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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', 'x', or 'y' are given.

rbox- generate various point distributions. Default is random in cube. args (any order, space separated): 3000 number of random points in cube, lens, spiral, sphere or grid D3 dimension 3-d c add a unit cube to the output ('c G2.0' sets size) d add a unit diamond to the output ('d G2.0' sets size) l generate a regular 3-d spiral r generate a regular polygon, ('r s Z1 G0.1' makes a cone) s generate cospherical points x generate random points in simplex, may use 'r' or 'Wn' y same as 'x', plus simplex Pn,m,r add point [n,m,r] first, pads with 0 Ln lens distribution of radius n. Also 's', 'r', 'G', 'W'. Mn,m,r lattice (Mesh) rotated by [n,-m,0], [m,n,0], [0,0,r], ... '27 M1,0,1' is {0,1,2} x {0,1,2} x {0,1,2}. Try 'M3,4 z'. W0.1 random distribution within 0.1 of the cube's or sphere's surface Z0.5 s random points in a 0.5 disk projected to a sphere Z0.5 s G0.6 same as Z0.5 within a 0.6 gap Bn bounding box coordinates, default 0.5 h output as homogeneous coordinates for cdd n remove command line from the first line of output On offset coordinates by n t use time as the random number seed (default is command line) tn use n as the random number seed z print integer coordinates, default 'Bn' is 1e+06

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.For example,

rbox c 10 D2generates2 RBOX c 10 D2 14 -0.4999921736307369 -0.3684622117955817 0.2556053225468894 -0.0413498678629751 0.0327672376602583 -0.2810408135699488 -0.452955383763607 0.17886471718444 0.1792964061529342 0.4346928963760779 -0.1164979223315585 0.01941637230982666 0.3309653464993139 -0.4654278894564396 -0.4465383649305798 0.02970019358182344 0.1711493843897706 -0.4923018137852678 -0.1165843490665633 -0.433157762450313 -0.5 -0.5 -0.5 0.5 0.5 -0.5 0.5 0.5

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 1000 L100000 s G1e-6 1000 random points near the edge 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} 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.

Some combinations of arguments generate odd results.

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 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

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Comments to: qhull@geom.umn.edu

Created: Sept. 25, 1995 --- Last modified: August 12, 1998