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rbox(1) 		     General Commands Manual			 rbox(1)

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 inte-
	    ger 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

Geometry Center 		 August 10, 1998			 rbox(1)

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