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# Rbox manual

    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 given. The
           format of the output is the following: first line contains
           the dimension and a comment, second line contains the num-
           ber of points, and the following lines contain the points,
           one  point per line. Points are represented by their coor-
           dinate 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} 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.

    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}.

           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

           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

    BUGS
           Some combinations of arguments generate odd results.

           Report bugs to  qhull_bug@geom.umn.edu,	other  correspon-
           dence to qhull@geom.umn.edu

    SEE ALSO
           qhull(1)

    AUTHOR
           C. Bradford Barber
           c/o The Geometry Center
           400 Lind Hall
           207 Church Street S.E.
           Minneapolis, MN 55455

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Comments to: qhull@geom.umn.edu
Created: Sept. 25, 1995 --- Last modified: August 12, 1998