278 lines
9.3 KiB
HTML
278 lines
9.3 KiB
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<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML//EN">
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<html>
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<head>
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<title>rbox -- generate point distributions</title>
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</head>
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<body>
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<!-- Navigation links -->
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<p><b><a name="TOP">Up:</a></b> <a href="http://www.qhull.org">Home page</a> for Qhull<br>
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<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
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<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
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• <a href="qh-quick.htm#options">Options</a>
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• <a href="qh-opto.htm#output">Output</a>
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• <a href="qh-optf.htm#format">Formats</a>
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• <a href="qh-optg.htm#geomview">Geomview</a>
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• <a href="qh-optp.htm#print">Print</a>
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• <a href="qh-optq.htm#qhull">Qhull</a>
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• <a href="qh-optc.htm#prec">Precision</a>
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• <a href="qh-optt.htm#trace">Trace</a>
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• <a href="../src/libqhull_r/index.htm">Functions</a><br>
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<b>To:</b> <a href="#synopsis">sy</a>nopsis • <a href="#outputs">ou</a>tputs
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• <a href="#examples">ex</a>amples • <a href="#notes">no</a>tes
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• <a href="#options">op</a>tions
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<hr>
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<!-- Main text of document -->
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<h1><a
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href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/cone.html"><img
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src="qh--cone.gif" alt="[CONE]" align="middle" width="100"
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height="100"></a>rbox -- generate point distributions</h1>
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<blockquote>
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rbox generates random or regular points according to the
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options given, and outputs the points to stdout. The
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points are generated in a cube, unless 's', 'x', or 'y'
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are given.
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</blockquote>
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<h3><a href="#TOP">»</a><a name="synopsis">rbox synopsis</a></h3>
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<pre>
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rbox- generate various point distributions. Default is random in cube.
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args (any order, space separated):
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3000 number of random points in cube, lens, spiral, sphere or grid
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D3 dimension 3-d
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c add a unit cube to the output ('c G2.0' sets size)
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d add a unit diamond to the output ('d G2.0' sets size)
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l generate a regular 3-d spiral
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r generate a regular polygon, ('r s Z1 G0.1' makes a cone)
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s generate cospherical points
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x generate random points in simplex, may use 'r' or 'Wn'
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y same as 'x', plus simplex
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Cn,r,m add n nearly coincident points within radius r of m points
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Pn,m,r add point [n,m,r] first, pads with 0
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Ln lens distribution of radius n. Also 's', 'r', 'G', 'W'.
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Mn,m,r lattice (Mesh) rotated by [n,-m,0], [m,n,0], [0,0,r], ...
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'27 M1,0,1' is {0,1,2} x {0,1,2} x {0,1,2}. Try 'M3,4 z'.
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W0.1 random distribution within 0.1 of the cube's or sphere's surface
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Z0.5 s random points in a 0.5 disk projected to a sphere
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Z0.5 s G0.6 same as Z0.5 within a 0.6 gap
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Bn bounding box coordinates, default 0.5
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h output as homogeneous coordinates for cdd
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n remove command line from the first line of output
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On offset coordinates by n
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t use time as the random number seed (default is command line)
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tn use n as the random number seed
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z print integer coordinates, default 'Bn' is 1e+06
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</pre>
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<h3><a href="#TOP">»</a><a name="outputs">rbox outputs</a></h3>
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<blockquote>
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The format of the output is the following: first line contains
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the dimension and a comment, second line contains the
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number of points, and the following lines contain the points,
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one point per line. Points are represented by their coordinate values.
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<p>For example, <tt>rbox c 10 D2</tt> generates
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<blockquote>
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<pre>
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2 RBOX c 10 D2
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14
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-0.4999921736307369 -0.3684622117955817
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0.2556053225468894 -0.0413498678629751
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0.0327672376602583 -0.2810408135699488
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-0.452955383763607 0.17886471718444
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0.1792964061529342 0.4346928963760779
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-0.1164979223315585 0.01941637230982666
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0.3309653464993139 -0.4654278894564396
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-0.4465383649305798 0.02970019358182344
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0.1711493843897706 -0.4923018137852678
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-0.1165843490665633 -0.433157762450313
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-0.5 -0.5
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-0.5 0.5
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0.5 -0.5
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0.5 0.5
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</pre>
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</blockquote>
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</blockquote>
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<h3><a href="#TOP">»</a><a name="examples">rbox examples</a></h3>
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<pre>
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rbox 10
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10 random points in the unit cube centered at the
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origin.
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rbox 10 s D2
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10 random points on a 2-d circle.
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rbox 100 W0
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100 random points on the surface of a cube.
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rbox 1000 s D4
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1000 random points on a 4-d sphere.
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rbox c D5 O0.5
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a 5-d hypercube with one corner at the origin.
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rbox d D10
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a 10-d diamond.
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rbox x 1000 r W0
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100 random points on the surface of a fixed simplex
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rbox y D12
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a 12-d simplex.
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rbox l 10
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10 random points along a spiral
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rbox l 10 r
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10 regular points along a spiral plus two end
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points
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rbox 1000 L10000 D4 s
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1000 random points on the surface of a narrow lens.
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rbox 1000 L100000 s G1e-6
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1000 random points near the edge of a narrow lens
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rbox c G2 d G3
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a cube with coordinates +2/-2 and a diamond with
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coordinates +3/-3.
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rbox 64 M3,4 z
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a rotated, {0,1,2,3} x {0,1,2,3} x {0,1,2,3} lat-
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tice (Mesh) of integer points.
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rbox P0 P0 P0 P0 P0
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5 copies of the origin in 3-d. Try 'rbox P0 P0 P0
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P0 P0 | qhull QJ'.
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r 100 s Z1 G0.1
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two cospherical 100-gons plus another cospherical
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point.
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100 s Z1
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a cone of points.
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100 s Z1e-7
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a narrow cone of points with many precision errors.
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</pre>
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<h3><a href="#TOP">»</a><a name="notes">rbox notes</a></h3>
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<blockquote>
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Some combinations of arguments generate odd results.
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</blockquote>
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<h3><a href="#TOP">»</a><a name="options">rbox options</a></h3>
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<pre>
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n number of points
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Dn dimension n-d (default 3-d)
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Bn bounding box coordinates (default 0.5)
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l spiral distribution, available only in 3-d
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Ln lens distribution of radius n. May be used with
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's', 'r', 'G', and 'W'.
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Mn,m,r lattice (Mesh) rotated by {[n,-m,0], [m,n,0],
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[0,0,r], ...}. Use 'Mm,n' for a rigid rotation
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with r = sqrt(n^2+m^2). 'M1,0' is an orthogonal
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lattice. For example, '27 M1,0' is {0,1,2} x
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{0,1,2} x {0,1,2}.
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s cospherical points randomly generated in a cube and
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projected to the unit sphere
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x simplicial distribution. It is fixed for option
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'r'. May be used with 'W'.
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y simplicial distribution plus a simplex. Both 'x'
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and 'y' generate the same points.
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Wn restrict points to distance n of the surface of a
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sphere or a cube
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c add a unit cube to the output
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c Gm add a cube with all combinations of +m and -m to
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the output
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d add a unit diamond to the output.
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d Gm add a diamond made of 0, +m and -m to the output
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Cn,r,m add n nearly coincident points within radius r of m points
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Pn,m,r add point [n,m,r] to the output first. Pad coordi-
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nates with 0.0.
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n Remove the command line from the first line of out-
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put.
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On offset the data by adding n to each coordinate.
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t use time in seconds as the random number seed
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(default is command line).
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tn set the random number seed to n.
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z generate integer coordinates. Use 'Bn' to change
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the range. The default is 'B1e6' for six-digit
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coordinates. In R^4, seven-digit coordinates will
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overflow hyperplane normalization.
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Zn s restrict points to a disk about the z+ axis and the
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sphere (default Z1.0). Includes the opposite pole.
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'Z1e-6' generates degenerate points under single
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precision.
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Zn Gm s
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same as Zn with an empty center (default G0.5).
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r s D2 generate a regular polygon
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r s Z1 G0.1
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generate a regular cone
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</pre>
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<!-- Navigation links -->
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<hr>
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<p><b>Up:</b> <a href="http://www.qhull.org">Home page</a> for Qhull<br>
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<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
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<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
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• <a href="qh-quick.htm#options">Options</a>
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• <a href="qh-opto.htm#output">Output</a>
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• <a href="qh-optf.htm#format">Formats</a>
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• <a href="qh-optg.htm#geomview">Geomview</a>
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• <a href="qh-optp.htm#print">Print</a>
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• <a href="qh-optq.htm#qhull">Qhull</a>
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• <a href="qh-optc.htm#prec">Precision</a>
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• <a href="qh-optt.htm#trace">Trace</a>
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• <a href="../src/libqhull_r/index.htm">Functions</a><br>
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<b>To:</b> <a href="#synopsis">sy</a>nopsis • <a href="#outputs">ou</a>tputs
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|
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• <a href="#examples">ex</a>amples • <a href="#notes">no</a>tes
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• <a href="#options">op</a>tions
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<!-- GC common information -->
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<hr>
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<p><a href="http://www.geom.uiuc.edu/"><img src="qh--geom.gif"
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align="middle" width="40" height="40"></a><i>The Geometry Center
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Home Page </i></p>
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<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
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<br>
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Created: Sept. 25, 1995 --- <!-- hhmts start --> Last modified: August 12, 1998 <!-- hhmts end --> </p>
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</body>
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</html>
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