


rbox(1) 						  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 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



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rbox(1) 						  rbox(1)


	      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



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rbox(1) 						  rbox(1)


       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@qhull.org,	other  correspon-
       dence to qhull@qhull.org

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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