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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	 '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

       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 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

       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}. '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'	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

       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

       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

Geometry Center			August 10, 1998			       rbox(1)


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