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![[CONE]](qh--cone.gif) rbox -- generate point distributions
rbox -- generate point distributionsrbox generates random or regular points according to the options given, and outputs the points to stdout. The points are generated in a cube, unless 's', 'x', or 'y' are given.
rbox- generate various point distributions.  Default is random in cube.
args (any order, space separated):
  3000    number of random points in cube, lens, spiral, sphere or grid
  D3      dimension 3-d
  c       add a unit cube to the output ('c G2.0' sets size)
  d       add a unit diamond to the output ('d G2.0' sets size)
  l       generate a regular 3-d spiral
  r       generate a regular polygon, ('r s Z1 G0.1' makes a cone)
  s       generate cospherical points
  x       generate random points in simplex, may use 'r' or 'Wn'
  y       same as 'x', plus simplex
  Cn,r,m  add n nearly coincident points within radius r of m points
  Pn,m,r  add point [n,m,r] first, pads with 0
  Ln      lens distribution of radius n.  Also 's', 'r', 'G', 'W'.
  Mn,m,r  lattice (Mesh) rotated by [n,-m,0], [m,n,0], [0,0,r], ...
          '27 M1,0,1' is {0,1,2} x {0,1,2} x {0,1,2}.  Try 'M3,4 z'.
  W0.1    random distribution within 0.1 of the cube's or sphere's surface
  Z0.5 s  random points in a 0.5 disk projected to a sphere
  Z0.5 s G0.6 same as Z0.5 within a 0.6 gap
  Bn      bounding box coordinates, default 0.5
  h       output as homogeneous coordinates for cdd
  n       remove command line from the first line of output
  On      offset coordinates by n
  t       use time as the random number seed (default is command line)
  tn      use n as the random number seed
  z       print integer coordinates, default 'Bn' is 1e+06
The format of the output is the following: first line contains the dimension and a comment, second line contains the number of points, and the following lines contain the points, one point per line. Points are represented by their coordinate values.For example, rbox c 10 D2 generates
2 RBOX c 10 D2 14 -0.4999921736307369 -0.3684622117955817 0.2556053225468894 -0.0413498678629751 0.0327672376602583 -0.2810408135699488 -0.452955383763607 0.17886471718444 0.1792964061529342 0.4346928963760779 -0.1164979223315585 0.01941637230982666 0.3309653464993139 -0.4654278894564396 -0.4465383649305798 0.02970019358182344 0.1711493843897706 -0.4923018137852678 -0.1165843490665633 -0.433157762450313 -0.5 -0.5 -0.5 0.5 0.5 -0.5 0.5 0.5
       rbox 10
              10 random points in the unit cube centered  at  the
              origin.
       rbox 10 s D2
              10 random points on a 2-d circle.
       rbox 100 W0
              100 random points on the surface of a cube.
       rbox 1000 s D4
              1000 random points on a 4-d sphere.
       rbox c D5 O0.5
              a 5-d hypercube with one corner at the origin.
       rbox d D10
              a 10-d diamond.
       rbox x 1000 r W0
              100 random points on the surface of a fixed simplex
       rbox y D12
              a 12-d simplex.
       rbox l 10
              10 random points along a spiral
       rbox l 10 r
              10 regular points  along  a  spiral  plus  two  end
              points
       rbox 1000 L10000 D4 s
              1000 random points on the surface of a narrow lens.
           rbox 1000 L100000 s G1e-6
                  1000 random points near the edge of a narrow lens
       rbox c G2 d G3
              a cube with coordinates +2/-2 and  a  diamond  with
              coordinates +3/-3.
       rbox 64 M3,4 z
              a  rotated,  {0,1,2,3} x {0,1,2,3} x {0,1,2,3} lat-
              tice (Mesh) of integer points.
       rbox P0 P0 P0 P0 P0
              5 copies of the origin in 3-d.  Try 'rbox P0 P0  P0
              P0 P0 | qhull QJ'.
       r 100 s Z1 G0.1
              two  cospherical  100-gons plus another cospherical
              point.
       100 s Z1
              a cone of points.
       100 s Z1e-7
              a narrow cone of points with many precision errors.
Some combinations of arguments generate odd results.
       n      number of points
       Dn     dimension n-d (default 3-d)
       Bn     bounding box coordinates (default 0.5)
       l      spiral distribution, available only in 3-d
       Ln     lens  distribution  of  radius n.  May be used with
              's', 'r', 'G', and 'W'.
       Mn,m,r lattice  (Mesh)  rotated  by  {[n,-m,0],   [m,n,0],
              [0,0,r],  ...}.   Use  'Mm,n'  for a rigid rotation
              with r = sqrt(n^2+m^2).  'M1,0'  is  an  orthogonal
              lattice.   For  example,  '27  M1,0'  is  {0,1,2} x
              {0,1,2} x {0,1,2}.
       s      cospherical points randomly generated in a cube and
              projected to the unit sphere
       x      simplicial  distribution.   It  is fixed for option
              'r'.  May be used with 'W'.
       y      simplicial distribution plus a simplex.   Both  'x'
              and 'y' generate the same points.
       Wn     restrict  points  to distance n of the surface of a
              sphere or a cube
       c      add a unit cube to the output
       c Gm   add a cube with all combinations of +m  and  -m  to
              the output
       d      add a unit diamond to the output.
       d Gm   add a diamond made of 0, +m and -m to the output
       Cn,r,m add n nearly coincident points within radius r of m points
       Pn,m,r add point [n,m,r] to the output first.  Pad coordi-
              nates with 0.0.
       n      Remove the command line from the first line of out-
              put.
       On     offset the data by adding n to each coordinate.
       t      use  time  in  seconds  as  the  random number seed
              (default is command line).
       tn     set the random number seed to n.
       z      generate integer coordinates.  Use 'Bn'  to  change
              the  range.   The  default  is 'B1e6' for six-digit
              coordinates.  In R^4, seven-digit coordinates  will
              overflow hyperplane normalization.
       Zn s   restrict points to a disk about the z+ axis and the
              sphere (default Z1.0).  Includes the opposite pole.
              'Z1e-6'  generates  degenerate  points under single
              precision.
       Zn Gm s
              same as Zn with an empty center (default G0.5).
       r s D2 generate a regular polygon
       r s Z1 G0.1
              generate a regular cone
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Comments to: qhull@qhull.org
Created: Sept. 25, 1995 ---  Last modified: August 12, 1998