NAME

       rbox - generate point distributions for qhull

SYNOPSIS

       Command "rbox" (w/o arguments) lists the options.

DESCRIPTION

       rbox  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' or  'k' option is  given.
       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.

EXAMPLES

       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 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} lattice (Mesh) of integer points.
              'rbox 64 M1,0' is orthogonal.

       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.

OPTIONS

       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}. '27 M3,4 z' is a rotated integer
              lattice.

       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 coordinates with 0.0.

       n      Remove the command line from the first line of output.

       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

BUGS

       Some combinations of arguments generate odd results.

       Report bugs to qhull_bug@qhull.org, other correspondence to qhull@qhull.org

SEE ALSO

       qhull(1)

AUTHOR

       C. Bradford Barber
       bradb@shore.net