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rbox(1)			    General Commands Manual		       rbox(1)

       rbox - generate point distributions for qhull

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

       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
       number of points, and the following lines contain the points, one point
       per line. Points	are represented	by their coordinate values.

       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

       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 P0 P0 P0 P0	P0
	      5	copies of the origin in	3-d.  Try 'rbox	P0 P0 P0 P0 P0 | qhull

       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.

       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'	gener-
	      ate the same points.

       Wn     restrict points to distance n of the surface of a	 sphere	 or  a

       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 coordinates with

       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  com-
	      mand 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 (de-
	      fault Z1.0).  Includes the opposite pole.	 'Z1e-6' generates de-
	      generate 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

       Some combinations of arguments generate odd results.

       Report	bugs   to,   other   correspondence   to


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

Geometry Center			August 10, 1998			       rbox(1)


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