316 lines
12 KiB
HTML
316 lines
12 KiB
HTML
|
<html><head>
|
||
|
|
<meta http-equiv="content-type" content="text/html; charset=windows-1252">
|
||
|
|
<title>Drawing Graphs with gpic - Douglas B. West</title>
|
||
|
|
</head>
|
||
|
|
<body><h1>Drawing Graphs with gpic - Douglas B. West</h1>
|
||
|
|
|
||
|
|
Various people over the years have asked me how I draw the figures
|
||
|
|
for my books, such as
|
||
|
|
<a href="https://faculty.math.illinois.edu/~west/igt"><i>Introduction to Graph Theory</i></a>,
|
||
|
|
<a href="https://faculty.math.illinois.edu/~west/mt"><i>Mathematical Thinking: Problem-Solving and
|
||
|
|
Proofs</i></a> (with John D'Angelo),
|
||
|
|
and the forthcoming
|
||
|
|
<a href="https://faculty.math.illinois.edu/~west/0cont.ps"><i>Combinatorial Mathematics</i></a>.
|
||
|
|
All these figures are drawn using gpic, the GNU (Free Software Foundation)
|
||
|
|
version of the program pic developed originally by AT&T. gpic is part of
|
||
|
|
the freely available groff document formatting system.
|
||
|
|
|
||
|
|
<p>
|
||
|
|
The program pic was developed for drawing pictures in troff documents,
|
||
|
|
I believe in 1984. The original version of gpic was intended as a
|
||
|
|
preprocessor for groff. Sometime in the late 1990s, a command-line option
|
||
|
|
was added to gpic to allow it to serve as a preprocessor for TeX.
|
||
|
|
This allowed me to migrate my books from troff to TeX.
|
||
|
|
|
||
|
|
</p><p>
|
||
|
|
Since mostly I want to draw graphs, I wrote macros that facilitate drawing and
|
||
|
|
labeling graphs of various sorts in a few lines of gpic input.
|
||
|
|
I provide the <a href="https://faculty.math.illinois.edu/~west/tpics.txt">macro package</a> as a text file with
|
||
|
|
essentially no documentation. On this page I give a brief summary of how to
|
||
|
|
use it, plus a few examples at the end.
|
||
|
|
More extensive <a href="http://www.kohala.com/start/troff/troff.html">reference
|
||
|
|
materials</a> on pic and gpic themselves, including old user manuals, have been
|
||
|
|
gathered by Richard Stevens.
|
||
|
|
|
||
|
|
</p><p>
|
||
|
|
My macro package is inelegant and could be made cleaner and more sophisticated.
|
||
|
|
However, it does enable me to draw the pictures I want to draw rather quickly
|
||
|
|
and with very little code.
|
||
|
|
</p><p>
|
||
|
|
Please send feedback on how this page can be improved to
|
||
|
|
west @ math . uiuc . edu.
|
||
|
|
Also, please let me know if you use these macros.
|
||
|
|
|
||
|
|
|
||
|
|
</p><h2>Basics</h2>
|
||
|
|
|
||
|
|
<b>Locations and arguments</b><br>
|
||
|
|
gpic is coordinate-based. Locations are described as ordered pairs "(a,b)"
|
||
|
|
in the coordinate plane. Locations (or objects) can be named using colons, as
|
||
|
|
in "A:(a,b)". Names remain in effect until reassigned; in particular, they
|
||
|
|
persist into later pictures. To put multiple commands on a single line, end
|
||
|
|
each with a semicolon.
|
||
|
|
<p>
|
||
|
|
In order to facilitate placing vertices at grid points, I have defined
|
||
|
|
names for these locations. Available are "<b>p00</b>" through "<b>p99</b>"
|
||
|
|
and "<b>p100</b>" through "<b>p155</b>", where "<b>p</b>ij" denotes "(i,j)",
|
||
|
|
and the other locations are from (10,0) through (15,5). Offset locations
|
||
|
|
are also available, using "<b>op00</b>" through "<b>op99</b>"
|
||
|
|
and "<b>op100</b>" through "<b>op155</b>". Here "<b>op</b>ij" is defined
|
||
|
|
as "O+(i,j)" for the particular location named as "O", which can be viewed
|
||
|
|
as an "origin". A picture with several copies of the same structure can
|
||
|
|
be produced by using the same commands with a change in the specification of
|
||
|
|
"O".
|
||
|
|
</p><p>
|
||
|
|
Lines and arrows are drawn from location to location. gpic macros have a fixed
|
||
|
|
list of up to nine arguments, invoked as <b>macro</b>(arg1,arg2,...,argN).
|
||
|
|
Therefore, many of my macros come in sets indexed up to 9, depending
|
||
|
|
on how many points are being placed or connected by lines.
|
||
|
|
The syntax for macro definitions is
|
||
|
|
<br>
|
||
|
|
"define macroname #command1; command2; etc#"
|
||
|
|
|
||
|
|
|
||
|
|
</p><p>
|
||
|
|
<b> "spot", "spot2", . . ., "spot9"</b><br>
|
||
|
|
The arguments for these macros are locations in the plane. "<b>spotN</b>"
|
||
|
|
takes N such locations and puts bullets there as vertices. It also names those
|
||
|
|
locations in order, A, B, C, . . . Those names can be used as arguments
|
||
|
|
in later macros. This enables editing of pictures by moving vertices
|
||
|
|
around without retyping lots of locations. If more than nine vertices are
|
||
|
|
needed, than one can save the locations with other names, as in "A1:A;";
|
||
|
|
each use of a "<b>spotN</b>" macro assigns names starting from "A".
|
||
|
|
|
||
|
|
</p><p>
|
||
|
|
<b> "poly2", . . ., "poly20" </b><br>
|
||
|
|
"<b>polyN</b>(loc,rad)" places N equally spaced vertices around an invisible
|
||
|
|
circle with center "loc" and radius "rad", naming the locations beginning with
|
||
|
|
A at the top (as in <b>spotN</b>) and moving clockwise. This is done via a
|
||
|
|
small table of sines and cosines present in the macro package.
|
||
|
|
For odd N, only up to N=13 is provided.
|
||
|
|
When N is even, the (invisible) polygon sits on a horizontal base;
|
||
|
|
the version "<b>polyNv</b>" (and maybe also "<b>polyNh</b>" for N=12
|
||
|
|
and N=16") puts a point at the top and bottom.
|
||
|
|
|
||
|
|
|
||
|
|
</p><p>
|
||
|
|
<b> "edge", "degr", "matc", "path", "cycl"</b><br>
|
||
|
|
"<b>edge</b>(A,B)" draws a line segment connecting two locations A and B.
|
||
|
|
<br>
|
||
|
|
"<b>degrN</b>" draws edges from its first argument to the other N arguments,
|
||
|
|
up to N=8.
|
||
|
|
<br>
|
||
|
|
"<b>matcN</b>" draws a matching of size N on its 2N arguments, for N\in{2,3,4}.
|
||
|
|
For example, "<b>matc4</b>(A,B,C,D,E,F,G,H)" draws the edges AB, CD, EF, and GH.
|
||
|
|
<br>
|
||
|
|
"<b>pathN</b>" draws a path through the locations of its N arguments in order.
|
||
|
|
<br>
|
||
|
|
"<b>cyclN</b>" draws a cycle through the locations of its N arguments in order.
|
||
|
|
<br>
|
||
|
|
The gpic primitive for these macros is "line", as in "line from A to B to C
|
||
|
|
to D to E".
|
||
|
|
|
||
|
|
</p><p>
|
||
|
|
<b> "call", "call2", "call3"</b><br>
|
||
|
|
These place text at a specified location.
|
||
|
|
In "<b>call</b>(A,"text $v_1$",ne);" the text inside quotation marks is
|
||
|
|
placed near location A, in the northeast direction away from A.
|
||
|
|
There are eight compass directions plus "c" for center.
|
||
|
|
Note that text is passed through unchanged, to be processed by TeX (or troff),
|
||
|
|
and it will be produced in the fonts used by the subsequent program. Thus
|
||
|
|
notation is placed within dollar signs.
|
||
|
|
To place text at locations A,B or A,B,C, use
|
||
|
|
"<b>call2</b>(A,B,"text1","text2",direc1,direc2);" or
|
||
|
|
"<b>call3</b>(A,B,C,"text1","text2","text3",direc1,direc2,direc3);".
|
||
|
|
|
||
|
|
</p><p>
|
||
|
|
<b> "circ", "arch", "elli"</b><br>
|
||
|
|
"<b>circ</b>(A,rad)" draws a circle of radius "rad" centered at location A.
|
||
|
|
<br>
|
||
|
|
"<b>arch</b>(A,B,rad)" draws a circular arc of radius "rad" counterclockwise
|
||
|
|
from location A to location B.
|
||
|
|
<br>
|
||
|
|
"<b>elli</b>(A,ht,wid)" draws an ellips of height "ht" and width "wid"
|
||
|
|
centered at location A.
|
||
|
|
<br>
|
||
|
|
Circless and ellipse are objects with centers and directional corners.
|
||
|
|
The objects can be named, as in "C:circ(p00,2);" and then "C.ne" subsequently
|
||
|
|
refers to the northeast point on C.
|
||
|
|
|
||
|
|
</p><p>
|
||
|
|
<b>"spli3", . . ., "spli9"</b><br>
|
||
|
|
"<b>spliN</b>" draws a curved line (via splines) from
|
||
|
|
A to B to C, etc., those being its N arguments in order.
|
||
|
|
Only the first and last locations are actually touched by the curve.
|
||
|
|
Try it.
|
||
|
|
|
||
|
|
</p><p>
|
||
|
|
<b> Arrow, Bold, Dashed, Dotted</b><br>
|
||
|
|
Generally speaking, many of the macros for edge, path, cycl, degr, matc, spli,
|
||
|
|
can be modified by prepending "a", "b", "f", "d", "t" to obtain lines that
|
||
|
|
are arrows (directed edges), bold (thicker), fat (much thicker), dashed, or
|
||
|
|
dotted, respectively. In combination, <b>daedge</b>, <b>baedge</b>, and
|
||
|
|
<b>dapath</b> are also available.
|
||
|
|
<br>
|
||
|
|
The size of arrowheads is constant, but the extent of coordinates in pictures
|
||
|
|
is not. As a result, arrowheads may appear too large or too small. To fix
|
||
|
|
this, use "<b>sethead</b>(param)" to multiply the scale of arrowheads by
|
||
|
|
"param". At the end of the picture, use "<b>resethead</b>" to restore the
|
||
|
|
original scale; otherwise the new size arrowheads will be used in succeeding
|
||
|
|
pictures.
|
||
|
|
|
||
|
|
|
||
|
|
</p><h2>Invocation in TeX Documents</h2>
|
||
|
|
|
||
|
|
Within a TeX document, the source for a gpic picture appears as follows:
|
||
|
|
<br>\gpic{
|
||
|
|
<br>.PS x
|
||
|
|
<br>gpic commands
|
||
|
|
<br>.PE
|
||
|
|
<br>}
|
||
|
|
|
||
|
|
<p>
|
||
|
|
The "\gpic" macro is defined within the macro package. The "x" is the
|
||
|
|
desired width of the picture in inches. When the file is run through the
|
||
|
|
gpic program before sending it to tex or latex, the portion from
|
||
|
|
.PS to .PE will be replaced with the "specials" that direct tex to draw the
|
||
|
|
lines and other elements of the picture. Under tex, the macro "\gpic" then
|
||
|
|
creates a centered box with the picture inside it.
|
||
|
|
|
||
|
|
</p><p>
|
||
|
|
The command-line option "-t" instructs gpic to prepare its output for
|
||
|
|
TeX rather than for troff. To run the preprocessor and then tex, one therefore
|
||
|
|
uses something like the following script:
|
||
|
|
<br>gpic -t gpicmacros texsource > temp.tex
|
||
|
|
<br>tex temp
|
||
|
|
</p><p>
|
||
|
|
To get pdf output, the resulting dvi file should be hit with
|
||
|
|
<br>
|
||
|
|
dvips -Ppdf | ps2pdf
|
||
|
|
|
||
|
|
</p><h2>Further Macros and Comments</h2>
|
||
|
|
|
||
|
|
<b>Filled and Invisible</b><br>
|
||
|
|
"<b>icirc</b>(A,rad)" draws an invisible circle, which may be useful when
|
||
|
|
named in order to refer to directional locations.
|
||
|
|
<br>
|
||
|
|
"<b>fcirc</b>(A,rad,fill)" draws a circle of radius "rad" centered at location
|
||
|
|
A with the interior filled to density "fill", between 0 and 1. The use of
|
||
|
|
"fcirc" will overwrite anything that was previous put in the interior of the
|
||
|
|
circle.
|
||
|
|
<br>
|
||
|
|
"<b>ficirc</b>(A,rad,fill)" draw a filled interior without the boundary.
|
||
|
|
<br>
|
||
|
|
"<b>felli, fielli</b>" are the analogues for ellipses.
|
||
|
|
|
||
|
|
<p>
|
||
|
|
<b>"h1,...,h9", "v1,...,v9"</b><br>
|
||
|
|
Like "<b>p</b>ij", these are shorthand for coordinate pairs, with
|
||
|
|
"<b>h</b>j" being (.j,0) and "<b>v</b>j" being (0,.j).
|
||
|
|
They can be used for making slight adjustments to locations for placing
|
||
|
|
text labels.
|
||
|
|
|
||
|
|
</p><p>
|
||
|
|
"<b>spoto</b>(A)" puts an open circle (instead of a bullet) at location A.
|
||
|
|
<br>
|
||
|
|
"<b>mark</b>(A)" puts a square at location A (to distinguish a vertex).
|
||
|
|
<br>
|
||
|
|
"<b>cliqN</b>" draws a complete graph with vertices at its N arguments,
|
||
|
|
for N\in{4,5,6}.
|
||
|
|
<br>
|
||
|
|
<b>"k23", "k33", "k34", "k44"</b> draw complete bipartite graphs.
|
||
|
|
|
||
|
|
</p><h2>Examples</h2>
|
||
|
|
Below is the gpic code using these macros to produce several of the
|
||
|
|
figures in Section 1.1 of <i>Introduction to Graph Theory</i>,
|
||
|
|
second edition.
|
||
|
|
|
||
|
|
<p>
|
||
|
|
Petersen graph, page 13:
|
||
|
|
<br>
|
||
|
|
\gpic{
|
||
|
|
<br>
|
||
|
|
.PS 3.8
|
||
|
|
<br>
|
||
|
|
O:p00; poly5(O,2); cycl5(A,B,C,D,E); A1:A; B1:B; C1:C; D1:D; E1:E;
|
||
|
|
<br>
|
||
|
|
poly5(O,1); cycl5(A,C,E,B,D); matc3(A,A1,B,B1,C,C1); matc2(D,D1,E,E1);
|
||
|
|
<br>
|
||
|
|
call3(A1,B1+h1,C1+h1,"12","34","51",n,ne,se); call2(D1-h1,E1-h1,"23","45",sw,nw)
|
||
|
|
<br>
|
||
|
|
call3(A+h1,B-v1,C-h1,"35","52","24",e,s,sw); call2(D,E,"41","13",nw,n);
|
||
|
|
<br>
|
||
|
|
O:(5.5,0)+v1; poly3(op00,-.8); degr3(O,A,B,C); A1:A; B1:B; C1:C; spot(O);
|
||
|
|
<br>
|
||
|
|
poly6(op00,2); cycl6(A,B,C,D,E,F); path3(A,B1,D); path3(B,A1,E); path3(C,C1,F);
|
||
|
|
<br>
|
||
|
|
O:p110+v1; poly9(O,2); cycl9(A,B,C,D,E,F,G,H,I); spot(O); degr3(O,A,D,G);
|
||
|
|
<br>
|
||
|
|
matc3(B,F,E,I,H,C);
|
||
|
|
<br>
|
||
|
|
.PE
|
||
|
|
<br>
|
||
|
|
}
|
||
|
|
|
||
|
|
</p><p>
|
||
|
|
Decomposition of <i>K<sub>5</sub></i> and <i>K<sub>4</sub></i>, page 11:
|
||
|
|
<br>
|
||
|
|
\gpic{
|
||
|
|
<br>
|
||
|
|
.PS 2.6
|
||
|
|
<br>
|
||
|
|
poly5((0,.85),1.15); bcycl5(A,B,C,D,E); cycl5(A,C,E,B,D);
|
||
|
|
<br>
|
||
|
|
spot4(p30,p50,p52,p32); path3(A,B,D); dpath3(B,C,A); bpath3(C,D,A);
|
||
|
|
<br>
|
||
|
|
.PE
|
||
|
|
<br>
|
||
|
|
}
|
||
|
|
|
||
|
|
</p><p>K\"onigsberg Bridge Problem, page 2:
|
||
|
|
<br>
|
||
|
|
\gpic{
|
||
|
|
<br>
|
||
|
|
.PS 4.0
|
||
|
|
<br>
|
||
|
|
elli(p64,4,6); call3(p64,p96+h2,p92+h2,"$W$","$X$","$Z$",c,ne,se);
|
||
|
|
<br>
|
||
|
|
call3(p124+h2,p55-v3,p75-v3,"$Y$","1","2",e,nw,ne);
|
||
|
|
<br>
|
||
|
|
call3(p53+v1,p73+v1,p84-h2,"3","4","5",sw,se,e);
|
||
|
|
<br>
|
||
|
|
call3(p115+h2,p113+h2,p114,"6","7","$~$",s,n,w);
|
||
|
|
<br>
|
||
|
|
spli7((14,6.4),(12,5.4),(9.8,5.0),(9.2,4),(9.8,3.0),(12,2.6),(14,1.6));
|
||
|
|
<br>
|
||
|
|
spli7((1.0,3.6),(2.6,3.4),(4,2),(6,1.4),(9.2,2.6),(12,2),(14,.8));
|
||
|
|
<br>
|
||
|
|
spli7((1.0,4.4),(2.6,4.6),(4,6),(6,6.6),(9.2,5.4),(12,6),(14,7.2));
|
||
|
|
<br>
|
||
|
|
matc2((8.7,4.1),(9.6,4.1),(8.7,3.9),(9.6,3.9));
|
||
|
|
<br>
|
||
|
|
matc4((4.7,1.4),(5.0,2.4),(4.5,1.5),(4.8,2.5),(4.7,6.6),(5.0,5.6),(4.5,6.5),(4.8,5.5));
|
||
|
|
<br>
|
||
|
|
matc4((7.3,1.4),(7.0,2.4),(7.5,1.5),(7.2,2.5),(7.3,6.6),(7.0,5.6),(7.5,6.5),(7.2,5.5));
|
||
|
|
<br>
|
||
|
|
matc4((11.0,1.8),(11.5,3.1),(11.2,1.7),(11.7,3.0),(11.0,6.2),(11.5,4.9),(11.2,6.3),(11.7,5.0));
|
||
|
|
<br>
|
||
|
|
O:(17,1);
|
||
|
|
<br>
|
||
|
|
spot4(op30,op03,op36,op63); degr3(D,A,B,C); dbledge(A,B,6.5); dbledge(B,C,6.5);
|
||
|
|
<br>
|
||
|
|
call3(C+v1,D,A-v1,"$x$","$y$","$z$",n,e,s); E1:.5< B,C>; E3:.5< A,B >;
|
||
|
|
<br>
|
||
|
|
E5:.5< B,D>; E6:.5< C,D>; E7:.5< D,A>;
|
||
|
|
<br>
|
||
|
|
call3(B-h2,E1-h3+v3,E1+h2-v2,"$w$","$e_1$","$e_2$",w,nw,se);
|
||
|
|
<br>
|
||
|
|
call3(E3-h2-v2,E3+h2+v2,E5,"$e_3$","$e_4$","$e_5$",sw,ne,n);
|
||
|
|
<br>
|
||
|
|
call3(E6,E7,E5,"$e_6$","$e_7$","$~$",ne,se,s);
|
||
|
|
<br>
|
||
|
|
.PE
|
||
|
|
<br>
|
||
|
|
}
|
||
|
|
|
||
|
|
</p><div id="grammalecte_menu_main_button_shadow_host" style="width: 0px; height: 0px;"></div></body><script src="Drawing%20Graphs%20with%20gpic%20-%20Douglas%20B.%20West_files/api.js"></script></html>
|