rbox(1) General Commands Manual rbox(1)

# [NAME](#NAME)

rbox - generate point distributions for qhull

# [SYNOPSIS](#SYNOPSIS)

Command "rbox" (w/o arguments) lists the options.

# [DESCRIPTION](#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](#EXAMPLES)

[rbox 10](#rbox)

10 random points in the unit cube centered at the origin.

[rbox 10 s D2](#rbox~2)

10 random points on a 2‐d circle.

[rbox 100 W0](#rbox~3)

100 random points on the surface of a cube.

[rbox 1000 s D4](#rbox~4)

1000 random points on a 4‐d sphere.

[rbox c D5 O0.5](#rbox~5)

a 5‐d hypercube with one corner at the origin.

[rbox d D10](#rbox~6)

a 10‐d diamond.

[rbox x 1000 r W0](#rbox~7)

100 random points on the surface of a fixed simplex

[rbox y D12](#rbox~8)

a 12‐d simplex.

[rbox l 10](#rbox~9)

10 random points along a spiral

[rbox l 10 r](#rbox~10)

10 regular points along a spiral plus two end points

[rbox 1000 L10000 D4 s](#rbox~11)

1000 random points on the surface of a narrow lens.

[rbox c G2 d G3](#rbox~12)

a cube with coordinates +2/-2 and a diamond with coordinates +3/-3.

[rbox 64 M3,4 z](#rbox~13)

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](#rbox~14)

5 copies of the origin in 3-d. Try 'rbox P0 P0 P0 P0 P0 | qhull QJ'.

[r 100 s Z1 G0.1](#r)

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](#OPTIONS)

[n](#n)

number of points

[Dn](#Dn)

dimension n‐d (default 3‐d)

[Bn](#Bn)

bounding box coordinates (default 0.5)

[l](#l)

spiral distribution, available only in 3‐d

[Ln](#Ln)

lens distribution of radius n. May be used with 's', 'r', 'G', and 'W'.

[Mn,m,r](#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](#s)

cospherical points randomly generated in a cube and projected to the unit sphere

[x](#x)

simplicial distribution. It is fixed for option 'r'. May be used with 'W'.

[y](#y)

simplicial distribution plus a simplex. Both 'x' and 'y' generate the same points.

[Wn](#Wn)

restrict points to distance n of the surface of a sphere or a cube

[c](#c)

add a unit cube to the output

c Gm

add a cube with all combinations of +m and -m to the output

[d](#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](#Cn,r,m)

add n nearly coincident points within radius r of m points

[Pn,m,r](#Pn,m,r)

add point \[n,m,r] to the output first. Pad coordinates with 0.0.

[n](#n~2)

Remove the command line from the first line of output.

[On](#On)

offset the data by adding n to each coordinate.

[t](#t)

use time in seconds as the random number seed (default is command line).

[tn](#tn)

set the random number seed to n.

[z](#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](#Zn)

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](#Zn~2)

same as Zn with an empty center (default G0.5).

[r s D2](#r~2)

generate a regular polygon

[r s Z1 G0.1](#r~3)

generate a regular cone

# [BUGS](#BUGS)

Some combinations of arguments generate odd results.

Report bugs to qhull\_bug@qhull.org, other correspondence to qhull@qhull.org

# [SEE ALSO](#SEE_ALSO)

[qhull(1)](/man/os/qhull/qhull.1)

# [AUTHOR](#AUTHOR)

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

August 10, 1998 Geometry Center

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Document: rbox(1) from qhull 2020.2-r7 (Chainguard OS)
Source: https://github.com/qhull/qhull