# 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
```

## Referenced By

August 10, 1998 Geometry Center