graph Application
plot Program
tek2plot Program
plotfont Utility
spline Program
ode Program
libplot, a Function Library
The GNU plotting utilities consist of seven command-line programs: the
graphics programs graph, plot, tek2plot, and
plotfont, and the mathematical programs spline,
ode, and double. Distributed with these programs is GNU
libplot, the library on which the graphics programs are
based. libplot is a function library for device-independent
two-dimensional vector graphics, including vector graphics animations
under the X Window System.
The graphics programs and libplot can produce output in the
following seven formats.
idraw-editable Postscript format. Files in this format
may be sent to a Postscript printer, imported into another document, or
edited with the free idraw drawing editor. See section How to get idraw.
xfig drawing editor. See section How to get xfig.
xterm program
and some versions of kermit.
plot program
can translate it to any of the preceding formats.
Of the graphics programs, the most powerful is graph, which is an
application for plotting two-dimensional scientific data. It reads one
or more data files containing datasets, and outputs a plot. The above
output formats are supported. The corresponding commands are
graph -T X, graph -T ps, graph -T fig,
graph -T pcl, graph -T hpgl, graph -T tek, and
graph. graph without a `-T' option (referred to as
`raw graph') produces output in GNU metafile format.
graph can read datasets in both ASCII and binary format, and
datasets in the `table' format produced by the plotting program
gnuplot. It produces a plot with or without axes and labels.
You may specify labels and ranges for the axes, and the size and
position of the plot on the display. The labels may contain subscripts
and subscripts, Greek letters, and other special symbols; there is also
support for Cyrillic script (i.e., Russian) and Japanese. You may
specify the type of plotting symbol used for each dataset, and such
parameters as the style and thickness of the line (if any) used to
connect points in a dataset. The plotting of filled regions is
supported, as is the drawing of error bars. graph provides full
support for multiplotting. With a single invocation of graph,
you may produce a plot consisting of many sub-plots, either side by side
or inset. Each sub-plot will have its own axes and data.
graph -T X, graph -T tek, and raw graph have a
feature that most plotting programs do not have. They can accept input
from a pipe, and plot data points in real time. For this to occur, the
user must specify ranges for both axes, so that graph does not
need to wait until the end of the input before determining them.
The plot program is a so-called plot filter. It can translate
GNU graphics metafiles (produced for example by raw graph) into
any supported output format. The corresponding commands are plot
-T X, plot -T ps, plot -T fig, plot -T pcl,
plot -T hpgl, plot -T tek, and plot. The
plot program is useful if you wish to produce output in several
different formats while invoking graph only once. It is also
useful if you wish to translate files in the traditional `plot(5)'
format produced by, e.g., the non-GNU versions of graph provided
with some operating systems. GNU metafile format is compatible with
plot(5) format.
The tek2plot program can translate from Tektronix format to any
of the abovementioned output formats. The corresponding commands are
tek2plot -T X, tek2plot -T ps, tek2plot -T fig,
tek2plot -T pcl, tek2plot -T hpgl, and tek2plot.
tek2plot is useful if you have a legacy application that produces
drawings in Tektronix format.
The plotfont program is a simple utility that displays a
character map for any font that is available to graph,
plot, or tek2plot. If the -T X, -T ps, or
-T fig options are used, the 35 standard Postscript fonts are
available, and if the -T pcl or -T hpgl options are used,
the 45 standard PCL 5 fonts are available, as are a number of
Hewlett--Packard vector fonts. A set of 22 Hershey vector fonts,
including Cyrillic fonts and a Japanese font, is always available. When
producing output for an X Window System display, any of the graphics
programs can use scalable X fonts.
Of the mathematical programs, spline does spline interpolation of
scalar or vector-valued data. It normally uses either cubic spline
interpolation or exponential splines in tension, but like graph
it can function as a real-time filter under some circumstances. Besides
splining datasets, it can construct curves, either open or closed,
through arbitrarily chosen points in d-dimensional space.
ode provides the ability to integrate an ordinary differential
equation or a system of ordinary differential equations, when provided
with an explicit expression for each equation. It supplements the
plotting program gnuplot, which can plot functions but not
integrate ordinary differential equations. The final plotting utility,
double, is a filter for converting, scaling and cutting binary or
ASCII data streams. It is still under development and is not yet
documented.
The libplot function library is discussed at length elsewhere in
this documentation. It can draw such objects as lines, open and closed
polylines, arcs (both circular and elliptic), circles and ellipses,
points, marker symbols, and text strings. The filling of objects other
than points, marker symbols, and text strings is supported (fill color,
as well as pen color, can be set arbitrarily). The support for
drawing text strings is extensive. The X Window System, Postscript,
and xfig drivers support the 35 standard Postscript fonts, and
the PCL 5 and HP-GL/2 drivers support both the 45 standard PCL 5
fonts and a number of Hewlett--Packard vector fonts. All drivers,
including the Tektronix and metafile drivers, support a set of 22
Hershey vector fonts. Text strings may include subscripts and
superscripts, and may include characters chosen from more than one font
in a typeface. Many non-alphanumeric characters may be included. The
entire collection of over 1700 `Hershey glyphs' digitized by Allen
V. Hershey at the U.S. Naval Surface Weapons Center, which includes
many curious symbols, is built into libplot. Japanese text
strings in the so-called EUC (Extended Unix Code) format can be also be
drawn. Such strings may include both syllabic characters (Hiragana and
Katakana) and ideographic characters (Kanji). A library of over 600
Kanji is built into libplot.
The drawing editors idraw and xfig are not distributed
along with the GNU plotting utilities. However, they are free software,
and you may readily obtain them elsewhere (see section Obtaining Auxiliary Software).
graph Application
Each invocation of graph reads one or more datasets from files
named on the command line or from standard input, and prepares a plot.
There are many command-line options for adjusting the visual appearance
of the plot.
See section graph command-line options, for documentation on all options.
The following sections explain how to use the most frequently used
options, by giving examples.
graph
By default, graph reads ASCII data from the files specified on
the command line, or from standard input if no files are specified. The
data are pairs of numbers, interpreted as the x and y
coordinates of data points:
0.0 0.0 1.0 0.2 2.0 0.0 3.0 0.4 4.0 0.2 5.0 0.6
Data points do not need to be on different lines, nor do the x and y coordinates of a data point need to be on the same line. However, there should be no blank lines in the input if it is to be viewed as forming a single dataset.
To plot such a dataset with graph, you could do
graph -T ps ascii_data_file > plot.ps
or equivalently
graph -T ps < ascii_data_file > plot.ps
This will produce an encapsulated Postscript file plot.ps, which
you may include in another document, display on a screen, or send
directly to a printer. (The `--page-size' option, or the
PAGESIZE environment variable, specifies the size of the printed
page. The default is "letter", i.e., 8.5in by 11in, but
"a4" or other ISO or ANSI page sizes can be specified instead.)
You may also do
graph -T fig < ascii_data_file > plot.fig
to produce a file plot.fig that you may edit with the the
xfig drawing editor, or
graph -T hpgl < ascii_data_file > plot.plt
to produce a file plot.plt in the Hewlett--Packard Graphics
Language (HP-GL/2) that you may send to a Hewlett--Packard plotter.
Similarly, graph -T pcl will produce a file in PCL 5 format
that you may print on a LaserJet or other laser printer.
You may use graph -T X to pop up a window on an X
Window System display, and display the plot in it. For that, you
would do
graph -T X < ascii_data_file
If you use graph -T X, no output file will be produced; only a
window. The window will vanish if you type `q' or click your mouse
in it.
You may also use graph -T tek, to display a plot on a device that
can emulate a Tektronix 4014 graphics terminal. xterm, the X
Window System terminal emulator, can do this. Within an xterm
window, you would do
graph -T tek < ascii_data_file
xterm normally emulates a VT100 terminal, but when this command
is issued from within it, it will pop up a second window
(a `Tektronix window') and draw the plot in it. The Japanese
terminal emulator kterm should be able to do the same, provided
that it is correctly installed. Another piece of software that can
emulate a Tektronix 4014 terminal is the MS-DOS version of kermit.
graph may behave differently depending on the environment in
which it is invoked. We have already mentioned the PAGESIZE
environment variable, which affects the operation of graph -T ps,
graph -T fig, graph -T pcl, and graph -T hpgl. The
DISPLAY and BITMAPSIZE environment variables affect the
operation of graph -T X, and the TERM environment
variable affects the operation of graph -T tek. There are also
several environment variables that affect the operation of graph
-T pcl and graph -T hpgl. For a complete discussion of the
effects of the environment on graph, see section Environment variables.
The following remarks apply irrespective of which display type is
specified.
By default, successive points in the dataset are joined by solid line segments, which form a polygonal line or polyline that we call simply a `line'. You may choose the style of line (the `linemode') with the `-m' option:
graph -T ps -m 2 < ascii_data_file > plot.ps
Here `-m 2' indicates that linemode #2 should be used. If the dataset is rendered in monochrome, which is the default, the line can be drawn in one of five distinct styles. Linemodes #1 through #5 signify solid, dotted, dotdashed, shortdashed, and longdashed; thereafter the sequence repeats. If the `-C' option is used, the dataset will be rendered in color. For colored datasets, the line can be drawn in one of 25 distinct styles. Linemodes #1 through #5 signify red, green, blue, magenta, and cyan; all are solid. Linemodes #6 through #10 signify the same five colors, but dotted rather than solid. Linemodes #11 through #16 signify the same five colors, but dotdashed, and so forth. After linemode #25, the sequence repeats. Linemode #0, irrespective of whether the rendering is in monochrome or color, means that the line is not drawn.
If you wish to fill the polygon bounded by the line (i.e., shade it, or fill it with a solid color), you may use the `-q' option. For example,
echo .1 .1 .1 .9 .9 .9 .9 .1 .1 .1 | graph -T ps -C -m 1 -q 0.3 > plot.ps
will plot a square region with vertices (0.1,0.1), (0.1,0.9), (0.9,0.9), and (0.9,0.1). The repetition of the first vertex (0.1,0.1) at the end of the sequence of vertices ensures that the square will be closed: all four segments of its boundary will be drawn. The square will be drawn in red (since the colored version of linemode #1 is requested). The interior of the square will be filled with red to an intensity of 30%, as the `-q 0.3' option indicates. If the intensity were zero, the region would be filled with white, and if it were 1.0, the region would be filled with solid color. If the intensity were negative, the region would be unfilled, or transparent (the default).
You may choose the width of the line, whether it is filled or not, by using the `-W' option. For example, `-W 0.01' means that the line should have a width equal to 0.01 times the width of the display. Also, you may put symbols at each data point along the line by doing, for example,
graph -T ps -S 3 0.1 < ascii_data_file > plot.ps
where the first argument 3 indicates which symbol to plot. The optional second argument 0.1 specifies the symbol size as a fraction of the size of the `plotting box': the square within which the plot is drawn. Symbol #1 is a dot, symbol #2 is a plus sign, symbol #3 is an asterisk, symbol #4 is a circle, symbol #5 is a cross, and so forth. (See section Available marker symbols.) Symbols 1 through 31 are the same for all display types, and the color of a symbol will be the same as the color of the line it is plotted along.
Actually, you would probably not want to plot symbols at each point in the dataset unless you turn off the line joining the points. For this purpose, the `negative linemode' concept is useful. A line whose linemode is negative is not visible; however, any symbols plotted along it will have the color associated with the corresponding positive linemode. So, for example,
graph -T ps -C -m -3 -S 4 < ascii_data_file > plot.ps
will plot a blue circle at each data point. The circles will not be joined by line segments. By adding the optional second argument to the `-S' option, you may adjust the size of the circles.
graph will automatically generate abscissa (i.e., x)
values for you if you use the `-a' option. If this option is
used, no abscissa values should be given in the data file. The data
points will be taken to be regularly spaced along the abscissa. The two
arguments following `-a' on the command line will be taken as the
sampling interval and the abscissa value of the first data point. If
they are absent, they default to 1.0 and 0.0 respectively. For example,
the command
echo 0 1 0 | graph -T ps -a > plot.ps
produces exactly the same plot as
echo 0 0 1 1 2 0 | graph -T ps > plot.ps
graph will plot data with error bars, if the `-I e' option
is specified. If it is, the dataset should consist of triples
(x,y,error) rather than pairs (x,y). A
vertical error bar of the appropriate length will be plotted at each
data point. You may plot a symbol at each data point, along with the
error bar, by using the `-S' option in the usual way. The symbol
will be the same for each point in the dataset. You may use the
`-a' option in conjunction with `-I e', if you wish. If you
do, the dataset should contain no abscissa (i.e., x) values.
By default the limits on the x and y axes, and the spacing between the labeled ticks on each axis, are computed automatically. You may wish to set them manually. You may accomplish this with the `-x' and `-y' options.
echo 0 0 1 1 2 0 | graph -T ps -x -1 3 -y -1 2 > plot.ps
will produce a plot in which the x axis extends from -1
to 3, and the y axis from -1 to 2. By default,
graph tries to place about six numbered ticks on each axis. By
including an optional third argument to either `-x' or `-y',
you may manually set the spacing of these ticks, also. For example,
using `-y -1 2 1' rather than `-y -1 2' will produce a
y axis with labeled ticks at -1, 0, 1, and 2,
rather than at the locations that graph would choose by default.
In general, if a third argument is present then labeled ticks will
be placed at each of its integer multiples.
To make an axis logarithmic, you may use the `-l' option. For example,
echo 1 1 2 3 3 1 | graph -T ps -l x > plot.ps
will produce a plot in which the x axis is logarithmic, but the y axis is linear. To make both axes logarithmic, you would use `-l x -l y'. By default, the upper and lower limits on a logarithmic axis are powers of ten, and the tick marks at these powers of ten, and no other tick marks, are labeled. If you need more labeled ticks on a logarithmic axis, you should specify a tick spacing manually. For example, `-l x -x 1 9 2' will produce a plot in which the x axis is logarithmic and extends from 1 to 9. Labeled ticks will be located at each integer multiple of 2, i.e., at 2, 4, 6, and 8.
You may label the x and y axes with the `-X' and `-Y' options, respectively. For example,
echo 1 1 2 3 3 1 | graph -T ps -l x -X "A Logarithmic Axis" > plot.ps
will label the log axis in the preceding example. By default the label for the y axis (if any) will be rotated 90 degrees, unless you use the `--toggle-rotate-y-label' option. You may specify a `top label', or title for the plot, by using the `-L' option. Doing, for example,
echo 1 1 2 3 3 1 | graph -T ps -l x -L "A Simple Example" > plot.ps
will produce a plot with a title on top.
The size of the x axis and y axis labels is specified with the `-f' option, and the size of the title is specified with the `--title-font-size' option. For example,
echo 1 1 2 3 3 1 | graph -T ps -X "Abscissa" -f 0.1 > plot.ps
will produce a plot in which the font size of the x axis label, and each of the numerical tick labels, is very large (0.1 times the size of the plotting box, i.e., the square within which the plot is drawn).
The font in which the labels specified with the `-X', `-Y',
and `-L' options are drawn can be specified with the `-F'
option. For example, `-F Times-Roman' will make the labels appear
in Times-Roman instead of the default font (which is Helvetica, unless
`-T pcl', `-T hpgl' or `-T tek' is specified). Font
names are case-insensitive, so `-F times-roman' will work equally
well. The available fonts include 35 Postscript fonts (for all variants
of graph other than graph -T pcl, graph -T hpgl and
graph -T tek), 45 PCL 5 fonts and a number of
Hewlett--Packard vector fonts (for graph -T pcl and graph
-T hpgl), and 22 Hershey vector fonts. The Hershey fonts include
HersheyCyrillic, for Russian, and HersheyEUC, for Japanese. For a
discussion of the available fonts, see section Available text fonts. The
plotfont utility will produce a character map of any available
font. See section The plotfont Utility.
The format of the labels drawn with the `-X', `-Y', and `-L' options may be quite intricate. Subscripts, superscripts, square roots, and switching fonts within a typeface are all allowed. The above examples do not illustrate this, but for details, see section Text string format and escape sequences.
Each of the preceding examples produced a plot containing the default sort of grid (a square box, with ticks and labels drawn along its lower edge and its left edge). There are actually several sorts of grid you may request. The `-g 0', `-g 1', `-g 2', and `-g 3' options yield successively fancier grids. What they yield, respectively, is no grid at all, a pair of axes with ticks and labels, a square box with ticks and labels, and a square box with ticks, labels, and grid lines. As you can see, `-g 2' is the default. There is also a `-g 4' option, which yields a slightly different sort of grid: a pair of axes that cross at the origin. This last sort of grid is useful if the x or y coordinates of the data points you are plotting are both positive and negative.
To alter the linear dimensions of a plot, and also to position it in a different part of your display, you could do something like
graph -T ps -h .3 -w .6 -r .1 -u .1 < ascii_data_file > plot.ps
Here the `-h' and `-w' options specify the height and width of the plotting box, and the `-r' and `-u' options indicate how far up and to the right the lower left corner of the plotting box should be positioned. All dimensions are expressed as fractions of the size of the graphics display, which by convention is a square. By default, the height and width of the plotting box equal 0.6, and the `upward shift' and the `rightward shift' equal 0.2. So the above example will produce a plot that is half as tall as usual. Compared to its usual position, the plot will be shifted slightly downward and to the left.
The `graphics display', within which the plotting box is located, is an
abstraction. For graph -T X, it is a square window on an
X display, the size of which can be set by using the
--bitmap-size option, or by setting the BITMAPSIZE
environment variable. For graph -T tek, it is a square region
occupying the central part of a Tektronix display. (Tektronix displays
are 4/3 times as wide as they are high.) For graph -T ps, by
default it is a square region centered on an 8.5in by 11in
page (US letter size), occupying the full width of the page with
allowance being made for margins. For graph -T fig, by
default it is a square region of the same size, positioned in the upper
left corner of an xfig display. For graph -T pcl and
graph -T hpgl, by default it is a square region of the same
size, with position and orientation on the page being controlled by
environment variables. The page size used by graph -T ps,
graph -T fig, graph -T pcl, and graph -T hpgl can
be set by using the --page-size option, or by setting the
environment variable PAGESIZE. For example, setting
PAGESIZE to "a4" would position the graphics display
appropriately on an A4-size page (21cm by 29.7cm).
Changing the width of the plotting box may have unforeseen consequences. A number of command-line options specify sizes or dimensions as fractions of the width of the plotting box. For example, `-S 3 .01' specifies that the plotting symbols for the following dataset should be of type #3, and should have a fractional size equal to 0.01. If the `-w' option is employed to widen or narrow the plot, such dimensions or sizes will scale in tandem. That is presumably the right thing to do, but may be slightly disconcerting.
It is frequently the case that several datasets need to be displayed on the same plot. If so, you may wish to distinguish the points in different datasets by joining them by lines of different types, or by using plotting symbols of different types.
A more complicated example would be the following. You may have a file containing a dataset that is the result of experimental observations, and a file containing closely spaced points that trace out a theoretical curve. The second file is a dataset in its own right. You would presumably plot it with line segments joining successive points, so as to trace out the theoretical curve. But the first dataset, resulting from experiment, would be plotted without such line segments. In fact, a plotting symbol would be plotted at each of its points.
These examples, and others like them, led us to define a set of seven attributes which define the way in which a dataset should be plotted. These attributes, which can be set by command-line options, are the following.
Color/monochrome (a choice of one or the other) is the simplest. This choice is toggled with the `-C' option. The `linemode' (i.e., line style) specifies how the line segments joining successive points should be drawn; it is specified with the `-m' option. Linemode #0 means no linemode at all, for example. `Linewidth' is self-explanatory; it is specified with the `-W' option. `Symbol type' and `symbol size', which are specified with the `-S' option, specify the symbol plotted at each point of the dataset. `Symbol font name' refers to the font from which plotting symbols #32 and above, which are taken to be characters rather than geometric symbols, are selected. It is set with the `--symbol-font-name' option, and is relevant only if `-S' is used to request such special plotting symbols. Finally, the polygonal line joining the points in a dataset may be filled, to create a filled or shaded polygon. The `fill fraction' is set with the `-q' option. A negative fill fraction means no fill, or transparent; zero means white, and 1.0 means solid, or fully colored.
The preceding seven attributes refer to the way in which datasets are plotted. Datasets may also differ from one another in the way in which they are read from files. The dataset(s) in a file may or may not contain error bars, for example. If a file contains data with error bars, the `-I e' option should occur on the command line before the file name. (The `-I' option specifies the input format for the following files.)
The following illustrates how datasets in three different input files could be plotted simultaneously.
graph -T ps -m 0 -S 3 file_1 -C -m 3 file_2 -C -W 0.02 file_3 > output.ps
The dataset in file_1 will be plotted in linemode #0, so
successive points will not be joined by lines. But symbol #3 (an
asterisk) will be plotted at each point. The dataset in file_2
will be plotted in color, and linemode #3 will be used. In color
plotting, linemode #3 is interpreted as a solid blue line. The second
`-C' on the command line turns off color for file_3. The
points in the third dataset will be joined by a black line of width
0.02, as a fraction of the width of the graphics display.
The above command line could be made even more complicated by specifying additional options (e.g., `-q' or `-I') before each file. In fact the command line could also include such standard options as `-x' or `-y', which specify the range of each axis. Such options, which refer to the plot as a whole rather than to individual datasets, should appear before the first file name. For example, you could do
graph -T ps -x 0 1 0.5 -m 0 -S 3 file_1 -C -m 3 file_2 > output.ps
Note that it is possible to include the special file name `-',
which refers to standard input, on the command line. So you may produce
a plot in part from files, and in part from input that is piped to
graph from another program.
Each input file may include more than one dataset. If so, the command line options preceding a file on the command line will take effect for all datasets in that file. There are two exceptions to this. By default, the linemode is incremented (`bumped') from one dataset to the next. This feature is usually quite convenient. For example, if you do
graph -T ps -m 3 file_1 > output.ps
the first dataset in file_1 will appear in linemode #3, the
second in linemode #4, etc. In fact if you do
graph -T ps file_1 file_2 ... > output.ps
without specifying linemode explicitly, the successive datasets read from the files on the command line will appear in linemode #1, linemode #2, .... If you do not like this feature, you may turn it off, or in general toggle it, by using the `-B' option.
You may also control manually the linemode and symbol type used for the datasets within any file. You would do this by including directives in the file itself, rather than on the command line. For example, if the line
#m=-5,S=10
appeared in an ASCII-format input file, it would be interpreted as a
directive to switch to linemode #-5 and symbol type #10 for the
following dataset. Future releases of graph may provide the
ability to set each of the seven dataset attributes in this way.
It is occasionally useful to display several plots at once on a single page, or on a single graphics display. We call such a composite plot a multiplot. One common sort of multiplot is a small plot inset into a larger one. Another sort is two or more plots side by side.
graph can draw multiplots consisting of an arbitrarily large
number of sub-plots. When multiplotting, graph draws each
sub-plot in its own `virtual display'. When an ordinary plot is drawn,
the virtual display is the same as the physical display. But when a
multiplot is drawn, the virtual display may be any smaller square
region. The following example illustrates the idea.
graph -T ps data_file_1 --reposition .35 .35 .3 data_file_2
Here data_file_1 is plotted in the usual way. The
`--reposition' option specifies that when data_file_2 is
plotted, it will be drawn within a virtual display. For the purposes of
the `--reposition' option, the physical display is a square with
lower left corner (0.0,0.0) and upper right corner (1.0,1.0). In those
coordinates, the virtual display will be a square of size 0.3 with lower
left corner (0.35,0.35). So the second sub-plot will be inset into
the first.
Just as the `-w', `-h', `-r', and `-u' options may be used to set the size and position of a plotting box within the physical display, so they may be used to set the size and position of a plotting box within a virtual display. For example,
graph -T ps data_file_1 --reposition .35 .35 .3 -w .4 -r .3 data_file_2
will yield a multiplot in which the second sub-plot is significantly different. Its plotting box will have a width only 0.4 times the width of the virtual display. However, the plotting box will be centered within the virtual display, since the distance between the left edge of the plotting box and the left edge of the virtual display will be 0.3 times the width of the virtual display.
By convention, before each sub-plot of a multiplot other than the first is drawn, a `blankout region' surrounding its plotting box is erased. (That is, it is filled with white.) This erasure prevents the sub-plots from overlapping and producing a messy result. By default, the blankout region is a rectangular region 30% larger in each dimension than the plotting box for the sub-plot. This is appropriate if the sub-plot is a small one that is inset into the first sub-plot. It may not be appropriate, however, if you are preparing a multiplot in which several sub-plots appear side by side. You may use the `--blankout' option to adjust this parameter. For example, specifying `--blankout 1.0' will make the blankout region for a sub-plot coincide with its plotting box. Specifying `--blankout 0.0' will prevent any blanking out from occurring. The blankout parameter may differ from sub-plot to sub-plot.
It should be emphasized that every sub-plot in a multiplot is a plot in
its own right. All the usual options (`-m', `-S', `-x',
`-y', etc.) can be applied to each sub-plot separately. The
options for a sub-plot should occur on the graph command line
immediately after the `--reposition' option that applies to it.
Each sub-plot may be prepared from more than a single dataset, also.
The names of the data files for each subplot should occur on the command
line before the following `--reposition' option, if any.
By default, graph reads datasets in ASCII format. But it can
also read datasets in any of three binary formats (single precision
floating point, double precision floating point, and integer).
These three input formats are specified by the `-I d', `-I f',
and `-I i' options, respectively.
There are two advantages to using binary data: 1) graph runs
significantly faster because the computational overhead for converting
data from ASCII to binary is eliminated, and 2) the input files may
be significantly smaller. If you have very large datasets, using
binary format may reduce storage and runtime costs.
For example, you may create a single precision binary dataset as output from a C language program:
#include <stdio.h>
void write_point (float x, float y)
{
fwrite(&x, sizeof (float), 1, stdout);
fwrite(&y, sizeof (float), 1, stdout);
}
You may plot data written this way by doing:
graph -T ps -I f < binary_data_file > plot.ps
@ifnottex
The inclusion of multiple datasets within a single binary file is
supported. If a binary file contains more than a single dataset,
successive datasets should be separated by a single occurrence of the
the largest possible number. For single precision datasets this is the
quantity FLT_MAX, for double precision datasets it is the
quantity DBL_MAX, and for integer datasets it is the quantity
INT_MAX. On most machines FLT_MAX is approximately
3.4x10^38, DBL_MAX is approximately 1.8x10^308, and
INT_MAX is 2^32-1.
If you are reading datasets from more than one file, it is not required that the files be in the same format. For example,
graph -T ps -I f binary_data_file -I a ascii_data_file > plot.ps
will read binary_data_file in `f' (binary single precision)
format, and ascii_data_file in `a' (normal ASCII) format.
There is currently no support for reading and plotting binary data with
error bars. If you have data with error bars, you should supply the data
to graph in ASCII, and use the `-I e' option.
graph can also read data files in the ASCII `table' format
produced by the gnuplot plotting program. For this, you should
use the `-I g' option. Such a data file may consist of more than
one dataset.
To sum up: there are six supported data formats, `a' (normal
ASCII), `e' (ASCII with error bars), `g' (the ASCII `table'
format produced by gnuplot), `f' (binary single precision),
`d' (binary double precision), and `i' (binary integer).
Input files may be in any of these six formats.
graph command-line options
The graph program reads one or more datasets from files named on
the command line or from standard input, and prepares a plot. The
display type or output format is specified with the `-T' option.
There are many command-line options for adjusting the visual appearance
of the plot.
By default, graph reads ASCII data from the files specified on
the command line. The data are pairs of numbers, interpreted as the
x and y coordinates of data points. If no file names
are specified, or the file name `-' is specified, the standard
input is read.
The relative order of file names and command-line options is important. Only the options that precede a file name on the command line take effect for that file.
The following sections list the possible command-line options. Each option that takes an argument is followed, in parentheses, by the type and default value of the argument. There are five sorts of option.
graph, i.e., relevant only if no
display type or output format is specified with the `-T' option.
(See section Raw graph options.)
@ifnottex
The behavior of graph is also affected by a number of environment
variables, so there is a section discussing them as well.
The following options affect an entire plot. They should normally occur at most once, and should appear on the command line before the first file name. If a multiplot is being drawn, they may (with the exception of the `-T' option) occur more than once. If so, the second and later occurrences should be placed on the command line immediately after each `--reposition x y' option.
idraw-editable Postscript, the format used by the
xfig drawing editor, the Hewlett-Packard PCL 5 printer
language, the Hewlett--Packard Graphics Language, Tektronix format, and
device-independent GNU metafile format.
graph -T pcl, graph
-T hpgl and graph -T tek, for which "HersheySerif" is the
default.) Set the font used for the axis and tick labels, and for the
plot title (if any), to be font_name. The choice of font for
the plot title may be overridden with the `--title-font-name'
option (see below). Font names are case-insensitive. If the specified
font is not available, the default font will be used. Which fonts are
available depends on which `-T' option is used. For a list of all
fonts, see section Available text fonts. The plotfont utility will produce a
character map of any available font. See section The plotfont Utility.
graph not erase the
display device before it begins to plot. This is relevant only to
graph -T tek. It may be employed to perform a crude sort of
multiplotting, since Tektronix displays and emulators are persistent, in
the sense that previously drawn graphics remain visible.
graph is to act as a real-time filter.
graph is to act as a real-time filter.
graph -T X.
An unrecognized name sets the color to the default. For information
on what names are recognized, see section Specifying Colors by Name. The environment
variable BG_COLOR can equally well be used to specify the
background color.
graph -T X, for
which the graphics display is an X window. If you choose a
rectangular (non-square) window size, the fonts in the plot will be
scaled anisotropically, i.e., by different factors in the horizontal and
vertical direction. This requires an X11R6 display. Any font that
cannot be scaled in this way will be replaced by a default scalable
font, such as the Hershey vector font "HersheySerif".
The environment variable BITMAPSIZE can equally well be used to
specify the window size. For backward compatibility, the X resource
Xplot.geometry, which can be set by the user, may be used
instead.
libplot graphics library should be used. This
value is device-dependent. The interpretation of zero line width is
also device-dependent (on some devices, a zero-width line is the
thinnest line that can be drawn; on others, a zero-width line is
invisible).
graph -T tek does not support drawing lines with other than a
default width, and graph -T hpgl does not support doing so if
the environment variable HPGL_VERSION is set to a value less
than "2" (the default).
MAX_LINE_LENGTH can also
be used to specify the maximum line length. This option has no effect
on graph -T tek or raw graph, since they draw polylines in
real time and have no buffer limitations.
graph -T ps,
graph -T fig, graph -T pcl, and graph -T hpgl.
"letter" means an 8.5in by 11in page. Any ISO page size in
the range "a0"..."a4" or ANSI page size in the range "a"..."e"
may be specified ("letter" is an alias for "a" and "tabloid" is an
alias for "b"). "legal" and "ledger" are recognized page sizes
also. The environment variable PAGESIZE can equally well be used
to specify the page size.
For graph -T ps, the graphics display within which the plot is
drawn will be a square region centered on the specified page and
occupying its full width. For graph -T fig, the graphics display
will be a square region located in the upper left corner of an
xfig display, with width equal to the width of the specified
page. For graph -T pcl and graph -T hpgl, fine control
over the positioning of the graphics display on the page can be
accomplished by setting certain environment variables (see section Environment variables).
graph -T pcl, graph
-T hpgl and graph -T tek, for which "HersheySerif" is the
default.) Set the font used for the plot title (`top label') to be
font_name. Normally the font used for the plot title is the same
as that used for labelling the axes and the ticks along the axes, as
specified by the `-F' option. But the `--title-font-name'
option can be used to override this. Font names are case-insensitive.
If the specified font is not available, the default font will be used.
Which fonts are available depends on which `-T' option is used.
For a list of all fonts, see section Available text fonts. The plotfont
utility will produce a character map of any available font.
See section The plotfont Utility.
The following options affect the way in which individual datasets are read from files, and drawn as part of a plot. They should appear on the command line before the file containing the datasets whose reading or rendering they will affect. They may appear more than once on a command line, if more than one file is to be read.
The following three options affect the way in which datasets are read from files.
gnuplot plotting program.
FLT_MAX, which is the largest
possible single precision floating point number. On most machines this
is approximately 3.4x10^38.
DBL_MAX, which is the largest
possible double precision floating point number. On most machines this
is approximately 1.8x10^308.
INT_MAX,
which is the largest possible integer. On most machines this is 2^31-1.
The following options affect the way in which individual datasets are drawn as part of a plot. These options set the six `attributes' (symbol type, symbol font, linemode, line width, fill fraction, and color/monochrome) that each dataset has.
libplot graphics
library. See section Available marker symbols. Symbol numbers greater than or equal
to 32 are interpreted as characters to be selected from a symbol font,
which can be set with the `--symbol-font-name' option (see below).
libplot graphics
library should be used. This value is device-dependent. The
interpretation of zero line width is also device-dependent (on some
devices, a zero-width line is the thinnest line that can be drawn; on
others, a zero-width line is invisible).
graph -T tek does not support drawing lines with other than a
default width, and graph -T hpgl does not support doing so if
the environment variable HPGL_VERSION is set to a value less
than "2" (the default).
graph -T tek, and it is only
partly effective in graph -T hpgl if the environment variable
HPGL_VERSION is set to "1".
-T tek is specified, in which case it is "HersheySerif".) Set
the symbol font, from which plotting symbols numbered 32 and higher are
selected, to be symbol_font_name. Font names are
case-insensitive. If the specified font is not available, the default
font will be used. Which fonts are available depends on which `-T'
option is used. For example, if the -T pcl or -T hpgl
option is used then normally the Wingdings font, which is an alternative
source of symbols, becomes available. For a list of all fonts, see
section Available text fonts. The plotfont utility will produce a character
map of any available font. See section The plotfont Utility.
The following options are used for multiplotting (placing several plots on a display, or a page, at once).
graph -T tek
cannot clear regions, and graph -T hpgl cannot clear them if the
environment variables HPGL_VERSION and HPGL_OPAQUE_MODE
are set to non-default values (i.e., values other than "2" and
"yes", respectively).
graph options
The following option is relevant only to raw graph, i.e., is
relevant only if no display type or output format is specified with the
`-T' option. In this case graph outputs a graphics
metafile, which may be translated to other formats by invoking
plot. This option should appear on the command line before any
file names, since it affects the output of the plot (or multiplot) as a
whole.
The following options request information.
graph -T X, graph -T ps, and graph -T
fig each support the 35 standard Postscript fonts. graph -T pcl
and graph -T hpgl support the 45 standard PCL 5 fonts and a
number of Hewlett--Packard vector fonts. All five, together with
graph -Ttek, support a set of 22 Hershey vector fonts. Raw
graph in principle supports any of these fonts, since its
output must be translated to other formats with plot. The
plotfont utility will produce a character map of any available
font. See section The plotfont Utility.
graph and the plotting utilities
package, and exit.
The behavior of graph is affected by several environment
variables. We have already mentioned the environment variables
BITMAPSIZE, PAGESIZE, BG_COLOR, and
MAX_LINE_LENGTH. They serve as backups for the options
`--bitmap-size', `--page-size', `--bg-color', and
`--max-line-length'. The remaining environment variables are
specific to individual display types. They control device driver
parameters.
graph -T X, which pops up a window on an X Window System
display and draws graphics in it, checks the DISPLAY
environment variable. The value of this variable determines the display
on which the window will be popped up.
graph -T pcl, which produces PCL 5 output for
Hewlett--Packard printers and plotters, is affected by several
environment variables. The position of the graphics display on the page
can be adjusted by setting the PCL_XOFFSET and PCL_YOFFSET
environment variables, which may be specified in centimeters,
millimeters, or inches. For example, an offset could be specified as
"2cm" or "1.2in". Also, the display can be rotated 90 degrees
counterclockwise on the page by setting the PCL_ROTATE
environment variable to "yes". Besides "no" and "yes", recognized
values for this variable are "0", "90", "180", and "270". "no"
and "yes" are equivalent to "0" and "90", respectively.
The variable PCL_ASSIGN_COLORS is also recognized. It should be
set to "yes" when producing PCL 5 output for a color printer or
other color device. This will ensure accurate color reproduction by
giving the output device complete freedom in assigning colors,
internally, to its "logical pens". If it is "no" then the device will
use a fixed set of colored pens, and will emulate other colors by
shading. The default is "no" because monochrome PCL 5 devices,
which are much more common than colored ones, must use shading to
emulate color.
graph -T hpgl, which produces Hewlett--Packard Graphics Language
output, is affected by several environment variables. The most
important is HPGL_VERSION, which may be set to "1", "1.5", or
"2" (the default). "1" means that the output should be generic
HP-GL, "1.5" means that the output should be suitable for the
HP7550A graphics plotter and the HP758x, HP7595A and HP7596A drafting
plotters (HP-GL with some HP-GL/2 extensions), and "2" means that
the output should be modern HP-GL/2. If the version is "1" or "1.5"
then the only available fonts will be vector fonts, and all lines will
be drawn with a default width (the `-W' option will not work).
Additionally, if the version is "1" then the filling of arbitrary
curves with solid color will not be supported (the `-q' option may
be used to fill circles and rectangles aligned with the coordinate axes,
though).
The position of the graph -T hpgl graphics display on the page
can be adjusted by setting the HPGL_XOFFSET and
HPGL_YOFFSET environment variables, which may be specified in
centimeters, millimeters, or inches. For example, an offset could be
specified as "2cm" or "1.2in". Also, the display can be rotated 90
degrees counterclockwise on the page by setting the HPGL_ROTATE
environment variable to "yes". Besides "no" and "yes", recognized
values for this variable are "0", "90", "180", and "270". "no"
and "yes" are equivalent to "0" and "90", respectively. "180" and
"270" are supported only if HPGL_VERSION is "2" (the
default).
Opaque filling and the drawing of visible white lines are
supported only if HPGL_VERSION is "2" and the environment
variable HPGL_OPAQUE_MODE is "yes" (the default). If the value
is "no" then opaque filling will not be used, and white lines (if
any), which are normally drawn with pen #0, will not be drawn.
This feature is to accommodate older HP-GL/2 devices. HP-GL/2 pen
plotters, for example, do not support opacity or the use of pen #0
to draw visible white lines. Some older HP-GL/2 devices reportedly
malfunction if asked to draw opaque objects.
By default, graph -T hpgl will draw with a fixed set of pens.
Which pens are present may be specified by setting the HPGL_PENS
environment variable. If HPGL_VERSION is "1", the default
value of HPGL_PENS is "1=black"; if HPGL_VERSION is "1.5"
or "2", the default value of HPGL_PENS is
"1=black:2=red:3=green:4=yellow:5=blue:6=magenta:7=cyan". The format
should be self-explanatory. By setting HPGL_PENS, you may
specify a color for any pen in the range #1...#31. For information
on what color names are recognized, see section Specifying Colors by Name. Pen #1
must always be present, though it need not be black. Any other pen in
the range #1...#31 may be omitted.
If HPGL_VERSION is "2" then graph -T hpgl will also be
affected by the environment variable HPGL_ASSIGN_COLORS. If the
value of this variable is "yes", then graph -T hpgl will not be
restricted to the palette specified in HPGL_PENS: it will
assign colors to "logical pens" in the range #1...#31, as
needed. The default value is "no" because other than color LaserJet
printers and DesignJet plotters, not many HP-GL/2 devices allow the
assignment of colors to logical pens.
graph -T tek, which produces output for a Tektronix terminal or
emulator, checks the TERM environment variable. If the value
of TERM is xterm, xterms, or kterm, it
is taken as a sign that the current application is running in an X
Window System VT100 terminal emulator: an xterm. Before
drawing graphics, graph -T tek will emit an escape sequence that
causes the terminal emulator's auxiliary Tektronix window, which is
normally hidden, to pop up. After the graphics are drawn, an escape
sequence that returns control to the original VT100 window will be
emitted. The Tektronix window will remain on the screen.
If the value of TERM is kermit, ansi.sys,
ansissys, ansi.sysk, or ansisysk, it is taken
as a sign that the current application is running in the VT100 terminal
emulator provided by the MS-DOS version of kermit. Before drawing
graphics, graph -T tek will emit an escape sequence that switches
the terminal emulator to Tektronix mode. Also, some of the Tektronix
control codes emitted by graph -T tek will be
kermit-specific. There will be a limited amount of color
support, which is not normally the case (the 16 ansi.sys colors
will be supported). After drawing graphics, graph -T tek will emit
an escape sequence that returns the emulator to VT100 mode. The key
sequence `ALT minus' can be employed manually within kermit
to switch between the two modes.
plot Programplot
The GNU plot filter plot displays GNU graphics metafiles, or
translates them to other formats. The `-T' option is used to
specify the display type or output format.
Graphics metafiles are produced by the graph utility if no
`-T' option is specified on its command line, and can also be
produced by the libplot library. The metafile format is a
device-independent format for storage of graphic data. By default, it
is a binary rather than an human-readable format (see section The Graphics Metafile Format).
plot, like the metafile format itself, is useful if you wish to
preserve a plot that is to be displayed or edited on more than one type
of display. The following illustrate how this is done.
To produce a plot of data arranged as alternating x and y
coordinates in an ASCII file, you may use raw graph as follows:
graph < ascii_data_file > test.plot
The file `test.plot' will be a GNU graphics metafile. Similarly, to create a plot consisting of a simple figure, you may do:
echo 0 0 1 1 2 0 | spline | graph > test.plot
To display any such plot on an X Window System display, you would do
plot -T X test.plot
or
plot -T X < test.plot
To print the plot on a Postscript printer, you would do something like
plot -T ps < test.plot | lpr
To edit it with the idraw drawing editor, you would do
plot -T ps < test.plot > test.ps idraw test.ps
And to produce a plot that can be edited with the xfig drawing
editor, you would do
plot -T fig < test.plot > test.fig xfig test.fig
plot may behave differently depending on the environment in which
it is invoked. In particular, plot -T ps, plot -T fig,
plot -T pcl, and plot -T hpgl are affected by the
environment variable PAGESIZE. plot -T X is affected
by the environment variables DISPLAY and BITMAPSIZE, and
plot -T tek is affected by the environment variable TERM.
There are also several environment variables that affect the operation
of plot -T pcl and plot -T hpgl. For a complete
discussion of the effects of the environment on plot, see
section Environment variables.
plot command-line options
The plot filter plot translates GNU graphics metafiles to other
formats. The `-T' option is used to specify the display type or
output format. Files in metafile format are produced by GNU
graph and other applications that use the GNU libplot
graphics library. For technical details on the metafile format, see
section The Graphics Metafile Format.
Input file names may be specified anywhere on the command line. That is, the relative order of file names and command-line options does not matter. If no file names are specified, or the file name `-' is specified, the standard input is read.
The full set of command-line options is listed below. There are four sorts of option:
plot, i.e., relevant only if no
display type or output format is specified with the `-T' option.
Each option that takes an argument is followed, in parentheses, by the type and default value of the argument.
The following options set the values of drawing parameters.
idraw-editable Postscript, the format used by the
xfig drawing editor, the Hewlett-Packard PCL 5 printer
language, the Hewlett--Packard Graphics Language, Tektronix format, and
device-independent GNU metafile format.
plot -T X displays each page in its own X
window. If the -T fig option is used, the default behavior is
to display only the first page, since files to be edited by xfig
may contain only a single page of graphics.
Most metafiles produced by the GNU plotting utilities (e.g., by raw
graph) contain only a single page.
graph -T X, for
which the graphics display is an X window. If you choose a
rectangular (non-square) window size, the fonts in the plot will be
scaled anisotropically, i.e., by different factors in the horizontal and
vertical direction. This requires an X11R6 display. Any font that
cannot be scaled in this way will be replaced by a default scalable
font, such as the Hershey vector font "HersheySerif".
The environment variable BITMAPSIZE can equally well be used to
specify the window size. For backward compatibility, the X resource
Xplot.geometry, which can be set by the user, may be used
instead.
MAX_LINE_LENGTH can also
be used to specify the maximum line length. This option has no effect
on plot -T tek or raw plot, since they draw polylines in
real time and have no buffer limitations.
plot -T ps,
plot -T fig, plot -T pcl, and plot -T hpgl.
"letter" means an 8.5in by 11in page. Any ISO page size in
the range "a0"..."a4" or ANSI page size in the range "a"..."e"
may be specified ("letter" is an alias for "a" and "tabloid" is an
alias for "b"). "legal" and "ledger" are recognized page sizes
also. The environment variable PAGESIZE can equally well be used
to specify the page size.
For plot -T ps, the graphics display within which the plot is
drawn will be a square region centered on the specified page and
occupying its full width. For plot -T fig, the graphics display
will be a square region located in the upper left corner of an
xfig display, with width equal to the width of the specified
page. For plot -T pcl and plot -T hpgl, fine control over
the positioning of the graphics display on the page may be accomplished
by setting certain environment variables (see section Environment variables).
The following options set the initial values of additional drawing parameters. All of these may be overridden by directives in the metafile itself. In fact, these options are useful mostly for plotting old metafiles in the pre-GNU `plot(5)' format, which did not include such directives.
plot -T X. An unrecognized name sets the color to the
default. For information on what names are recognized, see section Specifying Colors by Name. The environment variable BG_COLOR can equally well be
used to specify the background color.
plot -T pcl, plot
-T hpgl and plot -T tek, for which "HersheySerif" is the
default.) Set the font initially used for text (i.e., for `labels') to
font_name. Font names are case-insensitive. If the specified
font is not available, the default font will be used. Which fonts are
available depends on which `-T' option is used. For a list of all
fonts, see section Available text fonts. The plotfont utility will produce a
character map of any available font. See section The plotfont Utility.
libplot graphics
library should be used. This value is device-dependent. The
interpretation of zero line width is also device-dependent (on some
devices, a zero-width line is the thinnest line that can be drawn; on
others, a zero-width line is invisible).
plot -T tek does not support drawing lines with other than a
default width, and plot -T hpgl does not support doing so if
the environment variable HPGL_VERSION is set to a value less
than "2" (the default).
The following option is relevant only to raw plot, i.e., relevant
only if no output type is specified with the `-T' option. In this
case plot outputs a graphics metafile, which may be translated to
other formats by a second invocation of plot.
plot will automatically determine which type of GNU metafile
format the input is in. There are two types: binary (the default)
and portable (human-readable). The binary format is machine-dependent.
See section The Graphics Metafile Format.
For compatibility with older plotting software, the reading of input files in the pre-GNU `plot(5)' format is also supported. This is normally a binary format, with each integer in the metafile represented as a pair of bytes. You may specify that input file(s) are in plot(5) format rather than ordinary GNU metafile format by using the `-l' option ("low byte first") or the `-h' option ("high byte first"). The former variant of plot(5) format is far more common than the latter. Some non-GNU systems support an ASCII (human-readable) variant of plot(5) format. You may specify that the input is in the ASCII variant of plot(5) format by using the `-A' option. Irrespective of the variant, a file in plot(5) format includes only one page of graphics.
The following options request information.
plot -T X, plot -T ps, and plot -T fig
each support the 35 standard Postscript fonts. plot -T pcl and
plot -T hpgl support the 45 standard PCL 5 fonts and a number
of Hewlett--Packard vector fonts. All five, together with plot -T
tek, support a set of 22 Hershey vector fonts. Raw plot in
principle supports any of these fonts, since its output may be
translated to any other format by a later invocation of plot.
plot and the plotting utilities
package, and exit.
The behavior of plot is affected by several environment
variables. We have already mentioned the environment variables
BITMAPSIZE, PAGESIZE, BG_COLOR, and
MAX_LINE_LENGTH. They serve as backups for the options
`--bitmap-size', `--page-size', `--bg-color', and
`--max-line-length'. The remaining environment variables are
specific to individual display types. They control device driver
parameters.
plot -T X, which pops up a window on an X Window System
display and draws graphics in it, checks the DISPLAY
environment variable. The value of this variable determines the display
on which the window will be popped up.
plot -T pcl, which produces PCL 5 output for
Hewlett--Packard printers and plotters, is affected by several
environment variables. The position of the graphics display on the page
can be adjusted by setting the PCL_XOFFSET and PCL_YOFFSET
environment variables, which may be specified in centimeters,
millimeters, or inches. For example, an offset could be specified as
"2cm" or "1.2in". Also, the display can be rotated 90 degrees
counterclockwise on the page by setting the PCL_ROTATE
environment variable to "yes". Besides "no" and "yes", recognized
values for this variable are "0", "90", "180", and "270". "no"
and "yes" are equivalent to "0" and "90", respectively.
The variable PCL_ASSIGN_COLORS is also recognized. It should be
set to "yes" when producing PCL 5 output for a color printer or
other color device. This will ensure accurate color reproduction by
giving the output device complete freedom in assigning colors,
internally, to its "logical pens". If it is "no" then the device will
use a fixed set of colored pens, and will emulate other colors by
shading. The default is "no" because monochrome PCL 5 devices,
which are much more common than colored ones, must use shading to
emulate color.
plot -T hpgl, which produces Hewlett--Packard Graphics Language
output, is affected by several environment variables. The most
important is HPGL_VERSION, which may be set to "1", "1.5", or
"2" (the default). "1" means that the output should be generic
HP-GL, "1.5" means that the output should be suitable for the
HP7550A graphics plotter and the HP758x, HP7595A and HP7596A drafting
plotters (HP-GL with some HP-GL/2 extensions), and "2" means that
the output should be modern HP-GL/2. If the version is "1" or "1.5"
then the only available fonts will be vector fonts, and all lines will
be drawn with a default width (the `-W' option will not work).
Additionally, if the version is "1" then the filling of arbitrary
curves with solid color will not be supported (circles and rectangles
aligned with the coordinate axes may be filled, though).
The position of the plot -T hpgl graphics display on the page can
be adjusted by setting the HPGL_XOFFSET and HPGL_YOFFSET
environment variables, which may be specified in centimeters,
millimeters, or inches. For example, an offset could be specified as
"2cm" or "1.2in". Also, the display can be rotated 90 degrees
counterclockwise on the page by setting the HPGL_ROTATE
environment variable to "yes". Besides "no" and "yes", recognized
values for this variable are "0", "90", "180", and "270". "no"
and "yes" are equivalent to "0" and "90", respectively. "180" and
"270" are supported only if HPGL_VERSION is "2" (the
default).
Opaque filling and the drawing of visible white lines are
supported only if HPGL_VERSION is "2" and the environment
variable HPGL_OPAQUE_MODE is "yes" (the default). If the value
is "no" then opaque filling will not be used, and white lines (if
any), which are normally drawn with pen #0, will not be drawn.
This feature is to accommodate older HP-GL/2 devices. HP-GL/2 pen
plotters, for example, do not support opacity or the use of pen #0
to draw visible white lines. Some older HP-GL/2 devices reportedly
malfunction if asked to draw opaque objects.
By default, plot -T hpgl will draw with a fixed set of pens.
Which pens are present may be specified by setting the HPGL_PENS
environment variable. If HPGL_VERSION is "1", the default
value of HPGL_PENS is "1=black"; if HPGL_VERSION is "1.5"
or "2", the default value of HPGL_PENS is
"1=black:2=red:3=green:4=yellow:5=blue:6=magenta:7=cyan". The format
should be self-explanatory. By setting HPGL_PENS, you may
specify a color for any pen in the range #1...#31. For information
on what color names are recognized, see section Specifying Colors by Name. Pen #1
must always be present, though it need not be black. Any other pen in
the range #1...#31 may be omitted.
If HPGL_VERSION is "2" then plot -T hpgl will also be
affected by the environment variable HPGL_ASSIGN_COLORS. If the
value of this variable is "yes", then plot -T hpgl will not be
restricted to the palette specified in HPGL_PENS: it will
assign colors to "logical pens" in the range #1...#31, as
needed. The default value is "no" because other than color LaserJet
printers and DesignJet plotters, not many HP-GL/2 devices allow the
assignment of colors to logical pens.
plot -T tek, which produces output for a Tektronix terminal or
emulator, checks the TERM environment variable. If the value
of TERM is xterm, xterms, or kterm, it
is taken as a sign that the current application is running in an X
Window System VT100 terminal emulator: an xterm. Before
drawing graphics, plot -T tek will emit an escape sequence that
causes the terminal emulator's auxiliary Tektronix window, which is
normally hidden, to pop up. After the graphics are drawn, an escape
sequence that returns control to the original VT100 window will be
emitted. The Tektronix window will remain on the screen.
If the value of TERM is kermit, ansi.sys,
ansissys, ansi.sysk, or ansisysk, it is taken
as a sign that the current application is running in the VT100 terminal
emulator provided by the MS-DOS version of kermit. Before drawing
graphics, plot -T tek will emit an escape sequence that switches
the terminal emulator to Tektronix mode. Also, some of the Tektronix
control codes emitted by plot -T tek will be
kermit-specific. There will be a limited amount of color
support, which is not normally the case (the 16 ansi.sys colors
will be supported). After drawing graphics, plot -T tek will
emit an escape sequence that returns the emulator to VT100 mode. The
key sequence `ALT minus' can be employed manually within
kermit to switch between the two modes.
tek2plot Programtek2plot is used for
GNU tek2plot is a command-line Tektronix translator. It displays
Tektronix graphics files, or translates them to other formats. The
supported output formats are the same formats that are supported by the
GNU graph and plot utilities. tek2plot will take
input from a file specified on the command line or from standard input,
just as the plot filter plot does.
Tektronix graphics files are produced by many legacy applications. A directory containing sample Tektronix files, which you may experiment with, is distributed along with the GNU plotting utilities. On most systems it is installed as `/usr/share/tek2plot' or `/usr/local/share/tek2plot'.
Tektronix graphics format is defined as a noninteractive version of the
graphics format understood by Tektronix 4010/4014 terminals, as
documented in the 4014 Service Manual, Tektronix Inc., 1974
(Tektronix Part #070-1648-00). tek2plot does not support
interactive features such as GIN mode and status enquiry. However, it
does support a few features of popular Tektronix emulators, such as the
color extensions supported by the Tektronix emulator contained in the
MS-DOS version of kermit.
tek2plot command-line options
The tek2plot program translates the Tektronix graphics files
produced by many legacy applications to other formats. The output
format or display type is specified with the `-T' option. The
possible output formats are the same seven formats that are supported by
the GNU graph and plot programs.
Input file names may be specified anywhere on the command line. That is, the relative order of file names and command-line options does not matter. If no file names are specified, or the file name `-' is specified, the standard input is read.
The full set of command-line options is listed below. There are three sorts of option:
tek2plot, i.e., relevant only if no
display type or output format is specified with the `-T' option.
Each option that takes an argument is followed, in parentheses, by the type and default value of the argument.
The following are general options.
idraw-editable Postscript, the format used by the
xfig drawing editor, the Hewlett-Packard PCL 5 printer
language, the Hewlett--Packard Graphics Language, Tektronix format, and
device-independent GNU metafile format.
tek2plot -T X
displays each page in its own X window. If the -T fig option
is used, the default behavior is to display only the first nonempty
Tektronix page, since files to be edited by xfig may contain only
a single page of graphics.
Most Tektronix files consist of either one page (page #0) or
two pages (an empty page #0, and page #1). Tektronix files
produced by the GNU plotting utilities (e.g., by graph -T tek)
are normally of the latter sort.
tek2plot -T pcl and
tek2plot -T hpgl, for which "HersheySerif" is the default.) Set
the font used for text to font_name. Font names are
case-insensitive. If a font outside the Courier family is chosen,
the `--position-chars' option (see below) should probably be used.
For a list of all fonts, see section Available text fonts. If the specified font is
not available, the default font will be used.
libplot graphics
library should be used. This value is device-dependent. The
interpretation of zero line width is also device-dependent (on some
devices, a zero-width line is the thinnest line that can be drawn; on
others, a zero-width line is invisible).
tek2plot -T hpgl does not support drawing lines with other than a
default width if the environment variable HPGL_VERSION is set to
a value less than "2" (the default).
tek2plot -T
X. An unrecognized name sets the color to the default. For
information on what names are recognized, see section Specifying Colors by Name. The
environment variable BG_COLOR can equally well be used to specify
the background color.
graph -T X, for
which the graphics display is an X window. If you choose a
rectangular (non-square) window size, the fonts in the plot will be
scaled anisotropically, i.e., by different factors in the horizontal and
vertical direction. This requires an X11R6 display. Any font that
cannot be scaled in this way will be replaced by a default scalable
font, such as the Hershey vector font "HersheySerif".
The environment variable BITMAPSIZE can equally well be used to
specify the window size. For backward compatibility, the X resource
Xplot.geometry, which can be set by the user, may be used
instead.
MAX_LINE_LENGTH can also
be used to specify the maximum line length. This option has no effect
on raw tek2plot, since it draws polylines in real time and has no
buffer limitations.
tek2plot -T ps,
tek2plot -T fig, tek2plot -T pcl, and tek2plot -T
hpgl. "letter" means an 8.5in by 11in page. Any ISO page
size in the range "a0"..."a4" or ANSI page size in the range
"a"..."e" may be specified ("letter" is an alias for "a" and
"tabloid" is an alias for "b"). "legal" and "ledger" are recognized
page sizes also. The environment variable PAGESIZE can equally
well be used to specify the page size.
For tek2plot -T ps, the graphics display within which the plot is
drawn will be a square region centered on the specified page and
occupying its full width. For tek2plot -T fig, the graphics
display will be a square region located in the upper left corner of an
xfig display, with width equal to the width of the specified
page. For tek2plot -T pcl and tek2plot -T hpgl, fine
control over the positioning of the graphics display on the page can be
accomplished by setting certain environment variables (see section Environment variables).
xfig or
idraw.
tek2plot -T X.
The four relevant bitmap fonts are distributed with most versions of the
plotting utilities package, under the names
tekfont0...tekfont3. They can easily be installed on
any modern X Window System display. For this option to work
properly, you must also select a window size of 1024x1024 pixels, either
by using the --bitmap-size 1024x1024 option or by setting the
value of the Xplot.geometry resource. The reason for this
restriction is that bitmap fonts, unlike the scalable fonts that the
plotting utilities normally use, cannot be rescaled.
This option is useful only if you have a file in Tektronix format that
draws text using native Tektronix fonts. Tektronix files produced by
the GNU plotting utilities (e.g., by graph -T tek) do not use
native Tektronix fonts to draw text.
The following option is relevant only to raw tek2plot, i.e.,
relevant only if no display type or output format is specified with the
`-T' option. In this case tek2plot outputs a graphics
metafile, which may be translated to other formats by invoking
plot.
The following options request information.
tek2plot -T X, tek2plot -T ps, and
tek2plot -T fig each support the 35 standard Postscript fonts.
tek2plot -T pcl and tek2plot -T hpgl support the 45
standard PCL 5 fonts and a number of Hewlett--Packard vector fonts.
All five support a set of 22 Hershey vector fonts. Raw tek2plot
in principle supports any of these fonts, since its output must be
translated to other formats with plot.
tek2plot and the plotting utilities
package, and exit.
The behavior of tek2plot is affected by several environment
variables, which are the same as those that affect graph and
plot. For convenience, we list them here.
We have already mentioned the environment variables BITMAPSIZE,
PAGESIZE, BG_COLOR, and MAX_LINE_LENGTH. They
serve as backups for the options `--bitmap-size',
`--page-size', `--bg-color', and `--max-line-length'.
The remaining environment variables are specific to individual display
devices. They control device driver parameters.
tek2plot -T X, which pops up a window on an X Window
System display and draws graphics in it, checks the DISPLAY
environment variable. The value of this variable determines the display
on which the window will be popped up.
tek2plot -T pcl, which produces PCL 5 output for
Hewlett--Packard printers and plotters, is affected by several
environment variables. The position of the graphics display on the page
can be adjusted by setting the PCL_XOFFSET and PCL_YOFFSET
environment variables, which may be specified in centimeters,
millimeters, or inches. For example, an offset could be specified as
"2cm" or "1.2in". Also, the display can be rotated 90 degrees
counterclockwise on the page by setting the PCL_ROTATE
environment variable to "yes". Besides "no" and "yes", recognized
values for this variable are "0", "90", "180", and "270". "no"
and "yes" are equivalent to "0" and "90", respectively.
The variable PCL_ASSIGN_COLORS is also recognized. It should be
set to "yes" when producing PCL 5 output for a color printer or
other color device. This will ensure accurate color reproduction by
giving the output device complete freedom in assigning colors,
internally, to its "logical pens". If it is "no" then the device will
use a fixed set of colored pens, and will emulate other colors by
shading. The default is "no" because monochrome PCL 5 devices,
which are much more common than colored ones, must use shading to
emulate color.
tek2plot -T hpgl, which produces Hewlett--Packard Graphics
Language output, is affected by several environment variables. The most
important is HPGL_VERSION, which may be set to "1", "1.5", or
"2" (the default). "1" means that the output should be generic
HP-GL, "1.5" means that the output should be suitable for the
HP7550A graphics plotter and the HP758x, HP7595A and HP7596A drafting
plotters (HP-GL with some HP-GL/2 extensions), and "2" means that
the output should be modern HP-GL/2. If the version is "1" or "1.5"
then the only available fonts will be vector fonts, and all lines will
be drawn with a default width (the `-W' option will not work).
The position of the tek2plot -T hpgl graphics display on the page
can be adjusted by setting the HPGL_XOFFSET and
HPGL_YOFFSET environment variables, which may be specified in
centimeters, millimeters, or inches. For example, an offset could be
specified as "2cm" or "1.2in". Also, the display can be rotated 90
degrees counterclockwise on the page by setting the HPGL_ROTATE
environment variable to "yes". Besides "no" and "yes", recognized
values for this variable are "0", "90", "180", and "270". "no"
and "yes" are equivalent to "0" and "90", respectively. "180" and
"270" are supported only if HPGL_VERSION is "2" (the
default).
The drawing of visible white lines is supported only if
HPGL_VERSION is "2" and the environment variable
HPGL_OPAQUE_MODE is "yes" (the default). If the value is "no"
then white lines (if any), which are normally drawn with pen #0,
will not be drawn. This feature is to accommodate older HP-GL/2
devices. HP-GL/2 pen plotters, for example, do not support the use of
pen #0 to draw visible white lines. Some older HP-GL/2 devices may,
in fact, malfunction if asked to draw opaque objects.
By default, tek2plot -T hpgl will draw with a fixed set of
pens. Which pens are present may be specified by setting the
HPGL_PENS environment variable. If HPGL_VERSION is
"1", the default value of HPGL_PENS is "1=black"; if
HPGL_VERSION is "1.5" or "2", the default value of
HPGL_PENS is
"1=black:2=red:3=green:4=yellow:5=blue:6=magenta:7=cyan". The format
should be self-explanatory. By setting HPGL_PENS, you may
specify a color for any pen in the range #1...#31. For information
on what color names are recognized, see section Specifying Colors by Name. Pen #1
must always be present, though it need not be black. Any other pen in
the range #1...#31 may be omitted.
If HPGL_VERSION is "2" then tek2plot -T hpgl will also be
affected by the environment variable HPGL_ASSIGN_COLORS. If the
value of this variable is "yes", then tek2plot -T hpgl will not
be restricted to the palette specified in HPGL_PENS: it will
assign colors to "logical pens" in the range #1...#31, as
needed. The default value is "no" because other than color LaserJet
printers and DesignJet plotters, not many HP-GL/2 devices allow the
assignment of colors to logical pens.
plotfont Utilityplotfont
GNU plotfont is a simple utility that will produce a character
map for any font available to the GNU plotting utilities graph,
plot, and tek2plot, and the GNU libplot graphics
library on which they are based. The map may be displayed on an X
Window System display, or produced in any of five output formats.
Which fonts are available depends on the choice of display or output format. To get a list of the available fonts, use the `--help-fonts' option. For example,
plotfont -T ps --help-fonts
will list the fonts that are available when producing Postscript output. One of these fonts is "Times-Roman". Doing
plotfont -T ps Times-Roman > map.ps
will produce a character map of the lower half of this font, which consists of printable ASCII characters. The map will be a 12x8 grid, with a character centered in each grid cell. If you include the `-2' option, you will get a map of the upper half of the font.
Most built-in fonts are ISO-Latin-1 fonts, which means that the upper half is arranged according to the ISO-Latin-1 encoding. The "HersheyCyrillic" font is one that is not. If you do
plotfont -T ps -2 HersheyCyrillic > map.ps
you will get a map that illustrates its arrangment, which is called KOI8-R. The KOI8-R arrangement is the standard for Unix and networking applications in the former Soviet Union. So-called dingbats fonts, such as "ZapfDingbats" and "Wingdings", also have an individualistic layout. In most installations of the plotting utilities, the Wingdings font is not available when producing Postscript output. However, it is available when producing output in PCL 5 or HP-GL/2 format. If you do
plotfont -T hpgl Wingdings > map.plt
you will get a Wingdings character map, in HP-GL/2 format, that may be
imported into any application that understands HP-GL/2. Similarly,
plot -T pcl Wingdings will produce a Wingdings character map in
PCL 5 format, which may be printed on a LaserJet or other PCL 5
device.
In all, more than a hundred fonts are built into the plotting utilities. See section Available text fonts. If you are using the plotting utilities to display output on an X display, you are not restricted to the built-in fonts. Doing
plotfont -T X --help-fonts
produces a list of the built-in fonts that are available, including both
Hershey and Postscript fonts. But fonts available on your X display
may also be used. The xlsfonts command will list the fonts
available on your X display, most font names being given in what is
called XLFD format. The plotting utilities refer to X fonts by
shortened versions of their XLFD names. For example, the font
"Utopia-Regular" is available on many X displays. Its XLFD name is
"-adobe-utopia-medium-r-normal--0-0-0-0-p-0-iso8859-1", and its
shortened XLFD name is "utopia-medium-r-normal". If you do
plotfont -T X utopia-medium-r-normal
then a character map for this font will be displayed in a popped-up X window.
When using the `-T X' option, you may also use the `--bitmap-size' option to choose the size of the popped-up window. Modern X displays can scale fonts by different amounts in the horizontal and vertical directions. If, for example, you add `--bitmap-size 600x300' to the above command line, both the character map and the Utopia-Regular font within it will be scaled in this way. If your X display does not support font scaling, a scalable font will be substituted.
plotfont command-line options
The plotfont font display utility will produce a character map
for any of the fonts available to the GNU plotting utilities
graph, plot, and tek2plot, and the GNU
libplot graphics library on which they are based. The map may be
produced in any supported output format, or displayed on an X
Window System display. The display type or output format is specified
with the `-T' option.
The names of the fonts for which a character map will be produced may
appear anywhere on the plotfont command line. That is, the
relative order of font names and command-line options does not matter.
The possible options are listed below. There are three sorts of option:
plotfont, i.e., relevant only if no
display type or output format is specified with the `-T' option.
Each option that takes an argument is followed, in parentheses, by the type and default value of the argument.
The following are general options.
idraw-editable Postscript, the format used by the
xfig drawing editor, the Hewlett-Packard PCL 5 printer
language, the Hewlett--Packard Graphics Language, Tektronix format, and
device-independent GNU metafile format.
Files to be edited by xfig may contain only a single page of
graphics. So if the -T fig option is used, a character map will
be produced for only the first-specified font.
plotfont -T
X. An unrecognized name sets the color to the default. For
information on what names are recognized, see section Specifying Colors by Name. The
environment variable BG_COLOR can equally well be used to specify
the background color.
plot2font -T X,
for which the graphics display is an X window. If you choose a
rectangular (non-square) window size, the font in the character map will
be scaled anisotropically, i.e., by different factors in the horizontal
and vertical direction. This requires an X11R6 display. If the
font cannot be scaled in this way, it will be replaced by a default
scalable font, such as the Hershey vector font "HersheySerif".
The environment variable BITMAPSIZE can equally well be used to
specify the window size. For backward compatibility, the X resource
Xplot.geometry, which can be set by the user, may be used
instead.
plotfont -T pcl,
plotfont -T hpgl and plotfont -T tek, for which
"HersheySerif" is the default.) Set the font used for the numbering of
the characters in the character map(s) to be font_name.
plotfont -T ps, plotfont -T fig, plotfont -T pcl
and plotfont -T hpgl. "letter" means an 8.5in by
11in page. Any ISO page size in the range "a0"..."a4" or ANSI
page size in the range "a"..."e" may be specified ("letter" is an
alias for "a" and "tabloid" is an alias for "b"). "legal" and
"ledger" are recognized page sizes also. The environment variable
PAGESIZE can equally well be used to specify the page size.
For plotfont -T ps, the graphics display within which each
character map is drawn will be a square region centered on the page, and
occupying its full width. For plotfont -T fig, the graphics
display will be a square region located in the upper left corner of an
xfig display, with width equal to the width of the specified
page. For plotfont -T pcl, plotfont -T hpgl, fine control
over the positioning of the graphics display on the page can be
accomplished by setting certain environment variables (see section Environment variables).
The following option is relevant only to raw plotfont, i.e.,
relevant only if no display type or output format is specified with the
`-T' option. In this case plotfont outputs a graphics
metafile, which may be translated to other formats by invoking
plot.
The following options request information.
plotfont -T X, plotfont -T ps, and
plotfont -T fig each support the 35 standard Postscript fonts.
plotfont -T pcl and plotfont -T hpgl support the 45
standard PCL 5 fonts and a number of Hewlett--Packard vector fonts.
All five, together with plotfont -T tek, support a set of 22
Hershey vector fonts. Raw plotfont in principle supports any
of these fonts, since its output must be translated to other formats
with plot.
plotfont and the plotting utilities
package, and exit.
The behavior of plotfont is affected by several environment
variables, which are the same as those that affect graph,
plot, and tek2plot. For convenience, we list them here.
We have already mentioned the environment variables BITMAPSIZE,
PAGESIZE, and BG_COLOR. They serve as backups for the
options `--bitmap-size', `--page-size', and `--bg-color'.
The remaining environment variables are specific to individual display
devices. They control device driver parameters.
plotfont -T X, which pops up a window on an X Window
System display and draws a character map in it, checks the
DISPLAY environment variable. The value of this variable
determines the display on which the window will be popped up.
plotfont -T pcl, which produces PCL 5 output for
Hewlett--Packard printers and plotters, is affected by several
environment variables. The position of the graphics display on the page
can be adjusted by setting the PCL_XOFFSET and PCL_YOFFSET
environment variables, which may be specified in centimeters,
millimeters, or inches. For example, an offset could be specified as
"2cm" or "1.2in". Also, the display can be rotated 90 degrees
counterclockwise on the page by setting the PCL_ROTATE
environment variable to "yes". Besides "no" and "yes", recognized
values for this variable are "0", "90", "180", and "270". "no"
and "yes" are equivalent to "0" and "90", respectively.
The variable PCL_ASSIGN_COLORS is also recognized. It should be
set to "yes" when producing PCL 5 output for a color printer or
other color device. This will ensure accurate color reproduction by
giving the output device complete freedom in assigning colors,
internally, to its "logical pens". If it is "no" then the device will
use a fixed set of colored pens, and will emulate other colors by
shading. The default is "no" because monochrome PCL 5 devices,
which are much more common than colored ones, must use shading to
emulate color.
plotfont -T hpgl, which produces Hewlett--Packard Graphics
Language output, is affected by several environment variables. The most
important is HPGL_VERSION, which may be set to "1", "1.5", or
"2" (the default). "1" means that the output should be generic
HP-GL, "1.5" means that the output should be suitable for the
HP7550A graphics plotter and the HP758x, HP7595A and HP7596A drafting
plotters (HP-GL with some HP-GL/2 extensions), and "2" means that
the output should be modern HP-GL/2. If the version is "1" or "1.5"
then the only available fonts will be vector fonts.
The position of the plotfont -T hpgl character map on the page
can be adjusted by setting the HPGL_XOFFSET and
HPGL_YOFFSET environment variables, which may be specified in
centimeters, millimeters, or inches. For example, an offset could be
specified as "2cm" or "1.2in". Also, the map can be rotated 90
degrees counterclockwise on the page by setting the HPGL_ROTATE
environment variable to "yes". Besides "no" and "yes", recognized
values for this variable are "0", "90", "180", and "270". "no"
and "yes" are equivalent to "0" and "90", respectively. "180" and
"270" are supported only if HPGL_VERSION is "2" (the
default).
By default, plotfont -T hpgl will draw with a fixed set of
pens. Which pens are present may be specified by setting the
HPGL_PENS environment variable. If HPGL_VERSION is
"1", the default value of HPGL_PENS is "1=black"; if
HPGL_VERSION is "1.5" or "2", the default value of
HPGL_PENS is
"1=black:2=red:3=green:4=yellow:5=blue:6=magenta:7=cyan". The format
should be self-explanatory. By setting HPGL_PENS, you may
specify a color for any pen in the range #1...#31. For information
on what color names are recognized, see section Specifying Colors by Name. Pen #1
must always be present, though it need not be black. Any other pen in
the range #1...#31 may be omitted.
If HPGL_VERSION is "2" then plotfont -T hpgl will also be
affected by the environment variable HPGL_ASSIGN_COLORS. If the
value of this variable is "yes", then plotfont -T hpgl will not
be restricted to the palette specified in HPGL_PENS: it will
assign colors to "logical pens" in the range #1...#31, as
needed. The default value is "no" because other than color LaserJet
printers and DesignJet plotters, not many HP-GL/2 devices allow the
assignment of colors to logical pens.
plotfont -T tek, which produces output for a Tektronix terminal
or emulator, checks the TERM environment variable. If the
value of TERM is xterm, xterms, or kterm,
it is taken as a sign that the current application is running in an
X Window System VT100 terminal emulator: an xterm.
Before drawing graphics, plotfont -T tek will emit an escape
sequence that causes the terminal emulator's auxiliary Tektronix window,
which is normally hidden, to pop up. After the graphics are drawn,
an escape sequence that returns control to the original VT100 window
will be emitted. The Tektronix window will remain on the screen.
If the value of TERM is kermit, ansi.sys,
ansissys, ansi.sysk, or ansisysk, it is taken
as a sign that the current application is running in the VT100 terminal
emulator provided by the MS-DOS version of kermit. Before
drawing graphics, plotfont -T tek will emit an escape sequence
that switches the terminal emulator to Tektronix mode. Also, some of
the Tektronix control codes emitted by plotfont -T tek will be
kermit-specific. There will be a limited amount of color
support, which is not normally the case (the 16 ansi.sys colors
will be supported). After drawing graphics, plotfont -T tek will
emit an escape sequence that returns the emulator to VT100 mode. The
key sequence `ALT minus' can be employed manually within
kermit to switch between the two modes.
spline Programspline
GNU spline is a program for interpolating between the data points
in one or more datasets. Each dataset would consist of values for an
independent variable and a dependent variable, which may be a vector of
specified fixed length. When discussing interpolation, we call these
variables `t' and `y', respectively. To emphasize:
t is a scalar, but in general the dependent variable
y may be a vector.
The simplest case is when there is a single input file, which is in ASCII format, and the vector y is one-dimensional. This is the default. For example, the input file could contain the dataset
0.0 0.0 1.0 1.0 2.0 0.0
which are the coordinates (t,y) of the data points (0,0), (1,1), and (2,0). Data points do not need to be on different lines, nor do the t and y coordinates of a data point need to be on the same line. However, there should be no blank lines in the input if it is to be viewed as forming a single dataset. Also, by default the t coordinate should be monotonically increasing, so that y may be viewed as a function of t.
You would construct a spline (the graph of an `interpolating function') passing through the points in this dataset by doing
spline input_file > output_file
To produce a Postscript plot of the spline with the graph
utility, you would do
spline input_file | graph -T ps > output.ps
To display a spline on an X Window System display, you could do
echo 0 0 1 1 2 0 | spline | graph -T X
Notice that the last example avoids the use of the input file
altogether. spline will read from standard input if no files are
specified on the command line, or if the special file name `-'
is specified.
What exactly does spline do? First, it fits a curve (the graph
of an interpolating function) through the points in the dataset. Then
it splits the interval over which the independent variable t
ranges into 100 sub-intervals, and computes the y values at
each of the 101 subdivision points. It then outputs each of the
pairs (t, y). These are the coordinates of 101 points that lie
along a curve that interpolates between the points in the dataset. If
there is more than one dataset in the input (separated by blank lines),
each dataset is interpolated separately.
You may use the `-n' option to replace `100' by any other integer. You may also use the `-t' option to specify an interpolation interval that differs from the default (the interval over which the independent variable ranges). For example, the command
echo 0 0 1 1 2 0 | spline -n 20 -t 1.0 1.5 > output_file
will produce a dataset consisting of 21 (rather than 101) data points, with t values spaced regularly between 1.0 and 1.5 (rather than between 0.0 and 2.0). The data points will lie along a curve passing through (0,0), (1,1), and (2,0). This curve will be a parabola.
In general, the interpolating function will be a piecewise cubic spline. That is, between each pair of adjacent `knots' (points in the input dataset), y will be a cubic function of t. This function will differ, depending on which pair of knots y lies between. At each knot, both the slope and curvature of the cubic pieces to either side will match. In mathematical terms, the interpolating curve will be twice continuously differentiable.
spline supports `adding tension' to the interpolating curve.
A nonzero value for the tension can be specified with the `-T'
option. For example, a spline under considerable tension can be
computed and displayed by doing
echo 0 0 1 0 2 0 | spline -T 10 | graph -T X
As the tension parameter is increased to positive infinity, the spline will converge to a polygonal line. You are meant to think of the spline as being drawn taut. Actually, tension may be negative as well as positive. A spline with negative tension will tend to bow outward, in fact to oscillate sinusoidally. But as the tension decreases to negative infinity, the spline, though oscillatory, will again converge to a polygonal line.
If the tension is positive, its reciprocal will be the maximum range of the independent variable t over which the spline will `like to curve'. Increasing the tension far above zero will accordingly force the spline to consist of short curved sections, centered on the data points, and sections that are almost straight. It follows that tension is a `dimensionful' quantity. If the tension is nonzero, then when the values of the independent variable are multiplied by some common positive factor, the tension should be divided by the same factor to obtain a scaled version of the original spline. If the tension is zero (the default, or cubic spline case), then the computation of the spline will be unaffected by linear scaling of the data.
In mathematical terms, a spline under tension will satisfy the differential equation @ifnottex y""=sgn(tension)*(tension^2)y" between each successive pair of knots. If the tension equals zero, which is the default, the fourth derivative of y with respect to t will equal zero at every point. In this case, y as a function of t will reduce to a cubic polynomial between each successive pair of knots. But if the tension is nonzero, y will not be a polynomial function of t. It may be expressed in terms of exponential functions, however.
Irrespective of whether or not the spline is under tension, you may specify the `-p' option if you wish the spline to be a periodic function of t. This will only work if the y values for the first and last points in the dataset are equal. Otherwise, it would make no sense to compute a periodic interpolation.
It is sometimes useful to interpolate between data points at the same
time as they are generated by an auxiliary program. That is, it is
useful for spline to function as a real-time filter.
spline does not normally act as a filter, since computing an
interpolating curve that is as smooth as possible is a global task. But
if the `-f' option is specified, spline will indeed function
as a filter. A different interpolation algorithm (cubic Bessel
interpolation, which is local rather than global) will be used. If
`-f' is specified, `-p' may not be specified. Also, if
`-f' is specified then an interpolation interval (a range of
t values) must be requested explicitly with the `-t'
option.
Cubic Bessel interpolation is inherently less smooth than the construction of a global cubic spline. If the `-f' option is specified, the slope of the spline at each knot will be chosen by fitting a parabola through that knot, and the two adjacent knots. The slopes of the two interpolating segments to either side of each interior knot will match at that knot, but typically their curvatures will not. In mathematical terms, the interpolating curve will be continuously differentiable, but in general not twice continuously differentiable. This loss of differentiability is the price that is paid for functioning as a real-time filter.
spline
The preceding section explains how spline can be employed to
interpolate a function y of a scalar variable t, in the
case when y is a scalar. In this section we explain how to
perform more sophisticated interpolations. This includes
multidimensional interpolations, and interpolations that are splinings
of curves, rather than of functions.
spline can handle the case when y is a vector of
arbitrary specified dimensionality. The dimension can be specified with
the `-d' option. For example, an input file could contain the
multidimensional dataset
0.0 0.0 1.0 1.0 1.0 0.0 2.0 0.0 1.0
which are the coordinates (t,y) of the data points (0,0,1), (1,1,0), and (2,0,1). You would construct a spline (the graph of an interpolating function) passing through the points in this dataset by doing
spline -d 2 input_file > output_file
The option `-d 2' is used because in this example, the dependent variable y is a two-dimensional vector. Each of the components of y will be interpolated independently, and the output file will contain points that lie along the graph of the resulting interpolating function.
When doing multidimensional splining, you may use any of the options
that apply in the default one-dimensional case. For example, the
`-f' option will yield real-time cubic Bessel interpolation. As
in the one-dimensional case, if the `-f' option is used then the
`-t' option must be used as well, to specify an interpolation
interval (a range of t values). The -p option
will yield a periodic spline, i.e., the graph of a periodic
vector-valued function. For this, the first and last dataset
y values must be the same.
spline can also be used to draw a curve through arbitrarily
chosen points in the plane, or in general through arbitrarily chosen
points in d-dimensional space. This is not the same as splining,
at least as the term is conventionally defined. The reason is that
`splining' refers to construction of a function, rather than the
construction of a curve that may or may not be the graph of a function.
Not every curve is the graph of a function.
The following example shows how you may `spline a curve'. The command
echo 0 0 1 0 1 1 0 1 | spline -d 2 -a -s | graph -T X
will construct a curve in the plane through the four points (0,0), (1,0), (1,1), and (0,1), and graph it on an X Window System display. The `-d 2' option specifies that the dependent variable y is two-dimensional. The `-a' option specifies that t values are missing from the input, and should be automatically generated. By default, the first t value is 0, the second is 1, etc. The `-s' option specifies that the t values should be stripped from the output.
The same technique may be used to spline a closed curve. For example, doing
echo 0 0 1 0 0 1 0 0 | spline -d 2 -a -s -p | graph -T X
will construct and graph a closed, lozenge-shaped curve through the three points (0,0), (1,0), and (0,1). The construction of a closed curve is guaranteed by the `-p' (i.e., `--periodic') option, and by the repetition of the initial point (0,0) at the end of the sequence.
When splining a curve, whether open or closed, you may wish to substitute the `-A' option for the `-a' option. Like the `-a' option, the `-A' option specifies that t values are missing from the input and should be automatically generated. However, the first t value will be zero, and the increment from one t value to the next will be the distance between the corresponding values of y. This scheme for generating t values, when constructing a curve through a sequence of points, is the scheme that is used in the well known FITPACK subroutine library. It is probably the best approach when the distances between successive points fluctuate considerably.
A curve through a sequence of points in the plane, whether open or closed, may cross itself. Some interesting visual effects can be obtained by adding negative tension to such a curve. For example, doing
echo 0 0 1 0 1 1 0 0 | spline -d 2 -a -s -p -T -14 -n 500 | graph -T X
will construct a closed curve through the three points (0,0), (1,0), and (0,1), which is wound into curlicues. The `-n 500' option is included because there are so many windings. It specifies that 501 points should be generated, which is enough to draw a smooth curve.
spline command-line options
The spline program will interpolate vector-valued functions of a
scalar variable t, and curves in d-dimensional space.
The algorithms used by spline are similar to those discussed in
D. Kincaid and [E.] W. Cheney, Numerical Analysis (2nd
ed., Brooks/Cole, 1996), section 6.4, and C. de Boor, A
Practical Guide to Splines (Springer-Verlag, 1978), Chapter 4.
Input file names may be specified anywhere on the command line. That is, the relative order of font names and command-line options does not matter. If no file names are specified, or the file name `-' is specified, the standard input is read.
An input file may contain more than a single dataset. Unless the `-a' or `-A' options are used (see below), each dataset is expected to consist of a sequence of data points, given as alternating t and y values. t is the scalar independent variable, and y is the vector-valued dependent variable. The dimensionality of y is specified with the `-d' option (the default is 1).
If the input file is in ASCII format (the default), its datasets are separated by blank lines. An input file may also contain any number of comment lines, which must begin with the comment character `#'. Comment lines are ignored. They are not treated as blank, i.e., they do not interrupt a dataset in progress.
The options to spline are listed below. There are three sorts of
option:
Options that take an argument are followed, in parentheses, by the type and default value of the argument.
The following options specify the type of interpolation to be performed on each dataset.
spline can be used as a real-time filter. The slope of the
interpolating curve at each point in a dataset will be chosen by fitting
a quadratic function through that point and the two adjacent points in
the dataset. If `-f' is specified then the `-t' option,
otherwise optional, must be used as well. Also, if `-f' is
specified then the `-k', `-p', and `-T' options may not
be used.
If `-f' is not specified, then a different (global)
interpolation algorithm will be used.
The following options specify the format of the input file(s) and the output file.
FLT_MAX, which is the largest possible single precision floating
point number. On most machines this is approximately 3.4x10^38.
DBL_MAX, which is the largest possible double
precision floating point number. On most machines this is approximately
1.8x10^308.
INT_MAX, which is the largest
possible integer. On most machines this is 2^31-1.
spline).
spline).
The following options request information.
spline and the plotting utilities
package, and exit.
ode Program
The GNU ode utility can produce a numerical solution to the
initial value problem for many systems of first-order ordinary
differential equations (ODE's). ode can also be used to solve
systems of higher-order ODE's, since a simple procedure converts an
n'th-order equation into n first-order equations. The
output of ode can easily be piped to graph, so that one or
more solution curves may be plotted as they are generated.
Three distinct schemes for numerical solution are implemented: Runge--Kutta--Fehlberg (the default), Adams--Moulton, and Euler. The Runge--Kutta--Fehlberg and Adams--Moulton schemes are available with adaptive stepsize.
We begin with some standard definitions. A differential equation
is an equation involving an unknown function and its derivatives. A
differential equation is ordinary if the unknown function
depends on only one independent variable, often denoted t.
The order of the differential equation is the order of the
highest-order derivative in the equation. One speaks of a family, or
system of equations when more than one equation is involved. If
the equations are dependent on one another, they are said to be
coupled. A solution is any function satisfying the
equations. An initial value problem is present when there exist
subsidiary conditions on the unknown function and its derivatives, all
of which are given at the same value of the independent variable. In
principle, such an `initial condition' specifies a unique solution.
Questions about the existence and uniqueness of a solution, along with
further terminology, are discussed in any introductory text. (See
Chapter 1 of Birkhoff and Rota's Ordinary Differential
Equations. For this and other references relevant to ode, see
section Bibliography on ode and solving differential equations.)
In practical problems, the solution of a differential equation is usually not expressible in terms of elementary functions. Hence the need for a numerical solution.
A numerical scheme for solving an initial value problem produces an
approximate solution, using only functional evaluations and the
operations of arithmetic. ode solves first-order initial value
problems of the form:
@ifnottex
x' = f(t,x,y,...,z) y' = g(t,x,y,...,z) . . . z' = h(t,x,y,...,z)
given the initial values for each dependent variable at the initial value of the independent variable t, i.e.,
x(a) = b
y(a) = c
.
.
.
z(a) = d
t = a
@ifnottex where a,b,c,...,d are constants.
@ifnottex
For ode to be able to solve such a problem numerically, the
functions f,g,...,h must be expressed, using the usual operators
(+, -, *, /, and ^), in terms of
certain basic functions that ode recognizes. These are the same
functions that the plotting program gnuplot recognizes.
Moreover, each of f,g,...,h must be given explicitly. ode
cannot deal with a system in which one or more of the first derivatives
is defined implicitly rather than explicitly.
All schemes for numerical solution involve the calculation of an
approximate solution at discrete values of the independent variable
t, where the `stepsize' (the difference between any two
successive values of t, usually denoted h) may be
constant or chosen adaptively. In general, as the stepsize
decreases the solution becomes more accurate. In ode, the
stepsize can be adjusted by the user.
ode
The following examples should illustrate the procedure of stating an
initial value problem and solving it with ode. If these
examples are too elementary, see section The ode input language formally specified, for a formal
specification of the ode input language. There is also a
directory containing examples of ode input, which is distributed
along with the GNU plotting utilities. On most systems it is
installed as `/usr/share/ode' or `/usr/local/share/ode'.
Our first example is a simple one, namely
y'(t) = y(t)
with the initial condition
y(0) = 1
The solution to this differential equation is
@ifnottex
y(t) = e^t.
In particular
@ifnottex
y(1) = e^1 = 2.718282
to seven digits of accuracy.
You may obtain this result with the aid of ode by typing on the
command line the sequence of commands
ode y' = y y = 1 print t, y step 0, 1
Two columns of numbers will appear. Each line will show the value of the independent variable t, and the value of the variable y, as t is `stepped' from 0 to 1. The last line will be
1 2.718282
as expected. You may use the `-p' option to change the precision. If, for example, you type `ode -p 10' rather than `ode', you will get ten digits of accuracy in the output, rather than seven (the default).
After the above output, ode will wait for further instructions.
Entering for example the line
step 1, 0
should yield two more columns of numbers, containing the values of t and y that are computed when t is stepped back from 1 to 0. You could type instead
step 1, 2
to increase rather than decrease t. To exit ode,
you would type a line containing only `.', i.e. a single period,
and tap `return'. ode will also exit if it sees an end-of-file
indicator in its input stream, which you may send from your terminal by
typing control-D.
Each line of the preceding example should be self-explanatory. A
`step' statement sets the beginning and the end of an interval
over which the independent variable (here, t) will range, and
causes ode to set the numerical scheme in motion. The initial
value appearing in the first `step' statement (i.e., 0) and the
assignment statement
y = 1
are equivalent to the initial condition y(0) = 1. The statements
`y' = y' and `y = 1' are very different: `y' = y'
defines a way of computing the derivative of y, while `y
= 1' sets the initial value of y. Whenever a `step'
statement is encountered, ode tries to step the independent
variable through the interval it specifies. Which values are to be
printed at each step is specified by the most recent `print'
statement. For example,
print t, y, y'
would cause the current value of the independent variable t, the variable y, and its derivative to be printed at each step.
To illustrate ode's ability to take its input or the initial part
of its input from a file, you could prepare a file containing the
following lines:
# an ode to Euler y = 1 y' = y print t, y, y'
Call this file `euler'. (The `#' line is a comment line,
which may appear at any point. Everything from the `#' to the
end of the line on which it appears will be ignored.) To process
this file with ode, you could type on your terminal
ode -f euler step 0, 1
These two lines cause ode to read the file `euler', and the
stepping to take place. You will now get three quantities (t,
y, and y') printed at each of the values of t
between 0 and 1. At the conclusion of the stepping, ode
will wait for any further commands to be input from the terminal. This
example illustrates that
ode -f euler
is not equivalent to
ode < euler
The latter would cause ode to take all its input from the file
`euler', while the former allows subsequent input from the
terminal. For the latter to produce output, you would need to include a
`step' line at the end of the file. You would not need to include
a `.' line, however. `.' is used to terminate input only
when input is being read from a terminal.
A second simple example involves the numerical solution of a second-order differential equation. Consider the initial value problem
y''(t) = -y(t) y(0) = 0 y'(0) = 1
Its solution would be
@ifnottex
y(t) = sin(t)
To solve this problem using ode, you must express this
second-order equation as two first-order equations. Toward this end you
would introduce a new function, called yp say, of the independent
variable t. The pair of equations
y' = yp yp' = -y
would be equivalent to the single equation above. This sort of reduction of an n'th order problem to n first order problems is a standard technique.
To plot the variable y as a function of the variable t, you could create a file containing the lines
# sine : y''(t) = -y(t), y(0) = 0, y'(0) = 1 sine' = cosine cosine' = -sine sine = 0 cosine = 1 print t, sine
(y and yp have been renamed sine and cosine, since that is what they will be.) Call this file `sine'. To display the generated data points on an X Window System display as they are generated, you would type
ode -f sine | graph -T X -x 0 10 -y -1 1 step 0, 2*PI .
After you type the ode line, graph -T X will pop up a
window, and after you type the `step' line, the generated dataset
will be drawn in it. The `-x 0 10' and `-y -1 1' options,
which set the bounds for the two axes, are necessary if you wish to
display points in real time: as they are generated. If the axis
bounds were not specified on the command line, graph -T X would wait
until all points are read from the input before determining the bounds,
and drawing the plot.
A slight modification of this example, showing how ode can
generate several datasets in succession and plot them on the same graph,
would be the following. Suppose that you type on your terminal the
following lines.
ode -f sine | graph -T X -C -x 0 10 -y -1 1 step 0, PI step PI, 2*PI step 2*PI, 3*PI .
Then the sine curve will be traced out in three stages. Since the
output from each `step' statement ends with a blank line,
graph -T X will treat each section of the sine curve as a
different dataset. If you are using a color display, each of the three
sections will be plotted in a different color. This is a feature
provided by graph, which normally changes its linemode after each
dataset it reads. If you do not like this feature, you may turn it off
by using `graph -T X -B' instead of `graph -T X'.
In the above examples, you could use any of the other variants of
graph instead of graph -T X. For example, you could use
graph -T ps to obtain a plot in encapsulated Postscript format,
by typing
ode -f sine | graph -T ps > plot.ps step 0, 2*PI .
You should note that of the seven variants of graph, graph
-T ps, graph -T fig, graph -T pcl and graph -T
hpgl do not produce output in real time, even when the axis bounds are
specified with the `-x' and `-y' options. So if
graph -T ps, graph -T fig, graph -T pcl, or
graph -T hpgl is used, the plot will be produced only when input
from ode is terminated, which will occur when you type
`.'.
In the preceding examples, the derivatives of the dependent variables
were specified by comparatively simple expressions. They are allowed to
be arbitrarily complicated functions of the dependent variables and the
independent variable. They may also involve any of the functions that
are built into ode. ode has a fair number of functions
built in, including abs, sqrt, exp, log, log10,
sin, cos, tan, asin, acos, atan, sinh,
cosh, tanh, asinh, acosh, and atanh. Less familiar
functions which are built into it are besj0, besj1,
besy0, besy1, erf, erfc, inverf, lgamma,
gamma, norm, invnorm, ibeta, and igamma. These have
the same definitions as in the plotting program gnuplot. (All
functions take a single argument, except for ibeta, which takes
three, and igamma, which takes two). ode also knows the
meaning of the constant `PI', as the above examples show. The
names of the preceding functions are reserved, so, e.g., `cos' and
`sin' may not be used as names for variables.
Other than the restriction of avoiding reserved names and keywords, the
names of variables may be chosen arbitrarily. Any sequence of
alphanumeric characters starting with an alphabetic character may be
used; the first 32 characters are significant. It is worth noting
that ode identifies the independent variable by the fact that it
is (or should be) the only variable that has not appeared on the left
side of a differential equation or an initial value assignment. If
there is more than than one such variable then no stepping takes place;
instead, an error message is printed. If there is no such variable,
a dummy independent variable is invented and given the name
`(indep)', internally.
ode
We explain here how to use some additional features of ode.
However, the discussion below does not cover all of its capabilities.
For a complete list of command-line options, see section ode command-line options.
It is easy to use ode to create plots of great beauty. An
example would be a plot of a strange attractor, namely the Lorenz
attractor. Suppose that a file named `lorenz' contains the
following lines.
# The Lorenz model, a system of three coupled ODE's with parameter r. x' = -3*(x-y) y' = -x*z+r*x-y z' = x*y-z r = 26 x = 0; y = 1; z = 0 print x, y step 0, 200
Then executing the command
ode < lorenz | graph -T X -C -x -10 10 -y -10 10
would produce a plot of the Lorenz attractor (strictly speaking, a plot of one of its two-dimensional projections). You may produce a Postscript plot of the Lorenz attractor, and print it, by doing something like
ode < lorenz | graph -T ps -x -10 10 -y -10 10 -W 0 | lpr
The `-W 0' ("zero width") option requests that graph -T ps
use the thinnest line possible, to improve the visual appearance of the
plot on a printer or other Postscript device.
Besides plotting a visually striking object in real time, the Lorenz
attractor example shows how statements may be separated by semicolons,
rather than appearing on different lines. It also shows how to use
symbolic constants. In the description read by ode the
parameter r is a variable like x, y, and
z. But unlike them it is not updated during stepping, since no
formula for its derivative r' is given.
Our second example deals with the interactive construction of a `phase portrait': a set of solution curves with different initial conditions. Phase portraits are of paramount interest in the qualitative theory of differential equations, and also possess @ae{}sthetic appeal.
Since a description read by ode may contain any number of
`step' statements, multiple solution curves may be plotted in a
single run. The most recent `print' statement will be used with
each `step' statement. In practice, a phase portrait would be
drawn from a few well-chosen solution curves. Choosing a good set of
solution curves may require experimentation, which makes interactivity
and real-time plotting all-important.
As an example, consider a so-called Lotka--Volterra predator--prey model. Suppose that in a lake there are two species of fish: A (the prey) who live by eating a plentiful supply of plants, and B (the predator) who eat A. Let x(t) be the population of A and y(t) the population of B at time t. A crude model for the interaction of A and B is given by the equations
x' = x(a-by) y' = y(cx-d)
where a, b, c, d are positive constants. To draw a phase portrait for this system interactively, you could type
ode | graph -T X -C -x 0 5 -y 0 5 x' = (a - b*y) * x y' = (c*x - d) * y a = 1; b = 1; c = 1; d = 1; print x, y x = 1; y = 2 step 0, 10 x = 1; y = 3 step 0, 10 x = 1; y = 4 step 0, 10 x = 1; y = 5 step 0, 10 .
Four curves will be drawn in succession, one per `step' line. They
will be periodic; this periodicity is similar to the fluctuations
between predator and prey populations that occur in real-world
ecosystems. On a color display the curves will appear in different
colors, since by default, graph changes the linemode between
datasets. That feature may be turned off by using `graph -T X
-B' rather than `graph -T X'.
It is sometimes useful to use ode and graph to plot
discrete points, which are not joined by line segments to form a curve.
Our third example illustrates this. Suppose the file `atwoods'
contains the lines
m = 1 M = 1.0625 a = 0.5; adot = 0 l = 10; ldot = 0 ldot' = ( m * l * adot * adot - M * 9.8 + m * 9.8 * cos(a) ) / (m + M) l' = ldot adot' = (-1/l) * (9.8 * sin(a) + 2 * adot * ldot) a' = adot print l, ldot step 0, 400
The first few lines describe the functioning of a so-called swinging Atwood's machine. An ordinary Atwood's machine consists of a taut cord draped over a pulley, with a mass attached to the cord at each end. Normally, the heavier mass (M) would win against the lighter mass (m), and draw it upward. A swinging Atwood's machine allows the lighter mass to swing back and forth as well as move vertically.
The `print l, ldot' statement requests that the vertical position and vertical velocity of the lighter mass be printed out at each step. If you run the command
ode < atwoods | graph -T X -x 9 11 -y -1 1 -m 0 -S 1 -X l -Y ldot
you will obtain a real-time plot. The `-m 0' option requests that successive data points not be joined by line segments, and the `-S 1' option requests that plotting symbol #1 (a dot) be plotted at the location of each point. As you will see if you run this command, the heavy mass does not win against the lighter mass. Instead the machine oscillates non-periodically. Since the motion is non-periodic, the plot benefits from being drawn as a sequence of unconnected points.
We conclude by mentioning a few features of ode that may be
useful when things are not going quite right. One of them is the
`examine' statement. It may be used to discover pertinent
information about any variable in a system. For details, see section The ode input language formally specified.
Another useful feature is that the `print' statement may be used to print out more than just the value of a variable. As we have seen, if the name of the variable is followed by `'', the derivative of the variable will be printed instead. In a similar way, following the variable name with `?', `!', or `~' prints respectively the relative single-step error, the absolute single-step error, or the accumulated error (not currently implemented). These quantities are discussed in section Numerical error and how to avoid it.
The `print' statement may be more complicated than was shown in the preceding examples. Its general structure is
print <pr-list> [every <const>] [from <const>]
The bracket notation `[...]' means that the enclosed statements are optional. Until now we have not mentioned the `every' clause or the `from' clause. The <pr-list> is familiar, however; it is simply a comma-separated list of variables. For example, in the statement
print t, y, y' every 5 from 1
the <pr-list> is <t, y, y'>. The clauses `every 5' and `from 1' specify that printing should take place after every fifth step, and that the printing should begin when the independent variable t reaches 1. An `every' clause is useful if you wish to `thin out' the output generated by a `step' statement, and a `from' clause is useful if you wish to view only the final portion of a solution curve.
ode command-line options
The command-line options to ode are listed below. There are
several sorts of option:
The following option affects the way input is read.
The following options affect the output format.
The following options specify the numerical integration scheme. Only one of the three basic option `-R', `-A', and `-E' may be specified. The default is `-R' (Runge--Kutta--Fehlberg).
The following options set the error bounds on the numerical solution scheme.
ode to
continue even if this ceiling is exceeded. This may result in large
numerical errors.
Finally, the following options request information.
ode and the plotting utilities
package, and exit.
ode is always in one of two states:
ode moves from the first to the second state after it sees and
processes a `step' line. It returns to the first state after
the generated output has been printed. Errors may occur in either the
`reading' state or the `solving' state, and may terminate computations
or even cause ode to exit. We now explain the possible sorts of
error.
While reading input, ode may encounter a syntax error: an
ungrammatical line that it is unable to parse. (For a summary of its
input grammar, see section The ode input language formally specified.) If so, it emits the error
message
ode::nnn: syntax error
where `nnn' is the number of the line containing the error. When the `-f filename' option is used to specify an input file, the error message will read
ode:filename:nnn: syntax error
for errors encountered inside the input file. Subsequently, when
ode begins reading the standard input, line numbers will start
over again from 1.
No effort is made to recover from syntax errors in the input. However, there is a meager effort to resynchronize, so that more than one syntax error in a file may be found at the same time.
It is also possible that a fatal arithmetic exception (such as a
division by zero, or a floating point overflow) may occur while
ode is reading input. If such an exception occurs, ode
will print an "Floating point exception" error message and exit.
Arithmetic exceptions are machine-dependent. On some machines, the
line
y = 1/0
would induce an arithmetic exception. Also on some machines (not necessarily the same ones), the lines
y = 1e100 z = y^4
@ifnottex
would induce an arithmetic exception. That is because on most
machines, the double precision quantities that ode uses
internally are limited to a maximum size of approximately 1.8x10^308.
When ode is in the `solving' state, i.e., computing a numerical
solution, similar arithmetic exceptions may occur. If so, the solution
will be interrupted and a message resembling
ode: arithmetic exception while calculating y'
will be printed. However, ode will not exit; the exception will
be `caught'. ode itself recognizes the following exceptional
conditions: square root of a negative number, logarithm of a
non-positive number, and negative number raised to a non-integer power.
ode will catch any of these operations before it is performed,
and print an error message specifying which illegal operation it has
encountered.
ode: square root of a negative number while calculating y'
would be a typical error message.
If the machine on which ode is running supports the
`matherr' facility for reporting errors in the computation of
standard mathematical functions, it will be used. This facility reports
domain errors and range errors (overflows, underflows, and losses of
significance) that could occur when evaluating such functions as
`log', `gamma', etc.; again, before they are performed. If
the matherr facility is present, the error message will be fairly
informative. For example, the error message
ode: range error (overflow) in lgamma while calculating y'
could be generated if the logarithmic gamma function `lgamma' is evaluated at a value of its argument that is too large. The generation of any such message, except a message warning of an underflow, will cause the numerical solution to be interrupted.
There is another sort of error that may occur during numerical solution:
the condition that an error ceiling, which the user may set with the
`-r' option or the `-e' option, is exceeded. This too will
cause the numerical solution to be abandoned, and ode to switch
back to reading input.
This discussion is necessarily incomplete. Entire books exist on any
subject mentioned below (e.g., floating point error). Our goals are
modest: first, to introduce the basic notions of error analysis as they
apply to ode; second, to steer you around the more obvious
pitfalls. You should look through a numerical analysis text (e.g.,
Atkinson's Introduction to Numerical Analysis) before beginning
this discussion.
We begin with some key definitions. The error of greatest concern is the difference between the actual solution and the numerical approximation to the solution; this is termed the accumulated error, since the error is built up during each numerical step. Unfortunately, an estimate of this error is usually not available without knowledge of the actual solution. There are, however, several more usable notions of error. The single-step error, in particular, is the difference between the actual solution and the numerical approximation to the solution after any single step, assuming the value at the beginning of the step is correct.
@ifnottex
The relative single-step error is the single-step error, divided
by the current value of the numerical approximation to the solution.
Why not divided by the current value of the solution itself? The reason
is that the solution is not exactly known. When free to choose a
stepsize, ode will do so on the basis of the relative single-step
error. By default, it will choose the stepsize so as to maintain an
accuracy of eight significant digits in each step. That is, it will
choose the stepsize so as not to violate an upper bound of
10^(-9) on the relative single-step error. This ceiling may be
adjusted with the `-r' option.
Where does numerical error come from? There are two sources. The first
is the finite precision of machine computation. All computers work with
floating point numbers, which are not real numbers, but only an
approximation to real numbers. However, all computations performed by
ode are done to double precision, so floating point error tends
to be relatively small. You may nonetheless detect the difference
between real numbers and floating point numbers by experimenting with
the `-p 17' option, which will print seventeen significant digits.
On most machines, that is the precision of a double precision
floating point number.
The second source of numerical error is often called the
theoretical truncation error. It is the difference between
the actual solution and the approximate solution due solely to the
numerical scheme. At the root of many numerical schemes is an infinite
series; for ordinary differential equations, it is a Taylor expansion.
Since the computer cannot compute all the terms in an infinite series,
a numerical scheme necessarily uses a truncated series; hence the
term. The single-step error is the sum of the theoretical truncation
error and the floating point error, though in practice the floating
point error is seldom included. The single-step error estimated by
ode consists only of the theoretical truncation error.
We say that a numerical scheme is stable, when applied to a particular initial value problem, if the error accumulated during the solution of the problem over a fixed interval decreases as the stepsize decreases; at least, over a wide range of step sizes. With this definition both the Runge--Kutta--Fehlberg (`-R') scheme and the Adams--Moulton (`-A') scheme are stable (a statement based more on experience than on theoretical results) for a wide class of problems.
After these introductory remarks, we list some common sources of accumulated error and instability in any numerical scheme. Usually, problems with large accumulated error and instability are due to the single-step error in the vicinity of a `bad' point being large.
ode should not be used to generate a numerical solution on any
interval containing a singularity. That is, ode should not be
asked to step over points at which the system of differential equations
is singular or undefined.
You will find the definitions of singular point, regular singular point,
and irregular singular point in any good differential equations text.
If you have no favorite, try Birkhoff and Rota's Ordinary
Differential Equations, Chapter 9. Always locate and classify the
singularities of a system, if any, before applying ode.
ode to yield an accurate numerical solution on an interval,
the true solution must be defined and well-behaved on that interval.
The solution must also be real. Whenever any of these conditions is
violated, the problem is said to be ill-posed. Ill-posedness may
occur even if the system of differential equations is well-behaved on
the interval. Strange results, e.g., the stepsize suddenly shrinking to
the machine limit or the solution suddenly blowing up, may indicate
ill-posedness.
As an example of ill-posedness (in fact, an undefined solution) consider
the innocent-looking problem:
@ifnottex
y' = y^2 y(1) = -1The solution on the domain t > 0 is
y(t) = -1/t.With this problem you must not compute a numerical solution on any interval that includes t=0. To convince yourself of this, try to use the `step' statement
step 1, -1on this system. How does
ode react?
As another example of ill-posedness, consider the system
y'=1/ywhich is undefined at y=0. The general solution is @ifnottex
y = +/- (2(t-C))^(1/2),@ifnottex so that if the condition y(2)=2 is imposed, the solution will be (2t)^(1/2). Clearly, if the domain specified in a `step' statement includes negative values of t, the generated solution will be bogus. In general, when using a constant stepsize you should be careful not to `step over' bad points or bad regions. When allowed to choose a stepsize adaptively,
ode will often spot bad points, but not
always.
y' = 2x x' = 2yhas only one critical point, at (x,y) = (0,0). A critical point is sometimes referred to as a stagnation point. That is because a system at a critical point will remain there forever, though a system near a critical point may undergo more violent motion. Under some circumstances, passing near a critical point may give rise to a large accumulated error. As an exercise, solve the system above using
ode, with the
initial condition x(0) = y(0) = 0. The solution should be
constant in time. Now do the same with points near the critical point.
What happens?
You should always locate the critical points of a system before
attempting a solution with ode. Critical points may be
classified (as equilibrium, vortex, unstable, stable, etc.) and this
classification may be of use. To find out more about this, consult
any book dealing with the qualitative theory of differential equations
(e.g., Birkhoff and Rota's Ordinary Differential Equations,
Chapter 6).
ode are bad in the sense that
instability appears to be present, or an unusually small stepsize needs
to be chosen needed in order to reduce the single-step error to
manageable levels, it may simply be that the numerical scheme being used
is not suited to the problem. For example, ode currently has no
numerical scheme which handles so-called `stiff' problems very well.
As an example, you may wish to examine the stiff problem:
y' = -100 + 100t + 1 y(0) = 1on the domain [0,1]. The exact solution is @ifnottex
y(t) = e^(-100t) + t.It is a useful exercise to solve this problem with
ode using
various numerical schemes, stepsizes, and relative single-step error
bounds, and compare the generated solution curves with the actual
solution.
There are several rough and ready heuristic checks you may perform on
the accuracy of any numerical solution produced by ode. We
discuss them in turn.
# an equation arising in QCD (quantum chromodynamics) f' = fp fp' = -f*g^2 g' = gp gp' = g*f^2 f = 0; fp = -1; g = 1; gp = -1 print t, f step 0, 5Next make a file named `stability', containing the lines:
: sserr is the bound on the relative single-step error for sserr do ode -r $sserr < qcd done | spline -n 500 | graph -T X -CThis is a `shell script', which when run will superimpose numerical solutions with specified bounds on the relative single-step error. To run it, type:
sh stability 1 .1 .01 .001and a plot of the solutions with the specified error bounds will be drawn. The convergence, showing stability, should be quite illuminating.
The time required for ode to solve numerically a system of
ordinary differential equations depends on a great many factors. A
few of them are: number of equations, complexity of equations (number
of operators and nature of the operators), and number of steps taken
(a very complicated function of the difficulty of solution, unless
constant stepsizes are used). The most effective way to gauge the time
required for solution of a system is to clock a short or imprecise run
of the problem, and reason as follows: the time required to take two
steps is roughly twice that required for one; and there is a
relationship between the number of steps required and the relative error
ceiling chosen. That relationship depends on the numerical scheme being
used, the difficulty of solution, and perhaps on the magnitude of the
error ceiling itself. A few carefully planned short runs may be
used to determine this relationship, enabling a long but imprecise run
to be used as an aid in projecting the cost of a more precise run over
the same region. Lastly, if a great deal of data is printed, it is
likely that more time is spent in printing the results than in computing
the numerical solution.
ode input language formally specified
The following is a formal specification of the grammar for ode's
input language, in Backus--Naur form. Nonterminal symbols in the
grammar are enclosed in angle brackets. Terminal tokens are in all
capitals. Bare words and symbols stand for themselves.
<program> ::= ... empty ...
| <program> <statement>
<statement> ::= SEP
| IDENTIFIER = <const> SEP
| IDENTIFIER ' = <expression> SEP
| print <printlist> <optevery> <optfrom> SEP
| step <const> , <const> , <const> SEP
| step <const> , <const> SEP
| examine IDENTIFIER SEP
<printlist> ::= <printitem>
| <printlist> , <printitem>
<printitem> ::= IDENTIFIER
| IDENTIFIER '
| IDENTIFIER ?
| IDENTIFIER !
| IDENTIFIER ~
<optevery> ::= ... empty ...
| every <const>
<optfrom> ::= ... empty ...
| from <const>
<const> ::= <expression>
<expression> ::= ( <expression> )
| <expression> + <expression>
| <expression> - <expression>
| <expression> * <expression>
| <expression> / <expression>
| <expression> ^ <expression>
| FUNCTION ( <expression> )
| - <expression>
| NUMBER
| IDENTIFIER
Since this grammar is ambiguous, the following table summarizes the precedences and associativities of operators within expressions. Precedences decrease from top to bottom.
Class Operators Associativity Exponential ^ right Multiplicative * / left Additive + - left
As noted in the grammar, there are six types of nontrivial statement. We now explain the effects (the `semantics') of each type, in turn.
"y" is a dynamic variable value:2.718282 prime:2.718282 sserr:1.121662e-09 aberr:3.245638e-09 acerr:0 code: push "y"The phrase `dynamic variable' means that there is a differential equation describing the behavior of y. The numeric items in the table are:
The grammar for the ode input language contains four types of
terminal token: FUNCTION, IDENTIFIER, NUMBER, and
SEP. They have the following meanings.
gnuplot. All functions take a
single argument, except for ibeta, which takes three, and
igamma, which takes two. For trigonometric functions, all arguments
are expressed in radians. The atan function is defined to give a
value between -PI/2 and PI/2 (inclusive).
In the ode input language, upper and lower-case letters are
distinct. Comments begin with the character `#' and continue to
the end of the line. Long lines may be continued onto a second line by
ending the first line with a backslash (`\'). That is because
the combination backslash-newline is equivalent to a space.
Spaces or tabs are required in the input whenever they are needed to separate identifiers, numbers, and keywords from one another. Except as separators, they are ignored.
ode and solving differential equationsode.
ode: A
numerical simulation of ordinary differential equations,"
pp. 480--481 in Proceedings of the Conference on Computers in
Physics Instruction, Addison--Wesley, 1990.
libplot, a Function Librarylibplot: An overview
GNU libplot is a library of functions for drawing two-dimensional
vector graphics. It can produce smooth, double-buffered animations
for the X Window System, and graphical output in many different file
formats. It is `device-independent' in the sense that its API
(application programming interface) is to a large extent independent of
the display type or output format.
The graphical objects which libplot can draw include paths,
circles and ellipses, points, markers, and `adjusted labels' (justified
text strings). A path is a sequence of line segments,
circular arcs, and/or elliptic arcs. Paths may be open or closed.
User-specified filling of paths, circles, and ellipses is supported
(fill color, as well as pen color, may be specified). There is
support for maintaining a Postscript-style stack of graphics contexts,
i.e., a stack of drawing attribute sets. User-specifiable
attributes other than pen color and fill color include path-related
attributes such as line type and line width, and text-related attributes
such as font name, font size, and text angle.
The fundamental abstraction provided by libplot is that of a
Plotter. A Plotter is an object with an interface for the
drawing of vector graphics which is similar to the interface provided by
a traditional pen plotter. There are many types of Plotter, which
differ in the display type they produce output for. Any number of
Plotters, of the same or different types, may exist simultaneously in an
application.
The drawing operations supported by Plotters of different types are
identical, in agreement with the principle of device independence.
So a graphics application that is linked with libplot may
easily be written so as to produce output in any or all of the
supported output formats.
The following are the currently supported types of Plotter.
idraw drawing editor.
xfig drawing editor. The xfig editor will export
drawings in various other formats for inclusion in documents.
xterm, the X Window System terminal
emulation program. The MS-DOS version of kermit also includes
such an emulator.
plot. (See section The plot Program.)
A distinction among these types of Plotter is that all except X and X Drawable Plotters write graphics to a file or other output stream. An X Plotter pops up its own windows, and an X Drawable Plotter draws graphics in one or two X drawables.
Another distinction is that X, X Drawable, Tektronix and Metafile Plotters are real-time. This means that they draw graphics or write to an output stream as the drawing operations are invoked on them. Postscript, Fig and HP-GL Plotters are not real-time, since their output streams can only be emitted after all functions have been called. For a Postscript Plotter this is because a `bounding box' line must be placed at the head of the output file. For a Fig Plotter it is because color definitions must be placed at the head of the output file.
The most important operations supported by any Plotter are openpl
and closepl, which open and close it. Graphics may be drawn,
and drawing attributes set, only within an
openpl...closepl pair. The graphics produced within
each openpl...closepl pair constitute a `page'. In
principle, any Plotter may be opened and closed arbitrarily many times.
An X Plotter displays each page in a separate X window, and
Postscript, PCL, and HP-GL Plotters render each page as a separate
physical page. X Drawable Plotters and Tektronix Plotters
manipulate a single drawable or display, on which pages are displayed in
succession. Plotters that do not draw in real time (Postscript, Fig,
PCL, and HP-GL Plotters) may wait until their existence comes to an end
(i.e., until they are deleted) before outputting their pages of
graphics.
In the current release of libplot, Postscript Plotters delay
outputting graphics in this way, but PCL and HP-GL Plotters output each
page of graphics individually, i.e., when closepl is invoked.
Fig Plotters are similar, but output at most one page of graphics. That
is because Fig format currently supports only a single page. On
account of this potential problem with Fig Plotters, all Plotters
support an additional operation: outfile. The output stream for
a Plotter, if it has one, may be altered by invoking outfile
on it. outfile may only be invoked outside an
openpl...closepl pair. By using outfile, a
programmer may produce multipage graphics output from Fig Plotters by
directing output to a sequence of output streams, one per page. The use
of outfile in other contexts is strongly deprecated.
There are several other basic operations which any Plotter supports. The `graphics display' drawn in by a Plotter is a square or rectangular region on a display device. But when using any Plotter to draw graphics, a user will specify the coordinates of graphical objects in device-independent `user coordinates', rather than in device coordinates. A Plotter relates the user coordinate system to the device coordinate system by performing an affine transformation, which must be specified by the user.
Immediately after invoking openpl to open a Plotter, an
application should invoke the space operation to initialize this
affine transformation. This invocation specifies the rectangular region
(in user coordinates) that will be mapped by the Plotter to the graphics
display. The affine transformation may be updated at any later time by
invoking space again, or by invoking fconcat. The
fconcat operation will `concatenate' (i.e., compose) the current
affine transformation transformation with any specified affine map.
This sort of concatenation is a capability familiar from, e.g.,
Postscript.
Each Plotter maintains a Postscript-style stack of graphics contexts.
This makes possible the rapid, efficient drawing of complicated pages of
graphics. A graphics context includes the current affine
transformation from the user coordinate system to the device coordinate
system. It also includes such modal drawing attributes as graphics
cursor position, linemode, line width, pen and fill colors, and the
font used for drawing text. The state of any uncompleted path (if
any) is included as well, since paths may be drawn incrementally,
one portion (line segment or arc) at a time. The current graphics
context is pushed onto the stack by calling savestate, and popped
off by calling restorestate.
To permit vector graphics animation, any page of graphics may be split
into `frames'. A frame is ended, and a new frame is begun, by
invoking the erase operation. On a Plotter that does
real-time plotting (i.e., an X, X Drawable, Tektronix, or
Metafile Plotter), this erases all plotted objects from the graphics
display, allowing a new frame to be drawn. Displaying a sequence of
frames in succession creates the illusion of smooth animation.
On a Plotter that does not do real-time plotting (i.e., a
Postscript, Fig, PCL or HP-GL Plotter), invoking erase deletes
all plotted objects from an internal buffer. For this reason, Plotters
that do not do real-time plotting will display only the last frame of
any multiframe page.
libplot
libplot has bindings for several programming languages.
Regardless of which language binding is used, the concepts behind
libplot (Plotters, and a fixed set of operations that can be
applied to any Plotter) remain the same. However, the ways in which
Plotters are manipulated (created, selected for use, and deleted)
may differ between bindings.
If you are writing an application in C that will use libplot to
draw vector graphics, the first thing you need to know is how, in the
C binding, Plotters are manipulated. There are four functions for
this: newpl, selectpl, deletepl, and the
parameter-setting function parampl.
The newpl function will create a Plotter of specified type. Its
first argument may be "X", "Xdrawable", "ps", "fig", "pcl", "hpgl",
"tek", or "meta". It returns an integer (a "handle") that may be
used to refer to the Plotter. Before using a Plotter that you have
created (i.e., before invoking any of the libplot operations
on it), you must select the Plotter for use by calling
selectpl. Only one Plotter may be selected at a time, but by
calling selectpl you may switch from Plotter to Plotter at any
time, even when the selected Plotter is open. A Plotter that is not
currently selected can be deleted, and its storage freed, by calling
deletepl.
Strictly speaking, you do not need to call newpl,
selectpl, or deletepl in order to draw graphics. That is
because at startup, a single Metafile Plotter that writes to standard
output (with handle `0') is automatically created and selected. The
presence of this default Plotter is for compatibility with pre-GNU
versions of libplot. Of course, you may not wish to obtain
output in metafile format, and you may not wish to write to standard
output.
You should get into the habit of calling deletepl whenever you
are finished using a Plotter. In general, Plotters that do not plot
graphics in real time (Postscript Plotters in particular) write out
graphics only when the plot is finished, and deletepl is called.
The following table summarizes the action of the four functions in the C binding that are used for Plotter manipulation.
libplot operations is subsequently invoked, it
will be applied to the selected Plotter. Only one Plotter may be
selected at a time. A negative return value indicates the Plotter
could not be selected.
At startup, a single Metafile Plotter that writes to standard output
(with handle `0') is automatically created and selected.
char *, i.e., a string. Unrecognized
parameters are ignored. For a list of the recognized parameters and
their meaning, see section Device driver parameters.
Up to now we have not discussed the fourth function, parampl.
Even though the Plotter interface is largely Plotter-independent, it
is useful to be able to specify certain aspects of a Plotter's behavior
at the time it is created. Plotter behavior is captured by a manageable
number of parameters, which we call device driver parameters.
A value for any parameter can be specified by calling
parampl. This function does not operate on any particular
Plotter: it belongs to the C binding as a whole. The parameter
values used by any Plotter are constant over the lifetime of the
Plotter, and are those that were in effect when the Plotter was created.
Actually, a slightly more sophisticated rule applies. If at Plotter
creation time a parameter is set, the value specified by the most recent
call to parampl will be the value used by the Plotter. If at
Plotter creation time a parameter is not set, its default value
will be used, unless there is an environment variable of the same name,
in which case the value of that environment variable will be used. This
rule increases run-time flexibility: an application programmer may
allow non-critical driver parameters to be specified by the user via
environment variables. Once set, a parameter may be unset by the
programmer by calling parampl with a value argument of NULL.
This further increases flexibility.
The source code for a graphics application written in C, if it is to use
libplot, must contain the lines
#include <stdio.h> #include <plot.h>
The header file plot.h is distributed with libplot, and
should have been installed on your system where your C compiler will
find it. It contains prototypes for each of the functions in
libplot and some miscellaneous definitions. It may be used
with C++ programs as well as C programs.
To link your application with libplot, you would use the
appropriate `-l' option(s) on the command line when compiling it.
You would use
-lplot -lXaw -lXmu -lXt -lXext -lX11 -lm
or, in recent versions of the X Window System,
-lplot -lXaw -lXmu -lXt -lSM -lICE -lXext -lX11 -lm
(Alternatively, you may need to use `-lplot -lXm -lXt -lXext -lX11 -lm', `-lplot -lXm -lXt -lXext -lX11 -lm -lc -lgen', or `-lplot -lXm -lXt -lXext -lX11 -lm -lc -lPW', on systems that provide Motif widgets instead of Athena widgets. In recent versions of the X Window System, you may need to insert `-lXp' and `-lSM -lICE' also.)
On most systems libplot is installed as a DLL (dynamically linked
library, or `shared' library). This means that the linking with your
application will take place at run time rather than compile time. The
environment variable LD_LIBRARY_PATH lists the directories which
will be searched for DLL's at run time. For your application to be
executable, this environment variable should include the directory in
which libplot is stored.
The following is a sample application, written in C, that invokes
libplot operations to draw vector graphics. It draws an
intricate and beautiful path (Bill Gosper's "C" curve, discussed
as Item #135 in HAKMEM, MIT Artificial Intelligence Laboratory
Memo #239, 1972). As the numeric constant MAXORDER (here
equal to 12) is increased, the path will take on the shape of a
curly letter "C", which is the envelope of a myriad of epicyclic
octagons.
#include <stdio.h>
#include <plot.h>
#define MAXORDER 12
void draw_c_curve (double dx, double dy, int order)
{
if (order >= MAXORDER)
fcontrel (dx, dy); /* continue path along (dx, dy) */
else
{
draw_c_curve (0.5 * (dx - dy), 0.5 * (dx + dy), order + 1);
draw_c_curve (0.5 * (dx + dy), 0.5 * (dy - dx), order + 1);
}
}
int main ()
{
int handle;
/* set a Plotter parameter */
parampl ("PAGESIZE", "letter");
/* create a Postscript Plotter that writes to standard output */
if ((handle = newpl ("ps", stdin, stdout, stderr)) < 0)
{
fprintf (stderr, "Couldn't create Plotter\n");
return 1;
}
selectpl (handle); /* select the Plotter for use */
if (openpl () < 0) /* open Plotter */
{
fprintf (stderr, "Couldn't open Plotter\n");
return 1;
}
fspace (0.0, 0.0, 1000.0, 1000.0); /* specify user coordinate system*/
flinewidth (0.25); /* width of lines in user coordinates */
pencolorname ("red"); /* path will be drawn in red */
erase (); /* erase Plotter's graphics display */
fmove (600.0, 300.0); /* position the graphics cursor */
draw_c_curve (0.0, 400.0, 0);
if (closepl () < 0) /* close Plotter */
{
fprintf (stderr, "Couldn't close Plotter\n");
return 1;
}
selectpl (0); /* select default Plotter */
if (deletepl (handle) < 0) /* delete Plotter we used */
{
fprintf (stderr, "Couldn't delete Plotter\n");
return 1;
}
return 0;
}
As you can see, this application begins by calling the newpl
function to create a Postscript Plotter. The Postscript Plotter will
produce output for a US letter-sized page, though any other standard
page size, e.g., "a4", could be substituted. This would be arranged by
altering the call to parampl. The PAGESIZE parameter is
one of several Plotter parameters that an application programmer may set
by calling parampl. For a complete list, see section Device driver parameters.
After the Plotter is created, the application selects it for use,
opens it, and draws the "C" curve recursively. The drawing of
the curve is accomplished by invoking fmove on the Plotter to
position the graphics cursor, and then calling draw_c_curve.
This subroutine repeatedly invokes fcontrel. The fcontrel
operation continues a path by adding a line segment to it. The
endpoint of each line segment is specified in relative coordinates,
i.e., as an offset from the previous point. After the "C" curve
is drawn, the Plotter is closed. A Postscript file is written to
standard output when deletepl is called to delete the Plotter.
Specifying "fig", "pcl", "hpgl", "tek", or "meta" as the first argument
in the call to newpl, instead of "ps", would yield a Plotter that
would write graphics to standard output in the specified format, instead
of Postscript. The PAGESIZE parameter is relevant to the first
three of these output formats, but is ignored for the latter two.
Specifying "meta" as the Plotter type may be useful if you wish to avoid
recompilation for different output devices. Metafile output may be
piped to the plot utility and converted to any other supported
output format, or displayed in an X window. See section The plot Program.
If "X" were specified as the first argument of newpl, the
curve would be drawn in a popped-up X window, and the output stream
argument would be ignored. Which X Window System display the window
would pop up on would be determined by the DISPLAY parameter,
or if that parameter were not set, by the DISPLAY environment
variable. The size of the X window would be determined by the
BITMAPSIZE parameter, or if that parameter were not set, by the
BITMAPSIZE environment variable. The default value is "570x570".
You could also specify "Xdrawable" as the Plotter type. For you to make
this work, you would need to know a bit about X Window System
programming. You would need to create at least one X drawable
(i.e., window or a pixmap), and by invoking the parampl function
before newpl is called, set it as the value of the parameter
XDRAWABLE_DRAWABLE1 or XDRAWABLE_DRAWABLE2. For other
parameters that affect X Drawable Plotters, see section Device driver parameters.
The following is another sample application, written in C, that invokes
libplot operations to draw vector graphics. It draws a
spiral consisting of elliptically boxed text strings, each of which
reads "GNU libplot!". This figure will be sent to standard output in
Postscript format.
#include <stdio.h>
#include <plot.h>
#include <math.h>
#define SIZE 100.0 /* nominal size of user coordinate frame */
#define EXPAND 2.2 /* expansion factor for elliptical box */
void draw_boxed_string (char *s, double size, double angle)
{
double true_size, width;
ftextangle (angle); /* text inclination angle (degrees) */
true_size = ffontsize (size); /* choose font size */
width = flabelwidth (s); /* compute width of text string */
fellipserel (0.0, 0.0, /* draw surrounding ellipse */
EXPAND * 0.5 * width, EXPAND * 0.5 * true_size, angle);
alabel ('c', 'c', s); /* draw centered text string */
}
int main()
{
int handle, i;
/* set a Plotter parameter */
parampl ("PAGESIZE", "letter");
/* create a Postscript Plotter that writes to standard output */
if ((handle = newpl ("ps", stdin, stdout, stderr)) < 0)
{
fprintf (stderr, "Couldn't create Plotter\n");
return 1;
}
selectpl (handle); /* select the Plotter for use */
if (openpl () < 0) /* open Plotter */
{
fprintf (stderr, "Couldn't open Plotter\n");
return 1;
}
fspace (-(SIZE), -(SIZE), SIZE, SIZE); /* specify user coor system */
pencolorname ("blue"); /* pen color will be blue */
fillcolorname ("white");
filltype (1); /* ellipses will be filled with white */
fontname ("NewCenturySchlbk-Roman"); /* choose a Postscript font */
for (i = 80; i > 1; i--) /* loop through angles */
{
double theta, radius;
theta = 0.5 * (double)i; /* theta is in radians */
radius = SIZE / pow (theta, 0.35); /* this yields a spiral */
fmove (radius * cos (theta), radius * sin (theta));
draw_boxed_string ("GNU libplot!", 0.04 * radius,
(180.0 * theta / M_PI) - 90.0);
}
if (closepl () < 0) /* close Plotter */
{
fprintf (stderr, "Couldn't close Plotter\n");
return 1;
}
selectpl (0);
if (deletepl (handle) < 0) /* delete Plotter we used */
{
fprintf (stderr, "Couldn't delete Plotter\n");
return 1;
}
return 0;
}
This example shows what is involved in plotting a text string or text
strings. First, the desired font must be retrieved. A font is
fully specified by invoking fontname, fontsize, and
textangle, or their floating point counterparts ffontname,
ffontsize, and ftextangle. Since these three operations
may be invoked in any order, each of them returns the size of the font
that it selects, as a convenience to the programmer. This may differ
slightly from the size specified in the most recent call to
fontsize or ffontsize, since many Plotters have only a
limited repertory of fonts. The above example plots each text string in
the "NewCenturySchlbk-Roman" font, which is available on Postscript
Plotters. See section Available text fonts.
If you replace "ps" by "X" in the call to newpl, an X Plotter
rather than a Postscript Plotter will be used, and the spiral will be
drawn in a popped-up X window. If your X display does not
support the "NewCenturySchlbk-Roman" font, you may substitute any other
scalable font, such as the widely available "utopia-medium-r-normal".
For the format of font names, see section Available text fonts for the X Window System. If the X
Plotter is unable to retrieve the font you specify, it will first
attempt to use a default scalable font ("Helvetica"), and if that fails,
use a default Hershey vector font ("HersheySerif") instead. Hershey
fonts are constructed from line segments, so each built-in Hershey font
is available on all types of Plotter.
If you are using an older (pre-X11R6) X Window System display, you will find that retrieving a scalable font is a time-consuming operation. The above example may run slowly on some older X displays, since a new font must be retrieved before each text string is drawn. That is because each text string has a different angle of inclination. It is possible to retrieve individual characters from an X11R6 display, rather than retrieving an entire rasterized font. If this feature is available, the X Plotter will automatically take advantage of it to save time.
You may use libplot to produce vector graphics animations on any
Plotter that does real-time plotting (i.e., an X, X Drawable,
Tektronix, or Metafile Plotter). By definition, the `frames' in any
page of graphics are separated by invocations of erase. So
the graphics display will be cleared after each frame. If successive
frames differ only slightly, a smooth animation will result.
The following is a sample application, written in C, that produces an animation for the X Window System. It displays a `drifting eye'. As the eye drifts across a popped-up window from left to right, it slowly rotates. After the eye has drifted across twice, the window will vanish.
#include <stdio.h>
#include <plot.h>
int main ()
{
int handle, i = 0, j;
/* set Plotter parameters */
parampl ("BITMAPSIZE", "300x150");
parampl ("VANISH_ON_DELETE", "yes");
parampl ("USE_DOUBLE_BUFFERING", "yes");
/* create an X Plotter with the specified parameters */
if ((handle = newpl ("X", stdin, stdout, stderr)) < 0)
{
fprintf (stderr, "Couldn't create Plotter\n");
return 1;
}
selectpl (handle); /* select the Plotter for use */
if (openpl () < 0) /* open Plotter */
{
fprintf (stderr, "Couldn't open Plotter\n");
return 1;
}
space (0, 0, 299, 149); /* specify user coordinate system */
linewidth (8); /* width of lines in user coordinates */
filltype (1); /* objects will be filled */
bgcolorname ("saddle brown"); /* background color for the window */
for (j = 0; j < 300; j++)
{
erase (); /* erase window */
pencolorname ("red"); /* choose red pen, with cyan filling */
fillcolorname ("cyan");
ellipse (i, 75, 35, 50, i); /* draw an ellipse */
colorname ("black"); /* choose black pen, with black filling */
circle (i, 75, 12); /* draw a circle [the pupil] */
i = (i + 2) % 300; /* shift rightwards */
}
if (closepl () < 0) /* close Plotter */
{
fprintf (stderr, "Couldn't close Plotter\n");
return 1;
}
selectpl (0); /* select default Plotter */
if (deletepl (handle) < 0) /* delete Plotter we used */
{
fprintf (stderr, "Couldn't delete Plotter\n");
return 1;
}
return 0;
}
As you can see, this application begins by calling parampl
several times to set device driver parameters, and then calls
newpl to create an X Plotter. The X Plotter window will
have size 300x150 pixels. This window will vanish when the Plotter is
deleted. If the VANISH_ON_DELETE parameter were not set to
"yes", the window would remain on the screen until removed by the user
(by typing `q' in it, or by clicking with a mouse).
Setting the parameter USE_DOUBLE_BUFFERING to "yes" is very
important if you wish to produce a smooth animation, with no jerkiness.
Normally, an X Plotter draws graphics into a window in real time,
and erases the window when erase is called. But if double
buffering is used, each frame of graphics is written into an off-screen
buffer, and copied into the window, pixel by pixel, when erase is
called or the Plotter is closed. This is a bit counterintuitive, but is
exactly what is needed for smooth animation. On some high-end display
devices you may be able to do even better, by specifying "fast" rather
than "yes". This requests that the X Plotter take advantage of
special hardware support for double buffering. If no such support
is available, "fast" means the same as "yes".
After the Plotter is created, it is selected for use and opened. When
openpl is called, the window pops up, and the animation
begins. In the body of the for loop there is a call to
erase, and also a sequence of libplot operations that
draws the eye. The pen color and fill color are changed twice with each
passage through the loop. You may wish to experiment with the animation
parameters to produce the best effects on your video hardware.
The locations of the objects that are plotted in the animation are
expressed in terms of user coordinates, not pixel coordinates. But the
call to space defines user and pixel coordinates to be
effectively the same. User coordinates are chosen so that the lower
left corner is (0,0) and the upper right corner is (299,149). Since
this agrees with the window size, individual pixels may be addressed in
terms of integer user coordinates. For example, point(299,149)
would set the pixel in the upper right hand corner of the window to the
current pen color.
The following is another sample animation, this time of a rotating letter `A'.
#include <stdio.h>
#include <plot.h>
int main()
{
int handle, angle = 0;
/* set Plotter parameters */
parampl ("BITMAPSIZE", "300x300");
parampl ("BG_COLOR", "blue"); /* background color for window */
parampl ("USE_DOUBLE_BUFFERING", "yes");
/* create an X Plotter with the specified parameters */
handle = newpl ("X", stdin, stdout, stderr);
selectpl (handle);
/* open X Plotter, initialize coordinates, pen, and font */
openpl ();
fspace (0.0, 0.0, 1.0, 1.0); /* use normalized coordinates */
pencolorname ("white");
ffontsize (1.0);
fontname ("NewCenturySchlbk-Roman");
fmove (.50,.50); /* move to center */
while (1) /* loop endlessly */
{
erase ();
textangle (angle++); /* set new rotation angle */
alabel ('c', 'c', "A"); /* draw a centered `A' */
}
closepl(); /* close Plotter */
selectpl (0); /* select default Plotter */
deletepl (handle); /* delete Plotter we used */
return 0;
}
This animation serves as a good test of the capabilities of an X Window System display. On a modern X11R6 display, animation will be smooth and fast. That is because X11R6 displays can rasterize individual characters from a font without rasterizing the entire font. If your X display does not support the "NewCenturySchlbk-Roman" font, you may substitute any other scalable font, such as the widely available "utopia-medium-r-normal". For the format of font names, see section Available text fonts for the X Window System. If the X Plotter is unable to retrieve the font you specify, it will first attempt to use a default scalable font ("Helvetica"). If that too fails, it will use a default Hershey vector font ("HersheySerif") instead.
Animations that use Hershey fonts are normally faster than ones that use Postscript fonts or other X Window System fonts, since the Hershey fonts are constructed from line segments. Rasterizing line segments can be done rapidly. But if you use a scalable font such as "NewCenturySchlbk-Roman" or "utopia-medium-r-normal", you will notice that the rotation speeds up after the letter `A' has rotated through 360 degrees. That is because the `A' at angles past 360 degrees has already been rasterized.
Applications that run under the X Window System are normally built using Xt, the X Toolkit. In Xt, an application is constructed from `widgets' such as text entry fields, buttons, sliders, drawing areas, etc. When the application starts up, each widget is configured to respond appropriately to `events', which include key presses and mouse clicks. After the widgets are configured, control is transferred to the Xt event loop.
GNU libplot can be used within the Xt event loop to draw vector
graphics. For this, it would use one or more X Drawable Plotters.
An X Drawable Plotter is a Plotter that can plot into an off-screen
pixmap or an on-screen window, such as a window associated with a
widget.
The following sample application shows how an X Drawable Plotter would be used. The application draws a `C' curve, as defined in a previous section, in a popped-up window. The usual Xt command-line options may be used: the window background color is specified with the "-bg" option, the window geometry with "-geometry", etc. The curve is initially drawn in red, but clicking once with the mouse will redraw it in green. A second mouse click will redraw it in red, and so forth. The application will terminate when `q' is typed.
#include <stdio.h>
#include <plot.h>
#include <X11/Xlib.h>
#include <X11/Intrinsic.h>
#include <X11/Shell.h>
#include <X11/StringDefs.h>
#include <X11/Core.h>
int green = 0; /* draw in green, not red? */
#define MAXORDER 12
void draw_c_curve (double dx, double dy, int order)
{
if (order >= MAXORDER)
fcontrel (dx, dy); /* continue path along (dx, dy) */
else
{
draw_c_curve (0.5 * (dx - dy), 0.5 * (dx + dy), order + 1);
draw_c_curve (0.5 * (dx + dy), 0.5 * (dy - dx), order + 1);
}
}
void Redraw (Widget w, XEvent *ev, String *params, Cardinal *n_params)
{
/* draw C curve */
erase ();
pencolorname (green ? "green" : "red");
fmove (600.0, 300.0);
draw_c_curve (0.0, 400.0, 0);
endpath ();
}
void Toggle (Widget w, XEvent *ev, String *params, Cardinal *n_params)
{
green = (green ? 0 : 1);
Redraw (w, ev, params, n_params);
}
void Quit (Widget w, XEvent *ev, String *params, Cardinal *n_params)
{
exit (0);
}
/* mapping of events to actions */
static const String translations =
"<Expose>: redraw()\n\
<Btn1Down>: toggle()\n\
<Key>q: quit()";
/* mapping of actions to subroutines */
static XtActionsRec actions[] =
{
{"redraw", Redraw},
{"toggle", Toggle},
{"quit", Quit},
};
/* default parameters for widgets */
static String default_resources[] =
{
"Example*geometry: 250x250",
(String)NULL
};
int main (int argc, char *argv[])
{
Arg wargs[10]; /* storage of widget args */
Display *display; /* X display */
Widget shell, canvas; /* toplevel widget; child */
Window window; /* child widget's window */
XtAppContext app_con; /* application context */
int handle, i;
char *bg_colorname = "white";
/* take background color from command line */
for (i = 0; i < argc - 1; i++)
if (strcmp (argv[i], "-bg") == 0)
bg_colorname = argv[i + 1];
/* create toplevel shell widget */
shell = XtAppInitialize (&app_con,
(String)"Example", /* app class */
NULL, /* options */
(Cardinal)0, /* num of options */
&argc, /* command line */
argv, /* command line */
default_resources,
NULL, /* ArgList */
(Cardinal)0 /* num of Args */
);
/* set default widget parameters (including window size) */
XtAppSetFallbackResources (app_con, default_resources);
/* map actions to subroutines */
XtAppAddActions (app_con, actions, XtNumber (actions));
/* create canvas widget as child of shell widget; realize both */
XtSetArg(wargs[0], XtNargc, argc);
XtSetArg(wargs[1], XtNargv, argv);
canvas = XtCreateManagedWidget ((String)"", coreWidgetClass,
shell, wargs, (Cardinal)2);
XtRealizeWidget (shell);
/* for the canvas widget, map events to actions */
XtSetArg (wargs[0], XtNtranslations,
XtParseTranslationTable (translations));
XtSetValues (canvas, wargs, (Cardinal)1);
/* initialize GNU libplot */
display = XtDisplay (canvas);
parampl ("XDRAWABLE_DISPLAY", display);
window = XtWindow (canvas);
parampl ("XDRAWABLE_DRAWABLE1", &window);
parampl ("BG_COLOR", bg_colorname);
handle = newpl ("Xdrawable", NULL, NULL, stderr);
selectpl (handle);
openpl ();
fspace (0.0, 0.0, 1000.0, 1000.0);
flinewidth (0.25);
/* transfer control to X Toolkit event loop (doesn't return) */
XtAppMainLoop (app_con);
return 1;
}
Even if you are not familiar with X Window System programming, the
structure of this application should be clear. It defines three
callbacks: Redraw, Toggle, and Quit. They are
invoked respectively in response to (1) a window expose event or
mouse click, (2) a mouse click, and (3) a typed `q'. The
first drawing of the `C' curve (in red) takes place because the
window receives an initial expose event.
This example could be extended to take window resizing into account. Actually, X Drawable Plotters are usually used to draw vector graphics in off-screen pixmaps rather than on-screen windows. Pixmaps, unlike windows, are never resized.
libplot: A detailed listing
In the current release of GNU libplot, any Plotter supports 81
distinct operations. A language binding for libplot
necessarily includes 81 functions that correspond to these operations.
A language binding may also include functions for creating,
selecting, and deleting Plotters. For example, the C binding
includes the four additional functions newpl, selectpl,
deletepl, and parampl. See section The C application programming interface.
The 81 functions that operate on a specified Plotter are divided into the four sets tabulated below.
Many functions come in two versions: integer and double precision
floating point. Internally, libplot uses double precision
floating point. The integer versions are provided for backward
compatibility. If there are two versions of a function, the name of the
floating point version begins with the letter `f'.
Many functions come in both absolute and relative versions, also. The latter use relative coordinates (i.e., coordinates relative to the current position of the graphics cursor), and in the C binding their names end in `rel'.
Currently, only a few of the 81 functions have meaningful return values.
The following are the "setup functions" in the C binding for
libplot. They are the basic functions that open, initialize, or
close an already-created Plotter. They are listed in the approximate
order in which they would be called.
openpl. Future releases may support window re-use.
openpl...closepl pair remain on the graphics display
even after a new page is begun by a subsequent invocation of
openpl. Currently, only X Drawable Plotters and Tektronix
Plotters are persistent. Future releases may support optional
persistence for X Plotters also.
On X Plotters and X Drawable Plotters the effects of invoking erase
will be altogether different if the device driver parameter
USE_DOUBLE_BUFFERING is set to "yes". In this case, objects
will be written to an off-screen buffer rather than to the graphics
display, and invoking erase will (1) copy the contents of this
buffer to the display, and (2) erase the buffer by filling it with
the background color. This feature facilitates smooth animation.
See section Device driver parameters.
plot.
libplot output pages of
graphics individually.
The following are the "drawing functions" in the C binding for
libplot. When invoked on a Plotter, these functions cause it to
draw objects (paths, circles, ellipses, points, markers, and text
strings) on the associated graphics display. A path is a
sequence of line segments and arcs (either circular or elliptic). Paths
may be drawn incrementally, one line segment or arc at a time.
textangle has
been called.
arc and farc, but use
cursor-relative coordinates.
pc=(xc,yc), p0=(x0,y0), and
p1=(x1,y1) that define a so-called quarter ellipse.
This is an elliptic arc from p0 to p1 with center
pc. If the graphics cursor is at point p0 and a path is
under construction, the quarter-ellipse is added to it. Otherwise the
path under construction (if any) is ended, and the quarter-ellipse
begins a new path. In all cases the graphics cursor is moved to
p1.
The quarter-ellipse is an affinely transformed version of a quarter
circle. It is drawn so as to have control points p0,
p1, and p0+p1-pc. This means that it
is tangent at p0 to the line segment joining p0 to
p0+p1-pc, and is tangent at p1 to the
line segment joining p1 to p0+p1-pc.
So it fits snugly into a triangle with these three control points as
vertices. Notice that the third control point is the reflection of
pc through the line joining p0 and p1.
ellarcrel and fellarcrel are similar to ellarc and
fellarc, but use cursor-relative coordinates.
The following are the "attribute functions" in the C binding for
libplot. When invoked on a Plotter, these functions set its
drawing attributes, or save them or restore them. Path-related
attributes include pen color, fill color, line width, line style, cap
style, and join style. Text-related attributes include pen color, font
name, font size, and text angle.
Setting any path-related drawing attribute automatically terminates the
path under construction (if any), as if the endpath
operation had been invoked.
HPGL_VERSION is set to a value less than "2"
(the default). See section Device driver parameters.
HPGL_VERSION is
equal to "1.5" or "2" (the default). (If the version is "1"
then only circles and rectangles aligned with the coordinate axes may be
filled.) Opaque filling, including white filling, is supported
only if the parameter HPGL_VERSION is "2" and the parameter
HPGL_OPAQUE_MODE is "yes" (the default). See section Device driver parameters.
HPGL_VERSION is set to a value less than "2"
(the default). See section Device driver parameters.
"solid" -------------------------------- "dotted" - - - - - - - - - - - - - - - - "dotdashed" ----------- - ----------- - "shortdashed" -------- -------- "longdashed" ------------ ------------For sufficiently wide lines, the distance over which a pattern repeats is scaled proportionately to the line width. A path that is drawn when the linemode is "disconnected" will be rendered as a set of filled circles, each of which has diameter equal to the nominal line width. One of these circles will be centered on each of the juncture points of the path (i.e., the endpoints of the line segments or arcs from which it is constructed). Circles and ellipses that are drawn when the linemode is "disconnected" will be invisible. Disconnected paths, circles, and ellipses are not filled.
HPGL_VERSION is set to a value less than "2" (the default;
see section Device driver parameters).
HPGL_VERSION is "2" (the default), and the value of
the parameter HPGL_OPAQUE_MODE is "yes" (the default).
See section Device driver parameters.
HPGL_VERSION is "2" (the default) and the value of
the parameter HPGL_OPAQUE_MODE is "yes" (the default).
See section Device driver parameters.
libplot's drawing attributes, which are set by the attribute
functions documented in this section. So popping off the graphics
context restores the drawing attributes to values they previously had.
A path under construction is regarded as part of the graphics
context. For this reason, calling restorestate automatically calls
endpath to terminate the path under construction, if any. All
graphics contexts on the stack are popped off when closepl is
called, as if restorestate had been called repeatedly.
libplot's drawing attributes, which are set by the attribute
functions documented in this section. A path under construction,
if any, is regarded as part of the graphics context. That is
because paths may be drawn incrementally, one line segment or arc at a
time. When a graphics context is returned to, the path under
construction may be continued.
The following are the "mapping functions" in the C binding for
libplot. When invoked on a Plotter, these functions affect the
affine transformation it employs for mapping from the user coordinate
system to the device coordinate system. They may be viewed as
performing transformations of the user coordinate system. Their names
resemble those of the corresponding functions in the Postscript
language. For information on how to use them to draw graphics
efficiently, consult any good book on Postscript programming, or the
Postscript Language Reference Manual.
In designing the libplot library, every effort was made to make
the Plotter interface independent of the type of Plotter. To the
extent that device dependence exists, it is captured by a manageable
number of device driver parameters.
In the C binding, a value for any parameter may be specified by
calling the parampl function. The parampl function does
not operate on any particular Plotter: it belongs to the C
binding as a whole. The parameter values used by any Plotter are
constant over the lifetime of the Plotter, and are those that were in
effect when the Plotter was created. Each driver parameter has a value
that is allowed to be a generic pointer (a void *). For most
parameters, this value should be a string (a char *).
parampl may be called any number of times. A parameter may
be unset by calling parampl with a value argument of NULL.
If at Plotter creation time a parameter is not set, its default value will be used, unless there is an environment variable of the same name, in which case the value of that environment variable will be used. This rule increases run-time flexibility: an application programmer may allow non-critical driver parameters to be specified by the user via environment variables.
The following are the currently recognized parameters (unrecognized ones
are ignored). The most important ones are DISPLAY and
BITMAPSIZE, which affect X Plotters, and PAGESIZE,
which affects Postscript, Fig, and HP-GL Plotters. These three
parameters are listed first and the others alphabetically. Many of the
parameters, such as the several whose names begin with "HPGL", affect
only a single type of Plotter.
DISPLAY
BITMAPSIZE
Xplot.geometry. This is for backward compatibility.
PAGESIZE
xfig display, with width equal to the
width of the specified page. For PCL Plotters, fine control over the
positioning of the graphics display on the page may be accomplished by
setting the PCL_XOFFSET and PCL_YOFFSET parameters. For
HP-GL Plotters, HPGL_XOFFSET and HPGL_YOFFSET are used
similarly.
BG_COLOR
erase is invoked. The
background color may be changed at any later time by invoking the
bgcolor (or bgcolorname) and erase operations. An
unrecognized color name sets the background color to the default. For
information on what names are recognized, see section Specifying Colors by Name.
HPGL_ASSIGN_COLORS
HPGL_VERSION is "2". "no" means to draw with a fixed
set of pens, specified by setting the HPGL_PENS parameter. "yes"
means that pen colors will not restricted to the palette specified in
HPGL_PENS: colors will be assigned to "logical pens" in the
range #1...#31, as needed. Other than color LaserJet printers
and DesignJet plotters, not many HP-GL/2 devices allow the assignment of
colors to logical pens. So this parameter should be used with
caution.
HPGL_OPAQUE_MODE
HPGL_VERSION is "2". "yes" means that the HP-GL/2 output
device should be switched into opaque mode, rather than transparent
mode. This allows objects to be filled with opaque white and other
opaque colors. It also allows the drawing of visible white lines,
which by convention are drawn with pen #0. Not all HP-GL/2 devices
support opaque mode or the use of pen #0 to draw visible white
lines. In particular, HP-GL/2 pen plotters do not. Some older
HP-GL/2 devices reportedly malfunction if asked to switch into opaque
mode. If the output of an HP-GL Plotter is to be sent to such a
device, a "no" value is recommended.
HPGL_PENS
HPGL_VERSION is "1.5" or "2" and "1=black" if the
value of HPGL_VERSION is "1". Relevant only to HP-GL
Plotters. The set of available pens; the format should be
self-explanatory. The color for any pen in the range #1...#31 may
be specified. For information on what color names are recognized, see
section Specifying Colors by Name. Pen #1 must always be present, though it need
not be black. Any other pen in the range #1...#31 may be omitted.
HPGL_ROTATE
HPGL_VERSION is "2".
HPGL_VERSION
HPGL_XOFFSET, HPGL_YOFFSET
MAX_LINE_LENGTH
META_PORTABLE
PCL_ASSIGN_COLORS
PCL_ROTATE
PCL_XOFFSET, PCL_YOFFSET
TERM
xterm, xterms, or kterm, it is taken as a sign
that the current application is running in an X Window System VT100
terminal emulator: an xterm. Before drawing graphics, a
Tektronix Plotter will emit an escape sequence that causes the terminal
emulator's auxiliary Tektronix window, which is normally hidden, to
pop up. After the graphics are drawn, an escape sequence that
returns control to the original VT100 window will be emitted. The
Tektronix window will remain on the screen.
If the value of is kermit, ansi.sys, ansissys,
ansi.sysk, or ansisysk, it is taken as a sign that the
current application is running in the VT100 terminal emulator provided
by the MS-DOS version of kermit. Before drawing graphics, a
Tektronix Plotter will emit an escape sequence that switches the
terminal emulator to Tektronix mode. Also, some of the Tektronix
control codes emitted by the Plotter will be kermit-specific.
There will be a limited amount of color support, which is not normally
the case (the 16 ansi.sys colors will be supported). After
drawing graphics, the Plotter will emit an escape sequence that returns
the emulator to VT100 mode. The key sequence `ALT minus' may be
employed manually within kermit to switch between the two modes.
USE_DOUBLE_BUFFERING
VANISH_ON_DELETE
XDRAWABLE_COLORMAP
Colormap *, a pointer to a
colormap from which colors should be allocated. NULL indicates that the
colormap to be used should be the default colormap of the default screen
of the X display.
XDRAWABLE_DISPLAY
Display *, a pointer to the X display with which the
drawable(s) to be drawn in are associated.
XDRAWABLE_DRAWABLE1
XDRAWABLE_DRAWABLE2
Drawable *, a
pointer to a drawable to be drawn in. A `drawable' is either a
window or a pixmap. At the time an X Drawable Plotter is created,
at least one of the two parameters must be set.
X Drawable Plotters support simultaneous drawing in two drawables
because it is often useful to be able to draw graphics simultaneously in
both an X window and its background pixmap. If two drawables are
specified, they must have the same dimensions and depth, and be
associated with the same screen of the X display.
@ifnottex The following appendices contain miscellaneous information on the GNU plotting utilities.
The libplot vector graphics library and applications built on
it, such as graph and plot, can draw text strings in a
wide variety of fonts. Text strings may include characters from more
than one font in a typeface, and may include superscripts, subscripts,
and square roots. A wide variety of plotting symbols can also be
drawn. The following sections explain how to use these features.
The libplot library and applications built on it, such as
graph and plot, can use many fonts. These include 22
Hershey vector fonts, 35 Postscript fonts, 45 PCL 5 fonts, and 18
Hewlett--Packard vector fonts. We call these 120 fonts the
`built-in' fonts. The Hershey fonts are constructed from stroked
characters digitized c. 1967 by Dr. Allen V. Hershey at the
U.S. Naval Surface Weapons Center in Dahlgren, VA. The 35
Postscript fonts are the outline fonts resident in all modern Postscript
printers and plotter, and the 45 PCL 5 fonts are the outline fonts
resident in most modern Hewlett--Packard LaserJet printers. (The old
LaserJet III, which was Hewlett--Packard's first PCL 5 printer,
supported only 8 of the 45; most Hewlett-Packard plotters do not
support PCL 5 at all.) The 18 Hewlett--Packard vector fonts are
fonts that are resident in Hewlett--Packard printers and plotters
(mostly the latter).
The Hershey fonts can be used by all types of Plotter object supported
by libplot, and the Postscript fonts can be used by all types of
Plotter object except PCL, HP-GL and Tektronix. So all variants of
graph can use the Hershey fonts, and all variants of graph
except graph -T pcl, graph -T hpgl and graph -T tek
can use the Postscript fonts. The PCL 5 and Hewlett--Packard vector
fonts can be used by PCL and HP-GL Plotters, and by graph -T pcl
and graph -T hpgl. X Plotters and graph -T X are
not restricted to the built-in fonts. They can use any X Window
System font.
The plotfont utility, which accepts the `-T' option, will
print a character map of any font that is available in the specified
output format. See section The plotfont Utility.
For the purpose of plotting text strings (see section Text string format and escape sequences), the 120 built-in fonts are divided into typefaces. As you can see from the following tables, our convention is that in any typeface with more than a single font, font #1 is the normal font, font #2 is italic or oblique, font #3 is bold, and font #4 is bold italic or bold oblique. Additional variants (if any) are numbered #5 and higher.
The 22 Hershey fonts are divided into typefaces as follows.
Nearly all Hershey fonts except the Symbol fonts use the ISO-Latin-1 encoding, which is a superset of ASCII. The Symbol fonts consist of Greek characters and mathematical symbols, and use the symbol font encoding documented in the Postscript Language Reference Manual. By convention, each Hershey typeface contains a symbol font (HersheySerifSymbol or HersheySansSymbol, as appropriate) as font #0.
HersheyCyrillic, HersheyCyrillic-Oblique, and HersheyEUC (which is a Japanese font) are the only non-Symbol Hershey fonts that do not use the ISO-Latin-1 encoding. For their encodings, see section Cyrillic and Japanese fonts.
The 35 Postscript fonts are divided into typefaces as follows.
All Postscript fonts except the ZapfDingbats and Symbol fonts use the ISO-Latin-1 encoding. The encodings used by the ZapfDingbats and Symbol fonts are documented in the Postscript Language Reference Manual. By convention, each Postscript typeface contains the Symbol font as font #0.
The 45 PCL 5 fonts are divided into typefaces as follows.
All PCL 5 fonts except the Wingdings and Symbol fonts use the ISO-Latin-1 encoding. The encoding used by the Symbol font is the symbol font encoding documented in the Postscript Language Reference Manual. By convention, each PCL typeface contains the Symbol font as font #0.
The 18 Hewlett--Packard vector fonts are divided into typefaces as follows.
The Hewlett--Packard vector fonts with an asterisk (the ANK and Symbol
fonts) are not available when producing output in PCL 5 or HP-GL/2
format. They are only available when producing HP-GL output for the
HP7550A graphics plotter and the HP758x, HP7595A and HP7596A drafting
plotters, which used HP-GL with some HP-GL/2 extensions. To ensure
that these fonts are available, you must set the environment variable or
driver parameter HPGL_VERSION to "1.5". The ANK fonts are
Japanese fonts (see section Cyrillic and Japanese fonts), and the Symbol fonts
contain a few miscellaneous mathematical symbols.
All Hewlett--Packard vector fonts except the ANK and Symbol fonts use
the ISO-Latin-1 encoding. The Arc fonts are proportional
(variable-width) fonts, and the Stick fonts are fixed-width fonts. If
HPGL_VERSION is "1.5" then the Arc fonts will be kerned. But if
HPGL_VERSION is "2" (the default), there will be no kerning.
Apparently Hewlett--Packard dropped support for device-resident kerning
tables when moving from HP-GL to modern HP-GL/2 and PCL 5. For
information about Hewlett--Packard vector fonts and the way in which
they are kerned (in pen plotters, at least), see the article by
L. W. Hennessee et al. in the Nov. 1981 issue of the
Hewlett--Packard Journal.
To what extent do the fonts supported by libplot contain
ligatures? The Postscript fonts, the PCL 5 fonts, and the
Hewlett--Packard vector fonts, at least as implemented in
libplot, do not contain ligatures. However, six of the 22
Hershey fonts contain ligatures. The character combinations "fi", "ff",
"fl", "ffi", and "ffl" are automatically drawn as ligatures in
HersheySerif and HersheySerif-Italic. (Also in the two HersheyCyrillic
fonts and HersheyEUC, since insofar as printable ASCII characters are
concerned, they are identical [or almost identical] to HersheySerif.)
In addition, "tz" and "ch" are ligatures in HersheyGothicGerman.
The German double-s character `@ss{'}, which is called an `eszet',
is not treated as a ligature in any font. To obtain an eszet, you
must either request one with the escape sequence "\ss" (see section Text string format and escape sequences), or, if you have an 8-bit keyboard, type an eszet
explicitly.
The built-in fonts discussed in the previous section include Cyrillic
and Japanese vector fonts. This section explains how these fonts are
encoded, i.e., how their character maps are laid out. You may use
the plotfont utility to display the character map for any font,
including the Cyrillic and Japanese vector fonts. See section The plotfont Utility.
The HersheyCyrillic and HersheyCyrillic-Oblique fonts use an encoding called KOI8-R, a superset of ASCII that has become the de facto standard for Unix and networking applications in the former Soviet Union. Insofar as printable ASCII characters go, they resemble the HersheySerif vector font. But their upper halves are different. The byte range 0xc0...0xdf contains lower-case Cyrillic characters and the byte range 0xe0...0xff contains upper case Cyrillic characters. Additional Cyrillic characters are located at 0xa3 and 0xb3. For more on the encoding scheme, see the official KOI8-R Web page and the document known as Internet RFC 1489.
The HersheyEUC font is a vector font that is is used for displaying Japanese text. EUC stands for `extended Unix code', which is a scheme for encoding Japanese, and also other character sets (e.g., Greek and Cyrillic) as multibyte character strings. The format of EUC strings is explained in Ken Lunde's Understanding Japanese Information Processing (O'Reilly, 1993), which contains much additional information on Japanese text processing. See also his on-line supplement.
In the HersheyEUC font, characters in the printable ASCII range,
0x20...0x7e, are similar to HersheySerif (their encoding is
`JIS Roman', an ASCII variant standardized by the Japanese Industrial
Standards Committee). Each successive pair of bytes in the
0xa1...0xfe range defines a single character in the
JIS X0208 standard. The characters in the JIS X0208 standard include
Japanese syllabic characters (Hiragana and Katakana), ideographic
characters (Kanji), Roman, Greek, and Cyrillic alphabets, punctuation
marks, and miscellaneous symbols. For example, the JIS X0208 standard
indexes the 83 Hiragana as 0x2421...0x2473. To
obtain the EUC code for any JIS X0208 character, you would add
0x80 to each byte (i.e., `set the high bit' on each byte). So
the first of the 83 Hiragana (0x2421) would be encoded as the
successive pair of bytes 0xa4 and 0xa1.
The implementation of the JIS X0208 standard in the HersheyEUC font is based on Dr. Hershey's digitizations, and is complete enough to be useful. All 83 Hiragana and 86 Katakana are available, though the little-used `half-width Katakana' are not supported. Also, 603 frequently used Kanji are available. The Hiragana, the Katakana, and the available Kanji all have the same width. The file `kanji.doc', which on most systems is installed in `/usr/share/libplot' or `/usr/local/share/libplot', lists the 603 available Kanji. Each JIS X0208 character that is unavailable will be drawn as an `undefined character' glyph (several horizontal lines).
The eight Hewlett--Packard vector fonts in the ArcANK and StickANK
typefaces are also used for displaying Japanese text. They are
available when producing HP-GL output for the HP7550A graphics plotter
and the HP758x, HP7595A and HP7596A drafting plotters. To ensure
that they are available, you must set the environment variable or driver
parameter HPGL_VERSION to "1.5".
ANK stands for Alphabet, Numerals, and Katakana. The ANK fonts use the `Kana-8' encoding. The lower half of each font uses the JIS Roman encoding, and the upper half contains half-width Katakana. Half-width Katakana are simplified Katakana that may need to be equipped with diacritical marks. The diacritical marks are included in the encoding as separate characters.
The plotting utilities graph -T X and plot -T X,
and the libplot library that they are built on, can draw text
on an X Window System display in a wide variety of fonts. This
includes the 22 built-in Hershey vector fonts. They can use the 35
built-in Postscript fonts too, if those fonts are available on the X
display. Most releases of the plotting utilities include freely
distributable versions of the 35 Postscript fonts, in Type 1 format,
which are easily installed on any X display.
In fact, the plotting utilities can use most fonts that are available on the current X display. This includes all scalable fonts that have a so-called XLFD (X Logical Font Description) name. For example, the "CharterBT-Roman" font is available on many X displays. It has a formal XLFD name, namely "-bitstream-charter-medium-r-normal--0-0-0-0-p-0-iso8859-1". The plotting utilities would refer to it as "charter-medium-r-normal". The command
echo 0 0 1 1 2 0 | graph -T X -F charter-medium-r-normal
would draw a plot in a popped-up X window, in which all axis ticks are labeled in this font.
You may determine which fonts are available on an X display by using
the xlsfonts command. Fonts whose names end in
"-0-0-0-0-p-0-iso8859-1" or "-0-0-0-0-m-0-iso8859-1" are scalable
ISO-Latin-1 fonts that can be used by libplot's X Plotters
and by graph -T X and plot -T X. The two sorts of
font are variable-width and fixed-width fonts, respectively. Fonts
whose names end in "iso8859-2", etc., and "adobe-fontspecific", may also
be used, even though they do not employ the standard ISO-Latin-1
encoding.
The escape sequences that provide access to the non-ASCII `8-bit' characters in the built-in ISO-Latin-1 fonts may be employed when using any ISO-Latin-1 X Window System font. For more on escape sequences, see section Text string format and escape sequences. As an example, "\Po" will yield the British pounds sterling symbol `@pounds{'}. The command
echo 0 0 1 1 | graph -T X -F charter-medium-r-normal -L "A \Po1 Plot"
shows how this symbol could be used in a graph label. In the same way, the escape sequences that provide access to mathematical symbols and Greek characters may be employed when using any X Window System font, whether or not it is an ISO-Latin-1 font.
The plotting utilities, including graph, support a
--bitmap-size option. It is meaningful only if the
`-T X' option is used, since it sets the size of the popped-up
X Window. You may use it to obtain some interesting visual effects.
graph assumes that it is drawing in a square region, so if you
use the `--bitmap-size 800x400' option, your plot will be scaled
anisotropically, by a larger factor in the horizontal direction than in
the vertical direction. The fonts in the plot will be scaled in the
same way. Actually, this requires a modern (X11R6) display. If
your X display cannot scale a font, a default scalable font
(such as "HersheySerif") will be substituted.
Text strings that are drawn by libplot, and by such applications
as graph and plot that are built on libplot, must
consist of printable characters. No embedded control characters, such
as newlines or carriage returns, are allowed. Technically, a character
is `printable' if it comes from either of the two byte ranges
0x20...0x7e and 0xa0...0xff. The former is the
printable ASCII range and the latter is the printable `8-bit' range.
Text strings may, however, include embedded `escape sequences' that
shift the font, append subscripts or superscripts, or include non-ASCII
characters and mathematical symbols. As a consequence, the axis labels
on a plot prepared with graph may include such features.
The format of the escape sequences should look familiar to anyone who is
familiar with the TeX or groff document formatters. Each
escape sequence consists of three characters: a backslash and two
additional characters. The most frequently used escape sequences are as
follows.
For example, the string "x\sp2\ep" would be interpreted as `x squared'. Subscripts on subscripts, etc., are allowed. Subscripts and superscripts may be vertically aligned by judicious use of the "\mk" and "\rt" escape sequences. For example, "a\mk\sbi\eb\rt\sp2\ep" produces "a sub i squared", with the exponent `2' placed immediately above the subscript.
There are also escape sequences that switch from font to font within a typeface. For an enumeration of the fonts within each typeface, see section Available text fonts. Suppose for example that the current font is Times-Roman, which is font #1 in the `Times' typeface. The string "A \f2very\f1 well labeled axis" would be a string in which the word `very' appears in Times-Italic rather than Times-Roman. That is because Times-Italic is the #2 font in the typeface. Font-switching escape sequences are of the form "\fn", where n is the number of the font to be switched to, in the current font. There is currently no support for switching between fonts in different typefaces.
There are also a few escape sequences for horizontal shifts, which are useful for improving horizontal alignment, such as when shifting between fonts. "\r1", "\r2", "\r4", "\r6", "\r8", and "\r^" are escape sequences that shift right by 1 em, 1/2 em, 1/4 em, 1/6 em, 1/8 em, and 1/12 em, respectively. "\l1", "\l2", "\l4", "\l6", "\l8", and "\l^" are similar, but shift left instead of right. "A \f2very\r8\f1 well labeled axis" would look better than "A \f2very\f1 well labeled axis".
Square roots are handled with the aid of a special pair of escape sequences, together with the "\mk" and "\rt" sequences discussed above. A square root symbol is begun with "\sr", and continued arbitrarily far to the right with the overbar (`run') escape sequence, "\rn". For example, the string "\sr\mk\rn\rn\rtab" would be plotted as `the square root of ab'. To adjust the length of the overbar, you may need to experiment with the number of times "\rn" appears.
To underline a string, you would use "\ul", the underline escape sequence, one or more times. The "\mk"..."\rt" trick would be employed in the same way. So, for example, "\mk\ul\ul\ul\rtabc" would yield an underlined "abc". To adjust the length of the underline, you may need to experiment with the number of times "\ul" appears. You may also need to use one or more of the abovementioned horizontal shifts. For example, if the "HersheySerif" font were used, "\mk\ul\ul\l8\ul\rtabc" would yield a better underline than "\mk\ul\ul\ul\rtabc".
Besides the preceding escape sequences, there are also escape sequences for the printable non-ASCII characters in each of the built-in ISO-Latin-1 fonts (which means in every built-in font, except for the symbol fonts, ZapfDingbats, and the Cyrillic and Japanese fonts). The useful non-ASCII characters include accented characters, among others. Such `8-bit' characters, in the 0xa0...0xff byte range, may be included directly in a text string. But if your terminal does not permit this, you may use the escape sequences for them instead.
There are escape sequences for the mathematical symbols and Greek characters in the symbol fonts, as well. This is how the symbol fonts are usually accessed. Which symbol font the mathematical symbols and Greek characters are taken from depends on whether your current font is a Hershey font or a non-Hershey font. They are taken from the HersheySerifSymbol font or the HersheySansSymbol font in the former case, and from the Symbol font in the latter.
The following are the escape sequences that provide access to the non-ASCII characters of the current font, provided that it is an ISO-Latin-1 font. Each escape sequence is followed by the position of the corresponding character in the ISO-Latin-1 encoding (in decimal), and the official Postscript name of the character. Most names should be self-explanatory. For example, `eacute' is a lower-case `e', equipped with an acute accent.
The following are the escape sequences that provide access to mathematical symbols and Greek characters in the current symbol font, whether HersheySerifSymbol or HersheySansSymbol (for Hershey fonts) or Symbol (for Postscript fonts). Each escape sequence is followed by the position (in octal) of the corresponding character in the symbol encoding, and the official Postscript name of the character. Many escape sequences and names should be self-explanatory. "\*a" represents a lower-case Greek alpha, for example. For a table displaying each of the characters below, see the Postscript Language Reference Manual.
Finally, there are escape sequences that apply only if the current font is a Hershey font. Most of these escape sequences provide access to special symbols that belong to no font, and are accessible by no other means. These symbols are of two sorts: miscellaneous, and astronomical or zodiacal. The escape sequences for the miscellaneous symbols are as follows.
The final escape sequence in the table above, "\s-", yields a letter rather than a symbol. It is provided because in some Hershey fonts, the shape of the lower-case letter `s' differs if it is the last letter in a word. This is the case for HersheyGothicGerman. The German word "besonders", for example, should be written as "besonder\s-" if it is to be rendered correctly in this font. The same is true for the two Hershey symbol fonts, with their Greek alphabets (in Greek text, lower-case final `s' is different from lower-case non-final `s'). In Hershey fonts where there is no distinction between final and non-final `s', "s" and "\s-" are equivalent.
The escape sequences for the astronomical symbols, including the signs for the twelve constellations of the zodiac, are listed in the following table. We stress that that like the preceding miscellaneous escape sequences, they apply only if the current font is a Hershey font.
The preceding miscellaneous and astronomical symbols are not the only
special non-font symbols that can be used if the current font is a
Hershey font. The entire library of glyphs digitized by Allen Hershey
is built into GNU libplot. So text strings may include any
Hershey glyph. Each of the available Hershey glyphs is identified by a
four-digit number. Standard Hershey glyph #1 would be specified as
"\#H0001". The standard Hershey glyphs range from "\#H0001" to
"\#H3999", with a number of gaps. Some additional glyphs designed by
others appear in the "\#H4000"..."\#H4194" range. Syllabic Japanese
characters (Kana) are located in the "\#H4195"..."\#H4399" range.
You may order a table of nearly all the Hershey glyphs in the "\#H0001"..."\#H3999" range from the U.S. National Technical Information Service, at +1 703 487 4650. Ask for item number PB251845; the current price is about US$40. By way of example, the string
"\#H0744\#H0745\#H0001\#H0002\#H0003\#H0869\#H0907\#H2330\#H2331"
when drawn will display a shamrock, a fleur-de-lys, cartographic (small) letters A, B, C, a bell, a large circle, a treble clef, and a bass clef. Again, this assumes that the current font is a Hershey font.
You may also use Japanese syllabic characters (Hiragana and Katakana) and ideographic characters (Kanji) when drawing strings in any Hershey font. In all, 603 Kanji are available; these are the same Kanji that are available in the HersheyEUC font. The Japanese characters are indexed according to the JIS X0208 standard for Japanese typography, which represents each character by a two-byte sequence. The file `kanji.doc', which is distributed along with the GNU plotting utilities, lists the available Kanji. On most systems it is installed in `/usr/share/libplot' or `/usr/local/share/libplot'.
Each JIS X0208 character would be specified by an escape sequence which
expresses this two-byte sequence as four hexadecimal digits, such as
"\#J357e". Both bytes must be in the 0x21...0x7e
range in order to define a JIS X0208 character. Kanji are located at
"\#J3021" and above. Characters appearing elsewhere in the JIS X0208
encoding may be accessed similarly. For example, Hiragana and Katakana
are located in the "\#J2421"..."\#J257e" range, and Roman characters
in the "\#J2321"..."\#J237e" range. The file `kana.doc', which
is installed in the same directory as `kanji.doc', lists the
encodings of the Hiragana and Katakana. For more on the JIS X0208
standard, see Ken Lunde's Understanding Japanese Information
Processing (O'Reilly, 1993), and
his on-line
supplement.
The Kanji numbering used in A. N. Nelson's Modern Reader's Japanese-English Character Dictionary, a longtime standard, is also supported. (This dictionary is published by C. E. Tuttle and Co., with ISBN 0-8048-0408-7. A revised edition [ISBN 0-8048-2036-8] appeared in 1997, but uses a different numbering.) `Nelson' escape sequences for Kanji are similar to JIS X0208 escape sequences, but use four decimal instead of four hexadecimal digits. The file `kanji.doc' gives the correspondence between the JIS numbering scheme and the Nelson numbering scheme. For example, "\#N0001" is equivalent to "\#J306c". It also gives the positions of the available Kanji in the Unicode encoding.
All available Kanji have the same width, which is the same as that of the syllabic Japanese characters (Hiragana and Katakana). Each Kanji that is not available will print as an `undefined character' glyph (a set of horizontal lines). The same is true for non-Kanji JIS X0208 characters that are not available.
The GNU libplot library supports a standard set of marker
symbols, numbered 0 through 31. These are the symbols that the
graph program will plot at each point of a dataset, if the
`-S' option is used. The list is as follows (by convention, marker
symbol #0 means no symbol at all).
The interpretation of marker symbols 1 through 5 is the same as in the well known GKS (Graphical Kernel System).
Symbols 32 and up are interpreted as characters in a certain text font.
For libplot, it is the current font. For graph, it is the
font selected with the `--symbol-font-name' option. By default,
this is the ZapfDingbats font except in graph -T pcl, graph
-T hpgl and graph -T tek. These three variants of graph
normally have no access to Postscript fonts, so they use the
HersheySerif font instead.
Many of the characters in the ZapfDingbats font are suitable for use as marker symbols. For example, character #74 is the Texas star. Doing
echo 0 0 1 2 2 1 3 2 4 0 | graph -T ps -m 0 -S 74 0.1 > plot.ps
will produce a Postscript plot consisting of five data points, not joined by line segments. Each data point will be marked by a Texas star, of a large font size (0.1 times the width of the plotting box).
If you are using graph -T pcl or graph -T hpgl and wish to
use font characters as marker symbols, you should consider using the
Wingdings font, which is available when producing PCL 5 or HP-GL/2
output. Doing
echo 0 0 1 2 2 1 3 2 4 0 |
graph -T pcl -m 0 --symbol-font Wingdings -S 181 0.1 > plot.pcl
will produce a PCL 5 plot that is similar to the preceding Postscript plot. The Wingdings font has the Texas star in location #181.
Many of the plotting utilities allow colors to be specified by name.
For example, graph supports the `--frame-color' option.
plot -T hpgl checks the value of the HPGL_PENS environment
variable, as do the HP-GL Plotter objects available in the
libplot library. Also, the libplot library includes the
pencolorname, fillcolorname, and bgcolorname
functions.
In any of these contexts, 665 distinct color names are recognized, including obscure ones like "dark magenta", "forest green", and "olive drab". Color names are case-insensitive, and spaces are ignored. So, for example, "RosyBrown" is equivalent to "rosy brown", and "DarkGoldenrod3" to "dark goldenrod 3".
The file `colors.txt', which is distributed along with the GNU plotting utilities, lists the available color names. On most systems it is installed in `/usr/share/libplot' or `/usr/local/share/libplot'. The color names are essentially those recognized by recent releases of the X Window System, which on most machines are listed in the file `/usr/lib/X11/rgb.txt'. However, for every color name containing the string "gray", a version containing "grey" has been included. For example, both "dark slate gray 4" and "dark slate grey 4" are recognized color names.
GNU metafile format is produced by the raw variants of graph,
plot, tek2plot, and plotfont, and by any other
graphics application that uses the Metafile Plotter support contained in
GNU libplot. A file in this format is a sort of audit trail:
a sequence of plotting commands, each of which may be followed by
data. Each plotting command is an `op code': a single ASCII
character, indicating a Plotter operation. The data following the
command are the arguments passed to the operation, if any.
There are two sorts of GNU metafile: binary (the default) and portable
(human-readable). Binary metafiles begin with the magic string
"#PLOT 1\n", and portable metafiles with the magic string "#PLOT 2\n".
If you wish to transfer metafiles between machines of different types,
you should use portable rather than binary format. Portable metafiles are
produced by GNU graph and the other plotting utilities if the
`-O' option is specified, and by Metafile Plotters if the
META_PORTABLE parameter is set to "yes". Both binary and
portable metafiles can be translated to other formats by GNU
plot.
In the portable format, the arguments of each operation (integers,
floating point numbers, or strings) are printed in a human-readable
form, separated by spaces, and each argument list ends with a newline.
In the binary format, the arguments are represented as integers, single
precision floating point numbers, or newline-terminated ASCII strings.
Using the newline character as a terminator is acceptable because each
libplot operation includes a maximum of one string among its
arguments, and such a string may not include a newline. Also, the
string must come last among the arguments.
The openpl and closepl operations open and close a
Plotter, i.e., begin and end a page of graphics. They are represented
by the op codes `o' and `x', respectively. Each of
the other 79 Plotter operations has a corresponding op code, with 10
exceptions. These exceptions include (1) the setup operations
flushpl and outfile, (2) the operations
havecap, labelwidth, and flabelwidth, which merely
return information, and (3) the colorname,
pencolorname, fillcolorname, and bgcolorname
operations, which are internally mapped to pencolor,
fillcolor, and bgcolor, and (4) the ffontname
operation, which in a metafile would be indistinguishable from
fontname. So besides `o' and `x', there are 69
possible op codes, for a total of 71. The following table lists
10 of the op codes other than `o' and `x', followed by
the name of the libplot operation they stand for.
arc
circle
erase
linemod
line
move
cont
point
space
label
The full set of 71 op codes is listed in the header file `plot.h', which is distributed along with the plotting utilities. On most systems it is installed in `/usr/include' or `/usr/local/include'.
It is worth noting that of the 71 op codes, only 46 are used in
portable metafiles. That is because in ASCII format, there is no point
in distinguishing the floating point libplot operations from
their integer counterparts.
The 10 op codes in the table above are actually the op codes of the
traditional `plot(5)' format produced by pre-GNU versions of
graph and libplot. The use of these op codes make GNU
metafile format compatible with plot(5) format. The absence of a magic
string, and of the `o' and `x' op codes, makes it
possible to distinguish files in plot(5) format from GNU metafiles. GNU
plot can convert files in plot(5) format to GNU metafiles in
either binary or portable format.
idraw
The idraw utility mentioned several times in this documentation
is a freely distributable interactive drawing editor for the X
Window System. It may be used to edit the output of graph -T
ps, or, in general, the output of any application that uses the
Postscript Plotter support contained in libplot.
The current version of idraw is maintained by Vectaport, Inc.,
and is available at their Web site.
It is part of the ivtools package, which is a framework for
building custom drawing editors. idraw was originally part of
the InterViews package, developed by Stanford University and
Silicon Graphics. The InterViews package is available at
a distribution site but is no
longer supported. Retrieving the ivtools package instead is
recommended.
Also available at Vectaport's Web site
is an enhanced version of idraw called drawtool. Unlike
idraw, drawtool can import bitmapped graphics in
PBM/PGM/PPM, TIFF, and X11 bitmap formats.
xfig
The xfig utility mentioned several times in this documentation is
a freely distributable interactive drawing editor for the X Window
System. It may be used to edit the output of graph -T fig,
or in general the output of any application that uses the
Fig Plotter support contained in libplot.
The current version is available at
ftp://ftp.x.org/contrib/applications/drawing_tools/. It can
import graphics in GIF, X11 bitmap, and Postscript formats.
Accompanying the editor is a package called transfig, which
allows xfig graphics to be exported in many formats. GIF, X11
bitmap, LaTeX, and Postscript formats are supported.
There is a Web page on Fig
format, which discusses application software packages that can
interoperate with xfig.
Several of the GNU plotting utilities were inspired by Unix plotting
utilities. A graph utility and various plot filters were present
in the first releases of Unix from Bell Laboratories, going at least
as far back as the Version 4 distribution (1973). Most of the work
on tying them together and breaking out device-dependent versions of
libplot was performed by Lorinda
Cherry. By the time of Version 7 Unix (1979) and the subsequent
Berkeley releases, the package consisting of graph, plot,
spline, and several device-dependent versions of libplot
was a standard Unix feature. The first display device supported by the
package was a Versatec storage scope. By the early 1980's, supported
devices included Tektronix storage scopes, 200dpi electrostatic
printer/plotters from Versatec and Varian, pen plotters from
Hewlett--Packard, and early graphics terminals.
In 1989, Rich Murphey wrote the first GNU
versions of graph, plot, and spline, and the
earliest documentation. Richard Stallman further directed development
of the programs and provided editorial support for the documentation.
John Interrante, of the InterViews
team at Stanford, generously provided the idraw Postscript
prologue now included in libplot, and helpful comments. The
package as it stood in 1991 was distributed under the name `GNU graphics'.
In 1995 Robert Maier took over
development of the package, and designed and wrote the current,
maximally device-independent, standalone version of libplot.
He also rewrote graph from scratch, turning it into a real-time
filter that would use the new library. He fleshed out spline
too, by adding support for splines in tension, periodicity, and cubic
Bessel interpolation.
Most development work on ode was performed by
Nick Tufillaro in 1978--1994, on a sequence of
platforms that extended back to a PDP-11 running Version 4 Unix.
In 1997 Robert modified Nick's 1994 version to agree with GNU conventions
on coding and command-line parsing, extended it to support the full set
of special functions supported by gnuplot, and extended the
exception handling.
Many other people aided the development of the plotting utilities
package along the way. The Hershey vector fonts now in libplot
are of course based on the characters digitized in the mid to late
1960's by Allen V. Hershey, who deserves a vote of thanks.
Additional characters and/or marker symbols were taken from the SLAC
Unified Graphics System developed by Robert C. Beach in the
mid-1970's, and from the fonts designed by
Thomas Wolff for Ghostscript. The
interpolation algorithms used in spline are based on the
algorithms of Alan K. Cline, as
described in his papers in the Apr. 1974 issue of Communications
of the ACM. The table-driven parser used in tek2plot was
written at Berkeley in the mid-1980's by Edward Moy. The `sagitta' algorithm used in an extended form in
libplot for drawing circular and elliptic arcs was developed by
Peter Karnow of URW and Ken Turkowski of Apple.
Ray Toy helped with the tick mark spacing
code in graph and was the first to incorporate GNU getopt.
Arthur Smith, formerly of LASSP at Cornell, provided code for his
xplot utility. Nelson Beebe
exhaustively tested the package installation process.
Robert Maier wrote the documentation, which now incorporates Nick
Tufillaro's ode manual. Julie Sussmann checked over the
documentation for style and clarity.
This document was generated on 7 November 1998 using the texi2html translator version 1.52.