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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   '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
              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
              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' gener-
              ate 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  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 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
              (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)

qhull 2010.1 - Generated Sat Jan 9 07:55:49 CST 2010
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