rbox - generate point distributions for qhull

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

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 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.

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 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.

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}.

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

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

Some combinations of arguments generate odd results.

Report bugs to qhull_bug@qhull.org, other correspondence to qhull@qhull.org

qhull(1)

C. Bradford Barber
c/o The Geometry Center
400 Lind Hall
207 Church Street S.E.
Minneapolis, MN 55455