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' 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 [email protected], other correspondence to [email protected]

AUTHOR

C. Bradford Barber
[email protected]