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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 no normal for facet f%d qhull input error (qh_printafacet): option 'Fp' needs qh feasible_point %d %d %d %6.16g 1 %d %d Vertices and facets: qhull warning: output for ridges and intersections not implemented in 2-d qhull warning: output for outer/inner planes and centrums not implemented in 4-d qhull warning: output for vertices not implemented in 4-d qhull warning: 'Gnh' generates no output in 4-d {appearance {linewidth 3} LIST # %s | %s {appearance {+edge -evert linewidth 2} LIST # %s | %s LIST # %s | %s 4VECT %d %d 1 VECT %d %d 1 # 1 point per line 1 0 # 1 color for all 0 1 1 1 # color of points 4OFF %d %d 1 qhull warning: writing Delaunay. Use 'p' or 'o' for Voronoi centers %s | %s begin %d %d real qhull warning: output is the Delaunay triangulation PLOT(CURVES( PLOT3D(POLYGONS( { %d %d %d %d %s | %s begin %d %d real qhull internal error (qh_printbegin): can not use this format for dimension %d 0 {appearance {-normal -edge normscale 0} {INST geom { define centrum CQUAD # f%d -0.3 -0.3 0.0001 0 0 1 1 0.3 -0.3 0.0001 0 0 1 1 0.3 0.3 0.0001 0 0 1 1 -0.3 0.3 0.0001 0 0 1 1 } transform { {INST geom { : centrum } transform { # f%d %8.4g %8.4g %8.4g 0 1 }}} qhull warning: no facets printed qhull internal error (qh_printend): number of ridges %d != number printed %d and at end %d } end )); 3 %d %d %d %8.4g %8.4g %8.4g 1 # f%d f%d 3 %d %d %d %8.4g %8.4g %8.4g 1 #r%d f%d f%d qh_printextremes_2d: loop in facet list. facet %d nextfacet %d VECT 1 2 1 2 1 # f%d %8.4g %8.4g %8.4g %8.4g %8.4g %8.4g %8.4g %8.4g %8.4g 1.0 ,[[%16.8f, %16.8f], [%16.8f, %16.8f]] Line[{{%16.8f, %16.8f}, {%16.8f, %16.8f}}] { OFF %d 1 1 # f%d %8.4g %d %8.4g %8.4g %8.4g 1.0 } , [[%16.8f, %16.8f, %16.8f]]Polygon[{{%16.8f, %16.8f, %16.8f}}]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 - f%d - flags: top bottom simplicial tricoplanar 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 - owner of normal & centrum is facet 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: MERGE DUP f%d - ridges (ids may be garbage): r%d - ridges: - all ridges:qhull warning: CDD format is not available for centrums, halfspace intersections, and OFF file format. %d 1 Options selected for Qhull %s: %s %s | %s 0 2 10 %d %d %d %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@qhull.org Precision problems were detected during construction of the convex hull. This occurs because convex hull algorithms assume that calculations are exact, but floating-point arithmetic has roundoff errors. To correct for precision problems, do not use 'Q0'. By default, Qhull selects 'C-0' or 'Qx' and merges non-convex facets. With option 'QJ', Qhull joggles the input to prevent precision problems. See "Imprecision in Qhull" (qh-impre.htm). If you use 'Q0', the output may include coplanar ridges, concave ridges, and flipped facets. In 4-d and higher, Qhull may produce a ridge with four neighbors or two facets with the same vertices. Qhull reports these events when they occur. It stops when a concave ridge, flipped facet, or duplicate facet occurs. When computing the Delaunay triangulation of coordinates > 1.0, - use 'Qbb' to scale the last coordinate to [0,m] (max previous coordinate) When computing the Delaunay triangulation: - use 'Qz' to add a point at-infinity. This reduces precision problems. If you need triangular output: - use option 'Qt' to triangulate the output - use option 'QJ' to joggle the input points and remove precision errors - use option 'Ft'. It triangulates non-simplicial facets with added points. If you must use 'Q0', try one or more of the following options. They can not guarantee an output. - use 'QbB' to scale the input to a cube. - use 'Po' to produce output and prevent partitioning for flipped facets - use 'V0' to set min. distance to visible facet as 0 instead of roundoff - use 'En' to specify a maximum roundoff error less than %2.2g. - options 'Qf', 'Qbb', and 'QR0' may also help To guarantee simplicial output: - use option 'Qt' to triangulate the output - use option 'QJ' to joggle the input points and remove precision errors - use option 'Ft' to triangulate the output by adding points - use exact arithmetic (see "Imprecision in Qhull", qh-impre.htm) The input to qhull appears to be less than %d dimensional, or a computation has overflowed. Qhull could not construct a clearly convex simplex from points: The center point is coplanar with a facet, or a vertex is coplanar with a neighboring facet. The maximum round off error for computing distances is %2.2g. The center point, facets and distances to the center point are as follows: center pointfacet p%d distance= %4.2g These points are the dual of the given halfspaces. They indicate that the intersection is degenerate. These points either have a maximum or minimum x-coordinate, or they maximize the determinant for k coordinates. Trial points are first selected from points that maximize a coordinate. Because of the high dimension, the min x-coordinate and max-coordinate points are used if the determinant is non-zero. Option 'Qs' will do a better, though much slower, job. Instead of 'Qs', you can change the points by randomly rotating the input with 'QR0'. The min and max coordinates for each dimension are: %d: %8.4g %8.4g difference= %4.4g If the input should be full dimensional, you have several options that may determine an initial simplex: - use 'QJ' to joggle the input and make it full dimensional - use 'QbB' to scale the points to the unit cube - use 'QR0' to randomly rotate the input for different maximum points - use 'Qs' to search all points for the initial simplex - use 'En' to specify a maximum roundoff error less than %2.2g. - trace execution with 'T3' to see the determinant for each point. If the input is lower dimensional: - use 'QJ' to joggle the input and make it full dimensional - use 'Qbk:0Bk:0' to delete coordinate k from the input. You should pick the coordinate with the least range. The hull will have the correct topology. - determine the flat containing the points, rotate the points into a coordinate plane, and delete the other coordinates. - add one or more points to make the input full dimensional. 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 # p%d VECT 1 1 1 1 1 %8.4g %8.4g %8.4g 1 p%d: %8.4g - 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 1 }}} qh_printvdiagram: unknown print format %d. NULLvertex - p%d (v%d): %5.2g deleted ridgedeleted neighbors: p%d (v%d)1 %d {appearance {+edge -face} OFF %d %d 1 # Voronoi centers and cells %d %d %d 1 0 # infinity not used # %d f%d # p%d (v%d) # p%d is coplanar or isolated %d %d %d %d %d %dqhull input error: 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. beginBEGINqhull 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 endENDqhull 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 comment, line %d is the first short line, 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@qhull.org. 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'. 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