rbox(1) 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 given. The format of the output is the following: first line contains the dimension and a comment, second line contains the num- ber of points, and the following lines contain the points, one point per line. Points are represented by their coor- dinate 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 Geometry Center August 10, 1998 1 rbox(1) rbox(1) coordinates +3/-3. rbox 64 M3,4 z a rotated, {0,1,2,3} x {0,1,2,3} x {0,1,2,3} lat- tice (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. 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}. 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 Geometry Center August 10, 1998 2 rbox(1) rbox(1) 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 coordi- nates with 0.0. n Remove the command line from the first line of out- put. 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 correspon- dence to qhull@qhull.org SEE ALSO qhull(1) AUTHOR C. Bradford Barber bradb@shore.net Geometry Center August 10, 1998 3