial hull created and points partitioned qh_initialhull: initial orientation incorrect. Correct all facets 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: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 qhull internal error (qh_matchduplicates): missing dupridge at f%d skip %d for new f%d skip %d hash %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 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 qh_matchduplicates: duplicate f%d skip %d matched with new f%d skip %d keep 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. 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 errror (point_add): point p%d is out of bounds (%d) qh_prependfacet: prepend f%d before f%d hash %d f%d neighbors:qh_printlists: facets: new facets %d visible facets %d next facet for addpoint %d vertices (new %d):qh_vertexneighbors: determing neighboring facets for each vertex 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 neighborsmaximum number of 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 facetaverage 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 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 area maximum standard deviationbuild 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 iterationave. visible vertices per iteration 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 balanceaverage partition balance 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 neighbors average merge distance maximum merge distancemerges due to angle coplanar facetsmerges due to coplanar facetsmerges due to concave facetscoplanar/concave merges due to avoiding old mergemerges due to degenerate facetsmerges due to removing flipped facetsmerges due to duplicated ridgesrenamed 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 sets max. angle to ridge ave. angle to ridgeVoronoi 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 normalbounded ridges with near-zero normal %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: *0 cnt*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. ERRONEOUS%s set is null %s set=%p maxsize=%d size=%d elems=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 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 error (qh_memalloc): insufficient memory qhull internal error (qh_memalloc): qhmem has not been initialized. qh_memalloc long: %d bytes at %p qh_memfree long: %d bytes at %p 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):qh_backnormal: zero diagonal at column %d. zero diagonal on back substitutionyyzz{{L{{|<qh_distplane: 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: neighbors of f%d, bestdist %2.2g cutoff %2.2g searchdist %2.2g 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. qh_findbest: horizon facet f%d 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 qh_gausselim: 0 pivot at column %d. (%2.2g < %2.2g) zero pivot for Gaussian eliminationqh_gausselem: resultqh_getangle: %2.2g 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 merge was #%d. Current summary is: qh_setfacetplane: flipped orientation after testing interior_point 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: 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. qh_new_qhull: start qhull_cmd argument with "qhull " qh_new_qhull: build new Qhull for %d %d-d points with %s qhull error while processing previous error. Exit program ERRONEOUS While executing: %s | %s Options selected for %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 error while ending program. Exit program %s FACET: %s OTHER FACET: %s RIDGE: %s VERTEX: ERRONEOUS and NEIGHBORING FACETS to output qhull internal error (qh_clock): use qh_CLOCKtype 2 in user.h 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 qhull input error: more than %d characters in command line D Ɍ@ذ |p$XƌƼdelaunayincidencemathematicaqhull warning: no maximum cosine angle given for option 'An'. Ignored. Angle-premerge-Angle-postmergeqhull warning: no centrum radius given for option 'Cn'. Ignored. Centrum-premerge-Centrum-postmergeqhull warning: negative maximum roundoff given for option 'An'. Ignored. qhull warning: no maximum roundoff given for option 'En'. Ignored. Error-roundoffqhull warning: origin for Halfspace intersection should be 'Hn,n,n,...' qhull error: insufficient memory for 'Hn,n,n' Halfspace-aboutHalfspaceqhull warning: missing random perturbation for option 'Rn'. Ignored Random_perturbqhull warning: missing visible distance for option 'Vn'. Ignored qhull warning: missing coplanar distance for option 'Un'. Ignored U-coplanarqhull warning: negative outside width for option 'Wn'. Ignored. qhull warning: missing outside width for option 'Wn'. Ignored W-outside h|hhh`hhhhDдh@hhѼhhhhhhhhhh4hLάhhhh4hhhόϸЄhhthѤhFArea-totalFcoplanarsFCentrumsFd-cdd-inFD-cdd-outFFacets-xridgeFneighborsFNeighbors-vertexFOptionsFpoint-intersectFPoint-nearestFsummaryFtrianglesFVertex-averageFxtremesqhull warning: unknown 'F' output option %c, rest ignored ԸXl҄Ә<dԐGall-pointsGcentrumsGintersectionsGno-planesGtransparentGverticesqhull input error: missing dimension for option 'GDn' qhull warning: can only drop one dimension. Previous 'GD%d' ignored GDrop-dimqhull warning: unknown 'G' print option %c, rest ignored ,<<h<׀<<<<<<<<<<<<<<<<<<<<<<<<<<<h<<ְ<<<<<<<Pdrop-facets-dim-lessPDrop-facets-dim-morePgood-facetsPGood-facet-neighborsPoutput-forcedPprecision-ignoreqhull input error: missing facet count for keep area option 'PAn' PArea-keepqhull input error: missing facet area for option 'PFn' PFacet-area-keepqhull input error: missing merge count for option 'PMn' PMerge-keepqhull warning: unknown 'P' print option %c, rest ignored `܀ܤ4llllllllllllXllݔlllllllllllllllllllll0llTxlڜllllllll,PltlۜQbBound-unit-boxQbbound-lastqh_initflags: project dimension %d Qb-project-dimQbound-dim-lowQBound-dim-highQcoplanar-keepQfurthest-outsideQgood-facets-onlyQinterior-keepQmax-outside-onlyQrandom-outsideQsearch-initial-simplexQupperDelaunayQvertex-neighbors-convexQxact-mergeQz-infinity-pointQ0-no-premergeQ1-no-angle-sortQ2-no-merge-independentQ3-no-merge-verticesqhull warning: can not follow '1', '2', or '3' with a digit. '%c' skipped. Q4-avoid-old-into-newQ5-no-check-outerQ6-no-concave-mergeQ7-no-breadth-firstQ8-no-near-insideQ9-pick-furthestqhull warning: good point already defined for option 'QGn'. Ignored qhull warning: missing good point id for option 'QGn'. Ignored QGood-if-dont-see-pointQGood-if-see-pointqhull warning: missing random seed for option 'QRn'. Ignored QRotate-idQRandom-seedqhull warning: good vertex already defined for option 'QVn'. Ignored qhull warning: no good point id given for option 'QVn'. Ignored QV-good-facets-not-pointQV-good-facets-pointqhull warning: unknown 'Q' qhull option %c, rest ignored T4x DhTcheck-frequentlyTstatisticsqhull warning: output file undefined (stdout). Option 'Tz' ignored. Tz-stdoutqhull warning: missing point id for cone for trace option 'TCn'. Ignored TCone-stopqhull warning: missing frequency count for trace option 'TFn'. Ignored TFacet-logqhull warning: option 'TO' mistyped. Use 'TO', one space, file name, and space or end-of-line. The file name may be enclosed in single quotes. Do not use double quotes. Option 'FO' ignored. qhull error: filename for 'TO' too long. qhull error: missing end quote for option 'TO'. Rest of line ignored. qhull error: could not open file "%s".TOutput-fileqhull warning: missing point id for trace option 'TPn'. Ignored Trace-pointqhull warning: missing merge id for trace option 'TMn'. Ignored Trace-mergeqhull warning: missing rerun count for trace option 'TRn'. Ignored qhull warning: missing furthest point id for trace option 'TVn'. Ignored TV-stop-before-pointTV-stop-after-pointqhull warning: missing max width for trace option 'TWn'. Ignored TWide-traceqhull warning: unknown 'T' trace option %c, rest ignored qhull warning: unknown flag %c (%x) qhull warning: missing space after flag %c (%x); reserved for menu. Skipped. qhull warning: additional output formats are not compatible with Geomview qh_initqhull_globals: for %s | %s _pre-merge_merge-exactQbbound-last-qj_zero-centrumqhull input error: can not use Delaunay ('d') or Voronoi ('v') with halfspace intersection ('H') qhull input error: use upper-Delaunay ('Qu') or infinity-point ('Qz') with Delaunay ('d') or Voronoi ('v') qhull input error: can not use infinity-point ('Qz') with upper-Delaunay ('Qu') qhull input warning: option 'Qbb' (scale-last-coordinate) is normally used with 'd' or 'v' qhull input error: test vertex neighbors ('Qv') needs a merge option qhull error: dimension %d must be > 1 qh_initqhull_globals: initialize globals. dim %d numpoints %d malloc? %d projected %d to hull_dim %d Q3-no-merge-vertices-dim-highQRotate-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 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 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-merging Testing all coplanar points. qhull internal error (qh_qhull): temporary sets not empty (%d) qh_qhull: algorithm completed qh_addpoint: NULL facet. Use qh_findbestfacet qh_addpoint: added p%d new facets %d new balance %2.2g point balance %2.2g 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 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 ERRONEOUSqh_buildhull: stop point or cone P%d in initial hull 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 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. qh_findhorizon: find horizon for point p%d facet f%d coplanar horizonqh_findhorizon: point p%d is coplanar to horizon f%d, dist=%2.7g < qh MINvisible (%2.7g) empty horizonqhull precision error (qh_findhorizon): empty horizon Point p%d was above all facets. qh_findhorizon: %d horizon facets (good %d), %d visible (good %d), %d coplanar qhull internal error (qh_nextfurthest): num_outside %d incorrect or random %2.2g >= 1.0 qh_partitionall: partition all points into outside sets qh_partitioncoplanar: ====== p%d increases max_outside to %2.2g of f%d last p%d qh_partitioncoplanar: point p%d is coplanar with facet f%d (or inside) dist %2.2g nearly incident point (narrow hull)qh_partitionpoint: point p%d is outside facet f%d nearly incident pointqh_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 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: and at-infinity Number of Voronoi regions%s: %d 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 Number of Delaunay facets: %d Halfspace intersection by the convex hull of %d points in %d-d: Number of nonredundant halfspaces: %d similar and redundantredundant 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 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 Approximate %s facet area: %2.8g %s volume: %2.8g Maximum distance of %spoint above facet: %2.2g (%.1fx) Maximum distance of %svertex below facet: %2.2gqh_premerge: premerge centrum %2.2g angle %2.2g for apex v%d facetlist f%d %s with 'C%.2g' and 'A%.2g' 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 qhull error: f%d is not attached to the new facets qh_checkzero: skip convexity check until first pre-merge not concave, flipped, or duplicate ridgedclearly convexqh_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: find new vertex for v%d from qh_find_newvertex: vertices not in ridges for v%d qh_find_newvertex: found v%d for old v%d from %d vertices and %d ridges. qh_find_newvertex: no vertex for renaming v%d (all duplicated ridges) during p%d 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 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 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 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. qhull internal error (qh_merge_degenredunant): f%d redundant but f%d has no replacement 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: ========= trace merge %d of samecycle %d into trace f%d, furthest is p%d same cycle:MERGING CYCLEqh_mergecycle: end of trace facet qh_mergecycle_all: begin qh_mergecycle_all: f%d without normal 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 qhull internal error (qh_mergecycle_ridges): bad ridge r%d qh_mergecycle_ridges: found %d old ridges and %d new ones qh_mergecycle_vneighbors: update vertex neighbors for newfacet qh_mergecycle_vneighbors: deleted v%d when merging cycle f%d into f%d qh_mergecycle_vneighbors: merged vertices from cycle f%d into f%d qh_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. qh_mergefacet: end of wide tracing 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_mergevertex_neighbors: of f%d and f%d at furthest p%d f0= %p qhull internal error (qh_mergevertices): facets did not share a ridge qh_neighbor_intersections: %d vertices in neighbor intersection of v%d qh_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 qhull internal error (qh_rename_sharedvertex): v%d's neighbors not in f%d ERRONEOUSqh_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_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 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_tracemerge: trace facet and vertex after merge of f%d and f%d, 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. The hull contains %d facets and %d vertices. qh_vertexridges: found %d ridges for v%d version 2.6 1998/8/12 qhull- compute convex hulls and related structures. http://www.geom.umn.edu/locate/qhull %s input (stdin): first lines: dimension and number of points (or vice-versa). other lines: point coordinates, best if one point per line comments: start with a non-numeric character halfspaces: use dim plus one and put offset after coefficients. May be preceeded by a single interior point ('H'). options: d - Delaunay triangulation by lifting points to a paraboloid v - Voronoi diagram from the Delaunay triangulation Hn,n,... - halfspace intersection about [n,n,0,...] d Qu - furthest-site Delaunay triangulation (upper convex hull) v Qu - furthest-site Voronoi diagram QJ - joggle input instead of merging facets Qopts- Qhull control options: Qbk:n - scale coord k so that low bound is n QBk:n - scale coord k so that upper bound is n (QBk is %2.2g) QbB - scale input to unit cube Qbb - scale last coordinate to [0,m] for Delaunay triangulations Qbk:0Bk:0 - remove k-th coordinate from input QJn - randomly joggle input in range [-n,n] QRn - random rotation (n=seed, n=0 time, n=-1 time/no rotate) %s%s%s%s Qc - keep coplanar points with nearest facet Qf - partition point to furthest outside facet Qg - only build good facets (needs 'QGn', 'QVn', or 'PdD') Qm - only process points that would increase max_outside Qi - keep interior points with nearest facet Qr - process random outside points instead of furthest ones Qs - search all points for the initial simplex Qu - for 'd', compute upper hull without point at-infinity returns furthest-site Delaunay triangulation Qv - test vertex neighbors for convexity Qx - exact pre-merges (skips coplanar and angle coplanar facets) Qz - add point-at-infinity to Delaunay triangulation QGn - good facet if visible from point n, -n for not visible QVn - good facet if it includes point n, -n if not Q0 - turn off default premerge with 'C-0'/'Qx' Q1 - sort merges by type instead of angle Q2 - merge all non-convex at once instead of independent sets Q3 - do not merge redundant vertices Q4 - avoid old->new merges Q5 - do not correct outer planes at end of qhull Q6 - do not pre-merge concave or coplanar facets Q7 - depth-first processing instead of breadth-first Q8 - do not process near-inside points Q9 - process furthest of furthest points Topts- Trace options: T4 - trace at level n, 4=all, 5=mem/gauss, -1= events Tc - check frequently during execution Ts - print statistics Tv - verify result: structure, convexity, and point inclusion Tz - send all output to stdout TFn - report summary when n or more facets created TO file - output results to file, may be enclosed in single quotes TPn - turn on tracing when point n added to hull TMn - turn on tracing at merge n TWn - trace merge facets when width > n TRn - rerun qhull n times. Use with 'QJn' TVn - stop qhull after adding point n, -n for before (see TCn) TCn - stop qhull after building cone for point n (see TVn) Precision options (default detects precision problems without correction): Cn - radius of centrum (roundoff added). Merge facets if non-convex An - cosine of maximum angle. Merge facets if cosine > n or non-convex C-0 roundoff, A-0.99/C-0.01 pre-merge, A0.99/C0.01 post-merge En - max roundoff error for distance computation Rn - randomly perturb computations by a factor of [1-n,1+n] Vn - min distance above plane for a visible facet (default 3C-n or En) Un - max distance below plane for a new, coplanar point (default Vn) Wn - min facet width for outside point (before roundoff, default 2Vn) Output formats (may be combined; if none, produces a summary to stdout): f - all fields of all facets i - vertices incident to each facet m - Mathematica output (2-d and 3-d) o - OFF file format (dim, points and facets; Voronoi regions) n - normals with offsets p - point coordinates (Voronoi vertices) s - print summary to stderr Fopts- additional input/output formats: Fa - print area for each facet FA - compute total area and volume for option 's' Fc - print count and coplanar points for each facet FC - print centrum or Voronoi center for each facet Fd - use cdd format for input (homogeneous with offset first) FD - use cdd format for normals (offset first) FF - print facets w/o ridges Fi - print inner planes for each facet Fi - print inner ridge normals (bounded) for Voronoi diagram FI - print id for each facet Fm - print merge count for each facet (511 max) Fn - print count and neighbors for each facet FN - print count and vertex neighbors for each point Fo - print outer planes (or max_outside) for each facet Fo - print outer ridge normals (unbounded)for Voronoi diagram FO - print all options Fp - print point for each halfspace intersection FP - print nearest vertex for each coplanar point (v,p,f,d) FQ - print Qhull and input command Fs - print summary: #int (6), dimension, #points, tot vertices, tot facets, #vertices in output, #facets #real (2), max outer plane and min vertex FS - print sizes: #int (0), #real(2) tot area, tot vol Ft - print Delaunay triangulation with added centrums Fv - print count and vertices for each facet Fv - print Voronoi diagram as vertices for each pair of sites FV - print average vertex (feasible point for 'H') Fx - print extreme points by point id (2-d, in order) Gopts- Geomview output (2-d, 3-d and 4-d; 2-d Voronoi) Ga - all points as dots Gp - coplanar points and vertices as radii Gv - vertices as spheres Gi - inner planes only Gn - no planes Go - outer planes only Gc - centrums Gh - hyperplane intersections Gr - ridges GDn - drop dimension n in 3-d and 4-d output Gt - transparent outer ridges to view 3-d Delaunay Popts- Print options: PAn - keep n largest facets by area Pdk:n - drop facet if normal[k] <= n (default 0.0) PDk:n - drop facet if normal[k] >= n Pg - print good facets (needs 'QGn' or 'QVn') PFn - keep facets whose area is at least n PG - print neighbors of good facets PMn - keep n facets with most merges Po - force output. If error, output neighborhood of facet Pp - do not report precision problems . - list of all options - - one line descriptions of all options qhull- compute convex hulls and related structures. %s input (stdin): dimension, number of points, point coordinates comments start with a non-numeric character halfspace: use dim plus one and put offsets after coefficients options (qh-opt.htm): d - Delaunay triangulation by lifting points to a paraboloid v - Voronoi diagram from the Delaunay triangulation H1,1 - Halfspace intersection about [1,1,0,...] via polar duality d Qu - furthest-site Delaunay triangulation (upper convex hull) v Qu - furthest-site Voronoi diagram QJ - randomly joggle input by a small amount . - concise list of all options - - one-line description of all options output options (subset): FA - compute total area and volume Fx - extreme points (convex hull vertices) G - Geomview output (2-d, 3-d and 4-d) Fp - halfspace intersections m - Mathematica output (2-d and 3-d) n - normals with offsets o - OFF file format (if Voronoi, outputs regions) TO file- output results to file, may be enclosed in single quotes f - print all fields of all facets s - summary of results (default) Tv - verify result: structure, convexity, and point inclusion p - vertex coordinates i - vertices incident to each facet examples: rbox c d D2 | qhull Qc s f Fx | more rbox 1000 s | qhull Tv s FA rbox 10 D2 | qhull d QJ s i TO result rbox 10 D2 | qhull v QJ p rbox 10 D2 | qhull d Qu QJ m rbox 10 D2 | qhull v Qu QJ o rbox c | qhull n rbox c | qhull FV n | qhull H Fp rbox d D12 | qhull QR0 FA rbox c D7 | qhull FA TF1000 rbox y 1000 W0 | qhull rbox 10 | qhull v QJ o Fv Qhull %s. Except for 'F.' and 'PG', upper-case options take an argument. delaunay voronoi Halfspace facet_dump Geomview incidences mathematica normals points off_file summary Farea FArea-total Fcoplanars FCentrums Fd-cdd-in FD-cdd-out FFacet-xridge Finner FIds Fmerges Fneighbors FNeigh-vertex Fouter FOptions Fpoint-intersect FPoint_near FQhull Fsummary FSize Ftriangles Fvertices Fvoronoi FVertex-ave Fxtremes Gvertices Gpoints Gall_points Gno_planes Ginner Gcentrums Ghyperplanes Gridges Gouter GDrop_dim Gtransparent PArea-keep Pdrop d0:0D0 Pgood PFacet_area_keep PGood_neighbors PMerge-keep Poutput_forced Pprecision_not QbBound 0:0.5 QbB-scale-box Qbb-scale-last Qcoplanar Qfurthest Qgood_only QGood_point Qinterior Qmax_out QJoggle Qrandom QRotate Qsearch_1st QupperDelaunay QVertex_good Qvneighbors Qxact_merge Qzinfinite Q0_no_premerge Q1_no_angle Q2_no_independ Q3_no_redundant Q4_no_old Q5_no_check_out Q6_no_concave Q7_depth_first Q8_no_near_in Q9_pick_furthest T4_trace Tcheck_often Tstatistics Tverify Tz_stdout TFacet_log TPoint_trace TMerge_trace TOoutput_file TRerun TWide_trace TVertex_stop TCone_stop Angle_max Centrum_size Error_round Random_dist Visible_min Ucoplanar_max Wide_outside It$???`bM$3E@?zG{@È@$?PbM?񙙙@L=L?(\)<@@@<?zG{??A@TAA.\(\.H@@@A333A@Y??ИfXt |~Ӽ<TFHd<`ۘ >\PI=C|X4& Hp|=8P |^,Yp\0a0d@mnqwx{ |@ `` p  p°Ƞʰ̀p`0`  00p@  @ !p#`$`% %(P)/12`3035<<?BDpGHKLO`OW@XZp[\]c f0ffg@hik`kmrtPxz`P@` P  pp P`@pp@@ ` P   Pp%P(`+@0 37:P:@@BCCDFI@J0JLMNOPQR0RS`T`UWXY@Y[[p[\0]]_abcd`effgphhi@j@lmnnoqsux|p@`pP@pð0 P` @P$'+P.`/8:=pACFK`L0N PVWY] a@df`ghkn ptpwpzp}@ppP@   @@P\P$X p %6.16g 0 %d %d%d 1 %d %d 0 { 0 1 }}} } end ,%8.4g %d , }]- f%d top bottom new tested notG seen MERGE DUP f%d r%d%d 1 0 2 facet p%d # p%d p%d: %8.4g1 }}} %5.2g1 %d beginBEGINendENDQJoggle%s %6.3g %s p%d %d %6.2g%6.16g center:pointsgood %6.4g v%d %d%6.2e %s %7.2g%7d%7.3g %s %p set: %d->%d %6.16g Matrix:DISTANT%2.2g qhull .EXE.exe facetsnormalsoffFilepointssummaryvoronoiVisibleFareaFinnerFIdsFmergesFouterFQhullFSizeGinnerGouterGpointsGridgesQJoggleTverifywTRerunPgoodqhull %s %d %2.2g _runvisiblehorizonDISTANTsimilar QR%d Totalmerged reasonv%d r%d f%dMERGINGTRACEMERGED   ?   8    8 W   ؂  h /` h  x  X { x ? 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