\let\MFmanual=\!

\input manmac.tex

\input size.tex

\pagewidth=\hsize \pageheight=\vsize \def\onepageout#1{\shipout\vbox{ % here we define one page of output
    \offinterlineskip % butt the boxes together
%    \vbox to 3pc{ % this part goes on top of the 44pc pages
%      \iftitle % the next is used for title pages
%        \global\titlefalse % reset the titlepage switch
%        \setcornerrules % for camera alignment
%      \else\ifodd\pageno \rightheadline\else\leftheadline\fi\fi
%      \vfill} % this completes the \vbox to 3pc
    \vbox to \pageheight{
      \ifvoid\margin\else % marginal info is present
        \rlap{\kern31pc\vbox to\z@{\kern4pt\box\margin \vss}}\fi
      #1 % now insert the main information
      \ifvoid\footins\else % footnote info is present
        \vskip\skip\footins \kern-3pt
        \hrule height\ruleht width\pagewidth \kern-\ruleht \kern3pt
        \unvbox\footins\fi
      \boxmaxdepth=\maxdepth
      } % this completes the \vbox to \pageheight
    }
  \advancepageno}

\proofmodefalse

\ifproofmode\message{Proof mode is on!}\fi
\titlepage
\def\rhead{Preface}
\vbox to 8pc{
\rightline{\titlefont Preface}\vss}
%{\topskip 9pc % this makes equal sinkage throughout the Preface
\vskip-\parskip
\tenpoint
\noindent\hang\hangafter-2
\smash{\lower12pt\hbox to 0pt{\hskip-\hangindent\cmman G\hfill}}\hskip-16pt
{\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.

%} % end of the special \topskip

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has been replaced by purely combinatorial patterns of zeroes and ones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. Moreover, the shapes can be defined in terms of variable
parameters; computers can ``draw'' new fonts of characters
in seconds, making it possible for designers 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}. This manual has
been written for people who would like to help advance the art of
mathematical type design.

A top-notch designer of typefaces 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 of a typeface.
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 consistency can readily be obtained
where consistency is desirable, and a font can readily be extended 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
let us also hope 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 and heroines, 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
run 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.

\bigskip
\hrule
\line{\vrule\hss\vbox{\medskip\ninepoint
\leftskip=\parindent \rightskip=\parindent
\noindent\strut W{\sc ARNING}: Type design can be hazardous to your other
interests.  Once you get hooked, you will develop intense feelings about
letterforms; 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

\bigskip

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\null).
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 September 1985\hfil}

%} % end of the special \topskip
%\endchapter

\vfill
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

\vskip 4cm
\goodbreak
\vskip -4cm
\bigskip
~
\vfil

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


\end