# rbox man page

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' 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

- 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 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 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 correspondence to qhull@qhull.org

## See Also

## Author

C. Bradford Barber bradb@shore.net