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<h1><a
href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/cone.html"><img
src="qh--cone.gif" alt="[CONE]" align="middle" width="100"
height="100"></a>rbox -- generate point distributions</h1>
<blockquote>
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.
</blockquote>
<h3><a href="#TOP">»</a><a name="synopsis">rbox synopsis</a></h3>
<pre>
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
</pre>
<h3><a href="#TOP">»</a><a name="outputs">rbox outputs</a></h3>
<blockquote>
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.
<p>For example, <tt>rbox c 10 D2</tt> generates
<blockquote>
<pre>
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
</pre>
</blockquote>
</blockquote>
<h3><a href="#TOP">»</a><a name="examples">rbox examples</a></h3>
<pre>
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.
</pre>
<h3><a href="#TOP">»</a><a name="notes">rbox notes</a></h3>
<blockquote>
Some combinations of arguments generate odd results.
</blockquote>
<h3><a href="#TOP">»</a><a name="options">rbox options</a></h3>
<pre>
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
</pre>
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