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[CONE]rbox -- generate point distributions

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 synopsis

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

rbox outputs

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 D2 generates

2 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 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 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.

rbox notes

Some combinations of arguments generate odd results.

rbox 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

       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