---
name: "rbox"
section: "1"
platform: "linux"
package: "qhull"
version: "2020.2-6"
release: "Arch Linux 2026-11-01"
platforms: ["linux"]
url: "https://new.carta.tech/rbox"
---

# rbox(1)

generate point distributions for qhull

## 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' 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

[qhull(1)](/qhull/1.md)

## AUTHOR

```
C. Bradford Barber
bradb@shore.net
```