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C00002 00002	% This manual is copyright (C) 1984 by the American Mathematical Society.
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C00052 00010	\beginchapter Chapter 1. The Name of\\the Game
C00069 00011	\beginchapter Appendix J. Joining the\\\TeX\ Community
C00072 00012	\end
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% copyright
\titlepage
\eightpoint
\vbox to 8pc{}
\noindent\strut
The quotation on page xxx is copyright $\copyright$ 19xx by Xxxx,
and used by permission.
\medskip
\noindent
\TeX\ is a trademark of the American Mathematical Society.
\bigskip\medskip
\noindent
{\bf Library of Congress cataloging in publication data}
\medskip
{\tt\halign{#\hfil\cr
Knuth, Donald Ervin (1938-\cr
\ \ \  The METAFONTbook.\cr
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ISBN 0-201-xxxxx-x\cr}}
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%{\sl \kern-1pt Second printing, Someday?}
%\smallskip
\noindent
Copyright $\copyright$ 1985 by the American Mathematical Society
\smallskip
\noindent
This book is published jointly by the American Mathematical Society
and Addison-\kern-1ptWesley Publishing Company.
All rights reserved. No part of this publication may be reproduced, stored in
a retrieval system, or transmitted, in any form or by any means,
electronic, mechanical, photocopying, recording, or otherwise, without
the prior written permission of the publishers. Printed in the United
States of America. Published simultaneously in Canada.
\medskip
\noindent
ISBN 0-201-xxxxx-x\par
\noindent
ABCDEFGHIJ--HA--89876543
↑↑{Knuth, Donald Ervin}
\eject
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\rightline{\strut\eightssi To Hermann Zapf}
↑↑{Zapf, Hermann}
\vskip2pt
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% the preface
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\tenpoint
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{\sc ENERATION} {\sc OF} {\sc LETTERFORMS} \strut by mathematical means
was first tried in the fifteenth century; it became popular in the
sixteenth and seventeenth centuries; and it was abandoned (for good
reasons) during the eighteenth century. Perhaps the twentieth century
will turn out to be the right time for this idea to make a comeback,
now that mathematics has advanced and computers are able to
do the calculations.

Modern printing equipment based on raster lines---in which metal ``type''
has been replaced by purely combinatorial patterns of zeroes and ones
that specify the desired position of ink in a discrete way---makes
mathematics and computer science increasingly relevant to printing.
We now have the ability to give a completely precise definition of letter
shapes that will produce essentially equivalent results on all raster-based
machines. Furthermore it is possible to include variable parameters in the
definitions of those shapes; computers can ``draw'' new fonts of characters
in seconds, so that a designer is now able to perform valuable experiments
that were previously unthinkable.

\MF\ is a system for the design of alphabets suited to raster-based
devices that print or display text. The characters that you are reading
were all designed with \MF\!, in a completely precise way; and they
were developed rather hastily by the author of the system, who is a rank
amateur at such things. It seems clear that further work with \MF\ has
the potential of producing typefaces of real ↑{beauty}, so this manual has
been written for people who would like to help advance the art of
mathematical type design.

A top-notch designer of types needs to have an unusually good eye
and a highly developed sensitivity to the nuances of shapes.
A top-notch user of computer languages needs to have an unusual
talent for abstract reasoning and a highly-developed ability to
express intuitive ideas in formal terms. Very few people have both
of these unusual combinations of skills; hence the best products of
\MF\ will probably be collaborative efforts between two
people who complement each other's abilities. Indeed, this situation
isn't very different from the way types have been created for many
generations, except that the r\↑ole of ``punch-cutter'' is now being
played by skilled computer specialists instead of by skilled
metalworkers.

A \MF\ user writes a ``program'' for each letter or symbol that is
desired. These programs are different from ordinary computer programs,
because they are essentially {\sl declarative\/} rather than imperative.
In the \MF\ language you explain where the major components of a
desired shape are to be located, and how they relate to each other,
but you don't have to work out the details of exactly where the lines
cross, etc.; the computer takes over the work of solving equations as it
deduces the consequences of your specifications. One of the advantages of
\MF\ is that it provides a discipline according to which the principles
of a particular alphabet design can be stated precisely---the underlying
intelligence does not remain hidden in the mind of the designer, it is
spelled out in the programs. Thus it is comparatively easy to obtain
consistency where consistency is desirable, and to extend a font to
new symbols that are compatible with the existing ones.

It would be nice if a system like \MF\ were to simplify the task of
type design to the point where beautiful new alphabets could be
created in a few hours. This, alas, is impossible; an enormous
amount of subtlety lies behind the seemingly simple letter shapes that
we see every day, and the designers of high-quality typefaces have
done their work so well that we don't notice the underlying complexity.
One of the disadvantages of \MF\ is that a person can easily use it
to produce poor alphabets, cheaply and in great quantity. Let us hope
that such experiments will have educational value as they reveal why the
subtle tricks of the trade are important, but that they will not cause
bad workmanship to proliferate. Anybody can now produce a book in which
all of the type is home-made, but a person or team of persons should
expect to spend a year or more on the project if the type is actually
supposed to look right. \MF\ won't put today's type designers out of work;
on the contrary, it will tend to make them heroes, as more and more people
come to appreciate their skills.

Although there is no royal road to type design, there are some things that
can, in fact, be done well with \MF\ in an afternoon. Geometric designs
are rather easy; and it doesn't take long to make modifications to letters
or symbols that have previously been expressed in \MF\ form. Thus,
although comparatively few users of \MF\ will have the courage to do an
entire alphabet from scratch, there will be many who will enjoy
customizing someone else's design.

This book is not a text about mathematics or about computers. But if
you know the rudiments of those subjects (namely, contemporary high school
mathematics, together with the knowledge of how to use the text
editing or word processing facilities on your computing machine),
you should be able to use \MF\ with little difficulty after reading
what follows. Some parts of the exposition in the text are more obscure than others,
however, since the author has tried to satisfy experienced \MF\!ers
as well as beginners and casual users with a single manual. Therefore
a special symbol has been used to warn about esoterica: When you see the sign
$$\vbox{\hbox{\dbend}\vskip 11pt}$$
at the beginning of a paragraph, watch out for a ``↑{dangerous bend}''
in the train of thought---don't read such a paragraph unless you need to.
You will be able to use \MF\ reasonably well, even to design characters like
the dangerous-bend symbol itself, without reading the fine print in such
advanced sections.

Some of the paragraphs in this manual are so far out that they are rated
$$\vcenter{\hbox{\dbend\kern1pt\dbend}\vskip 11pt}\;;$$
everything that was said about single dangerous-bend signs goes double
for these. You should probably have at least a month's experience with
\MF\ before you attempt to fathom such doubly dangerous depths
of the system; in fact, most people will never need to know \MF\
in this much detail, even if they use it every day. After all, it's
possible to fry an egg without knowing anything about biochemistry.
Yet the whole story is here in case you're curious. \ (About \MF, not eggs.)

The reason for such different levels of complexity is that people change
as they grow accustomed to any powerful tool. When you first try to use
\MF\!, you'll find that some parts of it are very easy, while other things
will take some getting used to. At first you'll probably try to control
the shapes too rigidly, by overspecifying data that has been copied from
some other medium.  But later, after you have begun to get a feeling for
what the machine can do well, you'll be a different person, and you'll be
willing to let \MF\ help contribute to your designs as they are being
developed. As you gain more and more experience working with this unusual
apprentice, your perspective will continue to change and you will be
running into different sorts of challenges.  That's the way it is with any
powerful tool: There's always more to learn, and there are always better
ways to do what you've done before.  At every stage in the development
you'll want a slightly different sort of manual.  You may even want to
write one yourself.  By paying attention to the dangerous bend signs in
this book you'll be better able to focus on the level that interests you
at a particular time.

Computer system manuals usually make dull reading, but take heart:
This one contains {\sc ↑{JOKES}} every once in a while. You might actually
enjoy reading it. \ (However, most of the jokes can only be appreciated
properly if you understand a technical point that is being made---so
read {\sl carefully}.)

Another noteworthy characteristic of this book is that it doesn't
always tell the ↑{truth}. When certain concepts of \MF\ are introduced
informally, general rules will be stated; afterwards you will find that the
rules aren't strictly true. In general, the later chapters contain more
reliable information than the earlier ones do. The author feels that this
technique of deliberate lying will actually make it easier for you to
learn the ideas. Once you understand a simple but false rule, it will not
be hard to supplement that rule with its exceptions.

In order to help you internalize what you're reading,
{\sc ↑{EXERCISES}} are sprinkled through this manual. It is generally intended
that every reader should try every exercise, except for questions that appear
in the ``dangerous bend'' areas. If you can't solve a problem, you
can always look up the answer.
But please, try first to solve it by yourself; then you'll learn more
and you'll learn faster. Furthermore, if you think you do know the solution,
you should turn to Appendix~A and check it out, just to make sure.

\medskip
\hrule
\line{\vrule\hss\vbox{\medskip
\leftskip=\parindent \rightskip=\parindent
\strut W{\sc ARNING}: Type design can be hazardous to your other interests.
Once you get hooked, you will develop intense feelings about typography;
the medium will intrude on the messages that you read. And you will perpetually
be thinking of improvements to the fonts that you see everywhere,
especially those of your own design.
\strut\medskip}\hss\vrule}
\hrule

\medskip

The \MF\ language described here has very little in common with the
author's previous attempt at a language for alphabet design, because
five years of experience with the old system has made it clear that a
completely different approach is preferable. Both languages have
been called \MF; but henceforth the old language should be called
\MF\kern.05em79, and its use should rapidly fade away. Let's keep the name \MF\
for the language described here, since it is so much better, and since
it will never change again. ↑↑{MF79}

I wish to thank the hundreds of people who have helped me to formulate
this ``definitive edition'' of \MF\!, based on their experiences with
preliminary versions of the system.  In particular, John ↑{Hobby}
discovered many of the algorithms that have made the new language
possible. My work at Stanford has been generously supported by the
↑{National Science Foundation}, the ↑{Office of Naval Research}, the ↑{IBM
Corporation}, and the ↑{System Development Foundation}. I also wish to
thank the ↑{American Mathematical Society} for its encouragement and for
publishing the {\sl ↑{TUGboat}\/} newsletter (see Appendix~J).
Above all, I deeply thank my wife, Jill, for the inspiration, ↑↑{Knuth, Jill}
understanding, comfort, and support she has given me for more than
25~years, especially during the eight years that I have been
working intensively on mathematical typography.

\medskip
\line{{\sl Stanford, California}\hfil--- D. E. K.}↑↑{Knuth, Don}
\line{\sl June 1985\hfil}

} % end of the special \topskip
\endchapter

It is hoped that Divine Justice may find
some suitable affliction for the malefactors
who invent variations upon the alphabet of our fathers.~.\thinspace.\thinspace.
The type-founder, worthy mechanic, has asserted himself
with an overshadowing individuality,
defacing with his monstrous creations and revivals
every publication in the land.
\author AMBROSE ↑{BIERCE}, {\sl The Opinionator.~Alphab\↑etes\/} %
  (1911) % vol 10 of his collected works, p69
  % probably written originally in 1898 or 1899

\bigskip

Can the new process yield a result that, say,
a Club of Bibliophiles would recognise as a work of art
comparable to the choice books they have in their cabinets?
\author STANLEY ↑{MORISON}, {\sl Typographic Design in Relation to
	Photographic Composition\/} (1958) % pp 4--5

\eject
% the table of contents
\titlepage
\vbox to 8pc{
\rightline{\titlefont Contents}
\vfill}
↑↑{Contents of this manual, table}
\def\rhead{Contents}
\tenpoint
\begingroup
\countdef\counter=255
\def\diamondleaders{\global\advance\counter by 1
  \ifodd\counter \kern-10pt \fi
  \leaders\hbox to 20pt{\ifodd\counter \kern13pt \else\kern3pt \fi
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    \hbox to\parindent{\bf\hbox to 1em{\hss#1}\hss}%
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\\1. The Name of the Game. 1.
\\2. Whatever. 3.
\\3. Thirdly. 7.
\\4. Fourthly. 13.
\\5. Fifthly. 19.
\\6. Running \MF. 23.
\\7. How \MF\ Reads What You Type. 37.
\\8. XXX. 43.
\\9. All These Titles are Garbage. 51.
\\10. Dimensions. 57.
\\11. Boxes. 63.
\\12. Glue. 69.
\\13. Modes. 85.
\\14. How \TeX\ Breaks Paragraphs into Lines. 91.
\\15. How \TeX\ Makes Lines into Pages. 109.
\\16. Typing Math Formulas. 127.
\\17. More about Math. 139.
\\18. Fine Points of Mathematics Typing. 161.
\\19. Displayed Equations. 185.
\\20. Definitions (also called Macros). 199.
\\21. Making Boxes. 221.
\\22. Alignment. 231.
\\23. Output Routines. 251.
\eject
\vbox to 8pc{}
\\24. Summary of Normal Mode. 267.
\\25. Summary of Abnormal Mode. 285.
\\26. Summary of Everything Else. 287.
\\27. Recovering from Errors. 289.
\null
\leftline{\indent\bf Appendices}
\\A. Answers to All the Exercises. xxx.
\\B. Basic Operations. xxx.
\\C. Character Codes. xxx.
\\D. Dirty Tricks. xxx.
\\E. Examples. xxx.
\\F. Font Metric Information. xxx.
\\G. Generic Font Files. xxx.
\\H. Hardcopy Proofs. xxx.
\\I\hskip 1pt. Index. xxx.
\\J. Joining the \TeX\ Community. xxx.
\null % 17 lines so far to balance the 23 on the other page
\null % 18
\null % 19
\null % 20
\null % 21
\null % 22
\null % 23
\eject
\endgroup
\beginchapter Chapter 1. The Name of\\the Game

\pageno=1 % This is page number 1, number 1,
This is a book about a computer system called \MF\!, just as {\sl The \TeX
book\/} is about \TeX.  \MF\ and \TeX\ are good friends who intend to live
together for a long time.  Between them they take care of the two most
fundamental tasks of typesetting:  \TeX\ puts characters into the proper
positions on a page, while \MF\ determines the shapes of the characters
themselves. ↑↑{TeX} ↑↑{METAFONT, the name}

Why is the system called \MF\thinspace? The `-{\mfmanual FONT}\thinspace'
part is easy to understand, because sets of related characters that are
used in typesetting are traditionally known as fonts of type. The
`{\mfmanual META}-' part is more interesting: It indicates that we are
interested in making high-level descriptions that transcend any of the
individual fonts being described.

Newly coined words beginning with `meta-' generally reflect our contemporary
inclination to view things from outside or above, at a more abstract level than
before, with what we feel is a more mature understanding. We now have
metapsychology (the study of how the mind relates to its containing body),
metahistory (the study of principles that control the course of events),
metamathematics (the study of mathematical reasoning), metafiction
(literary works that explicitly acknowledge their own forms), and so on.
A metamathematician proves metatheorems (theorems about theorems);
a computer scientist often works with metalanguages (languages for
describing languages). Similarly, a ↑{meta-font} is a schematic description
of the shapes in a family of related fonts; the letterforms change
appropriately as their underlying parameters change.

Meta-design is much more difficult than design; it's easier to draw something
than to explain how to draw it. One of the problems is that it's hard to
envision many different sets of potential specifications all at once;
another is that a computer has to be told absolutely everything.
However, once we have successfully explained how to draw something
in a sufficiently general manner, the same explanation will work for
related shapes, in different circumstances; so~the time spent in formulating
a precise explanation turns out to be worth it.

Typefaces intended for text are normally seen small, and our eyes can read
them best when the letters have been designed specifically for the size at
which they are actually used. Although it is tempting to get 7-point fonts
by simply making a 70\% reduction from the 10-point size, this shortcut
leads to a serious degradation of quality. Much better results can be
obtained by incorporating parametric variations into a meta-design.  In
fact, there are advantages to built-in variability even when you want to
produce only one font of type in a single size, because it allows you to
postpone making decisions about many aspects of your design. If you leave
certain things undefined, treating them as parameters instead of
``freezing'' the specifications at an early stage, the computer will be
able to draw lots of examples with different settings of the parameters,
and you will be able to see the results of all those experiments at the final
size. This will greatly increase your ability to edit and fine-tune the font.

If meta-fonts are so much better than plain old ordinary fonts, why weren't
they developed long ago? The main reason is that computers did not exist until
recently. People find it difficult and dull to carry out calculations with
a multiplicity of parameters, while today's machines do such tasks with ease.
The introduction of parameters is a natural outgrowth of automation.

OK, let's grant that meta-fonts sound good, at least in theory. There's still
the practical problem about how to achieve them. How can we actually
specify shapes that depend on unspecified parameters?

If only one parameter is varying, it's fairly easy to solve the problem in
a visual way, by overlaying a series of drawings that show graphically how
the shape changes. For example, if the parameter varies from 0 to~1, we
might prepare five sketches, corresponding to the parameter values 0,
$1\over4$, $1\over2$, $3\over4$, and~1. If these sketches follow a
consistent pattern, we can readily interpolate to find the shape for a
value like~$2\over3$ that lies between two of the given ones. We might
even try extrapolating to parameter values like 1$1\over4$.

But if there are two or more independent parameters, a purely visual solution
becomes too cumbersome. We must go to a verbal approach, using some sort
of language to describe the desired drawings. Let's imagine, for example,
that we want to explain the shape of a certain letter `a' to a friend in
a distant country, using only a telephone for communication; our friend
is supposed to be able to reconstruct exactly the shape we have in mind.
Once we figure out a sufficiently natural way to do that, for a particular
fixed shape, it isn't much of a trick to go further and make our verbal
description more general, by including variable parameters instead of
restricting ourselves to constants.

An analogy to cooking might make this point clearer. Suppose you have just
baked a delicious berry pie, and your friends ask you to tell them the
↑{recipe} so that they can bake one too. If you have developed your cooking
skills entirely by instinct, you might find it difficult to record exactly
what you did. But there is a traditional language of recipes in which you
could communicate the steps you followed; and if you take careful measurements,
you might find that you used, say, 1$1\over4$ cups of sugar. The next step,
if you were instructing a computer-controlled cooking machine, would be to
go to a meta-recipe in which you use, say, $.25x$ cups of sugar for $x$
cups of berries; or $.3x+.2y$ cups for $x$~cups of boysenberries and
$y$~cups of blackberries.

In other words, going from design to meta-design is essentially like
going from arithmetic to elementary algebra: Numbers are replaced
by simple formulas that involve unknown quantities. We will see
many examples of this.

A \MF\ definition of a complete typeface generally consists of three
main parts. First there is a rather mundane set of subroutines that take care
of necessary administrative details, such as assigning code numbers
to individual characters; each character must also
be positioned properly inside an invisible ``box,'' so that typesetting
systems will produce the correct spacing. Next comes a more interesting
collection of subroutines, designed to draw the basic strokes characteristic
of the typeface (e.g., the serifs, bowls, arms, arches, and so on).
These subroutines will typically be described in terms of their own special
parameters, so that they can produce a variety of related strokes;
a serif subroutine will, for example, be able to draw serifs of
different lengths, although all of the serifs it draws should
have the same ``feeling.'' Finally, there are routines for each of
the characters. If the subroutines in the first and second parts have been
chosen well, the routines of the third part will be fairly high-level descriptions
that don't concern themselves unnecessarily with details; for example, it
may be possible to substitute a different serif-drawing subroutine without
changing any of the programs that use that subroutine, thereby obtaining
a typeface of quite a different flavor. [A particularly striking example
of this approach has been worked out by John~D. ↑{Hobby} and ↑{Gu} Guoan
in ``A Chinese Meta-Font,'' {\sl TUGboat\/ \bf5} (1984), xx--xx. By
changing a set of 13 basic stroke subroutines, they were able to draw 128
sample ↑{Chinese characters} in three different styles (Song, Long Song,
and Bold), using the same programs for the characters.]

A well-written \MF\ program will express the designer's intentions more
clearly than mere drawings ever can, because the language of algebra has
simple ``idioms'' that make it possible to elucidate many visual relationships.
Thus, \MF\ programs can be used to communicate knowledge
about type design, just as recipes convey the expertise of a chef. But
algebraic formulas are not easy to understand in isolation; \MF\ descriptions
are meant to be read with an accompanying illustration, just as the
constructions in geometry textbooks are accompanied by diagrams.
Nobody is ever expected to read the text of a \MF\ program and say,
``Ah, what a beautiful letter!'' But with one or more enlarged pictures
of the letter, based on one or more settings of the parameters, a reader
of the \MF\ program should be able to say, ``Ah, I~understand how this
beautiful letter was drawn!'' We shall see that the \MF\ system makes it
fairly easy to obtain annotated proof drawings that you can hold in your
hand as you are working with a program.

Although \MF\ is intended to provide a relatively painless way to describe
meta-fonts, you can of course use it also to describe unvarying shapes that
have no ``meta-ness'' at all. Indeed, you need not even use it to produce
fonts; the system will happily draw geometric designs that have no relation
to the characters or glyphs of any alphabet or script. The author
occasionally uses \MF\ simply as a pocket calculator, to do elementary
arithmetic in an interactive way. A computer doesn't mind if its
programs are put to purposes that don't match their names.

\endchapter

[Tinguely] made some large, brightly coloured open reliefs,
juxtaposing stationary and mobile shapes.
He later gave them names like\/ %
{\rm Meta-↑{Kandinsky}}\kern-1pt\ and\/ {\rm Meta-↑{Herbin}}\kern-.5pt,
to clarify the ideas and attitudes %
that lay at the root of their conception.
\author K. G. PONTUS ↑{HULT\'EN}, {\sl Jean ↑{Tinguely}: M\'eta\/} (1972)
 % translated from German by Mary Whittall, 1975, p46

\bigskip

The idea of a meta-font shoud now be clear. But what good is it?
The ability to manipulate lots of parameters may be interesting and fun,
but does anybody really need a 6\/$\scriptstyle{\mkern2mu 1\mkern-2mu\over %
	\mkern-2mu 7\mkern2mu}$-point font
that is one fourth of the way between Baskerville and Helvetica?
\author DONALD E. ↑{KNUTH}, {\sl The Concept of a Meta-Font\/} (1982)
 % Visible Language 16, p19


\eject
\beginchapter Appendix J. Joining the\\\TeX\ Community

This appendix is about grouping of another kind: \TeX\ and \MF\ users from
around the world have banded together to form the \TeX\ Users Group (TUG),
in order to exchange information about common problems and solutions.

A semiannual newsletter called {\sl TUGboat\/} has been published
since 1980, featuring articles about all aspects of \TeX\ and \MF. ↑↑{TeX}
TUG has a network of ``site coordinators'' who serve as focal points of
communication for people with the same computer configurations.
Occasional short courses are given in order
to provide concentrated training in special topics; videotapes of
these courses are available for rental.
Meetings of the entire TUG membership are held at least once a year.
You can buy \MF\ T-shirts at these meetings.

Information about membership in TUG and subscription to {\sl TUGboat\/}
is available from

\smallskip
{\obeylines
\TeX\ Users Group
c/o American Mathematical Society
P.O. Box 6248
Providence RI 02940, USA.
}

\endchapter

TUG is establishd to serve members having a common interest
in \TeX, a system for typesetting technical text,
and in\/ {\mfmanual opqrstuq}\!, a system for font design.
\author T\kern-.15em\lower.5ex\hbox{E}\kern-.005em X
 USERS GROUP, {\sl Bylaws, Article II\/} (1983) % TUGboat 4 (1983) p60

\bigskip

Don't delay, write today! That number again is
\TeX\ Users Group
c/o American Mathematical Society
P.O. Box 6248
Providence RI 02940, USA.
\author DONALD E. ↑{KNUTH}, {\sl The \TeX book\/} (1984) % Appendix J

\eject
\end