Boxes and Glue

Transcription

Boxes and Glue

Boxes and Glue
Copyright
2009
B.Bachler, E.Bonetti, L.Bontempi C.Haag, M.Hoogenboom, A.Jongstra, R.Monnikhof, D.Medic
Permission is granted to copy, distribute and/or modify this document under the
terms of the GNU Free Documentation License, Version 1.2 or any later version
published by the Free Software Foundation; A copy of the license is included in
the section entitled “GNU Free Documentation License”.
In February 2010 a workshop took place at the Piet Zwart Institute in Rotterdam. During three days we dealt with LATEX and the automated generation of
LATEX documents, especially regarding the possibilities for graphic design.
Boxes and Glue refers to Donald Knuth’s approach to typesetting1 and points
at the same time back to not-so-ancient days of graphic design. Printlaying as
analogue craft – glue, paper, scissors, rocks.Boxes of Stuff, Bags of Tricks, a
Bag of Pipes.2 Here is a snapshot of things, prepared for and done during the
workshop. Some simple examples, the students’ enhancements, two inspirational
texts from GOTO10’s Book FLOSS + Art and the great METAFONT Tutorial as
start for the next step.
You shouldn’t expect out-of-the-box solutions, for free, like beer and speech,
politically more correct than the Design SuiteTM and by the way the next hot
shit for human-computer interaction. This does NOT provide you with the newer
and better Processing for typesetting or Desktop Publishing. This is an introduction, especially for non-programmers, to the world of quick hacks, workarounds
and almost-good-enough solutions. Searching, finding and replacing, fundamental principles for computer based text processing and frequently used in forkable
tools, becomes here a style of working. Search for your tool, the almost-goodenough solution, hopefully find it and replace what does not fit your needs.
1 The TEX typesetting system uses a model of boxes and glue. Boxes contain typeset objects, such as
text, mathematical displays, and pictures, and glue is flexible space that can stretch and/or shrink by
amounts that are under user control.
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2 A pipe is a form of redirection that is used in Linux and other Unix-like operating systems to send the
output of one program to another program for further processing.
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3
The Shrink-Wrapped Design Process
Michael van Schaik
1 Preface
It takes us years of education to learn to read, write and talk as ways of interacting with our environment. Isn’t it strange, then, that one receives barely any kind
of education in interacting with computers (as a modern communication environment)? Instead most computer programs are built to use interfaces as translators
from computer to human. Although this is meant to help, in many cases this also
makes users less powerful because they can only consume set functions within
the program. You can only compute what the software lets you compute, and only
manipulate what you see.
This is especially the case in the world of graphic design; due to the global
monopoly of big firms like Adobe (which recently even bought it’s only real competitor Macromedia), all graphic designers seem forced to use the same software
to produce their work. Strangely enough, the lion’s share of designers don’t really
seems to care. Looking at my own education (in the Netherlands), a reason for
this could be that the discourse here seems to be focused on ideas more than
actual products (and the tools used to create them). Though there seems to be
a growing interest in alternatives such as open source software as a means to a
more independent design practice, the problem with these is that the few packages that are currently the killer apps in this field are often just free-er copies of
existing software, not much different from their proprietary counterparts.
What if designers actually learned to use the real power of the computer and
computational media instead of the ready-made physical workspace that it currently tries to represent? There is an interesting opportunity here for designers
to start using the computer as the universal machine that it really is instead of
a shrink-wrapped special purpose machine modelled on analogue tools, locking
them away from new creative possibilities specific to the field of computational
media. Why learn to use only the Adobe tool-chain if one can build one’s own
production-environment tool by tool?
2 Current Situation
The main software tool-chains used in the field of graphic design can be divided in
to “digital” and “print” oriented. Since most classically educated graphic designers
(like myself) are primarily educated in the field of print production, it shouldn’t
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come as a surprise that this is also the main focus of most software. The main,
widely used print-production software can be classified under three categories:
vector based (Illustrator, Freehand), bitmap based (Photoshop, Fireworks) and
software to gather and combine the two for prepress (X-press, inDesign). The
software that focuses more on digital-design such as design for websites and
CD-roms/DVDs generally tries to represent these media in a way designers are
already familiar with from the world of print. What these software programs have in
common is that they are an interface between a technical system and the visual
workspace of a designer. So placing an image on a website works in just the
same way as placing it in a book; the designer just imports the image and it’s
there. What actually happens beneath the surface of the Graphical User Interface
stays hidden. This might be considered a good thing, since it saves the designer
from having to learn a whole new way of working for any new technical system, it’s
just a matter of learning it once and then using the same techniques throughout
all media designs. And who wants to know what’s “under the hood” anyway? –
that’s the world of programmers, which is generally not of much interest to graphic
designers.
Without advocating Friedrich Kittler’s suggestion that computer users learn to
read the true (hexadecimal) language of the computer, hiding the real (raw) material of a medium from the user is indeed an important paradigm common in most
software engineering. 3
It can be considered the reason for the sort of fear
of programming code that seems to exist among designers (and lots of computer
users in general). Code is equal to problems. Code is where you see the actual
computer break through the graphical skin, like in the art of JODI, or the field of
glitch art, which is about errors and other things you’d like to prevent. 4 Take
a look at, for example, the Macintosh OS X operating system, where the “engine”
of the computer is almost invisible for the common user. You just do whatever you
want to do as if you were in the physical world, and, invisibly, the system takes
care of the technical layer. One never sees any program code, or even a glimpse
of how the system is built up, while the fact that this system is based on Unix
is considered one of its main advantages (The Unix-philosophy typically means
having simple applications doing their job as well as possible, instead of wasting
CPU power on things like dynamically resizing screens and using a “genie effect”
on hiding them).
The fear of program-code may originate from the first desktop systems, which
introduced this shrink-wrapping of program code in a nice GUI (Graphical User Interface). And this fear is also very much there among graphic designers. It is considered their job to work in the visual field, the field of texts, nice fonts and images,
and the computer is supposed to generate the appropriate code, say postscript
(for print) or html or actionscript etc. (for digital media). This way the designer has
the feeling of staying “above” the medium, calibrating it to their needs, unaffected
by its actual individual (technical) capabilities and way of working. However, if we
look at the historical context designers have worked in, things weren’t always like
this. On the contrary, well known designers such as Piet Zwart or Wim Crouwel,
for example, were actually working with new techniques (photography and photographic typesetting) and challenging, changing and creating the possibilities of
these techniques. Through their knowledge of these new media, they also learned
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3 FLOSS vs. Proprietary, or: Why it is Important to Study Our Software
their intrinsic qualities. Thus, photography introduced the photographic image into
design, but instead of taking that for granted, Piet Zwart re-appropriated these
images as design elements. And while photographic typesetting was invented to
easily reproduce existing type, Crouwel instead invented type specifically for the
capabilities and restrictions of this technique. These are things that wouldn’t have
been possible without a thorough (technical) knowledge of the medium.
So, taking fear of the actual medium of the computer, program code, as a given,
it is interesting to look at how this fear in fact restrains the designer nowadays. As
mentioned, artistic education is focused mainly on the development of the self,
and of original ideas. There is less interest in or time for studying the digital media used to communicate them. Because of the fear of being restrained by (the
absence of knowledge of) program code, instead of the freedom this knowledge
might give, the focus (at least in the Netherlands) is much more on concepts
and physical or visual techniques. But what is forgotten is the importance of the
medium in constituting part of the message. The computer is therefore, mistakenly, seen as just a meta-medium. One that reproduces all earlier media without
changing them. Think also here of how metaphors like the paper folder in the
desktop or the term “web pages” in the internet are used. And this last example is
also one of the more obvious illustrations of the constraint this disinterest in/fear
of the technical produces. The internet is, obviously, a totally different medium
from print but by applying this metaphor of a page as a piece of paper, designers
become its captive, in turn producing ideas such as websites that one can flip
through like pages in a book (next, previous). This places a huge restriction on
the actual âĂŸhyper-” quality of the web.
In order to understand the media we work in, there should be much more
focus on learning and understanding at least the basics of their intrinsic technical
layers. This way designers may acquire more of an insight into the constraints
GUI programs impose on the way they design our messages/media.
3 FLOSS vs. Proprietary, or: Why it is Important to
Study Our Software
The importance of knowledge for fully understanding and using or even designing
the medium may seem quite obvious. It is also important, however, for less obvious reasons. If we consider graphic design a form of communication, or even a
cultural activity, it is highly important for it to be totally free. Free to question, challenge and form critical opinions, free to question authority, free to protest and free
to question and shape the media it works with. Therefore, knowledge of technology should also be considered an important way to gain insight into how political
choices in software may invisibly inhibit a truly free and critical stance. To give an
example, according to Microsoft the new Windows Vista operating system
introduces a breakthrough user experience and is designed to help
you feel confident in your ability to view, find, and organize infor-
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mation and to control your computing experience.1
The last part of this claim in particular can be seen in a totally different light if
combined with the claim the Free Software Foundation makes on badvista.org:
Among other harms, BadVista.org will focus on the danger posed
by Treacherous Computing in Vista. Commonly called Trusted Computing in the industry, it is an attempt to turn computers from machines controlled by their user into machines that monitor their
user and refuse to operate in ways that manufacturers don’t authorize.2
Though the last claim (as well as the first) should be considered an opinion,
their combination gives a nice insight into how at least some technical knowledge
should be considered a necessity to gain insight into the political choices forming
the bases of software. Another way software can constrain its users may be found
in the example of big software companies “donating” computers to schools or institutes and thereby implicitly forcing them to learn, use and thus buy their specific
products. Or as Jaromil put it: “teaching them to use Sony cameras.”3 The strange
thing is that while there exist excellent alternatives to most proprietary software in
the form of Open Source software, this doesn’t seem to catch on very well. Open
Source software is free (libre) software because the source code of the software
is publicly available (or available after one has purchased the software). It is often free (gratis), created and maintained by networked communities of hackers
and programmers. The importance of this software lies in the fact that it makes
the user free to study or change it without being dependent on the original creators. Another important paradigm in this field is Open Standards, meaning the
file formats used are documented and can be freely studied and implemented.
An example of Open Standards can be found in the Open Document Format,
which originates from the xml-based file format used by Open Office. Open Office
is nowadays a fully working, Open Source alternative for closed proprietary software suites like Microsoft Office. The Open Document Format is a freely implementable file format that, because of its Open Standards, can be studied without
restrictions. The value of the transparency and freedom that comes with these
kinds of formats is underlined by the decision of the Dutch government to fully
adopt open source software and open standards by 2006 (the “Motie Vendrik”,
accepted in 2002). In June 2006 the Belgian government even decided to prohibit
closed formats in official government documents by 2008.
Though change takes time, this is also caused by the historic policy of deterring uptake of Open Source and Open Standards by those companies currently
holding the biggest market share. Much of the history of free software is about
1 http://www.microsoft.com/uk/windows/products/windowsvista/features/default.mspx
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2 http://badvista.fsf.org/
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3 in personal conversation with Jaromil, November 2006
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4 Software is the Message
circumventing restrictions put in place by companies. For example, at the time of
writing Microsoft Office still does not support Open Document Format, which may
be an important reason why the Dutch government’s progressive plans decided
back in 2002 have yet to be realised.
And if, for example, Adobe, nowadays the publisher of Flash and the Flashplayer, were to implement support for the (open standard) Scalable Vector Graphics format, the viewer-coverage for this Open Standard file format would instantly
be about 100 percent. Instead they have decided to cease development of their
svg plugin which was one of the few ways people using Internet Explorer were
able to view svg content (since IE, surprisingly, is the only browser which hasn’t
got any sort of basic native svg support). Luckily most other browsers have some
form of native support for svg graphics built in, it’s just too bad that about 70
percent of computer users are still using Internet Explorer.
The same story, by the way, goes for support of the (24-bit) png format (indeed,
also an open standard), which all browsers except IE support natively. With the
release of IE7 this seemed to have improved, except that this version is built not
to install on systems older than Windows XP which, in turn, will not run on older
hardware.
4 Software is the Message
To get an insight into how software shapes our message, it might be nice to take
a look at linguistics, for here the influence of the computer is quite remarkable.
“Browsing” as a word for finding information (as in a library), “system crash” for not
being able to remember something or even “ctrl-z” for undoing a mistake. These
terms have not only become part of the wider language, their influence reaches
far further. The software we use determines how we think. I personally noticed this
phenomenon when I once tried to use sticker-remover to remove some traces of
tape on a coffee-machine. The tape dissolved just fine, but so did the plastic of
the coffee-machine. The first thing that popped into my mind was to press Cmd-z
(I “Think different”).
According to Marshall McLuhan,
The new medium of TV as an environment creates new occupations.
As an environment, it is imperceptible except in terms of its content.
That is, all that is seen or noticed is the old environment, the movie.
But even the effects of the TV environment in altering the entire
character of human sensibility and sensory ratios is completely ignored. The content of any system or organization naturally consists
of the preceding system or organization, and in that degree acts as
a control on the new environment. It is useful to notice all of the arts
and sciences as acting in the role of anti-environments that enable
us to perceive the environment. 7
However, according to media theorist Arjen Mulder, while computers are indeed often said to also remediate the preceding media, they actually are a “metamedium”, a combination of all previous media:
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Only in this case, it is not so much a matter of remediation of all
old and new media, as it is a hybridization, a melting of unequal
media to a new unity. 8
Another example, which a friend with a background in architectural studies
recently pointed out to me, is that with the introduction of each new software used
in architecture, a new trend is born. For example, the release of Maya 3D sparked
blob-architecture, whose shapes were specific to this software and could easily
be traced back to the lines of software code from which they were generated.
This leads to another interesting question: who is the producer and who is
the consumer in this software setup? In a way the software companies are the
producers of the environment in which certain ideas develop. One could argue this
by saying software is just a tool in the process of developing and communicating
ideas, but in the case of Maya, the generative algorithm is created by a software
developer. Isn’t it true that the “designer” is actualising a potential form generated
by the software developer’s algorithm?
Of course this comparison might be seen as an exaggeration, but it illustrates
the basic point very well. What a user/consumer of software is actually doing
is placing his ideas in a preset environment. This works both ways, so (unconsciously) he is also conforming his ideas to this set environment. If we look at the
example of Maya, the ideas of blob-architecture might well be developed according to a certain “zeitgeist”, but by elaborating them with this software the resulting
physical shape becomes far from universal and is, as mentioned, sometimes very
specific to the software used. In this instance we might even wonder who the
actual producer of the blob-building is.
Software always (in a certain way) influences your thinking. Analogous to “the
medium is the message”, the software has become the medium (and thus, the
message).
5 Software Filters the Message
With the invention of the private computer, its developers started searching for
ways to make it understandable to non-scientists. Maybe the most important development in this field has been the desktop metaphor. So far it has seemed to
work fairly well; developers started to put all kinds of these metaphors into software and they made people understand computers better because of the references to existing physical objects. But the problem is that this imposes the idea of
the computer as meta-medium. As a result the computer as medium in itself has
become invisible behind all kinds of brush-metal windows and 3D-push buttons,
and we tend to forget to question their logic. We often take software as a given
fact, something that’s just there.
But software, apart from influencing messages because of it’s logic, has another layer of influence, which is now becoming more obvious every day; politics.
If we communicate using a software structure like the internet, aspects of the
wider world such as free speech become an important issue here, too. That’s
why it is so striking to see software companies functioning as an extension of less
free regimes, such as Google for the government of China. Here Google is developing ways to filter the content of the “free” web, so that its Chinese users will not
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6 OS / Free Software vs. Free Design / Libre
find results that are considered harmful by the Chinese government. (It should
be mentioned here that Google was one of the last search engines to submit to
these demands from the Chinese government, which is both admirable and an
index of the companies” power).
Without necessarily passing judgement on Google or the Chinese government
in this situation, it is a good example of why it is important for us to be able to look
“through” software, to study the environments that manipulate our thoughts and
that manipulate the information that is at the basis of formulating these thoughts.
The inner-workings of Google are a big secret and can therefore in no way be objectively monitored. Hypothetically, what would prevent them from filtering results
on, say, a person-to-person basis, or on an ip-location basis? These examples
might seem far-fetched, but if I search using the term “test” on google.nl I get
different and fewer results using the Safari browser than if I use Firefox (806 million results in Safari vs. 843 million in Firefox). This can be interpreted as at least
some sort of browser-specific filtering already going on. It’s also no big secret
that companies offering gratis services on the internet often generate money by
selling the data they gather through their services.
A friend gave me another recent example of software filtering of the message
that is fuelled by politics: part of his practice as an artist involves researching new
media. Another part involves photography, occasionally containing artistic nudity.
So when a new system like Flickr appeared, he became an early and extensive
user. It offered a very interesting way of combining two of his interests. But when
Flickr was acquired by Yahoo and so became subject to its rules he was asked
to remove his photos because they were considered sexually explicit content.
Though internet companies haven’t at present much to do with the software we
use to create graphic design, the situation is a strong example of the problem
of relying completely on proprietary software. We have no way to monitor how
they work, nor are we able to check what the major software companies might
be planning in the future for their services. Some nowadays repressive regimes
started out as ’Don’t be evil” revolutions (e.g. China) but power seems to have
strange effects on people.4 We should never blindly rely on a particular software
as our main let alone our only platform.
In the field of graphic design Open Source development can be regarded as
a healthy alternative to proprietary software because it offers the possibility of
studying / changing the source code, thereby disclosing how the program works,
and how it may influence its user. This makes users less dependent on the original developer to make changes or solve bugs. Also, because most open source
software uses Open Standards for saving files, users will not likely ’buy in” to a
specific software but are free to exchange files and projects between different
applications. At least, that is the idea of Open Standards.
4 Google’s corporate philosophy
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These are interesting times in the development of Open Source possibilities for
graphic designers. For quite a lot of proprietary software a fairly developed open
source alternative can be found. In the case of inDesign that would be Scribus, for
Photoshop, The Gimp and for Illustrator, Inkscape. Then there are a whole bunch
of less familiar but equally interesting software developments. For the purpose of
giving an overview of the basic design software, however, these three examples
should suffice.
Without wanting to deny the political and philosophical impact of these projects,
a practical issue is that they actually aren’t much more than a “free/libre” clone
of existing proprietary software. The reason for this is simple, as Craig Bradney,
part of the Scribus development team says:
Our aim is not to replace wholesale other applications, but to provide the best DTP experience for Linux users – to provide the same
kinds of tools users have had on other platforms and to use the
inherent strengths of “Open Source Software and Linux/Unix” to
Scribus advantage. 10
Though this is a perfectly legitimate reason for developers to create their software, the problem is twofold: firstly, the focus on “free as in libre”, is easily displaced to “free as in beer”. What is the importance of these developments, beside
the fact that it doesn’t cost money to use them? Of course there is the advantages
of it undermining the monopolistic landscape of (design) software, and that users
are not made dependent on big companies. Although most Linux users are aware
of this, and it may be a key consideration when they choose whether or not to use
a particular piece of software, I have my doubts about how important this aspect
really is to other users. Running Open Office on Windows is a lot less about being “free” and probably a lot more about being “gratis”. Though that’s as good
a reason as any, this can in some ways be compared to using a black market
reproduction of a product that has taken years of research and development. It
looks the same, it works the same, but it’s Open Source. This comparison opens
up another discussion in which one could argue that the way big companies have
been able to become this big and rich is by underpaying their workers and patenting (other) peoples” ideas. Here, a motive could also be found for pleading for the
right to take this knowledge back and make it public property. This is, however,
something which will probably remain a point of contention for a long time, and is
certainly not something I want to pass judgement on here.
The second problem, which is actually more important to me, is that as a clone
of existing software, these open source alternatives also copy the traps and mental models of their properietary counterparts. Therefore, in my opinion, for “free
software” to be a valid term, the open sourcing of closed software by reverseengineering should be seen as only a beginning; a way to make software available as a field of study in order to discover its inner logic; to redevelop it in order
to be really “free as in free speech”, or even thought. This doesn’t seem to be the
aim of the free software movement at the moment. Just as much as the proprietary software it resembles, it focuses on making computing understandable by
hiding it behind metaphors. These metaphors might actually be where the real
problem lies.
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If we take a look, for example, at Pure Data, a software developed as an open
source project intended to work with any data, we see that there is much less
hiding going on. The data is “wired” around by simple lines (like a pipe in the Unix
command line environment), resembling nothing other than a line. Data flowing
around can be manipulated in any conceivable way, if it don’t exist yet, it can be
programmed. This same kind of openness or freedom can also be found in another open source project: Processing. As the website explains: Processing is
an open source programming language and environment for people who want
to program images, animation, and sound. [...] It is created to teach fundamentals of computer programming within a visual context and to serve as a software
sketchbook and professional production tool.
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This description also suggests a shift that seems necessary in current design
education. In order to develop the design profession further in an interesting way
instead of the constant spiral of visual sampling that it is now, a better understanding of media should be developed. Now that everybody can use software, and the
pragmatic (theoretical) technical skills can be coded into computer systems, it
becomes more and more important to develop this software further. Because, if
software is the medium, it will be this software (digital media) that is part of the
future subject of design.
I’m not trying to say here that the formal study of conceptual thinking, or theoretical and technical knowledge, will become obsolete. Merely that, by getting a
better understanding of our media, we will be able to design them better and to
develop the design field further. To enable this understanding, it will be necessary
to stop superimposing physical metaphors on everything computer related. This,
as I have said, is causing an incorrect understanding of our media. This is the
reason why, when constructing a website, designers often fail to use the potential of hypertext and hyper structures. They are trained to create an all inclusive
conceptual idea and to communicate that within the technical possibilities of the
medium (print). This might be why a website is often called a “page” and why
designers often design them as if they were printed (preferably including kerning
and all kinds of custom typefaces). In the digital media this attitude can only be
seen as a dictatorial obsession, because part of (the strength of) digital media
such as hypertext is that it can look different on any computer. Users get a say
in how they would like to use the information you have designed, and therefore
the design should focus more on structure and route than on punctuation. This
obsessive focus on detail might be inherited from the physical world whose design and printing processes have been reproduced in computers. New media are
much more modular.
With the emerging generations of designers having been surrounded by computers all their life, it’s time to step out of representing the physical media within
the computer. Designers should be trained in (at least the basics of) the underlying codes that make up the digital media in order to be able to really understand
and use them. As Florian Cramer states:
The closer the software is to the daily needs and work methods
of programmers and system administrators, the higher typically its
quality. 12
This shows how important it is for designers to start taking a more critical
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stance toward their software and to study it. The best Open Source software
has been written in the field of programmers, simply because they found things
missing or not working the way they wanted it to. Just as designers have been
able to study and develop their processes and methodologies for years, now software (/programming) has become one of these processes and should be studied
and developed the same way and with the same understanding. Maybe that way
designers will learn to develop their own, really “free”, processes and escape the
physical metaphors.
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using the forkable repository
The forkable repository is not at all a stable system. It’s a collection of scripts,
tools, illustrations, documentation, an anarchive, perhaps a giant mess. The collection aims to be archive, production environment, documenation.
From a technical perspective it tries to learn from a more or less time-tested
design approach, that supports the kind of reuse I was looking for in the beginning. This set of design princliples gets to be talked about as the Unix Philosophy
and makes software as reusable as forkable should be.
The Unix Philosophy is present here as not the GNU in UNIX but in GNU/Linux,
operating system and anarchive of software. The collection has been tested so
far with Debian GNU/Linux and Ubuntu.
1 check it out
You should be running GNU/Linux with subversion1 installed.
sudo aptitude install subversion
Do a checkout:
svn co http://code.lafkon.net/subversion/forkable
You will be asked for username and password. If you do not have already one,
please send an email. Because we are currently on a test run, the subversion
repository is not completly open to the public while you can browse everything at
http://www.forkable.eu. The checkout may take some time because there is
a rather large collection of vector illustrations from http://vektordb.lafkon.
net included.
2 check the system
Because, what is forkable at the moment, is a diversity of tools, glued together
mostly inside bash scripts, there is a bunch of software that is actually needed to
get everything working.
1 What is subversion?
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using the forkable repository
prepare your LATEX installation
First you need a TEX installation for Debian and Ubuntu that is texlive.
sudo aptitude install texlive
Add the forkable TEXMF path to your local tex installation:
Open /etc/texmf/texmf.cnf with a text editor.
sudo nano /etc/texmf/texmf.cnf
Add the following:
TEXMFFORKABLE = /path/to/your/forkable/folder/utils/latex/TEXMF
look for a line something like this:
TEXMF = $TEXMFCONFIG,$TEXMFVAR,$TEXMFHOME,$TEXMFSYSCONFIG,!!$TEXMFSYSVAR,
and the variable for the forkable TEXMF folder:
TEXMF = $TEXMFCONFIG,$TEXMFVAR,$TEXMFHOME,$TEXMFFORKABLE,$TEXMFSYSCONFIG,
You must do this so that LATEX finds the packages that are distributed with
forkable.
Reload TeX.
sudo texhash
install software
you need to have java installed.
sudo aptitude install sun-java5-bin
you can the check_the_system.sh script to test which software you need
to install.
3 folder structure
generators Like the name says things that generate something. This is most
active part of forkable
release Finished stuff that is not really used anymore like a print layed book.
utils Things that are usefull. Has become right now kind of a wastedump, for all
stuff not matching categories.
i
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i/free + i/non-free For the distribution of projects i decided to differentiate data
into free and non-free. Most projects include data that is the property of a third
party like logos and therefore can not be put under free licenses. for the public svn
checkout the non-free directories are excluded. to get layouts and scripts working
nontheless these files are replaced by free supplementals.
i/*/v vector graphics. see jon phillips
i/*/p raster images to be included. p for pixel
i/tmp local temporary directory.
i/a – follow the donkey path
Der Esel geht im Zickzack, döst ein wenig, blöde vor Hitze und
zerstreut, geht im Zickzack, um den großen Steinen auszuweichen,
um sich den Anstieg sanfter zu machen, um den Schatten zu suchen.
13
i/a is a recursive link i use so far for linking documents. this link stays the
same for all documents what makes it easy to include documents into each other
without specifying an absolute link.
as far as i know latex resolves links not relative to the document path but relative to the root document.
if i include in release/osk/Offener_Schaltkreis.tex via \input the document generators/lacmachine/doc/lacmachine.tex that uses a graphic via \include{i/v/graphic.pdf
that is stored in generators/lacmachine/doc/i/v/graphic.pdf i can’t release/osk/Offener_Schaltkreis.tex because it searches for an image i/v/graphic.pdf that obviously does not exist. by providing each latex directory through a symlink with
the path i/a i can link images with the path i/a/generators/lacmachine/doc/i/v/graphic.pdf, that is the same for release/osk/Offener_Schaltkreis.tex AND generators/lacmachine/doc/lacmachine.tex.
Better solution welcome.
o
o/non-free output rendered with proprietary parts. not in the subversion repository. online at http://www.forkable.eu
o/free output directories used for scripts in the subversion directory.
17
flexcommentbox
1 use
This command creates a box that can be moved around the page.
\flexcommentbox{.5\paperwidth}{.5\paperheight}{.5\textwidth}
\flexcommentbox{1}{2}{3}{4}
•
•
•
•
1 is the X position
2 is the Y position
3 is the width
4 is what is inside (not outside) the box
Height adjusts to the content of the box.
2 macro code
\ newcommand \ flexcommentbox [4]
{%
\ deffootnote [1.5 em ]{1.5 em }{1 em }{\ textsuperscript {}}
\ footnotetext {
\ setlength \ fboxsep {10 pt }%
\ vspace {#2}
\ makebox [.5\ textwidth ][ l ]{
\ hspace {#1}
\ parbox {#3}{
\ vspace { -1\ textheight }
\ colorbox { white }{ %
{\ small
\ parbox {#3}{
\smallskip
#4 %
\smallskip
}
}
}
}
}
}
}
3 examples
19
\flexcommentbox{.1\textwidth}{.2\textheight}{.5\textwidth}{}
\flexcommentbox{.5\textwidth}{-.2\textheight}{.5\textwid
fullpage
1 use
This command creates a single image page. Takes 5 parametres.
\fullpage{path/to/image}{1.5}{80,angle=45}{120}{optional pag
\fullpage{1}{2}{3}{4}{5}
•
•
•
•
•
1 is the path to an image
2 is the scale
3 is the x offset
4 is the y offset
5 is an optional page command
Height adjusts to the content of the box.
2 macro code
\ newcommand {\ fullpage }[5]{
\ newpage
{\ renewcommand {\footnoterule}{\ rule {0 pt }{0 pt }} % REMOVE FOOTNOTERULE
\ includepdf [ scale =#2 , offset =#4 #3 , pagecommand ={
\ thispagestyle { empty }
#5
\ newpage
}]
{#1}
} % REMOVE FOOTNOTERULE
\ renewcommand {\footnoterule}{\ vspace *{10 pt }
% REMOVE FOOTNOTERULE
\hrule width 0.4\ columnwidth \ vspace *{10 pt }}
% REMOVE FOOTNOTERULE
}
3 examples
21
\fullpage{path/to/image}{1.5}{80}{120}{\flexcommentbox}
\fullpage{path/to/image}{1.5}{80}{120}{\flexcommentbox}
You can hack your own command by sneaking a parameter into the vertical offset brackets.
For more parametres see the pdfpages package
\fullpage{path/to/image}{1.5}{80,angle=45}{120}{\flexcommentbox}
doublepage
1 use
This command spreads an image over a double page. Takes 3 parametres, automatic recognition of even and odd pages is buggy, has been removed and should
be done by eye and hand.
\doublepage{path/to/image}{2.5}{-200}
\doublepage{1}{2}{3}
• 1 is the path to an image
• 2 is the scale factor
• 3 is the vertical
2 macro code
\ newcommand {\ doublepage }[3]{
\ ifthispageodd {
%\ hardpagebreak
% DOPPELSEITE %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\ includepdf [ scale =#2 , offset = -260 #3]
{#1}
{#1}
% DOPPELSEITE %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\ twocolumn [] % DEATH PROOF PAGEBREAK
}{
% DOPPELSEITE %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
{#1}
{#1}
% DOPPELSEITE %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\ twocolumn [] % DEATH PROOF PAGEBREAK
\ clearpage
}}
3 examples
25
gridpage
1 use
This command creates a 3x3 grid. 9 is the maximum number of arguments LATEX
takes by default.
\grid{einmal}{zweimal}{dreimal}{viermal}{f"unfmal}{sechsmal}
\gridpage{1}{2}{3}{4}{5}{6}{7}{8}{9}
•
•
•
•
•
•
•
•
•
1 is left top
2 is left center
3 is left right
4 is center top
5 is center center
6 is center bottom
7 is right top
8 is right center
9 is right bottom
2 macro code
\ newcommand {\ grid }[9]{ %
\ hspace { -.5\ universalgrid }
\ begin { picture }(0 ,0) %
\ put (0.2 , -2.4){#1} % |}
\ put (0.2 , -1.2){#4} % |}
\ put (0.2 , -3.6){#7} % |}
\ put (1.3 , -2.4){#2} % |}
\ put (1.3 , -1.2){#5} % |}
\ put (1.3 , -3.6){#8} % |}
\ put (2.4 , -2.4){#3} % |}
\ put (2.4 , -1.2){#6} % |}
\ put (2.4 , -3.6){#9} % |}
\end{ picture }%
\ twocolumn [] % DEATH PROOF PAGEBREAK
}
3 examples
29
gridpage
viermal
fünfmal
sechsmal
einmal
zweimal
dreimal
siebenmal
achtmal
neunmal
30
3 examples
31
gridpage
32
3 examples
33
gridpage
34
graphic
1 use
This command lets you include a graphic. It takes 5 parametres.
\graphic{0}{0}{400}{400}{path/to/graphic}{1pt}
\graphic{1}{2}{3}{4}{6}
•
•
•
•
•
•
1 is x start for the crop box
2 is y start for the crop box
3 is x end for the crop box
4 is y end for the crop box
5 is the path to the graphic
6 is weight for the border around the image
2 macro code
\ newcommand {\ graphic }[7]{
\ setlength \ fboxsep {0 pt }
\ setlength \ fboxrule {#7}
\ fbox {
\ includegraphics [ viewport =#2 #3 #4 #5 , clip , width =#6]{#1}
}
}
3 examples
35
graphic
36
3 examples
37
graphic
38
scalefontXtimes
1 use
This writes simply writes a string and an upcounting \scalefont{.} into a
texfile.
# !/ bin / bash
TEXGENERATED =o/ scalefontXtimes . tex
COUNT =10
rm $TEXGENERATED
while [ $COUNT -lt 90 ]
do
DEZ =‘echo 000 $COUNT | rev | cut -c 1 -2| rev ‘
SCALEFACTOR =‘echo $DEZ | cut -c 1 ‘. ‘echo $DEZ | cut -c 2 -3 ‘
echo " {\ scalefont {" $SCALEFACTOR "}" >> $TEXGENERATED
echo " Networked Media Master }"
>> $TEXGENERATED
COUNT =‘expr $COUNT + 5‘
done
exit 0;
39
scalefontXtimes
Networked Media Master
Networked Media Master
worked Media Master
dia Master
Net-
Networked Me-
Networked Media
Master Networked Me-
dia Master Networked
Media Master Net-
worked Media Master Networked Me-
dia Master Net-
worked Media Master Networked
Media Master
Networked Media Master Net-
worked Media Master Net40
1 use
worked Media Master
Networked
Media Master Networke
Media Master
41
Albert
# !/ bin / bash
TEXGENERATED = graphics . tex
COUNT =0
ROTATION =0
rm $TEXGENERATED
do
DEZ =‘echo 000 $COUNT | rev | cut -c 1 -2| rev‘
# echo "\ scalefont {" $SCALEFACTOR "}" >> $TEXGENERATED
# echo " Networked Media Master "
>> $TEXGENERATED
echo "\ graphic { albert & tineke . jpg }" >> $TEXGENERATED
echo " {0}{0}{500}{300 , angle =${ ROTATION }}{ $SCALEFACTOR \ linewidth }" >>
$TEXGENERATED
echo " {0 pt }" >> $TEXGENERATED
echo "\ graphic { ISHARD . jpeg }" >> $TEXGENERATED
$TEXGENERATED
echo "\ graphic { rdam . jpg }" >> $TEXGENERATED
$TEXGENERATED
$TEXGENERATED
echo " {0}{0}{505}{300 $RANDOM
, angle =${ ROTATION }}{ $SCALEFACTOR \ linewidth }" >> $TEXGENERATED
echo " ROTTERDAM = HARD " >> $TEXGENERATED
echo "{ ROTTERDAM = HARD }" >> $TEXGENERATED
ROTATION =‘expr $ROTATION + 36 ‘
done
exit 0;
43
1 blaaablabla
hahahaha
7777777
ROTTERDAM = HARD ROTTERDAM = HARD
ROTTERDAM = HARD ROT-
TERDAM = HARD
ROTTERDAM = HARD ROTTERDAM =
HARD
ROTTERDAM = HARD
ROTTERDAM = HARD
Birgit
# !/ bin / bash
TEXGENERATED = forgrid . tex
COUNT =1
rm $TEXGENERATED
echo "\ grid " >> $TEXGENERATED
do
for i in {1..9}
do
number1 =$[ (
number2 =$[ (
number3 =$[ (
number4 =$[ (
number5 =$[ (
$RANDOM
$RANDOM
$RANDOM
$RANDOM
$RANDOM
%
%
%
%
%
200 ) + 1 ]
200 ) + 1 ]
373 ) + $number1 ]
373 ) + $number2 ]
10 ) + 1 ]
echo "{" >> $TEXGENERATED
echo " \ graphic { broadwayy . pdf }" >> $TEXGENERATED
echo " {${ number1 }}{ ${ number2 }}{ ${ number3 }}{ ${ number4 }}{ $SCALEFACTOR \
universalgrid }" >> $TEXGENERATED
for j in {1.. ${ number5 }}
do
echo " \ graphic { broadwayy . pdf }" >> $TEXGENERATED
echo " {${ number2 }}{ ${ number1 }}{ ${ number3 }}{ ${ number4 }}{0.5\ universalgrid
}" >> $TEXGENERATED
done
echo "}" >> $TEXGENERATED
done
echo "\ newpage " >> $TEXGENERATED
done
exit 0;
59
60
61
62
63
64
Dar
1 The Guide for the manual
3 Dosing and how to use
The word “voda” (water) can, as a vocal inscription,
be interpreted in endless ways, by varying specific
sounds, rhythmically, by permutations, paying attention to the quality, length, intensity of the sound....
Only several possibilities will be questioned here.
This manual should be used as a combined sheetriver and lake writing*, intended for verbal interpretation. Every single letter-voice lasts for 1 second. The pause lasts in accordance to the number of
voices it stands instead of. The size corresponds to
sound intensity, and in the case of more successive
voices, a flow, fluid sound should be maintained.
Naturally, virtuosity shines through and there is a
great level of creative interpretation which can be
witnessed through gestures, attitude, dramatic elements, melodiousness ... Screaming is allowed. Typos represent the parts which are to be emphasized.
It is considered to have an immensely bigger effect on the younger population (i.e. if used from an
early age). That doesn’t mean that it has no effect on
adults, but it is less intense, due to some well constructed mechanisms of defense, prejudice, rejection
of new methods, change of linguistic identity and
habitual behavioral patterns. It showed interesting
results in the field of breaking through some verbal regularities and limitations. The impact of that
verbal flexibility on the thinking progress is being
examined momentarily, because it is considered to
have a beneficial effect in that field. There are also
indications of a larger percentage of brain activity
after longer use, which is certainly interesting, because humans use the minimum of their brain potential (2-3 percent, mostly passively). In the beginning it is necessary to read the manual several times
a day, both silently and out loud, in order to adapt
the vocal tract. Later, reading out fluently once a
day is sufficient. It’s possible to read mutually (with
one person), or collectively (with several persons),
simultaneously or completely separately, hierarchically or anarchically, in agreement or entirely free,
in improvisation (so-called jazz reading).
1 Effect
The manual for reading the word “voda” has a beneficial effect on the lip region, throat muscles, verbal
flexibility and diction, helps in the removal of rigidness in the vocal tract and potentially leads to creative forming of voices and sound units of a broad
spectrum, starting from monosyllabic and polysyl4 Counter indications and side-effects
labic, reaching complex sound units. In several cases
it has even led to the successful elimination of dyslexia, None have been proven so far, except among peoamnesia and autism, awakening the primal urge for ple with obsessive-compulsive disorder that can be
communication (which is in relation to the speaking triggered by use of the manual. It may also cause a
patterns of the collective unconscious). The effect vigorous, overwhelming creative urge which can be
can be felt immediately after the first reading.
controlled by paralleled reading of tabloids. There
were some cases of water on the and kidney gravel
among people with a predisposition toward psycho2 Uses
somatic diseases. There was one case of sea sickHabitual phraseology, uniform intonation, the spe- ness, but this is attributed to the domain of coinciech of merged vocals and mouth half open, stutter- dence (casus coincidentalis). It is recommended to
ing, losing of the sensibility for sonority, construc- pregnant women, but it is necessary to know that the
use of this manual, due to its acceleratory effect, can
tions of emotional dullness.
65
lead to premature birth. Not to be mixed with neither
alcohol nor psychoactive substances, because it can
lead to paranoid aspirations, and in severe cases to
verbal character separation of the personality.
5 Storage
Keep in a dry place at temperatures ranging from 5 to the limit of combustion, although optimally it
should be kept within moderate continental climate
of the middle upper class of democratic societies in
the post communist period. An issue for societies in
transition hasn’t been made yet, because it wasn’t
considered as a long term period. However, a new
issue is under serious consideration at the moment,
due to the movement of those societies on a path picturesquely named circulus vitiosus. Keep out of the
reach of pets, on a shelf or a workspace. Naturally, it
can be carried in a purse/briefcase, schoolbag, sports
bag, grocery bag, backpack, pouch or sack, but the
ambient for reading is of vital importance.
6 Best before
: There is no expiration date, which means that the
product can be used as long as eyesight and hearing
permit.
*rec̆ni is a homonym in Serbian meaning both
something in relation to word, and river ...
import sys , random
voda = ’voda ’
# def space ( number ):
#
gap = ""
#
for i in range ( number ):
#
gap = gap + " "
#
return gap
f = open (’ water .tex ’, ’w ’)
header = """\ documentclass [8 pt ]{ scrbook }
\ usepackage {i/a/ utils / latex / sty /LSI -191 x235 + crop }
\ usepackage {i/a/ workshop / bag / Boxes_and_Glue }
\ usepackage {00 _NEWCOMMANDS }
"""
f. write ( header )
f. write (" \\ begin { document }\ n")
# def letterfill () :
def pgfill (a ,b ,c):
for i in range (a):
f. write ("\ hfill ")
for i in range (b):
f. write (" \\ hspace {" + str ( random . random
() +0.001) + " \\ textwidth }" + voda
[ random . randint (0 ,c) ]* random .
randint (0 ,50) )
m = i
for j in range (m):
if random . randint (0 ,10) == 1:
f. write (" \\ vfill \n")
m = i +1
#
f. write ("\ scalefont {0.3}")
pgfill (60 , 1, 3)
pgfill (1 , 50 , 1)
# for i in range (20) :
#
pgfill (i , random . randint (0 , i) * 2,i%3 ,i)
f. write ("\n \\ end { document }")
66
vvv
vv
vv
v
vv
vv
vvv
vvv
vvvv
vvv
vvv
ooo
ooo
ooo
vvv
oo
oooo
vv
v
vvv
dddd
vvv
oooo
vvv
vvvv
vvvvv
vv
vv
vv
vvvv
vvvv
vvvvv
oo
dd
oo
ddd
ooo
o
o
ddd
vvvv
vv
vvvvv
vvvvv
vvvvvv
oo
vv
vvvvvvv
o
o
o
oooo
vvvv
vvvv
ooooo
o
oooo
o
ooo
vv
oooo
vvvv
ooooo
ooo
vvvvvvv
vvvvv
ooooo
vvvvv
vvvvv
oooooo
oooooo
vvvvvv
vvvvv
vvvv
ooooooo
oo
vvvvvv
vvvvvvv
vvvv
vvvvvvv
vvvvv
vvvvvvv
ooooo
vvv
vvvvvv
vvvvvvv
oooooo
oooo
vvvvv
ooo
ooo oo
vvvvvv
oooooo
oo
vv
vvvvv
vv
vvvv
oooo
vvvvvvv
vv
oooooo
ooooooo
vvv
ooo
ooooooo vvvvvv
vvvvv
ooo
o
vv
v
vvvvv
vv
vvv
oo
vvvvvvv
oooo
oooo
o
vvvvvv
ooo
oooooo
vvv
vvv
o
vvvvvvvv
vvvvvvv
vvvvvvv
ooo
ooooooo
vvvvvvv
dd
ooooooo
v
ddd
oo
vvvv
ddd
ooooooo
dddd
vvv
v
vvvvv
dddd
dddddddd
dddddd
vv
dddddd
ooooooo
vvvvvvvvvv
vvv
oooooo
vvvv
vvvvvvvvv
vv
vvvvv
oo
vvvvvvvvv
v
oo
oooooooooo
oooo
dd
d
v
vv
vvv
aaa
aa
aaa
aaaa
dd
aaa
oooo
o
vvvv
aaa
a
oo
ddd
dd
dd
dd
aaaa
dd
v
a
dd
aa
ooo
vvvv
vvv
vvv
vvv
d
ooo
ddd
aaaa
dddd
d
v
aaaa
ddd
dddd
aa
ooo
o
oooo
aaaa
vvv
a
vvvv
vvvv
vvv
vvvvvvvvvvv
dddddd
vvvvvvv
oooooooooooooo
vvvvvvvvvvvvvv
ooooooo
ooooooooo
vvvvvvvv
oooooooooooooo
ooooooooooooo
ooooooooooooooooooo
oooooooooooooooooo
o
v
vvvvvvvvvvvvvvvvv
oooooooooo
vvvvvv
vvvvvv
o
ooo
ooooooooooooo
vvvvvvvvvvvvvvvvvvv
vvvv
vvvvvvv
oooooooooooooooo
oo
vvvvvvvvvvv
oooo
ooooooooo
vvvvv
oooooooooooooooo
vvvv
vvvvvvvvvvvvvvvvv
vvv
vvvvvvvvvvvvvv
v
vvvvvvvvvvvv
ooooo
o
vvvvvvvvvvvvvvvvvv
oooooooooooooooooo
vvvvvvvvvvvvv
oooo
oooooooo
vvvvvvvvvvvvv
vvvvvvvvvvvv
vvvvvvvvvvvvvvv
vvvvvvvvv
oooooooooo
vvvvvvvvvvvvvvvvvv
vvvvvvvvvvvvvv
vvvvvvvvvvv
ooooo
vvvvvvvvvv
vvvvvvv
vvvvv
vvvvvvvvvvvvvvvvv
vvvvvvvvvvvvvvvvv
oooo
oooooooo
v
vvvvvvvvv
oo
vvvvvvvv
vvvvvvvvvvvv
oooooo
vvv
vvv
vvv
vvv
ooooo
ooooooooooo
vvvvvvvv
vvvvv
oooooooo
oooooooooooooooo
vvvvvvvvvvvvvv
oooooooooooooooo
vvvvvvvvvvvvvvvvvv
oooooooooo
vvvvvv
vvvvvvvvvvvvvvvvvvv
vvvvvvvv
vvvvvvvvvv
ooooooo
oooooooooo
vvvvvvvvvvv
ooooooooooooooooo
vvvvvvvvvvvvvvvv
oooooooooooooooooo
vvvvvvvvvvvvvvv
vvvvvvvvvvvvvvvvvv
ooooooooooooo
vvvvvvvvvvvvvvvv
oooooooooo
vvvvvvvvvvv
vvvvvvvvvvvvvvvvv
ooooooo
vvvvvvvvvvv
vvvvvvvvvvvvv
vvvvvvvv
oooooooo
Emanuele
import random
numpage =10
for i in range ( numpage ):
print " \\ section { square }"
print " \\ begin { picture }(0 ,0) "
for c in range ( random . randint (1 , 50) ):
print " \\ put ("+ str ( random . randint (0 , 30) /10.0) +" ,"+ str ( random .
randint (0 , 50) / -10.0) +"){"
print " \\ includegraphics [ scale ="+ str ( random . randint (1 , 100) /100.0)
+" , angle ="+ str ( random . randint (0 ,360) )+" ]{ i/a/ utils /
graphics / blank / black . pdf }"
print "}"
print " \\ end { picture }"
print " \\ newpage "
73
import random
numpage =10
print " \\ section { square }"
print " \\ begin { picture }(0 ,0) "
for c in range ( random . randint (1 , i +1) ):
print " \\ put ("+ str ( random . randint (0 , c +1) /10.0) +" ,"+ str ( random .
randint (0 , c +1) / -10.0) +"){"
print " \\ includegraphics [ scale ="+ str ( random . randint (1 ,10) /10.0) +" ,
angle ="+ str ( random . randint (0 ,360) )+" ]{ i/a/ utils / graphics /
blank / black . pdf }"
print "}"
74
import os
import random
numpage =10
colors = [’red ’,’ pink ’,’ purple ’]
print
print
print
print
print
" \\ section {} "
" \\ Huge \\ textbf { dT (Y) Tb }"
" \\ newline "
" \\ Huge \\ textbf { Feed The Bears !} "
" \\ begin { picture }(0 ,0) "
randomop = str ( random . randint (1 ,10) /10.0)
randomcolor = colors [ random . randint (0 ,2) ]
os . system (’ convert - size 100 x60 xc : transparent - fill ’+ randomcolor
+’ - stroke white - draw " polygon 0 , ’+ str ( random . randint (0 ,
60) )+’ ’+ str ( random . randint (0 , 100) )+ ’ ,0 60 , ’+ str ( random .
randint (0 , 60) )+’ 100 , ’+ str ( random . randint (0 , 60) )+’" flatten draw_polygon ’+ str (c)+ ’. gif ’)
os . system (’ autotrace -corner - threshold 1000 draw_polygon ’+ str (c)
+ ’. gif -output - file draw_polygon ’+ str (c)+ ’. pdf ’)
randint (0 , 50) / -10.0) +"){"
print " \\ includegraphics [ scale =1 , angle ="+ str ( random . randint
(0 ,360) )+" ]{ draw_polygon "+ str (c)+". pdf }"
print "}"
randint (0 , 50) / -10.0) +"){"
print " \\ includegraphics [ scale ="+ str ( random . randint (1 , 100) /100.0)
+" , angle ="+ str ( random . randint (0 ,360) )+" ]{ i/a/ utils /
graphics / blank / black . pdf }"
print "}"
75
import os
import random
numpage =10
print
print
print
print
print
" \\ section {} "
" \\ newline "
os . system (’ convert - size 100 x60 xc : transparent - fill black - stroke
black - draw " polygon 0 , ’+ str ( random . randint (0 , 60) )+’ ’+
str ( random . randint (0 , 100) )+ ’ ,0 60 , ’+ str ( random . randint (0 ,
60) )+’ 100 , ’+ str ( random . randint (0 , 60) )+’" - flatten
draw_polygon ’+ str (c)+ ’. gif ’)
if (c %2==0) :
print " \\ put ("+ str ( random . randint (0 , 30) / -10.0) +" ,"+ str (
random . randint (0 , 50) / -10.0) +"){"
print " \\ includegraphics [ scale =1 , angle ="+ str ( random .
randint (0 ,360) )+" ]{ draw_polygon "+ str (c)+". pdf }"
print "}"
random . randint (0 , 50) / -10.0) +"){"
print " \\ includegraphics [ scale ="+ str ( random . randint (1 , 50)
/100.0) +" , angle ="+ str ( random . randint (0 ,360) )+" ]{ i/
a/ utils / graphics / blank / black . pdf }"
print "}"
else:
print " \\ put ("+ str ( random . randint (0 , 30) /10.0) +" ,"+ str (
random . randint (0 , 50) / -10.0) +"){"
print "}"
random . randint (0 , 50) / -10.0) +"){"
print "}"
76
1
dT(Y)Tb
Feed The Bears!
77
2
dT(Y)Tb
Feed The Bears!
78
3
dT(Y)Tb
Feed The Bears!
79
4
dT(Y)Tb
Feed The Bears!
80
5
dT(Y)Tb
Feed The Bears!
81
6
dT(Y)Tb
Feed The Bears!
82
7
dT(Y)Tb
Feed The Bears!
83
8
dT(Y)Tb
Feed The Bears!
84
9
dT(Y)Tb
Feed The Bears!
85
10
dT(Y)Tb
Feed The Bears!
86
Loredana
import os
import random
numpage =10
print
print
print
print
print
" \\ section {} "
" \\ newline "
os . system (’ convert - size 100 x60 xc : transparent - fill black - stroke
black - draw " polygon 0 , ’+ str ( random . randint (0 , 60) )+’ ’+
str ( random . randint (0 , 100) )+ ’ ,0 60 , ’+ str ( random . randint (0 ,
60) )+’ 100 , ’+ str ( random . randint (0 , 60) )+’" - flatten
draw_polygon ’+ str (c)+ ’. gif ’)
if (c %2==0) :
random . randint (0 , 50) / -10.0) +"){"
print "}"
random . randint (0 , 50) / -10.0) +"){"
print "}"
else:
random . randint (0 , 50) / -10.0) +"){"
print "}"
random . randint (0 , 50) / -10.0) +"){"
print "}"
87
88
89
90
91
Megan
[
import random , sys
visual poetry
of
was
still
header = is’’’\
documentclass [8tends
pt ]{
scrbook }
\ usepackage {i/a/ utils / latex / sty /LSI
-191 x235 + crop }
\ usepackage {i/a/ workshop / bag /
Boxes_and_Glue }
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visual poetry ’, ’blurs ’, ’the
distinction ’, ’ between art ’, ’
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poetry ’, ’is still ’, ’
recognizable ’, ’as poetry ’, ’
being composed ’, ’of ’, ’purely
’, ’ typographic ’, ’ elements ’, ’
visual poetry ’, ’is generally ’,
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’, ’ remains some ’, ’debate ’, ’
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type’, ’( or sub - category ) ’, ’of
concrete ’, ’poetry ’, ’and ’, ’
the last ’, ’view ’, ’( adopted in
’, ’ this article ) ’, ’is that ’,
’ visual poetry ’, ’has ’, ’
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form distinct ’, ’ from concrete
’, ’poetry ’, ’this ’, ’view ’, ’
is supported ’, ’by work ’, ’
identified ’, ’as visual ’, ’
poetry ’, ’in which ’, ’
typographic ’, ’ elements ’, ’are
’, ’ secondary ’, ’to visual ’, ’
elements ’, ’are minimal ’, ’or
in some ’, ’cases ’, ’are absent
’, ’ altogether from ’, ’the work
’, ’!’, ’?’, ’!’, ’?’, ’!’,
’? ’]
as
by Fluxus
it is
in which
with itvisual poetry
described
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purely
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sometimes the work
art
whereas
\\ begin { document }
referred to
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blurs
intermedia
heavily influenced
}
images and symbols
visual
poetry
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\\ newcommand {\\ tib }[1]{
\ colorbox { black }{\ color { white }# 1}
}
’’’
f = open (’ mypage .tex ’, ’w ’)
poetry
f. write ( header )
is
and visual poetry
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that predates
f. write ( ’\\ begin { picture }(0 ,0) \n\n ’)
of text
# These words are from poems from
Shakespeare , Sir William Scott
and Sappho
in conveying
# let = [’ blow ’, ’thou ’, ’winter ’, ’
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is ’, ’not ’, ’keen ’, ’oh !’, ’
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come ’, ’out ’, ’of ’, ’the ’, ’
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all ’, ’ unarmed ’, ’and ’, ’he ’, ’
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’, ’ warning ’, ’as ’, ’a ’, ’
whirlwind ’, ’swoops ’, ’on ’, ’an
’, ’oak ’, ’love ’, ’shakes ’, ’my
’, ’heart ’ ]
# These words are from the Wikipedia
page on Visual Poetry
let = [’ visual ’, ’poetry ’, ’is poetry
’, ’or ’, ’art ’, ’in which ’, ’
the visual ’, ’ arrangement ’, ’of
text ’, ’ images and symbols ’, ’
to blur
work
was synonymous
the intended
93
for i in range (50) :
pos = random . randint (0 ,8)
letter = let [ pos ]
del let [ pos ]
#
print letter ,
f. write (" \\ put ("+ str ( random .
random () ) + " , "+ str (
random . random () -1) + ") {\\
tib {" + letter + " }}\ n")
f. write ( ’\n \\ end { picture }\n ’)
f. write ( ’\\ end { document }\n ’)
94
import random , sys
header = ’’’\ documentclass [8 pt ]{ scrbook }
\ usepackage {i/a/ utils / latex / sty /LSI -191 x235 + crop }
\ usepackage {i/a/ workshop / bag / Boxes_and_Glue }
\\ newcommand {\\ tib }[1]{
\ colorbox { black }{\ color { white }# 1}
}
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\ setlength {\ unitlength }{.5\ paperwidth }
’’’
f = open (’ mypage .tex ’, ’w ’)
f. write ( header )
f. write ( ’\\ begin { picture }(0 ,0) \n\n ’)
# These words are from poems from Shakespeare , Sir William Scott and Sappho
# let = [’ blow ’, ’thou ’, ’winter ’, ’wind ’, ’art ’, ’not ’, ’so ’, ’unkind ’, ’as ’, ’
mans ’, ’ ingratitude ’, ’thy ’, ’tooth ’, ’is ’, ’not ’, ’keen ’, ’oh !’, ’young ’,
’ Lochinvar ’, ’is ’, ’come ’, ’out ’, ’of ’, ’the ’, ’west ’, ’ through ’, ’all ’, ’
the ’, ’wide ’, ’border ’, ’his ’, ’steed ’, ’was ’, ’the ’, ’best ’, ’and ’, ’save
’, ’his ’, ’good ’, ’ broadsword ’, ’he ’, ’ weapons ’, ’had ’, ’none ’, ’he ’, ’rode
’, ’all ’, ’ unarmed ’, ’and ’, ’he ’, ’rode ’, ’all ’, ’alone ’, ’ without ’, ’
warning ’, ’as ’, ’a ’, ’ whirlwind ’, ’swoops ’, ’on ’, ’an ’, ’oak ’, ’love ’, ’
shakes ’, ’my ’, ’heart ’ ]
# These words are from the Wikipedia page on Visual Poetry
let = [’ visual ’, ’poetry ’, ’is poetry ’, ’or ’, ’art ’, ’in which ’, ’the visual ’, ’
arrangement ’, ’of text ’, ’ images and symbols ’, ’is ’, ’ important ’, ’in
conveying ’, ’the intended ’, ’ effect of ’, ’the work ’, ’it is ’, ’ sometimes ’,
’ referred to ’, ’as concrete ’, ’poetry ’, ’a term ’, ’ that predates ’, ’ visual
poetry ’, ’and ’, ’at one time ’, ’was synonymous ’, ’ with it ’ ’ visual poetry ’,
’was ’, ’ heavily influenced ’, ’by Fluxus ’, ’ which is ’, ’ usually ’, ’
described ’, ’as ’, ’ being intermedia ’, ’ intermedia ’, ’work ’, ’tends ’, ’to
blur ’, ’the distinctions ’, ’ between different ’, ’media ’, ’and visual poetry
’, ’blurs ’, ’the distinction ’, ’ between art ’, ’and text ’, ’ whereas ’, ’
concrete poetry ’, ’is still ’, ’ recognizable ’, ’as poetry ’, ’ being composed
’, ’of ’, ’purely ’, ’ typographic ’, ’ elements ’, ’ visual poetry ’, ’is
generally ’, ’ much less ’, ’text - dependent ’, ’visual ’, ’poems ’, ’ incorporate
’, ’text ’, ’but ’ ’the text ’, ’may have ’, ’ primarily ’, ’a visual ’, ’function
’, ’visual ’, ’poems ’, ’ often incorporate ’, ’ significant ’, ’ amounts ’, ’of
non - text ’, ’ imagery ’, ’in addition ’, ’to ’, ’text ’, ’there ’, ’ remains some ’,
’debate ’, ’ regarding ’, ’the distinction ’, ’ between concrete ’, ’poetry ’, ’
and visual ’, ’poetry ’, ’there ’, ’are ’, ’ three dominant ’, ’ views regarding ’,
’the issue ’, ’one view ’, ’is ’, ’ that visual ’, ’ poetry is ’, ’ synonymous
with ’, ’ concrete ’, ’poetry ’, ’a second ’, ’view ’, ’is ’, ’that ’, ’visual ’, ’
poetry ’, ’is ’, ’a type’, ’( or sub - category ) ’, ’of concrete ’, ’poetry ’, ’and
’, ’the last ’, ’view ’, ’( adopted in ’, ’ this article ) ’, ’is that ’, ’ visual
poetry ’, ’has ’, ’ evolved into ’, ’a visual ’, ’ form distinct ’, ’ from concrete
’, ’poetry ’, ’this ’, ’view ’, ’is supported ’, ’by work ’, ’ identified ’, ’as
visual ’, ’poetry ’, ’in which ’, ’ typographic ’, ’ elements ’, ’are ’, ’ secondary
’, ’to visual ’, ’ elements ’, ’are minimal ’, ’or in some ’, ’cases ’, ’are
absent ’, ’ altogether from ’, ’the work ’, ’!’, ’?’, ’!’, ’?’, ’!’, ’? ’]
for i in range (50) :
pos = random . randint (0 ,8)
letter = let [ pos ]
del let [ pos ]
#
print letter ,
f. write (" \\ put ("+ str ( random . random () ) + " , "+ str ( random . random () -1) + ") {\\
95
tib {" + letter + " }}\ n")
f. write ( ’\n \\ end { picture }\n ’)
f. write ( ’\\ end { document }\n ’)
96
[
was
is still
visual poetry
of
as
tends
by Fluxus
it is
described
usually
important
the distinctions
in which
with itvisual poetry
or
arrangement
which isconcrete poetry
purely
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being composed
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art
whereas
referred to
as
concrete
effect
of a term
between different
and
at one time
blurs
intermedia
heavily influenced
images and symbols
visual
poetry
being intermedia
poetry
is
of text
in conveying
and visual poetry
is poetry
that predates
to blur
work
was synonymous
the intended
97
Reneeom
# !/ bin / bash
TEXGENERATED =o/ scalefontXtimes . tex
TEXTTOFILLIN =" fill this page "
COUNT =10
rm $TEXGENERATED
do
SCALEFACTOR =‘echo $DEZ | cut -c 1 -2 ‘. ‘echo $DEZ | cut -c 2 -4 ‘
LINEWIDTH =. ‘expr 1000 \/ $COUNT ‘"\ linewidth "
LINEWIDTH =" \\ linewidth "
if [ $COUNT -eq 10 ]; then
LINEWIDTH =" \\ linewidth "
fi
#
echo "\ scalebox {" $SCALEFACTOR "}{"
>> $TEXGENERATED
echo " {\ scalefont {" $SCALEFACTOR "}"
>> $TEXGENERATED
CNT =0; while [ $CNT -lt 1 ]
do
echo " \\ vspace {${ COUNT } pt }"
echo "\ letterspace to " $LINEWIDTH "{"
echo $TEXTTOFILLIN " }} "
echo " \\ vfill "
>>
>>
>>
>>
$TEXGENERATED
$TEXGENERATED
$TEXGENERATED
$TEXGENERATED
CNT =‘expr $CNT + 1‘
done
#
echo "}"
echo "\ newpage "
COUNT =‘expr $COUNT + 50 ‘
>> $TEXGENERATED
>> $TEXGENERATED
done
exit 0;
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Appropriation and Type – Before and
Today
Ricardo Lafuente
Appropriation has been a recurring and accepted strategy in defining typography as an activity and a business. We can pinpoint four cases where appropriation has been key in defining landmarks in the history of type, not only aiding the
breaking of technical and creative boundaries but also helping to question legal
and moral ones.
A brief analysis of the current situation in typography will follow, focusing
on the approach to the subject by corporations, users and designers. The current
business model (digital foundries, font files with copyrights) is, as we’ll argue, a
remnant of a time where a typeface filled a whole drawer and fails to account for
the necessary changes that the information age demands.
Finally, we’ll conclude with the definition of an essentially contradictory business model that has a very strong stance against “font forging” and copyright issues, although it has historically – and now, more than ever – thrived on constant,
and often uncredited, appropriation of ideas and designs.
1 Appropriation in Type through History
We could certainly identify many more instances of inspiration or downright
copying of ideas in typography, but these four cases will suffice to demonstrate
the different uses of copy, inspiration and appropriation in general. Our focus
here will be on the issue of creative appropriation (inspiration) on one hand, and
corporate business models and copyright issues (plagiarism) on the other.
2 The Gutenberg Press
In 1450, Johannes Gutenberg produced the first commercially viable model of
his printing press, which was widely used for centuries until the advent of the
Linotype machine, the first way to automate, though only partially, the type setting and printing process. Gutenberg’s press was the result of the combination of
five key methods and processes, three, possibly four, of which were not original:
• The screw press, which was already used by the Greeks and Romans to
process olive oil and wine.
161
• Block printing, present in China since 594 AD. Gutenberg’s innovation
was to use metal cast types (instead of the Chinese traditional woodblock
printing technique), although metal typecasting was already developed in
Korea around 1230 AD.
• Letter punches, which were a goldsmithing technique – Gutenberg was a
goldsmith – used to engrave letters in metal pieces.
• Letter replica casting, a method to quickly create new individual characters, along with a particular metal alloy that made for durable pieces. This
method has been attributed to Gutenberg but recent studies shed doubts
on this fact.
• Metal-adherent ink, devised by Gutenberg.
This shows that originality, in a time before copyrights and patents existed, is
not a straightforward issue. It was not before 1700 that the first copyright statute
appeared in Britain – the protection of ideas could have changed the fate of this
invention and the combination of methods made. The point here is that they
were combined in a way that made typography as we know it possible, and there
seems to be absolutely no question regarding the legitimacy of this invention
made possible by appropriating previous methods and processes. Gutenberg’s
model of printing stood firm for centuries until the Linotype machine introduced
partial automation of the printing process.
3 Stanley Morison and Monotype
In 1886, the Linotype machine began to be produced by the Mergenthaler Printing Co. in the United States. This machine revolutionised the printing process
by introducing a degree of automation, allowing for quick composition of lines
of text. It wouldn’t take long (a year) for Lanston Monotype to begin production
of their own fully automated typesetting machine, devised by Tolbert Lanston,
which could typeset whole pages from a mechanical keyboard input.
In 1922, Stanley Morison was appointed as typographic advisor of the Monotype Corporation (the British branch of the Philadephia company), a post he
would keep until 1967. The Monotype Corporation built an extensive catalogue
of cuts made by Morison from classic references, such as Bodoni, Bembo, Baskerville, and several others. These revivals helped bring general interest to the
old masters” works They were also a key marketing strategy to try to push up the
value of the Monotype machine – the faces available would definitely determine
the decision of a buyer who fancies a particular style, and thus the Monotype
Corporation had no qualms about recruiting all the classics, which were by then
in the public domain.
It is tremendously unfair, though, to portray Morison as a hijacker – he was
one of the hallmarks of 20th century type, being responsible for the creation of
the Times typeface and hugely influencing the field of typography to the present
day through the efforts he dedicated to bringing the classics to the general public
– legitimately appropriating other designs. Without Morison’s endeavour, our
legacy would no doubt be poorer today.
162
4 Arial, Monotype and Microsoft
1982 is the year in which the Arial typeface was released by Monotype Typography, Monotype Corporation’s type design division. Designed by Robin Nicholas
and Patricia Saunders, this typeface had a remarkable impact. Not only does it
have obvious similarities to other modern sans serifs (sharing features with Helvetica, Univers and Akzidenz Grotesk), it exactly mirrors the glyph width tables
from Helvetica, which is the data included in a font file that describes each character’s dimensions – an exact match that gives little chance of coincidence.
Microsoft licensed Arial from Monotype instead of the more expensive Helvetica, and in 1990 it was bundled with Microsoft Windows 3.1. It has been a
staple of Windows systems until today. This is a specific case where a typeface
was chosen not for its genuine creative and/or practical value but based upon
external reasons, in this case driven by financial motives. Type designers are almost unanimous in shunning Arial as a lesser typeface: it is notably absent from
Robert Bringhurst’s typeface selection in The Elements of Typographic Style
(the current all round reference on type design from the designer’s perspective),
and is also only mentioned as a passing remark on Robin Nicholas’s entry on the
typographic encyclopaedic survey by Friedl et al. 14 p.409 This is pretty much
a clear indication of type designers’ consensus on the Arial issue; it’s also worth
noting that there has been, to date, no attempt to replace Arial as a standard font
in operating systems.1
In strict law and copyright terms, it’s appropriate to compare the Arial case
to a cheating student who argues that the fact that his exam has exact passages
from his nearest classmates” exams owes to coincidence. It is equally reasonable
to argue that borrowing from three sources rather than just one does not make
the situation more acceptable.
So Arial stands in mixed principles: the type community is almost unanimous
in calling shenanigans, but it has still made its way into our current operating
systems despite that fact – it didn’t face any legal actions as of 2008.
5 Segoe
In early 2006, Microsoft announced a significant effort to dignify type design
in their upcoming Vista operating system: six type designers – Lucas de Groot
and Robin Nicholas figuring among them – were commissioned to design appropriate typefaces for screen and print. The result was six very attractive fonts
that not only could appeal to general uses by less savvy people for simple word
processing tasks, but also suit the type designers” fancy.
Another font included in Vista is Segoe, a revival of Frutiger Next (which in
turn is a revival of Frutiger) that Microsoft licensed from Monotype and altered.
It’s not the first case in which Adrian Frutiger’s work has been remade, Adobe’s
Arial is now a ‘ standard” font of web typography, being part of a very limited set of fonts that most
browsers can read.
163
Myriad and Apple’s Podium Sans also bear a striking resemblance to Frutiger’s
structure. When Microsoft registered Segoe in Europe in 2004, Linotype sued for
copyright infringement since European law, unlike the American one, recognises
the rights to font designs (although patent law is often used to circumvent this
legal void in the U.S.).
The most significant fact is that Microsoft based their defence not on the issue
of originality – stating the differences between Segoe and Frutiger Next, but on
the fact that Linotype wasn’t selling its typeface in Europe when the request was
filed. This situation could very well be interpreted as an admission by Microsoft’s
part that the font in fact owes credit to Frutiger’s design.
This case becomes all more revealing in that it is both a high profile and current example of an attempt to settle the authenticity of a type design in courts.
Unlike Arial, it didn’t sneak past the critics and found serious hurdles while Microsoft tried to implement it in its Windows OS. The EU ended up rejecting
Segoe’s application, prompting the release of a modified version that bore less
resemblance to the Frutiger typeface. The plaintiff, Linotype, was acquired by
Monotype Imaging – the designers of Segoe – in 2006.
6 The Digital Typography Paradigm
Typography, and type design in particular, is historically defined by a constant
recursion of past themes and trends, be it as inspiration, revivals, or as a way
to question them – as in postmodern type examples, such as Emigre’s or David
Carson’s work. Nevertheless, modern designs still owe heavily (with or without
credit) to a tradition of arts and crafts spanning five centuries.
Meanwhile, during the last two decades, the type world hasn’t ceased discussing the issue of rights and plagiarism, a discussion that was sparked by the
digital revolution and the introduction of the personal computer as an all purpose
design and production tool. This shift implied that the tools used in typography
and book production ceased to be the sole domain of type makers, printers and
book publishers – the only ones who could afford the initial investment of a type
foundry, workshop or printing press and manage it effectively. Designing type
soon became cheaper and cheaper, as the physical and financial burden of the
new tools gradually became less and less significant. Nowadays, a computer and
a printer can do in minutes what a huge phototypesetting equipment would have
taken a lot of time, effort and money to produce ten years ago.
The key effect of the digital revolution in type design is that typefaces became fonts – a radical change in that they were no more lead blocks but data
– files that describe how each glyph should be drawn on screen or on a printer.
A free software solution to type design, FontForge, was released in 2004, doing
away with any software costs involved in font creation and editing, meaning the
only overhead for a type design business would be a PC, paper, drawing tools,
an image capture device (scanner or camera) and eventually an internet connection. This change has serious repercussions in the whole typography market: now
type design wouldn’t, in theory, require any kind of intermediaries between the
typographer/designer and its audience. Reality developed otherwise, as we will
see from three standpoints in typography usage and creation.
164
7 Corporate Type
The digital revolution made a deep redefinition of most areas of study possible. We will show, though, that the field of typography has been lagging behind
when it comes to taking advantage of the digital medium. Moreover, the corporate business model has failed to account for the specific needs and features
of information technology, sticking to an artificial market sustained by an inflated value attributed to digital files as if they still were physical objects that are
owned.
Nowadays, there are three major players in the type business: Microsoft, Adobe
and Monotype Imaging.
Apple Computer hasn’t been a key figure in the type market (concentrating
on developing font technology for its operating system), but it had an essential
role in developing the actual playing field. Apple heralded the personal computer
era in with their original Macintosh and has intermittently collaborated and competed with Microsoft and Adobe, being responsible for the development of the
TrueType font format along with Microsoft as a response to Adobe’s expensively
priced PostScript Type I font description format. The release of TrueType in 1991
forced Adobe to gradually reduce prices and eventually follow suit, releasing the
PostScript specifications so that software developers could implement it in their
programs without limitations.
Adobe Systems Inc., besides being responsible for a highly successful suite
of imaging and DTP software, has a very strong position in the type market:
not only is it a type vendor (through its typography division, Adobe Type) but
also the most influential company in the sense that it owns most digital design
solutions, especially after acquiring its main rival Macromedia in April 2005 and
facing no significant competition in its market.
Microsoft is responsible for creating the most widely used operating system in
personal computers, as well as the most popular office suite. Along with Adobe,
Microsoft developed the currently dominant OpenType file format, which is
freely available to developers as long as they agree to its rather restrictive licensing terms. Adobe converted its entire type collection to OpenType in a move
to spread the new standard.
Monotype Imaging is now a distant remnant of Tolbert Lanston’s original creation. It has adjusted technical breakthroughs in the 20th century and claimed
a staunch position in today’s digital type market. It was acquired by Agfa in
1999 forming Agfa Monotype, which in turn was acquired by T. A. Associates,
a North American investment firm, changing its name to Monotype Imaging and
developing a position in font software and rendering engines. It also secured a
strong standpoint in the font vendor market after acquiring its rival Linotype,
along with the rights to their entire type collection.
8 User Type
Most people get introduced to digital type by means of text editors. The digital
revolution would be the perfect reason to finally open typography to everyone
and make it a mainstream subject instead of a limited access craft. Things have
165
happened otherwise, though, and the inability to create a suitable interface for
allowing basic experimentation with type has severely crippled the possibilities
of the new medium.
The font selection paradigm has changed little during the years, offering a
whole collection of typefaces in a drop down menu. Such is the immediateness
of digital type: It’s just there, no need to open drawers with thousands of lead
characters. Users are encouraged, by means of a simple GUI, to just pick their
font and get to work on their document. Even more: you don’t even need to
choose, just stick with the default choice the software maker has made for you.
Word processing interfaces also assume the user doesn’t want to be bothered
with layout choices such as margins, structure – and they also make the choice
for us (incidentally, they also made it quite awkward to change these defaults). In
short: the standard word processing interface tells users not bother to with type.
This paradigm helps to build the general perception that a font is a finished,
shrinkwrapped and untouchable product – pretty much like pre-packaged software. Although font files can be opened and edited as long as we have an appropriate editor, most typeface editors are either crude or catering exclusively to
the type designer market. The user usually isn’t able to reach the underpinnings
and intricacies of type, instead being expected just to understand that the default
template is more than enough.
Such an approach to software designing effectively discourages any kind of
interest in typographic issues by the general public, and helps to fuel the thought
that fonts are “just there”. It’s worth noting that there is still no easy and streamlined way to buy, install and use fonts, unlike most other digital markets – iTunes
would be a good example of that kind of market strategy. There’s an obvious reluctance to develop alternative business models for type design.
9 Designer Type
The type designer community is centred on the study of classical and modern
examples and making attempts to postulate theory and practical guidelines for
the craft of type design, sitting somewhere between the methods of architecture
and those of poetry.
Fred Smeijers, a highly regarded Dutch type designer, analyses the type designer’s duty quite straightforwardly in his manifesto Type Now. On the issue of
the responsibilities of type designers and commitment to specific guidelines, he
states that
a type designer cannot escape this responsibility of judgement (...).
In the end, people – the society – either accept it or they don’t
15 p.25
Society, it seems, would be the ultimate judge of whether a typeface is a hallmark of craft or doomed to failure.
On the other hand, we find a curious account on Smeijers’s description on
Fontana, a typeface by Ruben Fontana inspired by Meta: he describes it as “uncomplicated”, “tres sympathique”, “sunny” and “open minded”. 15 p.40 This
certainly sounds more like a description of a person or a song than of an object,
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and indeed sheds some doubt on the much touted objectiveness of good type
design. It seems impossible to find serious and objective terms to classify a typeface’s features. Historical categorisations of design tendencies vary from author
to author, and although there are some widely used terms to describe historical
periods and typeface features, such as “transitional type” or “slab serifs”, there’s
a tendency to borrow from poetry and music to identify a type family’s “soul”
(which, though relevant from an artist or a historical point of view, is rather unscientific).
This is not a contradiction, though, since we can distinguish between type as a
creative activity (in which there would be no problem with this kind of analogy)
and type as an industry and commodity (where profit, market tendency, shareholder demands and legal requirements imply that things have a definite value
and purpose). Naturally, Smeijers’s interest is in the craft and art of typography,
and not the market and the economic relationships that it spawns. On the other
hand, our interest is definitely that which Smeijers doesn’t care for.
We must assert that defending the status of type as a functional solution to
practical problems requires an objective set of rules that derive from the way we
read and write. We cannot yet account for matters of objective legibility while
we do not possess all information on our mental processes and the mechanisms
in the brain involved in acquiring and processing written information – this is the
responsibility of cognitive psychology and neuroscience.
We know, from history, that a text with generous line spacing will certainly
read better than other with no line spacing at all. The German blackletter used by
Gutenberg in his Bible, however, is almost unreadable to a contemporary westerner’s eyes and definitely alien to someone from a non-Western background. In
the fifteenth century, though, it was certainly the norm. History can help to avoid
repeating our mistakes, but it also shows the relative importance of our current
standards. In short, we still cannot objectively define type, and won’t be able to
before a major breakthrough in neural science. However, copyright issues and
legal matters impose formal specifications on what a font is and what it is not.
Whether a typeface is a tweak, a revival or a work of art is left to the courts.
10 Tweaking and Reviving
In order to explain the type designer’s first reluctance to embrace the digital alternative, and also to understand how design processes are not as straightforward
as they are presented to us, we’ll concentrate on Fred Smeijers’s account on the
current state of events in typography. Specifically, we’ll borrow his term font
tweaking. 15 p.32 This process consists of loading a font, “tweaking” it – altering small details – and releasing it with different names, thereby circumventing
copyright laws, since U.S. Law protects font names as trademarks, but not font
designs. Smeijers is clear in pointing that font tweakers have nothing to do with
type design at all, reinforcing the distinction between doing type as a labour of
love and doing it for a profit.
Font revivals, on the other hand, are reinterpretations of existing designs, and
our best example would be Morison’s effort in bringing the classical designs into
the Monotype type library. Revivals matter to us because they aren’t original
167
productions (as they draw inspiration from existing designs) but aren’t copies
either (because no rights over them could be warranted otherwise, since there
would be no original idea).
Digital type foundries and vendors still maintain the tradition, digitising and
redoing the old masters” work. It’s worth noting that even if a certain typeface,
such as those with expired copyrights, resides in the public domain, anyone can
make a digital version – a revival – and claim the rights to it.
Digital type catalogues are rife with revivals: In Bringhurst’s inventory of digital foundries, we can find 14 that issue revivals, and 4 that only release original
designs. 16 p.309 This interest in resuscitating previous designs also has motives
that stand apart from simple typographic archaeology. Revivals are routinely issued by vendors and foundries to protect the rights of the rights holder when a
typeface’s copyright is about to expire. Such is the case with Avenir LT, Adobe
Garamond and Frutiger Next – which is what allowed Linotype to retain the
rights to the original design and be able to sue Microsoft in the Segoe case.
Revivals reside in a kind of legal no man’s land – some, like Arial (which is
more a tweak than a declared revival), manage to stick around while others, like
Segoe, raise copyright lawyers” eyebrows.
Given these two aspects, one cannot but wonder that a type designer wouldn’t
be thrilled with this perspective. One has also to question why there is such a rift
in reactions between font tweaking and font revivals, which can be interpreted
as no more than corporate font tweaking. A practical example of this is MyFonts.com’s description of the Avenir LT font (link, down the page) – a “recut
version of Avenir”, stating that “The “LT” was added to the name as the metrics
differ from the original version”. This definitely corresponds to Smeijers” description of font tweaking, despite the fact that the name change wasn’t intended
to avoid legal troubles, but to assert the brand of the author of the revival. What
is a revival, then, other than a corporate sanctioned font tweak?
11 Free software and Type Design
So far, we’ve kept our focus on corporate approaches to type design. As of 2008,
the digital design tools field is dominated by Adobe Systems Inc. with its Creative Suite bundle of applications targeting photo, video, vector and sound editing. Adding to that the fact that Adobe software is the staple in most design
courses in Europe and the United States, it can be stated that we are, indeed,
faced with stifled possibilities when choosing digital creative tools, a monoculture of sorts. Although there have been parallel efforts from the free software and
open source world to create alternatives, Adobe’s sole dominance in this market
remains unquestioned.
Going back to type design, we could point Donald Knuth’s TEX and METAFONT as the best examples of an alternative approach to designing type on
computers.
Having come from the UNIX crowd, and hailed as one of its most highly regarded representatives, Donald E. Knuth reflected this background in his efforts
to create a simple system for dynamic typesetting. TEX was first released in
1989, with several new versions being introduced during the ’90; its most recent
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update was released on 2002. It is still very popular among the academic and
scientist audience for typesetting papers, since TEX excels at accurately setting
and displaying mathematical formulae and including them in book layouts.
For an Adobe software user, TEX will definitely look alien, not least because
of its lack of a graphical user interface, instead relying on command line input
for operating. Instead of the mainstream point and click, drag and drop way of
laying out and manipulating text and image boxes, TEX is meant for processing
specifically crafted plaintext files, in turn outputting a printer-ready, typeset document. While requiring a rather steep learning curve, TEX introduced a model
of digital typesetting that would be mostly put aside by the software houses that
produced GUI page layout editors.
METAFONT was designed to be the font handling backend for TEX . It is
based on a modular method of generating letterforms, based on instructions fed
to the METAFONT processor, which outputs valid font files for use in TEX
documents. Computer Modern, the hallmark font of TEX , was created by Knuth
using METAFONT, and sports variable parameter such as stroke thickness, serif
dimensions and shape contrast. Thus, by tweaking the parameters, one could
create endless variations on letterforms, treating them as data to be manipulated,
in contrast with the commercial model of fonts as unique authored pieces.
Due to its lack of a GUI – an absence that a seasoned hacker would see as
a good feature – TEX and METAFONT presented little appeal for business
opportunities. As such, these two programs remain largely unknown to the noncomputer scientist audience since, among other reasons, you won’t easily find a
book introducing TEX as you would a book on Adobe InDesign.
Still, the METAFONT model can be the foundation of a new model of regarding typography and type design. Because of its simple input/output architecture,
it is only missing a proper interface for easy operation, along with compatibility with existing formats. Other projects, such as MetaType1 or LiveType – not
the Apple product, but a parametric approach to typeface construction, presented
in 1997 at SIGGRAPH – show that a modular, open-ended approach to fonts is
possible and has definite advantages over the manual creation process that’s the
norm in applications such as Fontographer, FontLab or its comprehensive free
software alternative, Fontforge.
12 Technology on Arcane Standards
The current terminology used in typography is also a clear signal of how it still
depends on former traditions instead of adapting to its new medium. Digital typography’s rules and terminology have been determined by its physical counterparts, and that still hasn’t changed. For example, we still talk about “leading” –
a term for the spacing between lines that takes its name from the lead strips used
for that purpose – although the term “line spacing” is gradually replacing it in
user oriented applications such as Microsoft Word.
Another example – while type foundries got that name because of their heavy
use of metal, single person studios with Macs are still referred to as “foundries”.
And fonts are described as being “cut” or “cast”, more than “digitised”. We talk
about “digital versions” instead of digital copies, perhaps to preserve their history
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and soul and not treat them as just another file in a user’s computer.
Although we can forgive this persistence in using traditional typesetting terms,
it also is a symptom that the type activity and business have failed to redefine
themselves for the digital medium. On the other hand, these examples can actually be interpreted as quite an artificial and linguistic way to value the work
of the typographer, probably with the aim of distinguishing between “true” type
designers and mere font tweakers, and not let “true” typography be contaminated
by the creeping tweaker threat.
13 What Now?
Given that digital type has been hanging around for thirty years, the progress in
improving on font technology and taking advantage of the digital medium has
been rather low. On the other hand, type designers in general (with the exception
of rare cases such as Emigre or Letterror) have not tried to get to grips with font
technology, rather limiting themselves to drawing and tracing their designs in
Fontographer and selling them on major font vendors (MyFonts, Monotype) or
independent ones (such as T26 and Veer). Worse still, issues of originality and
plagiarism have been discussed in type design circles, but corporate entities break
them routinely while trying, at the same time, to assert their rights in courts.
The difference between major and minor vendors is not substantial: though
distributors like Veer try to create a community and improve on the users” and
designers” experience through research, designer spotlights and support. Despite
these efforts, digital typefaces are still regarded in an esoteric limbo between
metal characters and abstract data. And though the price tags have steadily declined (and recently stabilised around the 20 dollar range in general), it is revealing that despite business models such as iTunes or Flickr, collaborative methods
in producing typefaces (many typographers are still lone workers) haven’t yet
developed, and file formats have changed so little in the face of recent, sleeker
solutions like XML and SVG. There’s little hope for innovation: the AdobeMacromedia and Monotype-Linotype mergers have paved the ground for a corporate monoculture ruled by software and typeface vendors and distributors, with
very little margin for competition.
We can also point a mutual apathy between commercial developers and designers as a possible reason – type designers try to adapt to outdated ways – file
formats and type tools – to create their works, while developers lag in keeping
up to date to new breakthroughs. Limiting the tools is limiting the imagination.
On the other hand, font vendors have an incredibly contradictory stance regarding font rights, using copyright law to protect their products while violating
it to borrow from others”. The different fate of Arial and Segoe begs the question:
are the vendors and distributors handling this as it should be handled?
This model’s obvious contradictions definitely invite serious questioning as to
the legitimacy and validity of the current type market and business model, which
cannot effectively release its standards and technology because of the threat of
competition. It is therefore left to users, designers and independent developers to
shape a new way of defining type and creating effective communication channels
between providers and users, be it through online communities or real world
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discussion in type designer’s circles and colleges.
If type design takes the free/open source route – and the wheels are already
in motion – how can type vendors sustain their profit margins and their markets?
With open fonts and free font editing software around, there would be little doubt
that typography can take a very interesting turn. Could we also see the open
approach and the business approach coexist, catering to specific users’ needs,
whether amateur or professional? And, finally, will the type world come to terms
with the fact that appropriation and use of other’s ideas have defined the activity
since its beginnings, and that it implies a serious rethinking of concepts such as
authorship, plagiarism and author’s rights?
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The METAFONT Tutorial
Christophe Grandsire
1 preface
METAFONT is the dark but indispensable brother of TEX , the well known
typesetting program written by Donald E. Knuth. Where TEX (most often
through its son LATEX ) works in the light, putting your words together in beautifully typeset documents, fully justified, with automatically generated tables of
contents (and so many other features), METAFONT works in the shadows, doing the dirty work of generating the fonts your documents are typeset with, and
without which you wouldn’t get anything but empty pages.
But METAFONT is much more than a blue-collar worker under the orders of
Manager TEX ! It is a true programming language, as much as TEX and LATEX
(and even more so!), devoted to the generation of entire families of fonts using a
single program and judiciously chosen sets of parameters.
Uh-oh! I already see the questioning looks in the audience, everyone is wondering what the heck I am talking about! ^
đ OK, so let’s go back to the beginning.
Once upon a time (read: in the late 1970s), there was a High Mage at the Stanford School of White Magic (read: a Professor of Computer Science at Stanford
University) named Donald Ervin participants/reneeom/scalefontXtimes.shKnuth
(read: Donald Ervin participants/reneeom/scalefontXtimes.shKnuth). This High
Mage was revising the second volume of his Book of White Magic Spells (read:
the second volume of his multivolume opus The Art of Computer Programming).
He had received the galleys, made using the new magical-aided scribes (read: the
new computer typesetting system) and was so horrified by the result that he immediately cast a Fire Spell on them, reducing them to ashes (read: he was not
happy by the result). The quality was far lower that of the first edition of this
second volume. Being himself a High Mage, he thought that he ought to be able
to do better than that. So he set out to learn as much as possible about the Art
of Scribes (read: the rules of typesetting and good typography) and, because
he could find no scribe whose style was good enough for writing the Hermetic
symbols he used daily (read: he couldn’t find symbol fonts with the characters
he needed), as much as he could about the Art of Calligraphy (read: type design). He figured that it would take about six months. It eventually took more
than ten years, and the help of plenty of other mages and wizards who had suffered from the same problem and saw the High Mage participants/reneeom/scalefontXtimes.shKnuth as their Saviour (read: they were too lazy to begin the
173
work by themselves and figured that it would be easier to help someone who had
already begun the job than do it all by themselves). But at the end of those ten
years, our High Mage had in his power the two best White Magic Spells ever created (read: the two best programs ever written): TEX and METAFONT. TEX
was the Scribe Spell, able to put together words and symbols on the parchment,
in Good Position and Alignment (read: TEX is the high-quality typesetting program). METAFONT was the Calligrapher Spell, able to create the wonderful
Hermetic shapes that TEX would align together, according to the best Rules
of the Art of Calligraphy (read: METAFONT is the high-quality type designer
program). And because our High Mage was of Good Alignment (read: he made
enough money from his books already that he didn’t have to make any more
with those programs), he released those spells and their components for free for
anyone to use and enhance (with a minimum of control, of course)! In a world
where Spells had mostly been proprietary and expensive, this was a revolution
which ensured a mass following, making eventually TEX (and its companion
spell LATEX , later created by the Wizard Leslie participants/reneeom/scalefontXtimes.shLamport to simplify the use of the basic TEX Spell and release
its true power) the spell used by the majority of Mages around the world for the
writing of their Books. The METAFONT Spell, on the other hand, wasn’t as
successful. Lacking helping spells like the ones that grew around the TEX Spell,
it was commonly seen as too Hermetic to be mastered, and thus was confined
to a helping role, being cast indirectly through the TEX Spell when needed to
produce beautiful Calligraphy.
Now, I hope this fairy tale has helped you understand the situation. ^
đ METAFONT is a type designer system whose power is wasted by being used only as a
helper program for TEX and LATEX . Being seen as too complicated for the common user, it has been ignored by most type-designers, whether amateurs or professional, despite having proved its qualities by its use by participants/reneeom/scalefontXtimes.shKnuth to create the Computer Modern font family, recognised
as one of the best for typesetting mathematical and scientific documents.
This tutorial is intended as a first step to correct this situation, by showing
that METAFONT is actually nothing to be scared of, and that it is actually an
easy-to-learn programming language, usable by anyone with a basic computer
knowledge to create high-quality fonts. After following this tutorial, anyone with
originally no knowledge of font design will be able to create simple fonts that
they will be able to include in their TEX documents, but also in any type of
documents they want, provided that a little more work is put into converting the
fonts in a format usable by other programs.
This tutorial is organised into lessons. Each lesson is divided into “descriptive” and “imperative” parts. The “descriptive” parts are the meat of the lessons,
they introduce and describe the commands and features you need to learn to
use METAFONT. The “imperative” parts appear generally in the form of exercises, which involve solving problems using the commands and features you’ve
been introduced to. Since this is not an official course, and that no diploma will
sanction it (although we can always dream, can’t we? ^
¨ ), the solutions to those
exercises are available in Appendix ??. You are of course allowed to look at them
whenever you want, but for the exercises to have any use, you are encouraged to
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try the exercises a while before checking the solutions, and to check them at the
very last resort, when even after a good night of sleep and re-reading the lesson
you are unable to find a working solution. You can of course also check the solutions even if you have a working solution yourself, if only to check whether your
solution is different from the author’s. In order to prevent you from looking too
fast at the solutions, the exercises are not hyperlinked to their solutions (the solutions, on the other hand, are hyperlinked to their respective exercises). At first,
you’ll probably have the impression that the lessons are pretty heavy and long.
This is done on purpose and reflects the nature of the METAFONT programming language. For this reason, you needn’t complete one lesson per day. Take
your time, and don’t hesitate to spend a few days on each lesson. Don’t jump to
the next lesson if you haven’t mastered completely the present one. Finally, I’m
talking here to fellow METAFONT experts. Don’t jump at my throat if this tutorial introduces small lies and oversimplifications. The approach here is the same
as the one taken by Donald E. participants/reneeom/scalefontXtimes.shKnuth in
The METAFONTbook, page viii:
When certain concepts of METAFONT 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.
A final word before I let you all begin to read the lessons in this tutorial: enjoy!
Despite the rather mathematical approach METAFONT takes for font design, it
is actually fun to create fonts with METAFONT!
2 Copyright Notice
Copyright © 2003–2004 Christophe Grandsire1 and all the Contributors to The
METAFONTtutorial.
Permission is granted to copy, distribute and/or modify this document under the
terms of the GNU Free Documentation License, Version 1.2 or any later version
published by the Free Software Foundation; with no Invariant Sections, no FrontCover Texts, and no Back-Cover Texts. A copy of the license is included in the
section entitled “GNU Free Documentation License”.
3 Thank you!
Some of the material from Lesson (including the example) comes from the first
two chapters of the METAFONT – guide pratique,2 by Bernard participants/re-
mailto:metafont.tutorial@free.fr
http://www.vuibert.com/livre515.html
175
neeom/scalefontXtimes.shDesgraupes, which are available online here.3 Other
material that helped me write this tutorial can be found here4 and here5 (two different “here”s ^
đ ). And of course the main source of information I used for this
tutorial is The METAFONTbook6 by Donald E. participants/reneeom/scalefontXtimes.shKnuth, the METAFONT bible from the very creator of METAFONT.
I would also like to thank all the members of the (La)TeX/METAFONT-forConlangers7 mailing list for their support and especially for their patience (Sorry
to have kept you waiting for so long!). I couldn’t have written this tutorial without
them. Naturally, all mistakes in this document are mine. If you ever find anything
correct, it must have been one of them dropping me a line.
4 Changes
v. 0.33 Corrected the bug that prevented some solutions to be linked to their
correct respective exercises.
v. 0.32 Changed the license to the GFDL and added it as an appendix.
v. 0.31 Slight changes in the description of the pk files and in the example in
Lesson ; some more corrections.
v. 0.3 Addition of Lesson .
v. 0.2 Even more corrections; change of the incorrect reference to RiscOS as an
unsupported operating system to a reference to TOPS-20, a truly unsupported operating system; modification of some internal references; addition of Lesson .
v. 0.12 More corrections of style (again thanks to Tristan participants/reneeom/s-
calefontXtimes.shMcLeay); change of the style of the smilies; modifications of the code to make it more robust; addition of Vim as text editor
with METAFONT syntax highlighting as default, and addition of links to
the sites of Vim and Emacs.
v. 0.11 Various corrections of style and contents (thanks to Tristan participants/re-
neeom/scalefontXtimes.shMcLeay); addition of a note about the new Adobe
Reader 6.0; addition of a “Changes” page.
v. 0.1 First appearance of The METAFONTtutorial.
http://www.vuibert.com/DOC/24-metafont_chap12.pdf
http://cgm.cs.mcgill.ca/∼luc/metafont.html
http://tex.loria.fr/english/fontes.html
http://www.amazon.com/exec/obidos/tg/detail/-/0201134446/103-1864765-6700651
http://groups.yahoo.com/group/latex-for-conlangers/
176
The Name of the Game
So, here it is, the very first lesson of The METAFONTtutorial. As its numbering
indicates, this is quite a special lesson, which lays the foundations for the rest
by explaining the nasty little technical details like what METAFONT actually
is and what you actually need to be able to use it. As such, it needs a basic
knowledge of computers. But don’t worry, when I say basic, I mean really basic.
If you know what a file, a program, a folder (also called directory) are, as well as
what an operating system is and which one you have on your computer, then you
know enough (knowledge of what it is to download something from the Internet
and of how to install programs on your platform is a plus ^
¨ ). The rest will be
explained here. If you don’t know what those things are, then you first need to
buy a computer, and how the heck have you managed to come here in the first
place?! ^
¨ Seriously, although you needn’t be a rocket scientist to understand this
tutorial, computer font design stays a specialised subject, and while this tutorial
is meant to bring METAFONT to the masses, you still need to understand a bit
about computers to fully appreciate its capacities.
So, now you’re warned, so let’s wait no longer and begin to work!
1 What does METAFONT mean?
I think the best way to understand what METAFONT is about is by understanding what its name means. So let’s do a bit of etymology (not much, don’t worry
đ ).
^
Let’s begin with the end, and we see that in METAFONT, there is FONT.
What a font is is a more difficult question than it seems at first. If you check
this online glossary,1 you’ll see a lot of terms that look very familiar and yet
have different definitions from what you’re used to. But since you’re interested
in font design (otherwise why are you reading this? ^
¨ ), you probably know
already some of this special vocabulary, don’t you? So let’s simply say that a
font is a collection of characters of similar “style”, or rather typeface in typographer’s speech. Or rather, a font is a particular realisation of a certain typeface
(in a physical—wood, lead, alloy—or electronic—a computer file usually simply called a “font”—medium), according to some parameters such as size, width,
weight (normal and bold are two examples of weight), contrast (the difference
between the thin parts and the thick parts of characters), style (normal, italic,
monospace or typewriter etc.) and the presence or absence of serifs (those little
http://nwalsh.com/comp.fonts/FAQ/cf_18.htm
177
decorative strokes that cross the ends of the main character strokes) and their
shapes. But you are not limited to this list and can make up your own parameters
too.
And that’s where the META- part comes in. “Meta-” is a prefix of Greek origin which originally meant simply “after”, but due to a strange turn of events
(read about it here2 ) came to mean “of a higher order, beyond” in Latin and
later in all modern languages (except Greek where it kept its original meaning).
So you have metalanguages (languages used to describe languages), metahistory
(the study of how people view and study history), metatheorems (theorems about
theorems), metarules (rules about rules) etc. Indeed, you can “meta-” about anything, making it quite a hype. ^
đ But there is one other place where “meta-” is
actually useful, and that’s font design. Conventional font design means that for
each value of the parameters I’ve listed before (and all the parameters that you
can invent yourself), you have to separately design a full font (i.e. a few hundred
characters), and that just for one typeface (the existence of scalable fonts, i.e.
fonts which can be used at any size, helps a little by taking care of the parameter “size”, but that’s only one out of a lot of parameters). Even with the help of
modern tools like font design programs, this is a tedious and boring job. It would
be so much nicer to do meta-design instead, i.e. design that is independent of
the parameter values. Instead of designing a font for each and every combination
of parameter values, you would describe a typeface once, and by entering separately a list of parameters, let the computer automatically create all the fonts you
need with all the combinations of parameters you want, and if you forget one
combination, instead of having to redesign the whole font again, you’d just have
to change some parameters and let the computer do the tedious job again. This
way would spare you a lot of work, and would ensure the unity of looks of each
of your typefaces, since you would describe them only once.
And yes, as you must have guessed by now, METAFONT is exactly about
font meta-design. METAFONT is a system that allows you to describe a typeface once, and create as many fonts as you like of this typeface by just changing
a set of well chosen parameters separately. How it is done is explained in the next
section.
2 How does METAFONT work?
So METAFONT is a system that allows you to create hundreds of related fonts
easily and with a minimum (which can be quite a lot nonetheless) of work from
the human creator. How does this work? Well, it may surprise you, but METAFONT is actually a single command-line application (called mf on most platforms, and mf.exe on Windows platforms). In short, it has no graphical interface
(no fancy windows and such!). It must be called from a command line or by a
helper program. So, how can you create fonts with such a program if you cannot
draw figures and such? Simple: this program is an interpreter. It takes a series
http://lists.tunes.org/archives/review/2000-April/000062.html
178
of instructions as input, and executes them one at a time, as it receives them.
In other words, METAFONT is also a programming language, like C, BASIC,
Pascal (in which the source of METAFONT was originally written), Perl, and
of course TEX .
So, how do you enter your programs so that mf can interpret them? Well, there
are various ways, but the most common is to make a file containing your instructions, and to give the file’s name to mf. The file itself must be plain text, and
must have the extension .mf. mf will then read this file and give back (if everything’s okay) two other files with the same name but different extensions (the
process is called compilation). One file will have the extension .tfm. It’s called
the font metrics file. It contains information like the size of the characters. The
second file will have an extension of the form .<number>gf where <number>
is a certain value with usually three figures. It contains the actual shapes of the
characters (or glyphs, as they are usually called). Both files form the font, and
both are necessary to have a working font.
So, is that it? Well, it would be too simple if it was. ^
¨ For historical reasons,
the gf file is not the one which is actually used. You need first to transform it
into a smaller file, containing the same information but in a packed way. You do
it with a second program called GFtoPK (GFtoPK.exe on Windows platforms of
course), and the resulting file has the same name as the original one, except that
its extension has become .<number>pk (with the same number as the gf file3 ).
The pk and tfm files form the actual font, and the last thing you have to do is to
put them in a place where they will be recognised by TEX and LATEX . Once
done, you can happily use your fonts in LATEX .
Does it look complicated? Well, like many things, it’s actually more complicated to explain than to do. And don’t worry if you don’t understand yet, the
method will be repeated at various times in the course of this tutorial, and you
will quickly get the hang of it. For now, here is a summary of the method:
1. Write one (or more) plain text file containing METAFONT instructions
(a METAFONT program thus) and save it (or them) with a .mf extension.
2. Call mf on this file. The result will be two files, ending respectively in
.tfm and .<number>gf.
3. Pack the gf file by calling GFtoPK on it. You will get another file ending
in .<number>pk or .pk.
4. Move your tfm and pk files to some place where they can be recognised
by TEX and LATEX .
5. Enjoy!
On some platforms, like Windows, the actual extension of the pk files must be .pk, without number. You
need to check the pk files already installed on your computer to find out which style you must adopt for
your own files.
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3 What do I need?
Well, I hear you saying now: “Well, that’s very nice, but how do I get those
programs in the first place?” Look no further, all the answers you need are here.
^
¨ But before looking for where you can get the programs you need and how to
set them up, let’s list what you need first:
• A computer, with some operating system on. OK, this may sound so obvious that it is painful, but the point here is that almost any computer will do.
LATEX and METAFONT have been ported to probably all the platforms
that are still in use today, including those that are not supported anymore
(like TOPS-20, a cousin of the WAITS operating system on which TEX
was originally developed). Those ports are more or less up-to-date, but
since TEX and METAFONT’s developments have been stopped (the versions existing today are final, except for the possible correction of a bug
once in a while—an extremely rare event, those two programs are nearly
completely bug-free), you will probably never experience the difference,
and your source files will compile in exactly the same way with exactly
the same results on every platform where METAFONT is installed.
• A plain text editor. It’s the simplest kind of text editor there is, and normally all platforms come with at least one included (like Notepad for Windows and vi for Unix). But nothing prevents you from using a fancier
editor with syntax-highlighting and project-tracking if you feel like it! ^
¨
• a LATEX distribution. Why LATEX if we’re interested in METAFONT?
Well, as I already said in the preface of this tutorial, TEX (and thus LATEX
) and METAFONT are essential to each other. TEX cannot work without
METAFONT, and METAFONT is useless without TEX . So METAFONT comes in full glory with every LATEX distribution and installing
a LATEX distribution will automatically install METAFONT on your
computer. Other needed programs like GFtoPK and GFtoDVI (necessary to
make proofsheets of your fonts) are also part of any LATEX distribution
and will be installed along with it.
• This tutorial! Otherwise you’ll have difficulties trying to learn the METAFONT language by yourself. ^
¨
As you see, the only thing you really need to get METAFONT up and going
is a LATEX distribution. So let’s see where you can get one suited for your
platform.4
Many platforms are still missing from this list. If you know how to install LATEX and METAFONT on a platform not yet listed, I would be glad if you could send the information at
metafont.tutorial@free.fr, so that I can update the list. Of course, the information will be properly attributed to you in this tutorial.
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1 Unix and clones
If you have a Unix platform of any flavour (Linux, Sun Solaris, BSD etc.), there’s
a big chance that you already have a full LATEX distribution installed, and a big
chance that this distribution is te TEX . In such a case, you have nothing special to
do and can safely skip this section. If you are unlucky enough not to have LATEX
already on your computer, then you must install it yourself, and of course I advise
you to install te TEX , as it’s the most up-to-date and easy-to-install distribution
for Unix systems. You can download it at the te TEX Homepage.5 But before
running there, I also advise you to check whether your particular Unix flavour has
some specific system or LATEX distribution tailored to its specificities. This will
probably save you some work (for instance, in Debian GNU/Linux and other
“apt-enabled distributions”, the simple command “apt-get install tetex-base”
will do all the work of downloading and installing te TEX for you). And if you
want a text editor with syntax-highlighting for METAFONT, no problem: both
Vim6 and Emacs7 have a METAFONT mode in their standard releases.
2 Windows
Windows doesn’t come with any LATEX distribution, so you have to download and install one yourself. The best one is without any doubt MiK TEX ,
available for free at http://www.miktex.org/ for all Windows versions (except Windows 3.1 and NT versions under 4.0). It includes a Package Manager and an Update Wizard which allow you to easily manage and update your
LATEX distribution with a graphical interface. And since Windows users are
usually rather uneasy with the command-line (the MS-DOS), I also advise two
other free programs which will provide you with a good graphical interface for
LATEX and METAFONT. The first one is Winshell,8 a text editor specialised
for LATEX , which is made to work automatically with MiK TEX , so that you
only have to download and install it and you can immediately work with it. It’s
simply a text editor which allows you to write your TEX sources (with syntaxhighlighting) and compile them with a click of the mouse, so that you needn’t
use the command-line anymore. The second one is the Crimson Editor,9 a customisable programmer’s editor. I advise it because it is easy to configure it to
run command-line programs, and also because I wrote syntax highlighter files
for it. You can get the custom highlighter files as well as instructions on how to
customise the Crimson Editor for use with METAFONT in Appendix ??.
http://www.tug.org/teTeX/
http://www.vim.org/
http://www.gnu.org/software/emacs/emacs.html
http://www.winshell.de/
http://www.crimsoneditor.com/
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3 Macintosh
If your operating system happens to be Mac OS X, then it’s your lucky day!
Since Mac OS X is based on the BSD flavour of Unix, porting Unix software is
easy and a lot of free software is available for Mac OS X this way. This includes
TEX , and the te TEX distribution is available for Mac OS X through the iInstaller10 or the fink11 package management tools. To use it, it seems a frontend is necessary, and my research pointed out i TEX Mac12 , which seems to be a
very good front-end for the te TEX distribution. However, I am not a Mac user,
and have never seen Mac OS X in function, so I cannot really tell if the good
reviews I’ve read about i TEX Mac are well-deserved or not. If you know more
than me, I’d be very happy to have your opinion!
If on the other hand the operating system on your Macintosh is an older version of Mac OS, then I am probably going to disappoint you, but there seems to
be no free Mac implementation of TEX for non-X Mac. Good implementations
seem to be CMac TEX 13 and Oz TEX ,14 but they are both shareware (CMac
TEX costs $35, Oz TEX $30, both for single user licences). They both come with
their own front-ends (basically replacing the command-line programs with menu
commands), but you still need a text editor to write your sources. More information is available at http://www.esm.psu.edu/mac-tex/default9.html.
Note also that those distributions have their little quirks. For instance, in the implementation of METAFONT for Oz TEX , called OzMF, the actual fontmaking
command is not called mf but Make TEX PK.
4 Other programs
The lists I’ve given here are only for a basic installation of TEX / LATEX and
METAFONT. Depending on your platform, you may need some other program
(like a Postscript viewer and/or a PDF viewer of some kind). But since those
concern strictly TEX and LATEX and not METAFONT, instead of explaining
everything here, I simply advise you to read completely the links I’ve provided.
Each implementation’s webpage usually explains very well what additional programs you may need to enjoy the full power of LATEX .15
http://www.rna.nl/ii.html
http://fink.sourceforge.net/
http://itexmac.sourceforge.net/
http://www.kiffe.com/cmactex.html
http://www.trevorrow.com/oztex/index.html
From now on, I’ll refer mostly to LATEX rather than TEX , since it’s the former rather than the latter which
is used by most people.
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4 METAFONT’s proof-mode
Rome wasn’t built in a day.
Genius is one percent inspiration and ninety-nine percent perspiration.
You’ve probably heard those quotes at least once in your life16 if you’re lucky,
thousands of times if you’re not. ^
¨ Despite the overuse they have been subject
of, they are quite valid here. Even when using METAFONT which does everything with equations, good typography stays an art, and it’s highly unlikely that
your first shots will be exactly what you want, even if you know all the intricacies of the METAFONT programming language, and even if you’re a genius in
typography! As with any art, you will have to train a lot, so that your understanding will become wider, your hand firmer, and your style more accomplished. In
other words, you will have to go through a long period of trial and error (also
called proofing) to create your first fonts.
However, with what you know right now, proofing is tedious with METAFONT. As it is, you would need to, for each modification or new character
you’ve put in your font:
• compile the whole font with the right parameters to get the gf and tfm
files;
• transform the gf file into a pk file;
• move the pk and tfm files where they can be found by TEX ;
• write a small TEX file to check how your font looks like.
This is due to the non-WYSIWYG17 nature of METAFONT (which is rather
WYGIWYW18 ). Moreover, font characters are usually small, and thus difficult
to check, and you have no way to check the position of the different points and
strokes you’ve put to make the characters. So what is needed here is some kind
of proofing capabilities that would bypass the usual font creation method and
provide us with more information than just the shapes of the characters.
Luckily, participants/reneeom/scalefontXtimes.shKnuth was well aware of the
necessity of proofing, and provided METAFONT with a built-in way to do that.
Actually, METAFONT’s default working mode is the proofing mode, so unless
you specify otherwise (Lesson 3 will explain how to do that) you will always
work in proofing mode. In this mode, METAFONT doesn’t produce a tfm file,
and the gf file it creates will have the extension .2602gf. You needn’t know anything about this file, except that it contains all the information a font file usually
For your edification, the second one is often attributed to Albert participants/reneeom/scalefontXtimes.shEinstein but it seems it would actually be from Thomas A. participants/reneeom/scalefontXtimes.shEdison.
What You See Is What You Get.
What You Get Is What You Want.
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contains, and is also fit for making proofsheets, by applying to it the program
GFtoDVI (GFtoDVI.exe on Windows). The result will be a DVI file (with the
same name but the .dvi extension), which you can view with the DVI viewer
that came with your LATEX distribution. On this file, each page is a proofsheet
devoted to a single character, printed very large (about 20 to 30 times the normal
size of font characters) and accompanied with some important information (at
least if you made your METAFONT program so that this information appears).
Section 5 will show an example of proofsheet and explain the information you
can find on it.
So, is that it? Well, that would just be too easy. Unfortunately, although METAFONT’s default mode is the proof-mode, you usually cannot use it immediately.
That’s because the proofsheets use a font called gray to show the characters in
large size and this font is usually not available in directly usable form in LATEX
distributions. Luckily, the METAFONT source for this font is always included,
so it is easy to compile it yourself to get a working font. Since the compilation
of this font is a technical problem which depends slightly on the characteristics of your distribution, it is best left out of this lesson, and you can find it in
Appendix ??.
5 An example
So, now you have a LATEX distribution with METAFONT working and a compiled gray font for your proofsheets. You are now ready to jump to Lesson . But
before you do that, maybe it’s a good idea to get a taste of METAFONT programming, just so as to help you digest what has been said until now. It will also
allow you to check whether your METAFONT installation works correctly.
xEXERCISE .1:
Note that although this is presented as an exercise, there is no solution as there is no real problem to be solved. The only thing you
need to do is follow the instructions and admire the results. ^
¨
Now open the text editor you have chosen to use to write METAFONT sources with, and write the following 26 lines (without the
line numbers):
Save the resulting file under the name beta.mf. Then open a
command-line window,19 go to the directory where you saved the
beta.mf file, type the following line:
I consider here that you will run METAFONT through the command line. If you do it differently
on your platform (for instance you’re on a Mac or you use the Crimson Editor configured for use with
METAFONT as explained in Appendix ??), just use the corresponding actions. You shouldn’t have
any trouble finding out what you must do.
184
mf beta.mf
and hit the “ENTER” key. If everything’s working correctly (and if
you didn’t make a mistake when copying the program), you should
get an output close to this: and possibly (on a Unix or Unix-like
platform) some graphics of a letter looking like a Greek beta. If you
check your directory, you will see that indeed, a beta.2602gf
file has appeared, as well as a beta.log file, which just contains
the same text as above. Carry on and enter now the following line:
gftodvi beta.2602gf
The resulting output is uninteresting, but you should find that you
now have also a beta.dvi file in your directory. View it with your
DVI viewer, and you should get something similar to Figure .1.
To understand how METAFONT drew this figure out of the program you fed it with, let’s have a closer look at the program itself:20
• Line 1 defines an algebraic parameter with which all the dimensions of the glyph will be defined. By doing so, you will
make it much easier to produce variants of your fonts, by
changing the values of a few parameters, rather than having
to look through a full complicated source where all the dimensions have been directly specified (one says “hard-wired”),
and as such multiplying the chances you will make a mistake
or will forget to change one value. Working with parameters
is the key ingredient to meta-design. This tutorial will slowly
teach you to think with parameters rather than direct values.
• As you can see, in the first line the parameter ends in #.
However, in the rest of the program, the parameter is simply called u. What is happening here is that “true” lengths
(i.e. device-independent values) in METAFONT are always
specified with parameters ending in # (called “sharped” variables). However, to get the same values on all devices (i.e.
screens, different kinds of printers etc.), you need to specify which device you create your font with, and then convert
your “sharped” values into “soft”, device-dependent, values.
That’s what the define_pixels command on Line 2 does. It
converts a “sharped” parameter into a “soft” one, of identical name but without a # sign at the end. This feature of
METAFONT, related to the modes you will learn about in
Lesson 3, is very much a sign of METAFONT’s age, created
This is the reason why the program lines were numbered here.
have numbered lines.
METAFONT sources must never
185
•
•
•
•
•
•
•
•
at a time when printing devices were far less flexible than they
are now. Still, it is necessary to learn how it works, and it is
still useful for meta-design.
Line 3 indicates that we start now creating a character in the
font. It defines the position of the character in that font, as
well as its dimensions (or rather the dimensions of an abstract “box” around the character called the bounding box,
which is what TEX actually manipulates when it puts characters together on a page. This line also defines a label for
this character (put just after the beginchar command between
double quotes), which appears on the proofsheets for this
character. It is a good idea to always label your characters,
as it facilitates navigation in your programs.
Lines 4 to 11 define the positions of various points through
which the “pen” will go to draw the glyph. For now, just observe how all point positions are defined only in terms of the
parameter u or of other points, rather than in terms of actual length values. This makes the character easily scalable
by just modifying the value of u# once.
Lines 12 to 21 define pen positions, i.e. the width of the pen
at the position of the point, and its inclination. This is what
defines the looks of the character, compared to similar characters using the same point positions.
Line 22 instructs METAFONT to take a certain pen (here
with a thin round nib). It’s with this pen that METAFONT
will draw the glyph. By changing the pen, you can achieve
different kinds of effects.
Line 23 is the actual (and only) drawing instruction. Its relative simplicity shows the strength of METAFONT, which
is able to interpolate the positions the pen has to go through
between two points without needing help from the user. Simply speaking, the command instructs METAFONT to draw
through all the different points in order, following the positions given by the different penpos instructions, and creating
the shape you can admire on Figure .1.
Line 24 instructs METAFONT to show, with their numbers,
the points used for the construction of the shape on the proofsheet. It is very good practice to do so as much as possible.
Line 25 tells METAFONT that it has finished drawing the
character, and that it can get ready to draw another one, or
to stop.
Line 26 instructs METAFONT that the job is finished and
it can go home. Don’t forget it, as without it METAFONT
will think there is still work to do and will wait patiently for
you to feed it with new instructions (METAFONT is a very
obedient servant).
Once again, don’t worry if you don’t understand everything which
is explained here. The goal of this tutorial is after all to teach you
186
what it means. ^
¨
Now, you probably fell in love with the shape you just produced,
and want to make a true font out of it, in order to sprinkle your
documents with eautiful etas.21 To do so, go back to your command line, and enter the following line:
mf \mode=ljfour; mode_setup; input beta.mf
Some command lines give a special signification to the backslash
character, and for them the above line will probably result in an
error. If you get this error, just put quotes around the arguments of
the mf command, like this:
mf ’\mode=ljfour; mode_setup; input beta.mf’
In the rest of this tutorial, I won’t use quotes around such arguments, but feel free to add them at need. For now, just remember that
the backslash indicates to METAFONT that it must expect instructions on the command line rather than a filename, that the first two
instructions put METAFONT in true fontmaking mode22 (rather
than proof-mode), and that the last one causes METAFONT to finally load and compile beta.mf. The output you will get should
look like this: It is slightly different from the output you got the first
time around, and indicates that two files have been created this
time. And indeed, if you check your directory, you should see that
a beta.tfm file and a beta.600gf (or similar with another
number) file have appeared. Now you still need to pack the gf file
into a usable format. You do so with this command:
gftopk beta.600gf beta.600pk
or this one:
gftopk beta.600gf beta.pk
if your platform needs unnumbered pk files. A beta.600pk or
beta.pk file should appear in your directory. And that’s it! Your
Don’t worry if the
doesn’t look good when you’re viewing this PDF document on screen. It is
the fault of the PDF viewer you use, which does a poor job displaying bitmap fonts like the ones
METAFONT creates (they will print beautifully, though). Luckily, Adobe®, the creators of the
PDF format, have now released a new version of their PDF viewer which solves this problem and
displays bitmap fonts on screen as well as on paper. So go and download the Adobe Reader 6.0 at
http://www.adobe.com/products/acrobat/readstep2.html, you won’t be disappointed!
Depending on your installation, you may need to choose a mode different from ljfour. Basically, you should
choose the same that you used to compile the gray font as explained in Appendix ??.
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font is now available to every LATEX document whose source is in
the same directory as the font files23 and you can test it with the
following LATEX program:
Just compile it and check the result with your DVI viewer. ^
¨
I said: “There is NO solution to this exercise!!!” ^
¨
6 Before you carry on. . .
Phew! This lesson is finally finished! You may have found it informative, challenging, just boring, or completely unintelligible. In any case, you have probably
found it extremely technical (and with reason). So before jumping to the real beginning of this tutorial, turn off your computer! Go out, do something else, some
sports, watch TV, read a book, do whatever you want as long as it isn’t related
to METAFONT. Have at least a full night of sleep before going back to this tutorial and start the real work. This will help you understand things you may not
have fully grasped while reading this lesson, or will help you realise what you
didn’t understand, and will have to look at again. And once again, don’t feel bad
because you didn’t understand everything that was explained here. This tutorial
will teach you everything in time, and you will come back to this lesson and be
surprised at how much more you understand after a few lessons. But for now, go
and rest! ^
¨
You will have to wait until Lesson 4 to learn how to make your font available to all LATEX files whatever
their location on your hard drive.
188
Figure .1: The Greek letter
.
189
My First Character
1 Before we begin
Before we actually start the lesson, let’s just give some remarks about the typographic conventions used to write METAFONT commands and programs.
As you may have guessed from the example in Section 5, there are two different typographic conventions used in this tutorial, both of which are taken
straight from the conventions in The METAFONTbook. Sometimes I’ll refer to
METAFONT commands and variables using a typewriter-like style of type, e.g.
‘z5=(10u,12u);’, ‘penpos9(1.5u,-180);’ or ‘beginchar(66,13u#,16u#,5u#);"Letter bet
Other times, I’ll use a fancier style where main commands and macros will appear in bold face or roman type, while variables, user-defined macros and less important macros will appear in italic types. In this style, subscripts and superscripts
will also be used. In this style, the same examples as given before will appear respectively as ‘z5 =(10u, 12u);’, ‘penpos9 (1.5u,−180);’ and ‘beginchar(66, 13u# ,
16u# , 5u# ); “Letter beta”;’. The typewriter style will be used when I talk about
what you will have to actually type on your keyboard, and how it will likely appear on your screen (without taking a possible syntax highlighting into account).
It will also be used when referring to the output the different programs you will
run will give you back, as well as to refer to filenames. The fancier style will be
used rather when I want to emphasize the logical structure and the meaning of
a program rather than its representation. Yet you will usually be able to directly
type what’s given to you in fancy style and obtain a correct program. You will
just have to pay attention to subscripts and superscripts as they may hide the actual order of the characters as you have to type them (for instance, a variable like
‘z01 ’ must by typed as ‘z1’’, not as ‘z’1’.
2 The command line
This section, as well as most of this lesson, will make use of the METAFONT
command line, and thus will be inaccessible for people with an OS without a
command line (users of MacOS until version 9 for instance). Those people can
solve this problem by writing programs containing the commands I will describe,
run them through METAFONT, and check the resulting logfile, however impractical that process is. But for the purpose of this lesson, I will suppose that
you have a command line.
Thus open your command line, go to a directory where you want to save your
METAFONT files, and then enter the command “mf”. You will receive a message which should look like: The “**” prompt indicates that METAFONT is
expecting a filename. But since in this case we don’t want to give it one, just type
191
“\relax” instead. The prompt will change to “*”, indicating that METAFONT
now expects to receive instructions directly from the keyboard. Go ahead and
type the following (admittedly useless) line:
1+1;
You will get the following output:
>> 2
! Isolated expression.
<to be read again>
;
<*> 1+1;
?
Don’t worry about the error (type “s” at the “?” prompt to enter scrollmode and
never have to worry about errors again. They will appear, but the normal prompt
will reappear afterwards). The important thing is that METAFONT calculated
the result of the addition (as you can see on the first line of output). Besides
the addition, you can of course make subtractions (“-”), multiplications (“*”)
and divisions (“/”). And as you’ll see later, METAFONT has a lot more mathematical abilities. But right now, METAFONT is nothing more than a glorified
calculator. So let’s get to the second step, the one which makes METAFONT so
different from other programming languages.
3 Some simple algebra
What? What’s happening? Why are you all running away? Is the word ‘algebra’
so frightening? I see, it reminds you of the nightmarish days at school and the
endless maths classes. Well, don’t worry, I’m not going to give an algebra class
here. But it is important to know at least a little about algebra in order to use
METAFONT to its full potential. So there.
But what is algebra anyway? Simply put, algebra is the idea that if we have
a set of related unknown quantities, we can label them using letters, and write
the relationships between those unknown quantities, which from now on will be
referred to as variables, using the language of mathematics, forming what we
call equations. And if we have enough of those equations, we can even, using
a process called solving, use our equations to obtain the values of the different
variables.
Well, that is exactly how METAFONT works: you write the equations, and it
takes on itself the job of solving them. But an example is better than theoretical
talk. Take back your METAFONT command line, and type:
tracingequations:=tracingonline:=1;
Don’t worry about what it means. It simply asks METAFONT to show you how
it works in the background when you give it equations to solve. Now enter the
following equation:
192
a+b-c=0;
METAFONT will reply:
## c=b+a
*
It just means that METAFONT has recognised that you have given it a relationship between some unknown quantities, and it has rearranged it in a way it likes
it. Then enter:
c=2a;
Note that METAFONT knows enough about mathematical notation to recognise
that ‘2a’ simply means ‘2*a’. Unlike many programming languages, it understands this kind of abbreviations, and will reply:
## b=a
In the process of solving the equations you have given to it, it has replaced in the
first equation the value of c that you gave with the second equation, thus making
a simpler equation depending only on a and b. Finally enter:
a=5;
METAFONT will reply:
## a=5
#### b=5
#### c=10
METAFONT is saying here that by giving it the actual value of a, it was able,
thanks to the other equations, to compute the value of b and c as well, so that now
all your variables are known. You have entered a system of equations to METAFONT, and it has solved it, giving you back the results. Since METAFONT is
doing all the dirty job, isn’t algebra looking much easier now? ^
¨
But now type in the following line:
c=0;
METAFONT won’t like it and will reply:
! inconsistent equation (off by -10).
<to be read again>
;
<*> c=0;
What does this mean? Simply that unlike in other programming languages, “=”
is not an assignment but a relation operator. It means that when you write a
line like “c=0;”, you are not telling “give to c the value 0”, but “I give you an
equation which poses a relationship of equality which between the variable c
and the value 0”. So if through other equations, the variable c has already been
found to have another specific value (here 10), the equation you add contradicts
193
previous results, and thus is inconsistent with the rest and causes an error. This,
with the ability to solve equations as they come, is the main difference between
METAFONT and other programming languages: while other languages are by
nature imperative, i.e. you order them to accomplish some tasks through different
commands (so that in those languages “c=0;” can mean “discard the previous
value of c and assign it the value 0”), METAFONT is by nature declarative, i.e.
you don’t order it around, but you describe things to it, in possibly complex ways,
yet simple to type, and let it find its way around all the relations you’ve given
it. As such, you let it do the dirty work, and you don’t have to bother with the
details. METAFONT does have some imperative commands, but I won’t talk
about them right now. Why? Because otherwise people used to an imperative
programming style would try to do the same with METAFONT, and would not
only make very inelegant programs, but would also prevent themselves from
using the full power of METAFONT, and would without realising it do much
too much work where METAFONT could have done it by itself, and faster.
Do try to remember the difference between declarative and imperative programming, even if you don’t understand very well yet what it means. With the
examples and exercises in this tutorial, you will soon find out how to program
declaratively.
xEXERCISE .1:
Here is a system of equations, presented in a mathematical way:

 a + b + 2c = 3
a − b − 2c = 1

b+c = 4
1. Is this system consistent (before you begin to feed the equations directly to METAFONT, try to solve that question by
yourself, and use METAFONT only to check your results.
It’s often easier to use a tool when you understand how it
works)?
2. If you were to enter the first equation as is in an imperative
programming language, what could be a problem?
1. Yes, the system is consistent, as no equation contradicts another. It is even completely solvable and leads to the solution:

 a=2
b=7

c = −3
2. Entering the first equation as is means entering the following sequence: “a+b+2*c=3’ (note that I wrote “2*c” because
unlike METAFONT, most programming languages don’t know
about those abbreviations), or something similar. The problem that would happen is that for most imperative languages,
‘=’ is an assignment operator, and assigning a single value
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to a sum of variables is something impossible to do (the language cannot guess what value each variable must receive).
Writing the equation as “a=3-b-2*c” would only be marginally
better, because for most imperative languages you cannot put
on the right of an assignment operator an unknown quantity,
and both b and c are unknown at this stage. Thus you see one
of the advantages of descriptive programming over imperative programming: you have much more freedom in entering
the relationships between variables, and are not restricted to
the rigid syntax imperative programming requests.
4 Coordinates and curves
Until now we have worked only with variables, equations and numbers. But isn’t
METAFONT about drawing characters? Indeed it is, so it is time we learn how
it does this.
But first, how does METAFONT know where to draw things? It uses coordinates. You probably already know about coordinates. For instance, you probably
know that the position of a person or a place on Earth or on a map can be described using 2 coordinates: the latitude and the longitude. You may also have
played games of Battleship, where each point on the board is located through
the combination of a letter (for the columns) and a number (for the rows). The
principle behind coordinates in METAFONT is the same: take a piece of graph
paper (with horizontal and vertical lines), and choose some point that you will
call the reference point. Once you’ve chosen this point, you can locate any other
point on the paper by counting the number of units to the right of the reference
point, and the number of units upward from the reference point. And if you need
to go to the left of the reference point, or downward, just use negative numbers,
i.e. count the number of units you need, and add a minus sign in front of them.
This way, you can uniquely locate each point on the paper relatively to the reference point using a set of two coordinates: the x coordinate, which is the number
of units to the right of the reference point, and the y coordinate, which is the
number of units upward from the reference point. And the notation used to write
down this pair is to put them in parentheses, separated by a comma, with the x
coordinate first: (x, y). So, for instance, the point located at the coordinates (5,
10) is the point at 5 units to the right of the reference point, and 10 units upward
from the reference point, while the point located at the coordinates (25, −10)
is located at 25 units to the right of the reference point, and 10 units downward
from that same point.
xEXERCISE .2:
True or false: all points that lie on a given vertical straight line
have the same y coordinate.
False. Check yourself on a piece of graph paper. To reach two different points on the same given vertical straight line from a given
reference point, you need to go up or down from different amounts,
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but for both points the number of units to the right or the left of
the reference point is the same. So all the points that lie on a given
vertical straight line have the same x coordinate. In the same way,
all the points that lie on a given horizontal straight line have the
same y coordinate.
xEXERCISE .3:
Here are the coordinates, relative to the same reference point, of
four different points, called A, B, C and D:
A: (10, 10)
C: (0, 10)
B: (0, 0)
D: (10, 20)
1. Explain where each point is located. Draw them on graph
paper.
2. Which is the top-most point?
3. Which of the four example points is closest to the point of
coordinates (7, 5)?
4. Explain where the point (−2, 6) is located. Which of the four
example points is it closest to?
5. (for the ones who still know a bit about geometry) How would
you call the figure ABCD?
1. In this case, a drawing is better than a long speech, so there!
Note that B is actually also the reference point.
2. D. It is the point with the highest y coordinate.
3. A. See Figure .1 for more details.
4. The point of coordinates (−2, 6) is located at two units to the
left of B, and 6 units upwards. It is closest to C. See Figure .1
for more details.
5. The shape ABCD is called a parallelogram.
METAFONT has its own internal graph paper, consisting of a grid of square
“pixels”. So the unit it naturally uses for its coordinates is the pixel. As for the
position of the reference point, it is also an absolute in METAFONT. We will
see later where it is located on the “internal graph paper”. So take again your
METAFONT command line, and type the following instructions:
drawdot (35,70); showit;
If your installation allows for online displays, you will see a circular dot appear on your screen. Otherwise, just wait for a few more lines. So now add the
instructions:
drawdot (65,70); showit;
You should see a new dot appear, at the right of the previous one (more exactly
at 30 pixels to its right). Finally, type:
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Figure .1: Positions of the different points.
draw (20,40)..(50,25)..(80,40); showit; shipit; end
This should draw a curve, show it if possible, and then ship the whole drawing
to an output file and stop METAFONT. The output file is called mfput.2062gf
and you should find it in the directory you were located at when you started
METAFONT. Now even the people who cannot have online display will be
able to see what they did. To do so, take your command line (with METAFONT
stopped, it should show again its normal prompt) and type:
gftodvi mfput.2602gf
This should create a mfput.dvi file which contains the result of your drawing
instructions. Display it to see METAFONT smile at you, as in Figure .2!
But wait a minute. The last line I made you type made a curve appear, and we
haven’t talked about curves yet! Well, here it comes! ^
đ
Curves are collections of points. Indeed, any curve, whatever its shape or
length, contains an infinity of points, and as such is much more complicated
to describe than points, which just require two numbers to describe their position. But luckily for us, METAFONT is quite intelligent and can do most of
the job for us. The main instruction to draw lines and curves in METAFONT,
as you’ve seen, is the draw instruction. It is incredibly powerful, while quite
innocent-looking. Indeed, all it needs is to receive a series of point coordinates
to draw a curve which will go through all the points you indicated, in the order
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Figure .2: Smile!
you typed them in. So if you simply want to draw a vertical straight line, 100
pixels long, beginning at the reference point, just type:
draw (0,0)..(0,100); showit; shipit; end
Go ahead and try it (to go back to the METAFONT prompt, type directly “mf \relax”
on your command line. Don’t forget to make the resulting output file into a DVI
for people without online display). Don’t worry yet about the “..” between the
two pairs of coordinates. We will come back to it in another lesson. For now,
just remember that the draw command needs to have those two dots between
coordinate pairs. So to draw a straight line, just give draw the location where it
starts and the one where it ends, and it will find out how to draw it by itself (this
is also descriptive programming). We will come back to the abilities of the draw
command in the next lesson. For now, we know enough for what we want to do.
xEXERCISE .4:
Describe the line which would be drawn by the following instruction:
draw (−100, 50)..(150, 50);
This instruction draws a 250-pixel-long horizontal line, beginning
at 100 pixels to the left of the reference point, and ending at 150
pixels to the right of that same point, and constantly at 50 pixels
above the reference point.
5 Just a remark
Before we carry on, let’s have a look at METAFONT’s syntax. As you have
probably seen by now, all instructions in METAFONT are followed with a semicolon ‘;’.1 This is mandatory. The semicolon in METAFONT, as in C, Java or
Except end and input instructions at the end of a program. Since end is used to end a program, it doesn’t
need anything after it (indeed, anything after it won’t be seen by METAFONT anyway). As for the
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Pascal (which happens to be the language the METAFONT source is written
in), is used to indicate the end of a statement. For now, just remember that it
means that each instruction in METAFONT must end with a semicolon, otherwise METAFONT will complain or act strangely.
6 What has Descartes got to do with METAFONT?
Descartes was a French philosopher and mathematician of the 17th century. Despite all the criticism he received during his life and after his death, he is in many
ways the father of the modern scientific thought. He left his mark even when his
theories were proved wrong while he was still living (for instance, his theories
about the weather, as presented in his treatise Les Météores, were completely
wrong, but it doesn’t change that we still call the study of the weather meteorology). But his main work was on geometry, from which we now have Cartesian
geometry.
The coordinate system we’ve been using until now is usually called Cartesian
coordinates. We don’t call it that way because Descartes invented the idea of
using coordinates (indeed, he didn’t), but because he got the idea of applying
algebra to geometry through the use of those coordinates! Indeed, by treating
coordinates as unknowns, i.e. as variables, and apply equations to them, he discovered that he could describe various lines and curves, and even easily prove
theorems of geometry through simple calculus, when until now all that had been
available was complex geometric methods. His work was to revolutionise both
physics and geometry, by providing a good base to describe geometric features
through numbers.
And that’s where we come back to METAFONT! Indeed, METAFONT uses
the full power of Cartesian geometry by allowing calculus to be done using point
coordinates. And so that’s where all this discussion about algebra using METAFONT and declarative programming comes back, because by using the power
of algebra and the ability to just describe a few features through equations that
METAFONT will be happy to solve itself, you can easily tell it where to locate
points without having yourself to know exactly where they are, just where they
are compared to other points! The gain is vital, as we are going to see in the rest
of this lesson.
7 Coordinates as variables
How do we refer to a point with unknown coordinates? We could of course take
two unknown variables a and b and use them as coordinates, defining a point of
coordinates (a, b). But if you needed a lot of points, you’d end up losing track of
what variable is associated to which coordinate of which point. Luckily, METAFONT helps you out in this case (again!). If you label your point with the number
input instructions we have seen until now, they all asked METAFONT to load a program which
contained an end command itself, and as such didn’t need a semicolon after them either.
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1 (for instance, any other value will do), its x coordinate will automatically be
x1 , and its y coordinate will automatically be y1 .2 Note that you don’t have to
declare any point to be labelled as ‘1’. As soon as you refer to x1 or y1 , METAFONT knows that it refers to a point labelled ‘1’.
So you can now define points using their coordinates and always keep track
of what belongs to what. See for instance:
(x 1 , y 1 ) = (0, 0);
(x 2 , y 2 ) = (50, 0);
(x 3 , y 3 ) = (100, 0);
(x 4 , y 4 ) = (0, 50);
(x 5 , y 5 ) = (50, 50);
(x 6 , y 6 ) = (100, 50);
Whatever the number of points you will have, you will never lose track of which
variables are associated to each of them. Also, as you see, you can define directly
pairs of coordinates by using the ‘=’ instruction, as long as on both sides of the
equal sign you have a pair of coordinates (otherwise you have a type mismatch,
and thus an error).
However, for how nice the use of x1 and y1 may be, if you have to write twenty
times the sequence “(xa , ya )”, with different values for a, it can get pretty long
and boring. Luckily, METAFONT provides a convenient shortcut. The notation
“z1 ” is completely equivalent to “(x1 , y1 )”, and can be used whenever the pair is
used. So the previous series of definitions could have been written:
z1
z2
z3
z4
z5
z6
= (0, 0);
= (50, 0);
= (100, 0);
= (0, 50);
= (50, 50);
= (100, 50);
However, if you still have to define your points like that, you are likely to
wonder what we have gained with all those conventions, apart from a little more
clarity. Well, the true advantages of those conventions are yet to come. ^
¨
8 Doing algebra with coordinates
Now that we have defined special variables for the x and y coordinates of points,
nothing obliges us to define them at the same time. Indeed, as long as you don’t
use a point in some drawing instruction, METAFONT will never complain, even
if the x coordinate of such point is defined 100 lines before its y coordinate! Also,
the coordinates are variables in their own right, which can go into all kinds of
Note that in METAFONT , x 1 is a shortcut for x[1]. This will be useful later.
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equations, and can thus be defined by solving those equations, what METAFONT can do in your place.
Figure .3: An upright rectangle
Here is an example. Imagine you want to draw an upright rectangle (i.e. a figure with opposite parallel sides, with one pair of horizontal sides and one pair of
vertical ones). You don’t know yet the exact lengths of the sides, just that it will
definitely be a rectangle. Indeed, the lengths of the sides may depend on an equation which will be solved only later in the program. In any other programming
language, you would just have to remember that you need a rectangle, and make
sure you don’t make a mistake at the end when you can finally define where the
corners of the rectangle will be. But METAFONT is not any programming language, and instead of leaving you the chore of remembering that you want an
upright rectangle, it can do it by itself. How? Well, just look at Figure .3, which
represents such a generic upright rectangle. What general features does it have
that don’t have to do with the lengths of its sides? What about corner alignment?
Indeed, in such an upright rectangle, the points 1 and 2 are horizontally aligned
(as well as 3 and 4), and the points 1 and 4 are vertically aligned (as well as 2
and 3). How does it translate in terms of coordinates? You just need to remember that horizontally aligned points have the same y coordinate, while vertically
aligned points have the same x coordinate. When you remember that, you will
realise that you only need 4 simple equations to tell METAFONT that the figure
formed by the four points 1, 2, 3 and 4 is a rectangle:
y 1 = y 2; y 3 = y 4;
x 1 = x 4; x 2 = x 3;
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And that’s all! From now on, METAFONT will remember that the figure 1234 is
a rectangle, and you will only need to finally get the coordinates of two opposite
points (either 1 and 3, or 2 and 4) to have your whole rectangle perfectly defined.
You can also give indications of distances. For instance, if you want to indicate
that whatever their exact positions, you want point 1 to be always at 100 pixels
to the right of point 2, you just have to write:
x 1 = x 2 + 100;
This last equation can also be written “x1 − x2 = 100;”, which shows that you
can specify the horizontal distance between two points by subtracting their x
coordinates (in the same way, you get the vertical distance between two points
by subtracting their y coordinates).
You can also say that point 1 will always be twice higher than point 2 by
specifying:
y 1 = 2y 2 ;
You can even make the coordinates of some point dependent on other parameters,
that you can define as you wish. For instance, you can say:
x 1 = 12 a;
which means that the x coordinate of point 1 will be equal to half the value of
a certain named a. As you see, thanks to the use of algebra, the possibilities are
infinite!
xEXERCISE .5:
Translate the following equations into “simple English”:
1.
2.
3.
4.
5.
6.
x1 = x2 − 20;
y1 = 3y2 − 100;
2x1 = a;
x2 − x1 = b;
x2 − x1 = y1 − y2 ;
b − y2 = y1 − a;
1. Point 1 is at 20 pixels to the left of point 2.
2. Point 1 is at 100 below a point which is three times higher
than point 2.
3. The parameter a is twice the value of the x coordinate of point
1. In other words, it is identical to “x1 = 12 a;”.
4. The horizontal distance between point 1 and point 2 is equal
to the parameter b, and point 2 will be to the right of point 1
if b is positive.
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5. The horizontal distance between point 1 and point 2 is equal
to the vertical distance between those same points. And if
point 2 is to the right of point 1, then point 1 is above point 2.
6. This is more complicated to describe, and the best way is to
consider the parameters a and b to refer to y coordinates as
well. They can be said to refer to horizontal lines, one at
height a, the other one at height b. Once said, you can describe this equation by saying that it means that point 2 is
below the line of height b by the same distance that point 1 is
above the line of height a.
Here’s another example. Now you have two vertically aligned points 1 and 2,
and you want to find the point exactly in the middle. Since they are vertically
aligned, said point will be vertically aligned with them:
x 3 = x 1 (= x 2 );
What is the condition on the y coordinate of 3 then? Since it’s in the middle,
exactly between 1 and 2, its y coordinate will be the mean of the y coordinates
of 1 and 2, i.e.:
y 3 = (y 1 + y 2 )/2;
Try this formula by drawing yourself some lines on graph paper and find their
middle to convince yourself that it is indeed correct.
xEXERCISE .6:
What if you would like to define an isosceles triangle rather than a
rectangle (reminder: an isosceles triangle is a triangle with at least
two equal sides). To simplify, such an isosceles triangle is represented in Figure .4, and you will just have to describe it in terms of
corner coordinates.
OK, even with the figure, it is slightly more complicated than describing a rectangle. Well, what do you expect? It’s an exercise, it’s
supposed to challenge you. ^
đ
The solution is actually simple. As you have probably seen already,
the points 1 and 2 are horizontally aligned, thus:
y 1 = y 2;
As for the point 3, the fact that the isosceles triangle has two equal
sides indicates that it must be at equal distance from both 1 and
2. In other words, its y coordinate stays unspecified, but its x coordinate is known: it must be exactly between the x coordinates of
the two other points, i.e. their mean. Translated into an equation, it
gives:
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Figure .4: An isosceles triangle
x 3 = (x 1 + x 2 )/2;
And that’s all! Those two equations are enough to describe this
isosceles triangle.
So we know that we can do algebra using coordinates. But what would really
be nice would be to be able to do algebra using pairs of coordinates directly!
After all, we can already use the equal sign between pairs of coordinates, so why
not other operators? Well, that’s what we are going to see in the next section.
9 Vectors
We already know that we can add x and y coordinates. “x1 + x2 ” and “y1 + y2 ”
are both clearly defined. So it’s not a big surprise to define “(x1 , y1 ) + (x2 , y2 )”
as “(x1 + x2 , y1 + y2 )”. This way, we have defined an addition operation on
coordinate pairs (and since the notation “z1 ” stands for “(x1 , y1 )”, we can also
write “z1 + z2 ” for the pair addition). But what does such an operation mean?
How does it translate on the graph paper?
To answer this question, we have to go back at how we defined coordinates.
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We said that the coordinates of a point are the amount of units we move to the
right of and upwards from some reference point. Because of this definition, this
reference point always has the coordinates (0, 0). But now let’s take any point
of coordinates (x, y). Because adding 0 to things doesn’t change anything, we
can also say that its coordinates are (0 + x, 0 + y). And because of the definition
of the addition of pairs we gave earlier, this can also be written as (0, 0) + (x,
y)! Isn’t it familiar? Yes, we see the reference point appearing, and this addition suddenly looks quite similar to the description of coordinates I gave at the
beginning of this paragraph. It’s not surprising. After all, we already know that
adding a certain amount to the x coordinate of a point means “move to the right
by this amount”, and that adding a certain amount to the y coordinate of a point
means “move upwards by this amount”. So adding a pair simply means doing
both additions at the same time, and thus moving both to the right and upwards
by both specified amounts. In other words, pairs of coordinates can describe not
only point locations, but also displacements. Depending on what we do with it,
the pair (5, 10) can mean “the point located at 5 units to the right of and 10 units
upwards from the reference point” or “move to the right by 5 units and upwards
by 10 units”. This second meaning appears as soon as you add this pair to another pair of coordinates. So now we know what an equation like “z2 = z1 + (5,
10)” means in simple English: to get to point 2, start from point 1, move to the
right by 5 units and upwards by 10 units. Try that on graph paper if you need to
by convinced that it’s really what the addition of pairs mean.
Displacements defined through pairs of coordinates are called vectors. You
can picture a vector as an arrow pointing to where the displacement leads, and
whose length is the actual amount of displacement. Vectors and points are completely equivalent, because the coordinates of a point are also the displacement
necessary to get from the reference point to the point in question. Note that just
like points can have negative coordinates, vectors can have negative coordinates
too, indicating displacement to the left and downwards rather than to the right
and upwards. Also, the pair (0, 0) is also a vector, namely the vector “don’t move
at all!” (also called null vector). ^
¨
xEXERCISE .7:
Just like we have defined an addition for pairs, we can easily define
a substraction, through the following definition: (x1 , y1 ) − (x2 , y2 )
= (x1 − x2 , y1 − y2 ). By defining it this way, the substraction of
pairs works exactly like the substraction of numbers, especially in
conjunction with the addition.
So, now that you know what substraction means, can you describe
what “z2 − z1 ” is?
The solution is easier than it may look. Since the substraction of
pairs works exactly like the substraction of numbers, you can write:
z1 + (z2 − z1 ) = z1 + z2 − z1 = z2 (because z1 − z1 = (0, 0), the null
vector). If you compare the resulting equation “z2 = z1 + (z2 − z1 )”
to the explanation of the addition we have given earlier, it becomes
clear that z2 − z1 is the displacement needed to go from point 1 to
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point 2, i.e. the vector that describes the displacement necessary to
go from point 1 to point 2. Please remember this result, it will be
quite useful in the future.
We have now defined both the addition and the substraction. But we can also
multiply coordinates with some value. So can we do that with pairs? Of course!
Simply define it this way: a(x1 , y1 ) = (ax1 , ay1 ), where a is some numerical value.
METAFONT allows you to use all those definitions, and treats pairs of coordinates as points and vectors according to their use, so that you can directly use
what you’ve learned here in METAFONT.
xEXERCISE .8:
1.
2.
3.
4.
z2 = z1 − (30, 50);
3z2 = z1 ;
z2 − z1 = (100, −100);
2(z2 − z1 ) = z4 − z3 ;
1. Point 2 is at 30 pixels to the left of and 50 pixels downwards
from point 1.
2. Point 2 is 3 times as far from the reference point as point 1 (if
this explanation surprises you, check it on graph paper).
3. The vector describing the displacement between point 1 and
point 2 has the coordinates (100, −100). It also means that
point 2 is at 100 pixels to the right and 100 pixels below point
1.
4. The vector describing the displacement between points 3 and
4 is twice the vector describing the displacement between
points 1 and 2 (it points to the same direction but is twice
as long). It also means that the lines 12 and 34 are parallel,
but that point 4 is twice as far from point 3 as point 2 is from
point 1.
We have already seen that we could find the y coordinate from a point halfway between two vertically aligned points by calculating the mean of their y
coordinates:
y = (y 1 + y 2 )/2;
In the same way, the point half-way two horizontally aligned points has the following x coordinate:
x = (x 1 + x 2 )/2;
But how do you do it when the two points are neither vertically nor horizontally
aligned? In this case, you need to use both equations to define both coordinates of
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the middle point. Indeed, the point half-way two other points 1 and 2 (whatever
their positions) has for coordinates the means of their x and y coordinates. Do
you need to specify both equations then? Of course not! Thanks to the definitions
that METAFONT uses for the addition and the multiplication, you can simply
write:
z 3 = (z 1 + z 2 )/2;
You can check yourself that the formula is correct.
However, calculating the middle point between two points is a little limited.
What if we want to specify a point on the line defined by points 2 and 3, but
at one-third of the distance between those points (closer to point 1 thus)? Or
at nine-tenths of this distance (and thus closer to point 2)? Or even a point on
this same line, but not between 1 and 2, like for instance a point aligned with
points 1 and 2, as far from point 1 as point 2, but in the other direction? Or 3
times as far from point 1 as point 2, and in the same direction? It may sound like
a complicated problem, but actually it is quite simple. Remember that z2 − z1
refers to the vector between point 1 and point 2. It has the direction of the line
made by those points, and its length is the distance between points 1 and 2. And
if you multiply it by a certain value, you will get a new vector, of same direction,
but with a different length. So if you add this new vector to z1 , you will get a
point on the line formed by 1 and 2, but depending on the chosen multiplicative
value you can reach any point on this line! Let’s see a few examples so that you
can understand what I mean:
• z1 + 0*(z2 − z1 ) = z1 . So if you take as value 0, you get point 1.
• z1 + 1*(z2 − z1 ) = z2 . So value 1 corresponds to point 2.
• z1 + .5*(z2 − z1 ) = .5(z1 + z2 ). This is the definition of the point half-way
between those two points, which is thus associated to the value .5.
• z1 − (z2 − z1 ) = 2z1 − z2 . You can check on Figure .5 that it corresponds
to the point as far from 1 as 2 but on the opposite direction.
• z1 + 2(z2 − z1 ) = 2z2 − z1 . You can check on Figure .5 that it corresponds
to the point twice as far from 1 as 2 and in the same direction.
What we have done here is called a parametrisation of the line defined by
the points 1 and 2. That’s because if we take a parameter t, we can define all
points of the line defined by the two points 1 and 2 through the formula z1 +
t(z2 − z1 ). It is a very important and useful formula in METAFONT (aligning
points together is one of the main things you’ll do when trying to find where to
put points to draw something with METAFONT). However, it is also a formula
difficult to remember. So METAFONT provides a practical shortcut for it: the
syntax “t[z1 , z2 ]” corresponds exactly to the formula “z1 + t(z2 − z1 )”. So you
can easily define any point aligned with points 1 and 2 by using this formula with
the correct parameter (which can be unknown). And note that this shortcut works
for coordinates separately too: “t[y1 , y2 ]” stands for “y1 + t(y2 − y1 )”.
xEXERCISE .9:
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Figure .5: The points on the line and their parameters
Redo Exercise .6, but this time using the “t[a, b]” notation (extremely easy).
The only difference from the first solution of this exercise is that you
can now simply write that the x coordinate of point 3 follows this
equation:
x 3 = .5[x 1 , x 2 ];
xEXERCISE .10:
1. z3 = 74 [z1 , z2 ];
2. z3 = .5[z1 , z2 ] − (0, 100);
3. z3 = (.2[x1 , x2 ], .8[y1 , y2 ]);
1. Point 3 is aligned with points 1 and 2, and between them at 47
of the distance between those two points (closer to 2 than to
1).
2. Point 3 is situated at 100 pixels below the middle point between points 1 and 2.
3. A drawing will give you a good idea of the situation, so check
Figure .6. As you can see, point 3 is vertically aligned with
the point at .2 of the distance between 1 and 2 (same x coordinate) and horizontally aligned with the point at .8 of the
distance between 1 and 2 (same y coordinate).
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Figure .6: Position of point 3 compared to points 1 and 2
xEXERCISE .11:
True or false: t[z1 , z2 ] = (1 − t)[z2 , z1 ].
True. You can check it by replacing the expression with its definition:
(1 − t)[z2 , z1 ] = z2 + (1 − t)(z1 − z2 )
= z2 + z1 − z2 + tz2 − tz1
= z1 + t(z2 − z1 )
= t[z1 , z2 ]
So, we can now define any point which is aligned with two other points. But
what if we just want to indicate that a point is aligned with two other points,
but you don’t know yet exactly where it is located? Of course, we could use
the formula “z = t[z1 , z2 ]” with an unknown t, and only later define the value
of this variable. This works perfectly, but only if we can eventually define t.
Indeed, you may want to finally define your point through alignment with other
points (thus finding the intersection between two lines), or through one of its
coordinates. In those cases, finding the actual value of t would be at best uneasy,
at worst impossible. Luckily, METAFONT provides a special variable exactly
for this purpose called whatever. The whatever variable means exactly what its
name says: “I don’t care what that actual value is”. ^
¨ So you can now specify
that a point will be aligned with the points 1 and 2 without having to specify
where exactly it will be found by using the equation: z = whatever[z1 , z2 ]. This
way, you will be able to define the actual position of this point through another
equation while you will always be sure that the point will always be aligned with
points 1 and 2. This whatever variable is very powerful and can be used in plenty
of situations, not only with the bracket notation, wherever you have to add a
parameter but don’t know yet its actual value, or that value is irrelevant at the
moment. We will encounter it quite often in the course of this tutorial (and you
will use it very often in your programs).
xEXERCISE .12:
209
What does the system of equations:
z 5 = whatever [z 1 , z 2 ];
z 5 = whatever [z 3 , z 4 ];
mean? Is it possible for such a system to be inconsistent?
If you read carefully the paragraph introducing the whatever variable, you should find the solution already written. ^
¨ The first equation says that point 5 is aligned with points 1 and 2 (without specifying exactly where it is). The second equation says that it is also
aligned with points 3 and 4. So point 5 is simply the intersection of
the lines defined by points 1 and 2 and points 3 and 4.
And yes, such a system may be inconsistent. If the two defined lines
happen to be parallel, they can never intersect and point 5 cannot
exist. That’s why for as powerful as it may be, try to make sure that
your lines do intersect before trying to find their intersection with
such a system of equations.
10 Finally, let’s draw a character!
So, we have learned about the command line of METAFONT, the basics of its
syntax, its descriptive rather than imperative nature, and have had a long (but
necessary) lesson about algebra and Cartesian geometry. Because of the theoretical nature of this lesson, you are probably wondering now whether it is actually
useful to know so much about algebra to draw characters. Well, let’s show that
by applying our newly acquired knowledge to the drawing of a character. In order to be simple but at the same time challenging, let’s draw a simple capital E,
of the kind you find in the name METAFONT. An example of what we want is
available in Figure .7.
But since we don’t want to be that simple, we’re going to add a little something: we are going to base our character on the golden number, a number which
is supposed to be indicative of “perfect” proportions. Some people see it everywhere, as you can check in this site.3 The golden number is usually written Φ
(Phi) and its value is:
√
1+ 5
Φ=
≈ 1.6180339887 . . .
2
So let’s take our METAFONT command line again (once again, type “mf \relax”
on your command line to obtain it), and begin with defining a variable which will
contain the value of Φ. Don’t worry about the square root, METAFONT provides us with a command called sqrt which calculates it. So just enter:
http://goldennumber.net/
210
Figure .7: A simple E character
Phi=(1+sqrt5)/2;
Note that METAFONT is case-sensitive, so that Phi and phi are two different
variables for it (be aware of it if you don’t want to make mistakes) and that
you needn’t put a space between sqrt and its argument (nor put its argument in
parentheses, as necessary in many other programming languages). METAFONT
commands can never contain figures, so METAFONT has no problem reading
that (but if you want to put a space “sqrt 5” or parentheses “sqrt(5)”, go
ahead! METAFONT is flexible enough to handle all those different syntaxes).
Now we are going to define the general dimensions of the character, namely its
width, and its height (we’ll see later that characters have two other dimensions,
but for this one two are enough). Let’s say that we want a character with a width
of 100 pixels. Let’s put that into a variable called w, by entering:
w=100;
As for its height, since we said this character should be based on the golden
number which is based on proportions, let’s define it by saying that it’s the width
multiplied by the golden number:
h=Phi*w;
So that the ratio height/width will be equal to the golden number.
Now let’s define the basic points needed to draw the character. The only points
we need are the extremities of the four strokes (1 vertical, 3 horizontal) necessary
to draw this character. So we only need six points, and we are numbering them
as in Figure .7. The E character contains three horizontal lines, which means that
211
those points must be horizontally aligned two by two. Indeed, points 1 and 6 are
aligned at the bottom of the character, points 3 and 4 are aligned at the top of the
character, and points 2 and 5 are aligned in between. Let’s enter the equations
that translate those alignments:
y1=y6=0;
y3=y4=h;
y2=y5;
As you see, we have not only translated the alignments, but also indicated that
points 1 and 6 are at the bottom of the character and points 3 and 4 at the top
(note how we concatenate equations to win space. METAFONT is happy to
allow those kinds of shortcuts ^
¨ ). We’ve not explicitly defined the y coordinates
of points 2 and 5 because we don’t know exactly yet where they are going to be
located at. The E character contains also a vertical stroke, which is translated by
saying that points 1, 2 and 3 are vertically aligned:
x1=x2=x3=0;
The vertical stroke is at the very left of the character, so we could also define
precisely those coordinates.
Now, we still have a few coordinates to define. First, we want the bottom and
top horizontal strokes to be both as long, and as long as the full width of the
character. But we don’t want the middle stroke to be as long, or the E character
would look a bit too wide. So we are going to make the middle stroke smaller,
so that the ratio of the width of the character over its width is again the golden
number (or that the width of the smaller stroke multiplied by the golden number
is the width of the character). We achieve that by writing:
x4=Phi*x5=x6=w;
So finally all that is left is to find how high points 2 and 5 must be. Since they
must have the same height according to the equations we already typed in, we
can work with a single point, 2 for instance. To put the golden number in there
too, we are going to define the height of point 2 so that the ratio of the area above
the middle stroke and the area under that same stroke is equal to the golden
number. If you remember that the substraction of coordinates allows to calculate
the distance between two points, you should agree that the two areas in question
have the following values: w*(y3 − y2 ) and w*(y2 − y1 ). Since the width w
appears in both formulae, it will disappear completely when you take the ratio of
those areas, and we can finally type in the right equation:
(y3-y2)=Phi*(y2-y1);
Now METAFONT has all the information it needs to locate all the points, so
that we can begin drawing. The four strokes are easy to draw, just type in:
draw
draw
draw
draw
212
z1..z6;
z2..z5;
z3..z4;
z1..z3;
The first three instructions draw the horizontal strokes, the last one the vertical
stroke. Let’s now label our points so that they’ll appear on the proofsheet we are
going to make (we will see in another lesson how the labels command works.
For now it’s unimportant):
labels(range 1 thru 6);
And let’s finish by displaying our beautiful job (if online display is available),
send it to the file mfput.2602gf and stop METAFONT:
showit; shipit; end
Now if you transform the resulting mfput.2602gf file into a DVI file and display
it, you should get a result identical to Figure .7. It’s done! You’ve created your
first character!!!4
Let’s sum up this section by putting together all the instructions necessary to
draw this E character:
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Phi=(1+sqrt5)/2;
w=100;
h=Phi*w;
y1=y6=0;
y3=y4=h;
y2=y5;
x1=x2=x3=0;
x4=Phi*x5=x6=w;
(y3-y2)=Phi*(y2-y1);
draw z1..z6;
draw z2..z5;
draw z3..z4;
draw z1..z3;
showit; shipit; end
xEXERCISE .13:
Let’s check that you have understood how things work by creating
another character by yourself, in this case a simple capital A as
shown in Figure .8. Like the E character defined in this section, this
character must be based on the golden number, so that:
• the ratio of its height by its width is equal to the golden number;
• its horizontal bar is at the same height as the horizontal bar
of the E character we drew earlier.
To make this character comparable with the E character, you can
make it with a 100-pixel width.
Note that in this form, it is not possible to make an actual font out of what we wrote. We will find out later
in this tutorial what we are still missing to make that possible).
213
Figure .8: A simple A character
To draw such a A character, we need five points, corresponding
once again to the ends of the three strokes we need to draw it. We
will label those points as in Figure .9.
First thing first, we need to define the golden number, as well as the
width and the height of the character. This part is identical to the
beginning of the definition of the E character:
Phi=(1+sqrt5)/2;
w=100;
h=Phi*w;
Then we need to position the points 1 and 5 at the bottom of the
character. They are horizontally aligned at the bottom of the character and on both sides of it, separated by a distance equal to the
width of the character. We could of course first indicate that they
are aligned, and then give their exact position, but we can actually
define them completely by a single line:
z1=z5-(w,0)=(0,0);
Remember that z refers to the pair of coordinates of a point, and
that you can add and subtract pairs as well as coordinates themselves. We use this here to define both points in a single line. The
first equality on the line says that point 1 is at w pixels to the left
214
Figure .9: A simple A character, with labels
of point 5 and at the same height (by subtracting 0 on the y coordinate). The second says that point 1 is at the coordinates (0, 0),
which at the same time completely defines point 5 through the first
equality.
We still have three points to define. Point 3 is easy to define: it must
be at the full height of the character, and horizontally it is exactly in
between points 1 and 5. We have already seen how to use the “t[a,
b]” notation for this kind of definitions:
z3=(.5[x1,x5],h);
Now only point 2 and 4 are left to be defined. Since they are used to
define the middle horizontal stroke, we must indicate that they are
horizontally aligned:
y2=y4;
Now, we also know that point 2 must be on the line defined by points
1 and 3, and point 4 on the line defined by points 3 and 5. But since
those lines are neither vertical nor horizontal, we cannot do that
through a direct equation on their coordinates. Luckily, we remember that we have a way to indicate alignment whatever the position
of the aligned points:
215
z2=whatever[z1,z3];
z4=whatever[z3,z5];
Finally, we must indicate that we want this horizontal stroke at
the same vertical position as the middle stroke of the E character
we created earlier. Actually, this is just a matter of copying and
pasting. Indeed, “same vertical position” means that the definition we’re interested in only involves y coordinates, and thus must
be identical to the definition of the vertical position of the middle
stroke of the E character! ^
¨
(y3-y2)=Phi*(y2-y1);
Since the definition involves only y coordinates, the fact that the
line defined by points 1 and 3 is slanted in this case, while it wasn’t
in the case of the E character, doesn’t change anything.
Now we can actually draw the three needed strokes:
draw z1..z3;
draw z3..z5;
draw z2..z4;
And we can finish by labelling all the points and ship the result to
mfput.2602gf:
showit; shipit; end
And we now have our A character exactly as we wanted it!
To sum up this whole exercise, here is the whole list of instructions
we used to define it:
1
2
3
4
5
6
7
8
9
10
11
12
13
14
216
Phi=(1+sqrt5)/2;
w=100;
h=Phi*w;
z1=z5-(w,0)=(0,0);
z3=(.5[x1,x5],h);
y2=y4;
z2=whatever[z1,z3];
z4=whatever[z3,z5];
(y3-y2)=Phi*(y2-y1);
draw z1..z3;
draw z3..z5;
draw z2..z4;
showit; shipit; end
11 Before you carry on. . .
Once again, this was a heavy lesson, introducing a lot of new concepts, and asking a lot from you. But you can now breathe again: the next lessons will be lighter
and more focussed in contents, thus easier to follow for you. Also, thanks to the
base this lesson has provided you, you should have little trouble following the
rest of this tutorial. This is why you must make sure to have understood everything which has been introduced in this lesson. So don’t hesitate to come back
to it after a night of sleep, and to work on it for several days. You can also try
to draw a few more characters according to the same principles, to check your
understanding of METAFONT. The capital F, H, K, L, N, T, V, X, Y and Z characters are good candidates for such a work. Take that as a sort of “homework”,
to do if you feel like doing it (but I strongly urge you to actually do it. The best
way to learn METAFONT is by using it, and you can never use it enough ^
¨ ).
And if you want a “correction” of this “homework”, just send me what you did at
metafont.tutorial@free.fr, and I’ll be happy to look at your programs and
correct them if necessary. You can also contact me if you have any question at
this same address (or through the (La)TeX/METAFONT-for-Conlangers5 mailing
list). But for now, go and have some rest! ^
¨
217
Pens and Curves
1 More algebra
In Lesson , we defined what algebra is, and saw some of the operations that can
apply to numerical values (like the addition, the subtraction, the multiplication
and the square root operator sqrt), and to pair (vectors or points) values (addition,
subtraction, multiplication by a numerical value and the “t[z1 , z2 ]” operation).
If those were the only operations METAFONT allows, we would be rapidly
very limited in what we can do. Luckily, METAFONT provides a wide range of
operations, and we are going to see a few of them here.
But first, in order not to drown in operations, we need to put some order into
them. An obvious way to classify operators is by the type of values they can
apply to. Let’s do it this way, and let’s put our operators in three categories:
• operators which apply to numerical values,
• operators which apply to pair values,
• angle-related operators (this category may surprise you, but you’ll see
soon enough why I put them in a separate category).
Note that those categories are not exclusive. Some operators, like sqrt, can apply
only to numerical values. Others (that we haven’t seen yet) can apply only to
pair values. But many (like the brackets operator) can apply to both numerical
and pair values, just like the addition, the subtraction and the multiplication by
a numerical value do. As for the angle-related operators, they are also separated
into operators which apply to numerical values and operators which apply to pair
values, but they are put in their own category because they use a special kind of
numerical values.
1 Numerical operators
Before talking about operators, let’s see two more special numerical variables
METAFONT defines that can be of some use. We have already seen the special variable whatever which is used when you don’t want to specify a value.
METAFONT has two other interesting variables. The first one is epsilon, which
corresponds to the smallest positive value different from zero METAFONT can
handle. As such, it’s also the precision of calculations with METAFONT, and
1
its value is 65536
. The second one is infinity, which despite its name is not really
219
infinite. Rather, it’s the highest value METAFONT can handle without complaining. By definition, infinity is equal to 4096 − epsilon.1
We have already seen that sqrt takes the square root of a numerical value. How
about the reciprocal operation, i.e. to take the square of a value? METAFONT
provides the “**” operator here, with “a**b” meaning: “a to the power of b”.
So to take the square of a, just write: “a**2”. If you rather want the cube of it,
simply write “a**3”. Other powers are as easily available with this operator.
xEXERCISE .1:
What is the value of “2**12;”? Feed METAFONT with such an
expression and look at the result. Is it surprising?
The value of “2**12” (of 2 to the 12th power) should be 4096.
However, if you feed it to METAFONT, you will rather get 4095.99998
as a result, which happens to be the value of infinity. This is due
to the definition of the “**” operator, which is defined in a way
that allows non-integer powers (i.e. METAFONT allows things
like “2**(1/3);”, which happens to compute the cubic root of 2)
and even negative ones, but loses precision at high values.
METAFONT provides the “/” operator for exact division. But sometimes
you’d rather want to do an integer division. You can do that with the “div” and
“mod” operations. “a div b” gives the result of the integer division, and “a mod
b” its remainder.
xEXERCISE .2:
How would you use those operations to ensure that a number will
be a multiple of another one (very easy)?
You only need the mod operator for that. If a number is a multiple of
another, the integer division of the first number by the other will be
exact, and the remainder will be zero. So we will have the equality:
“a mod b = 0”.
Other practical operators are “abs”, “max” and “min”. “abs” gets rid of possible minus signs (i.e. it leaves positive numbers alone and takes the opposite of
negative numbers, thereby making them positive). So for instance “abs(-7)” is 7.
“max” takes a list of values between parentheses and gets the highest value in the
list. ‘min” takes the lowest value instead. For instance, “max(2, 5, 8)” is 8, while
“min(2, 5, 8)” is 2.
xEXERCISE .3:
METAFONT can handle higher values during calculations, but the final result should always be
inferior or equal to infinity, otherwise it will strongly complain.
220
Give the results of the following operations:
1.
2.
3.
4.
5.
6.
abs(12).
1.
2.
3.
4.
5.
6.
12.
15.
2.
−5.
5.
5.
abs(−15).
max(−5, 2).
min(−5, 2).
max(abs(−5), 2).
abs(min(−5, 2)).
3.1416
−3.1416
1.5
1.49
floor
3
−4
1
1
ceiling
4
−3
2
2
round
3
−3
2
1
Table .1: Comparison of the effects of “floor”, “ceiling” and “round”.
Finally, despite the fact that METAFONT works happily with non-integer
values, you will sometimes want to round things up (or down ^
đ ). METAFONT
provides three different operators for rounding: “floor”, “ceiling” and “round”.
Their differences are illustrated in Table .1. “floor” rounds numbers to the closest
integer inferior to them. “ceiling” rounds them to the closest integer superior to
them. As for “round”, it rounds numbers to the integer absolutely closest to them
(and for numbers whose fractional part is exactly one half, like 1.5 or −2.5, it
rounds them to the integer immediately superior).
xEXERCISE .4:
The following cases define two variables a and b. In each case, find
out which of a and b has the highest value.
1.
2.
3.
4.
5.
a = floor(5.8) and b = round(5.8).
a = floor(−5.2) and b = round(−5.2).
a = max(floor(2.8), ceiling(3.2)) and b = round(min(3.2, 2.8)).
a = abs(floor(−6.1)) and b = ceiling(abs(−6.1)).
a = round(.5) and b = round(−1.5) + 1.
1. a = 5 and b = 6. Thus b has the highest value.
221
2.
3.
4.
5.
a = −6 and b = −5. Thus b has the highest value.
a = 4 and b = 3. Thus a has the highest value.
a = 7 and b = 7. Thus a and b are equal.
a = 1 and b = 0 (remember that for values with a fractional
part exactly equal to one half, “round” behaves exactly like
“ceiling”). Thus a has the highest value.
2 Pair operators
Just like with numerical values, METAFONT predefines a few practical pair
values. Those are called up, down, left, right and origin, and their respective
values are (0, 1), (0, −1), (−1, 0), (1, 0) and (0, 0). In other words, origin always
refers to the reference point (indeed, the reference point is often called “origin”,
and I will often call it that way in the rest of this tutorial), and the four other
variables are best described as vectors indicating the four simplest directions
(indeed, adding up to any pair simply means “move one pixel up”, and similarly
with the other variables).
We have already seen the “t[z1 , z2 ]” operator. This operator treats pair variables as points (it returns the coordinates of a point aligned with the two points
it took as operands). Another operator also important, but treating pair coordinates as vectors rather than points, is “length”. As its name indicates, the operator
“length” returns the length (a numerical value thus) of a vector. It is particularly
useful because it allows you to compute the distance between two points. Indeed, remember that if you have two points labelled 1 and 2, z2 − z1 is the
vector connecting the two points. So if you take “length(z2 − z1 )”, the length
of that vector, you will have computed the distance between those two points. It
can be very useful when you want to define a point according to its distance to
another point.
xEXERCISE .5:
Try to guess the value of “length up”, “length down”, “length left”
and “length right”. What about “length origin” (easy)?
The solution should be obvious: all those vectors have for length
1. Indeed, they correspond to a movement of only 1 pixel at a time,
which must correspond to a distance of 1 (if you are not convinced
yet, check it on some graph paper or by running METAFONT).
As for the length of origin, remember that (0, 0) can also be considered to be a vector meaning “don’t move at all”. When you don’t
move, the distance you make is obviously 0. And indeed, the length
of origin is 0.
xEXERCISE .6:
“length(z2 − z1 )” is the distance between two points labelled 1 and
2. What about “length(z1 − z2 )”? Whether you begin at point 1 to
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reach point 2 or at point 2 to reach point 1 doesn’t change anything,
if you always go in a straight line. So “length(z1 − z2 )” is also the
distance between points 1 and 2.
We have already seen that it’s possible to define the product of a vector by a
numerical value. But is it possible to define a product between vectors? Well, not
really. There is such a product, but the result of it is a numerical value rather than
another vector. Such a product is called the scalar product, usually noted with a
dot, and with the following definition:
(a, b) · (c, d) = ac + bd
In METAFONT, the scalar product is done using the operator “dotprod”, which
is put between its operands. In other words, the expression above would be written in METAFONT as “(a, b) dotprod (c, d)”. Now you probably wonder what
use such a strange definition could have. Well, it happens that with this definition, the scalar product of two vectors is equal to 0 when they are orthogonal,
i.e. when there is a right angle between them. It means that with this product,
you can easily define perpendicular lines. Imagine that you have a line defined
by two points 1 and 2, and that you want to define another line, passing by two
other points 3 and 4, and perpendicular to the first line. All you need is to enter
the equation “(z2 − z1 ) dotprod (z4 − z3 ) = 0”, and you will be sure that there
will always be a right angle between those two lines.
3 Angle operators
All the operations we have seen until now refer to numerical values taken as
lengths and distances. But in geometry, another important kind of numerical
values are angles, and many geometrical operations involve angles rather than
distances.
In METAFONT, angles are just numerical values. They are not formally differentiated from length values. However, they are treated differently by operators
which expect to receive angle values. The main difference is that METAFONT
measures angles in degrees, so a numerical value used as an angle value will
be taken to be degrees rather than pixels. What it basically means is that you
shouldn’t mix length and angle values, and thus shouldn’t use the same variable
as an angle value and as a length value at the same time. You will only create
confusion, for yourself and for anyone reading your code.
The basic operators involving angles are of course the cosine and the sine.
They are called “cosd” and “sind” respectively in METAFONT (the ‘d’ is there
to remind you that angles in METAFONT are measured in degrees, rather than
radians for instance). However, you will probably hardly ever use them in a
METAFONT program. That’s because METAFONT provides two other operators which will usually be enough for any font designer. Those operators are
called “dir” and “angle”. “dir” takes as value an angle, and returns a vector of
length 1 which is at the angle you defined with a horizontal line (note that angles
in METAFONT are measured positively counterclockwise, and that 0 corresponds to the horizontal position pointing to the right. It means that with a positive angle—at least one between 0 and 180◦ —the vector will point upwards, and
223
downwards with a negative angle). So for instance, up can be alternatively defined as “dir 90”. “angle” is the reciprocal operation: it takes a vector as operand,
and returns the angle this vector makes with horizontality, with angles once again
measured positively counterclockwise. So the expression “angle up” will return
90.
xEXERCISE .7:
Try to guess the results of the following expressions:
1. dir 25 dotprod dir 115.
2. angle (1, 1).
3. angle (0, 0).
1. 0. Indeed, angles can be added and substracted, and if two
vectors make respectively an angle of 25 and 115 degrees
with horizontality, it means that the angle between those two
vectors is 115 − 25 = 90, i.e. those vectors are orthogonal. So
their scalar product must be 0.
2. 45, i.e. exactly half a right angle.
3. This is a trick question. Indeed, since (0, 0) has a zero length,
it cannot make an angle with anything! ^
đ METAFONT recognises that by returning the value 0, but with an error message.
So if you want to use the “angle” operator with a vector, you
should try to make sure this vector is not (0, 0).
2 Transformations
Until now, we have only seen algebraic operations, i.e. operations which apply to
values, whether numerical or pairs, but have no other meaning then that. Transformations are something different. Transformations are geometric operations,
i.e. operations whose purpose is to modify the shape and/or position of a figure.
As such, they cannot apply to numerical values at all, but only to pair values,
whether those are to be taken as points or vectors. Transformations can of course
be described as algebraic operations (that’s after all the main point of Cartesian
geometry to describe everything geometric in algebraic terms), but this is only a
description. Transformations have mainly a geometrical definition, and it’s best
to introduce them that way. Indeed, the way they work in METAFONT allows
you to concentrate on the geometrical meaning of those transformations rather
than their algebraic details.
All transformations in METAFONT have a similar syntax: “pair value transformed some parameter(s)”. It means that the transformation must always be put
behind the pair value it applies to.
There are two transformations you have actually already been introduced to
without realising it. Those are called “shifted” and “scaled” in METAFONT.
“shifted” takes a vector as parameter and, when applying to a pair value, moves
it by the amounts defined by the vector. As such, it is in fact completely identical
to the addition of pairs. Indeed, we have: “(x, y) shifted (a, b) = (x + a, y + b)
224
= (x, y) + (a, b)”. As for “scaled”, it takes a numerical value as parameter, and
multiplies both coordinates of the pair it applies to by this value. As such, it is
identical to the multiplication of pairs by a numerical value: “(x, y) scaled s =
(sx, sy) = s(x, y)”. A reason why it is preferable to use the transformations rather
than the simple operations is that their syntax makes it clearer which kind of
geometric transformation we are talking about. Other reasons will become clear
in the rest of this tutorial.
(a)
(b)
Figure .1: Examples of (a) “shifted” and (b) “scaled” transformations.
“scaled” multiplies both coordinates of a pair by the same value. As such,
it effectively scales figures with the same coefficient in both the horizontal and
the vertical direction. But sometimes, you want to stretch or shrink a figure only
horizontally, or only vertically, or in both directions but with different coefficients in each direction. METAFONT provides the transformations “xscaled”
and “yscaled” for this job. They work like “scaled”, but they apply only to one
coordinate of a pair, the one in their name. So “(x, y) xscaled s = (sx, y)” and
“(x, y) yscaled s = (x, sy)”. And if you want to apply two different coefficients
to the coordinates at the same time, just put the two transformations one after
the other. It’s one of the advantages of the syntax of transformations that you can
concatenate them as you wish: “(x, y) xscaled s yscaled t = (sx, ty)”.
xEXERCISE .8:
When you concatenate “xscaled” and “yscaled” together, you can
do that in any order without changing the result (“xscaled s yscaled
t” is the same as “yscaled t xscaled s”). But is it true in general?
Is the result of two transformations always independent of their
order?
The solution in one word is: no. It’s easy to find a example:
(x, y ) shifted (a, b) scaled s = (x + a, y + b) scaled s = (s(x + a), s(y + b)),
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Figure .2: Examples of “xscaled” and “yscaled” transformations.
but:
(x, y ) scaled s shifted (a, b) = (sx, sy ) shifted (a, b) = (sx + a, sy + b),
obviously two quite different results!
As you see, the order in which the transformations are given is important to understand their final result. You just have to read the
transformations as they are given, step by step from left to right, to
understand their result.
With concatenations of shifts and the different kinds of scaling you have been
introduced to, you can accomplish quite a lot already. But you will always be
quite limited in what you can do unless you introduce rotations. Rotations, which
consist in turning a figure (while keeping all its dimensions equal) around some
point, are one of the most important and practical transformations there are. Of
course, METAFONT provides rotations. Actually, it provides us two rotation instructions. The first and simplest one is “rotated”. It takes an angle as parameter
and means: “rotate the point around the reference point (the point of coordinates
(0, 0)) by the given angle”. As usual, angles are measured positively counterclockwise. The second instruction is “rotatedaround”. It takes two parameters: a
pair and an angle. They must be separated by a comma and put in parentheses
(as such: “rotatedaround (z1 , 90)”). The angle has still the same meaning, while
the pair gives the coordinates of the point around which the rotation has to be
done. In other words, “rotated” is actually a special case of “rotatedaround” (indeed, “rotated angle” can be simply defined as “rotatedaround ((0, 0), angle)”).
Nevertheless, it’s a practical shortcut.
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Figure .3: Examples of “rotated” and “rotatedaround” transformations.
xEXERCISE .9:
Guess the result of “right rotated 90”. What about “right rotated
−90”?
By rotating right by 90° counterclockwise around the reference point,
you simply reach up. Similarly, by going clockwise (which is the
meaning of using a negative angle), you just reach down.
Last, but certainly not least, a very important transformation, very useful when
you create shapes with mirror symmetries, is the reflection, which consists in taking a point directly opposite to another point on the other side of a line (see Figure .4 to understand how it works). It is so important that the general term “symmetry” is usually used by people to refer exclusively to reflections, and objects
are called “symmetric” when they are unchanged through reflection about a certain line. For this purpose, METAFONT provides us with the “reflectedabout”
transformation, which takes as parameters two pair variables, which represent
two points defining the reflecting line. Those two variables must be separated by
a comma and between parentheses.
xEXERCISE .10:
List all the possible transformations which would transform a point
of coordinates (x, y) into a point of coordinates (−x, −y).
The two most obvious solutions to this problem are “(x, y) rotated
180” and “(x, y) scaled −1”. Of course, you can also choose inefficiency and write “(x, y) rotatedaround ((0, 0), 180)” and “(x, y)
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Figure .4: Examples of “reflectedabout” transformation.
xscaled −1 yscaled −1”, which are just longer ways to write the
same things as above. ^
đ
But that’s not all! Nothing says that your transformation cannot
depend on the coordinates of the point! In that case you can also
write “(x, y) shifted (−2x, −2y)”!
And if you are not afraid of letting METAFONT make a few calculations, you can even transform (x, y) into (−x, −y) through a
reflection! Indeed, remember the “dotprod” operation, which can
be used to define orthogonal vectors, i.e. perpendicular lines. And
as it happens, by definition of the reflection, the reflection line must
be perpendicular to the line defined by a point and its image by the
reflection. So if you define a line perpendicular to a point and its image and passing exactly in the middle between those two points (in
our case, passing by the origin), you will have the line necessary
for your reflection. This can be done with the following instructions:
z 1 dotprod ((x, y ) − (−x, −y )) = 0;
y1 = y;
Once done, as you can see in Figure .5, “(x, y) reflectedabout (z1 ,
(0, 0))” will indeed be (−x, −y).
Of course, the last two possibilities, and especially the last one,
are extremely contrived. Nobody in the right mind would want to
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Figure .5: A reflection transforming (x, y ) into (−x, −y ).
transform a point into its exact opposite around the origin through
such complicated operations! So for actual use, you are of course
urged to use the simple transformations given as first answers. They
are quick to type, and they don’t depend on the actual coordinates
of the point to work correctly! ^
¨
With those transformations, you are now equipped to define point positions
quickly and correctly by just translating into instructions the general characteristics of the characters you want to draw. It is thus time to learn a bit more about
drawing with METAFONT.
3 Curved lines
Curved lines, also simply called curves, are lines which are not straight. OK, this
is a rather silly definition, but I just wanted to make sure that it was clear for
everyone what I was talking about. In this tutorial, as you have probably guessed
by now, I usually reserve the word “line” to refer to straight lines only, and use
the word “curve” for curved ones. This is different from the usual use of the word
“line”, which in common speech refers to any kind of line, bent or not.2 Let’s
hope that with this paragraph the distinction I make between lines and curves
will now be clear. ^
¨
Until now, we have seen only how to draw straight lines (use the draw instruction with the coordinates of the extremities of the line separated by “..”).
However, in Section 4, we have had a glimpse of how to draw curves. In the
“Smile!” example, the actual smile was a curve drawn by the instruction:
Note that my use of the words “curve” and “line” is strictly personal and in no way representative of some
metaphysical distinction METAFONT would do between straight lines and bent curves. Indeed,
METAFONT doesn’t make a distinction at all and treats all curves and lines identically.
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draw (20, 40)..(50, 25)..(80, 40);
As you see, draw is here followed by the coordinates of three rather than two
points, also separated by “..”. This is the very secret of the powerful draw command of METAFONT. You can feed it with any number of coordinate pairs
(always separated two by two with “..”), and it will draw a smooth curve passing by all those points (in the order you typed them in) as well as it can! Check
Figure .6 to see the draw command in action.
draw z 0 ..z 1 ..z 2 ..z 3 ..z 4 ..z 5 ;
draw z 0 ..z 1 ..z 2 ..z 5 ..z 4 ..z 3 ;
draw z 0 ..z 5 ..z 2 ..z 1 ;
(a)
(b)
(c)
draw z 0 ..z 5 ..z 4 ..z 2 ..z 0 ;
draw z 0 ..z 5 ..z 3 ..z 4 ..z 2 ..z 1 ;
draw z 0 ..z 2 ..z 4 ..z 3 ..z 5 ..z 1 ;
(d)
(e)
(f)
Figure .6: Examples of curves and the commands that drew them.
As you see in those examples, METAFONT doesn’t mind bending the curve
quite a lot to get a very smooth result. That’s because as it is used right now,
it will always construct curves where bending is minimal at the positions of the
given points (you can check on Figure .6 that when a curve passes by one of the
labelled points, it will do that as straightly as possible). Another rule that METAFONT uses when it draws curves is that between two consecutive points given
in the draw command, it will try to draw a curve without inflection point, i.e. a
curve which bends in one direction only.3 METAFONT will break this rule only
when it has no other way to keep the curve smooth (as in (b)). This explains why
in (f), METAFONT drew such a large loop between points 0 and 2, and between
points 5 and 1. A more direct curve between those points would have created an
inflection point, and there was a better (in METAFONT’s point of view) way to
keep a smooth curve. On the other hand, METAFONT has no problem creating
an inflection point at the position of a point given in the draw command. Look
for instance at point 5 of (d). Try to remember those two drawing rules. They
will help you correctly translate the curves you want to draw into METAFONT
instructions.
an inflection point is a position on a curve where bending changes direction. The middle of the letter S is
a good example of inflection point.
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xEXERCISE .11:
Check Figure .7. Where would you put the additional points necessary to draw such a curve? (hint: only 2 additional points are
necessary) You only need to give a qualitative description of the
positions of the additional points.
Figure .7: A nice loop. Doesn’t it remind you of something? ^
đ
Once you have chosen the additional points, write down the instruction that will draw the curve.
It’s the perfect moment to remember the two principles METAFONT uses when it draws its curves. The first one is that it will
draw curves which are flatest at the position of the points you gave
in the draw instruction. To draw our loop as it is presented, you
must thus choose points that are positioned at the flatest places on
the curve. There are four such positions:
• on top of the loop;
• at both sides of the loop;
• where the curve crosses itself.
You may think the best idea would be to choose the positions on the
sides of the loop. This way, by labelling the point most to the right
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1 and the point most to the left 2, you could draw the curve with the
simple instruction:
draw z 0 ..z 1 ..z 2 ..z 3 ;
However, by doing so you forget the second principle of METAFONT: it will avoid inflection points at other positions than the
ones of the points you gave yourself at nearly any cost. As you
see in Figure .7, there is an inflection point (or rather two, if you
take the point of view of a small ant which would follow the curve
starting from point 0 and ending at point 3): the position where the
curve crosses itself. So if you chose the side points, METAFONT
would not draw the curve as it was asked. Instead, you would end
up with the curve of Figure .8.
Figure .8: The wrong loop.
So which points must we use instead? Well, the obvious choice,
since we do want the inflection point, is to choose that point (let’s
label it 1). Indeed, it’s a good design principle to remember: each
time you want to draw a curve with an inflection point, choose it
as one of the points you will put in your draw instruction. This is
the only way to get the result you want. As for the second point, the
only choice left is the top of the loop (choosing a side point would
have resulted in an asymmetric curve, not what was intended). We
will label it 2. And indeed, choosing those two points is the only
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way to get the loop as it is drawn. You can check Figure .9 to see
exactly the positions of those two points.
Figure .9: The right loop, with all the necessary points labelled.
Now for the exact instruction necessary to draw this loop, you have
to remember that you want the curve to cross itself for sure at point
1. The only way to achieve it correctly is to mention point 1 twice
in your drawing instruction. So the correct instruction (as you must
have guessed by now) is:
draw z 0 ..z 1 ..z 2 ..z 1 ..z 3 ;
The draw instruction is very powerful. However, if you have tried your hand
at a few curves, you have probably noticed that it is sometimes too powerful, in
the sense that METAFONT makes decisions about the shape of the curve you
want to draw which are against what you meant. That’s actually logical: giving
just the position of a few points is quite little information, and METAFONT
cannot read your mind! ^
¨ From the positions of the points you gave, it will try
to make a nice and smooth curve, but that will be according to its own criteria,
since it has no way to guess yours. The result is that it will sometimes draw
things differently from what you expected.
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So does that mean that METAFONT is the boss and that we can only accept
its ideas and hope that they sometimes look enough like ours? Of course not!
METAFONT is just a computer program, and will do as we want, if we tell it to
obey us. In other words, if you want METAFONT to draw exactly the curve you
want it to draw, you’ll have sometimes to give it more information than just the
positions of the points. How do we do that? Well, there are various ways, and we
will see only two of them in this lesson. We will learn more about those methods
of control in later lessons.
The most obvious way to control the shape of a curve is to specify its direction
(or slope) at some point(s). METAFONT allows you to specify the direction the
curve will take when it passes by the points you use to define your curve (in other
words, in order to control the slope of the curve at some position, you need to put
the coordinates of that position in your draw command). Specifying the direction itself is easy when you remember that coordinate pairs aren’t only used to
define point positions, but can also be used to define vectors, i.e. displacements.
And since displacements are always done according to a definite direction, using
vectors to specify directions is just natural. And indeed, to specify a direction at
some point named z in your draw command, you just need to put a coordinate
pair, which will be interpreted as a vector, in curly braces “{}”, and put the whole
thing next to z (nothing can go in between, especially not “..”!). Here is how this
syntax looks like:
draw <something >..{(a, b)}z..<something else>;
or
draw <something >..z{(a, b)}..<something else>;
where (a, b) is a coordinate pair defining a vector. For now, don’t worry about
the position of the {(a, b)} part. It doesn’t change anything if you put it before
or after the point coordinates (note, however, that if you put such a direction
specification with the first point coordinates of your draw instruction, you can
only add it after the point coordinates. A syntax like:
draw {(a, b)}z..<something >;
will result in an error).
Now, you may think that it’s great, but defining directions with pair coordinates is not that simple. After all, you probably can’t see at first sight what
direction corresponds to a vector of coordinates (−5.8, 12.3), and what vector
corresponds to a direction at 13.5° up from the horizontal, pointing to the left.
Well, it’s time then to remember Subsections 2 and 3, where you were introduced
to a series of predefined pair values and operators which are there to take care of
this job. If you need a simple direction, use the vectors up, down, left and right,
whose names correspond exactly to the directions they define. Remember also
that if you have two points labelled 1 and 2, z2 − z1 is the vector corresponding
to the displacement between point 1 and point 2, in the direction of point 2. You
can use this at your advantage if you want to force a curve to go in the direction
defined by those two points. And finally, if you know the angle the direction you
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want the curve to take has with the horizontal, don’t hesitate to use “dir” to create
a unit vector defining that direction. As you see, you already have all the tools
necessary to define directions without having to know exactly how to relate the
coordinates of a vector to the direction it defines.
xEXERCISE .12:
Answer the following questions as precisely as possible:
1. What is the difference between the directions defined by {left}
and {right}?
2. What direction is defined by {up + right}?
3. What is the difference between the directions defined by {up}
and {10up}?
1. {left} and {right} both define a horizontal direction, and thus
will force the curve to be horizontal at the point where they
are specified. But {left} also indicates that the curve will have
to go from right to left when it passes the specified point,
while {right} forces the curve to go from left to right at that
point. So {left} and {right} define both horizontal directions,
but of opposite sense. Check Figure .10 to see what tremendous consequences the difference of sense can have for the
overall shape of a curve.
draw z 0 {up}..{left}z 1 ..{down}z 2 ;
draw z 0 {up}..{right}z 1 ..{down}z 2 ;
Figure .10: An example illustrating the difference between {left} and {right}.
2. up is a vector meaning: “move 1 pixel upwards”, while right
means: “move 1 pixel to the right”. If you remember that the
addition of vector is simply the addition of displacements one
after the other, up + right means: “move 1 pixel upwards
then 1 pixel to the right.” You can check on some graph paper
that this corresponds to the direction exactly in between the
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upwards and rightwards directions, i.e. at 45° from the horizontal, pointing to the right. In other words, writing {up +
right} is exactly equivalent to writing {dir 45}.
3. None! The direction a vector defines is independent from its
length (up and 10up both point exactly upwards, regardless of
the fact that one is 10 times as long as the other), so {up} and
{10up} both define exactly the same direction. This means
that you needn’t worry about the length of your vectors when
you define directions4 (at least the length of the resulting vector, when it results from a calculation. But inside the calculation the lengths of the vectors are meaningful: up + right
defines a different direction from 10up + right).
xEXERCISE .13:
We have four points, labelled from 0 to 3, whose respective coordinates are given by the following lines:
z0
z1
z2
z3
= (0, 0);
= (100, 100);
= (50, 60);
= (120, 10);
We want to draw a curve going from point 0 to point 1, passing
exactly by the middle between points 2 and 3 and being at that point
perpendicular to the line defined by those points 2 and 3. Write the
instructions necessary to define the middle point between points 2
and 3 (that you will label 4) and to draw the wanted curve (hint:
you only need to write two instructions).
At first sight, this problem probably looks impossible to solve, especially with only two instructions. And with any other programming
language, it would probably be unsolvable indeed. But we’re using
METAFONT here, which has been designed to make such actually common problems easy to solve. Firstly, it’s very easy to define
the middle point between two points. You just need to remember the
brackets notation, which allows you to define any point on the line
defined by two other points. In our case, we can define point 4 as
the middle between points 2 and 3 through the instruction:
z 4 = .5[z 2 , z 3 ];
Just make sure your vector does have some length. A vector of length 0 like origin cannot define any
direction, and thus something equivalent to {origin} will just be ignored by METAFONT .
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The second instruction we have to write is obviously the actual
drawing instruction, which will be in the form “draw z0 ..{. . .}z4 ..z1 ;”,
where . . . will have to be replaced with a vector indicating the actual direction the curve takes at point 4. How are we going to define
this vector? Well, we want this vector to be perpendicular to the line
defined by points 2 and 3. So a good place to start is with the vector
z3 − z2 , which defines the direction of that line. You may be thinking of defining a vector orthogonal to that one using the “dotprod”
operator. It is indeed a possibility, but you would have to write a
few instructions more to implement it, and we don’t want that. So
we need something simpler. And when you want to do things simple
with directions, the first thing you should think about is. . . angles.
Indeed, having perpendicular curves means having a right angle,
i.e. an angle of 90°, between them. So if we could get the angle
of the direction defined by z3 − z2 and add it 90, we would get
the direction we want, and could transform it into a vector with
“dir”. Well, that’s what “angle” is for! So “angle(z3 − z2 ) + 90”
(Note the presence of parentheses. The “angle” operator doesn’t
need them per se, but they are there to make sure that it will take
the full expression z3 − z2 as operand, and not just z3 . Otherwise
the expression would be interpreted as “(angle z3 ) + z2 + 90”, and
would result in an error, since you can’t add together numerical
values and pair values. We will see in a later lesson how METAFONT treats priority between operations, but for now don’t hesitate to add parentheses to make sure an expression will be treated
as one by what’s around) is the angle of the direction we want the
curve to take at point 4, and we can replace the . . . in the drawing
instruction as follows:
draw z 0 ..{dir(angle(z 3 − z 2 ) + 90)}z 4 ..z 1 ;
Figure .11 was drawn using the two instructions we defined. You
can check on it that the curve does indeed pass exactly between
points 2 and 3 and perpendicularly to the line defined by those two
points (which has been drawn too to make the orthogonality more
obvious).
Let’s sum up by giving together the two instructions solution of this
exercise:
z 4 = .5[z 2 , z 3 ];
draw z 0 ..{dir(angle(z 3 − z 2 ) + 90)}z 4 ..z 1 ;
So, now you can control the shape of your curves, but you are still limited
by the fact that whatever you do, your curves will always be open. Even when
you make the curve end at the point where it began, like in Figure .6 (d), the
resulting curve will usually not be smooth at that point. That’s because METAFONT doesn’t care if it goes more than once through the same point. Each time
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Figure .11: The resulting curve.
it will be treated independently from the other times. So how do you do to draw
an O, or an 8, or for that matter any closed shape?
Well, your first idea, based on what we’ve seen until now, could be to fix the
direction the curve has to take on the point where the curve starts end ends (i.e.
force the same direction on starting and ending). For instance, taking again the
example of Figure .6 (d), if you write:
draw z 0 {right}..z 5 ..z 4 ..z 2 ..{right}z 0 ;
you will end up with a curve which looks smooth and closed (see Figure .12
for the result of that draw command). The problem with this approach is that it
obliges you to control the direction of the curve at its starting point, something
that you may not want to do (you may not even know how to describe the direction the curve should take). You could always, by a process of trial and error,
find the right angle and use “dir”, but this would be bad programming, especially since if you decided to change the position of some points of the curve,
you would probably have to change the angle you chose, again through trial and
error. Not much meta-ness in this! ^
đ Of course you could always calculate that
direction, but this would often ask you for a lot of work, and sometimes it would
just be impossible to do.5
OK, so I’ve been thoroughly explaining why the previous approach is wrong
and impractical, but I’ve not yet given an alternative. How on earth are we going
to make closed curves then?! Well, METAFONT has a simple way to do that.
Instead of mentioning twice the same point, at the beginning and the end of
Moreover, METAFONT would still treat the curve as open, even if it looks closed. METAFONT doesn’t care what the curve looks like. It considers a curve with a starting point and an ending
point as open, even if those two points are the same. For now, you needn’t care about it, but in later
lessons you will learn that it’s important to know what METAFONT considers open and closed.
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Figure .12: The resulting closed-looking curve.
the draw command, replace the last mention with “cycle”. The presence of this
word will tell METAFONT that we want to draw a closed curve, and it will
automatically connect the last point mentioned before “cycle” with the first point
of the curve, and in a smooth way.6 So if we take our example again, we will
write:
draw z 0 ..z 5 ..z 4 ..z 2 ..cycle;
and we will get the shape you can see on Figure .13. It is quite different from
the shape on Figure .12, because you let METAFONT decide the direction the
curve would take at point 0, and since there was a symmetry in the positions of
the points describing the curve, it drew it according to this symmetry.
xEXERCISE .14:
Use everything you have learned in this section to write a program
which draws a vertical closed 8 shape. The only conditions are that
the shape must be 200 pixels high and that you must try to use as
few points as possible to define your curve.
Check out Figure .9, as it nearly gives away a solution to this exercise. ^
¨ Indeed, if you take points 0 and 3 of that figure and bring
them together just under the two other points, the loop you have
would close and look like an 8 shape. This means that you can define your curve with only three points: the bottom point, the middle
point (where the curve crosses itself) and the top point. They have
And METAFONT will internally treat the curve as closed.
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Figure .13: The curve, as drawn using “cycle”.
the same x coordinate (since they are vertically aligned), so you
can just put it at 0 for simplicity:
x 0 = x 1 = x 2 = 0;
(don’t forget that you can define the two coordinates of a point separately). As for the y coordinate, let’s make the whole thing symmetric and put point 1 at the middle between point 0 and point
2:
y 0 = y 2 − 200 = 0;
y 1 = .5[y 0 , y 2 ];
Of course, this is only one way to define the point coordinates, and
you could simply have defined them more directly than I did.
Now comes the drawing instruction. Since we want a closed curve,
we know that it will end in “..cycle”. And since we want the curve to
cross itself at point 1, we will refer to z1 twice in the instruction. You
might be tempted to write simply: “draw z0 ..z1 ..z2 ..z1 ..cycle;”. Unfortunately, the shape that would result from this instruction would
only vaguely look like an 8 shape, and looking at it closely you
would realise that it actually doesn’t cross itself at all (try it if you
don’t believe me ^
¨ ), merely comes in contact with itself at point 1.
So how can we ensure that the curve actually crosses itself? Simply,
by specifying the direction it takes at points 0 and 2. Indeed, if we
force the curve to run from left to right (by giving it the “{right}”
direction) both at points 0 and 2 (or from right to left, as long as
both points receive the same direction), you will oblige the curve
to cross itself, as it’s the only way for it to obey the slopes you im-
240
posed (try it yourself on a piece of paper. If you force yourself to
draw a closed shape through two points vertically aligned while
going from left to right at both points, the only way to do it is to
make an 8 shape). So the correct drawing instruction is:
draw z 0 {right}..z 1 ..z 2 {right}..z 1 ..cycle;
And you can see the result on Figure .14.
Figure .14: The resulting 8 shape.
But wait a second! According to the previous paragraph, specifying
the same direction on the bottom and top point should be enough to
force the curve to take an 8-like shape. The middle point shouldn’t
be necessary at all! So what would happen if we didn’t mention the
point 1 in the drawing instruction, i.e. if we wrote instead:
draw z 0 {right}..z 2 {right}..cycle;
You can see the result of that instruction on Figure .15. This is indeed a curve which crosses itself exactly at the middle between the
definition points, but its shape is a little less 8-like, and it looks a
241
little like a sandglass. Why the presence or absence of the middle
point in the drawing instruction results in such different curves is a
complicated matter which has to do with the mathematical definition of the curves as they are handled by METAFONT. You needn’t
really worry about it. Just remember that METAFONT’s idea of
the “best” curve following your instructions is not always what you
expect, and that METAFONT is very sensitive to the curve definitions you give.
Figure .15: A sandglass-looking shape.
In any case, the 2-point solution to this exercise was not necessary to pass it. If you found its 3-point solution, you have correctly
solved the exercise already.
4 Pens
If you have been curious enough to try and reproduce some of the figures you’ve
seen until now, you must have noted that your results, while correct in shape,
are slightly different from what have seen in this tutorial. Namely, the curves
you have produced are thicker. For instance, if you tried to reproduce the closed
shape in Figure .13, what you have obtained was probably closer to Figure .16.
And you have been especially unable to reproduce the figures using thin lines
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that are present in this tutorial. Yet I have produced all those figures with METAFONT exclusively. So what have I done to get lines of a different thickness from
what you get?
Figure .16: A thick closed curve.
If you know a little about how computers work, and especially how they do
graphics, you probably have realised that the way I’ve been explaining how
METAFONT handles graphics is a metaphor, namely the metaphor of drawing. Indeed, METAFONT is not a man behind a desk with a sheet of paper in
front of him. It’s a program, and all it does when handling graphics is handle a
grid of pixels, small units of space which have only two states: white or black.
And what METAFONT does is tell which pixels are black and which ones stay
white. However, the metaphor of drawing is very useful, because from our perspective it looks exactly as if METAFONT was actually a man behind a desk
drawing on a piece of paper what we order him to draw. It’s not for nothing that
the main drawing instruction is called draw. ^
¨ For instance, just as when we
are drawing by hand, METAFONT’s curves behave just as if they are drawn in
a certain sense, from one point to the other (the order being of course the order
of the points as given behind the draw instruction). This explains why adding a
direction as a vector between braces works as we expect it, and why giving an
opposite sense can modify a curve so strongly (just check again Figure .10), and
exactly the same way as it would do if you draw the curve yourself by hand.
But this metaphor of drawing can be further extended. Indeed, when you want
to draw something, you need not only your hand and a piece of paper, but also a
pen, without which you could never mark anything on the paper! And depending
on the kind of pen you’re using (a pencil, a ballpoint pen, a fountain pen, or one
of those fancy calligraphic pens with special tips), you will get different results,
even if the shape you draw is always the same. Well, in METAFONT you just
do exactly the same! METAFONT has a command called pickup that allows
you to choose the pen it will use to draw the curves you ask it to draw with the
draw command. By using it, you can specify a pen whose tip is more or less big,
243
more or less circular (or of some other shape) etc. The pickup command must
simply be followed by the name of the pen you want to use.
But to choose a pen, you need pens to choose from! Well, it’s no problem,
because METAFONT has a few predefined pens ready for use, besides the default pen that it automatically uses when you don’t pick up another one, and that
you’ve been using until now. The two main predefined pens, that you will mostly
use, are called pencircle and pensquare. They correspond respectively to a pen
whose tip is a circle of 1 pixel of diameter and a pen whose tip is a square of side
1 pixel. Check out Figure .17 to see a familiar shape drawn this time using those
very thin pens. They were drawn by adding respectively “pickup pencircle;”
and “pickup pensquare;” in front of the actual drawing instruction.
(a)
(b)
Figure .17: The same loop as before, but drawn with (a) pencircle and (b) pensquare.
Now, for how useful tiny pens can be, what we want usually is bigger pens,
i.e. pens with a bigger tip, like the ones I’ve been using myself. But how can
you get such pens when all you have is pens with very small tips? The answer is
actually quite simple: transform them! Yes, you understood correctly. All those
transformations that we’ve seen in Section 2 can apply not only to pair values, but
also to pens! Or at least, the transformations that are meaningful in this situation
can be applied here. Indeed, since our goal is to change the shape and/or size of
our pens, a transformation like “shifted”, “rotatedaround” or “reflectedabout” is
useless. However, “scaled” (to change the global size of our pentip), “xscaled”
and “yscaled” (to stretch our pentip on one direction only) can be usefully used
with pens. For instance, by specifying:
244
pickup pencircle scaled 10;
you create a pen whose tip is a circle of 10 pixels of diameter. If you write:
pickup pensquare xscaled 20;
you will obtain a pen with a rectangular tip 20 pixels wide and 1 pixel tall. And
you can of course concatenate transformations, like in:
pickup pencircle xscaled 10 yscaled 35;
which makes subsequent drawing done with a pen whose tip is ellipsoidal, with
a horizontal axis 10 pixels long and a vertical axis 35 pixels long. Check out
Figure .18 to see how different pens can really change how otherwise identical
curves look like.
xEXERCISE .15:
List all the ways to pick up a 5-pixel-high, 20-pixel-wide, ellipsoidal pen.
The most obvious way to pick up such a pen is of course to use
the “xscaled” and “yscaled” transformations with a pencircle, as
such:
pickup pencircle xscaled 20 yscaled 5;
It is the easiest (and most advisable) way to do it, but certainly not
the only one! Indeed, you can also use “scaled” itself together with
a combination of “xscaled” and “yscaled” to obtain the same result. For instance, since the smallest dimension of the wanted pen is
5 pixels, you can first scale pencircle by 5, and then stretch it horizontally by a factor of 4 to obtain the wanted ellipsoidal pen:
pickup pencircle scaled 5 xscaled 4;
You can also scale it first by the biggest dimension (here 20) and
then shrink it vertically by scaling with a fractional factor:
pickup pencircle scaled 20 yscaled .25;
You could even go wild and make something strange like:
pickup pencircle scaled 56 xscaled 5/14 yscaled 5/56;
245
Go ahead, make the calculations, and you’ll see that it does create a 5-pixel-high, 20-pixel-wide pen. Depending on the factor you
first put with “scaled”, you actually have an infinity of possibilities
which all result in the wanted pen. But if you find them silly, don’t
worry: you’re not the only one! ^
đ The first three propositions were
the only ones necessary to correctly solve this exercise. ^
¨
However, if all you can do is scaling pencircle and pensquare, you’ll rapidly
be limited in what you can do. Even when scaling with different factors horizontally and vertically, all you can get is horizontal or vertical pens. And if you know
a little about calligraphy, you know that what influences most the looks of letters, besides the shapes of the curves, is the position of the thin and thick strokes.
And what fixes their positions is the angle the pen nib makes with horizontality.
Calligraphers will turn their pens differently depending on the result they want
to achieve. And it’s something METAFONT can easily do by rotating its pens.
Indeed, although the “rotatedaround” transformation cannot be used with pens,
the “rotated” transformation can, and has the expected effect of putting the pen
nib at an angle with horizontality. Figure .19 shows the effect the angle alone of
a pen can have on the looks of otherwise identical curves.
xEXERCISE .16:
Imagine that you want to pick up a rectangular pen 20 pixels wide
and 2 pixels high (a very thin pen thus). However, you want it tilted,
so that its longest side will be perpendicular to the direction defined by two points 1 and 2. Note that we don’t give any condition
on the positions of those two points, only that they have already
been defined before you pick up the pen. How would you solve this
problem?
Defining a rectangular 20-pixel-wide 2-pixel high pen is easy. The
line “pensquare xscaled 20 yscaled 2” solves that problem. However, you still have to add a “rotated” transformation to finish the
job. But how do we find the correct angle of rotation?
This problem is actually trivial if you remember the beginning of
this lesson, where we defined the “angle” operator. Remember also
that when you have two points labelled 1 and 2, the quantity z2 −
z1 is a vector whose direction is the one defined by the two points,
and that for this reason “angle(z2 − z1 )” is the angle this direction
makes with horizontality. And in order to have your pen perpendicular to that direction, you just need to rotate it by that angle plus
90°. So you finally pick up the correct pen through the following
command:
pickup pensquare xscaled 20 yscaled 2 rotated (angle(z 2 − z 1 ) + 90);
Note the use of parentheses to make sure that the addition is correctly interpreted.
246
5 Once more, with character!
Okay, I guess you’re all anxious to use your new knowledge to draw more characters, so let’s stop here for now and let’s come back at our characters. Let’s first
look back at our E from Section 10. It’s not bad, but it lacks something. So far,
its shape has been based on the golden number, but it has been drawn with the
dumb plain circular default pen. Let’s give it more class: let’s draw it with a pen
whose nib is also completely based on the golden number! To do that, we simply
need to add a pickup command somewhere before the first draw command used
to draw the character. Since we are not doing anything special, we will put it just
before that first draw command. Of course, this is the easy part. The difficult
part is the actual definition of the pen we will pick up.
First, we need to choose a predefined pen to start with. We want our strokes to
have smooth ends, so we shall start with a pencircle. The first thing we need to
do is to get it somewhat bigger, so we scale it:
pencircle scaled 15
But we said we didn’t want a plain circular pen, and we want it to be in some
way based on the golden number. We can easily fulfill both those conditions, if
we make the pen wider, and have its ratio width/height to be equal to the golden
number. Since we already scaled it equally in width and height, it’s easy to obtain
that by scaling it horizontally with the golden number, by adding to it:
xscaled Phi
(remember that it’s what we called the variable containing the golden number).
Finally, we can get a nice calligraphic effect if we rotate our pen a little. We
can do that by using “rotated”, but first we need to define an angle. Defining
an angle based on the golden number can be done in many ways, but we want
something simple that doesn’t need an extra line of calculations. In this case,
we are just going to define a simple vector with one of its coordinates being the
golden number and the other being 1, and get its angle with horizontality through
the “angle” operator. So we simply add:
rotated angle (Phi, 1);
Thus, when we add all those commands together, we finally get the following
line:
pickup pencircle scaled 15 xscaled Phi rotated angle (Phi, 1);
and if we add this line to the original program used to draw our E character, we
get:
1
2
3
Phi=(1+sqrt5)/2;
w=100;
h=Phi*w;
247
4
5
6
7
8
9
10
11
12
13
14
15
16
y1=y6=0;
y3=y4=h;
y2=y5;
x1=x2=x3=0;
x4=Phi*x5=x6=w;
(y3-y2)=Phi*(y2-y1);
pickup pencircle scaled 15 xscaled Phi rotated angle (Phi,1);
draw z1..z6;
draw z2..z5;
draw z3..z4;
draw z1..z3;
showit; shipit; end
The result of this program is shown in Figure .20. If you compare it with the
original character in Figure .7, although the positions of the contruction points
and the drawing instructions didn’t change, changing the pen has resulted in quite
a different overall shape for our character. It now has vertical strokes slightly
thicker than horizontal strokes, and the stroke ends have quite a different shape.
But the effects of changing the pen shape are even more obvious on characters
with oblique strokes like the A character you had to draw as an exercise. If you
apply the pen we just defined to it (I won’t show the resulting program here, as
adding a single line should now be obvious), you get Figure .21. If you compare
it with Figure .8, the difference is striking. A letter that looked quite plain looks
already much richer, and that only by drawing it with a different pen! ^
¨
However, as you’ve seen in Figure .19, you can only truly measure the effects
of calligraphic pens when your character contains curves rather than only straight
lines. And since we saw how to draw those curves, let’s draw our first character
with curves. The D is a good one to begin with. It is relatively simple, yet not as
obvious as an O. Since we want it to fit well with the E and A we defined before,
we begin with defining the same dimensions as we defined for them, and we will
base the other points on them:
Phi=(1+sqrt5)/2;
w=100;
h=Phi*w;
The next step is to define the construction points. The first question to answer
is how many points we need. The D is made out of a straight line and a curve,
so we need at least two points (the strict minimum necessary to define a straight
line). We could also, using directions, define the curve with those two points
alone (since the curve of the D has the same ending points as its straight line),
but then we would have difficulties to control the width of our character. So we
need at least a third point to define our curve. That is enough! We are going to
define our D using three points only.7 First we need to define the two points that
It is always good policy to define your character with as few points as possible. Too many points is often
248
make up the straight line on the left of the D. We’ll call them points 1 and 3,
to keep with the numbering on the E and A we already defined. They will be
placed at the same positions as they were placed when we defined our E. But this
time, we are not going to define them coordinate by coordinate. We are going to
use what we learned in this lesson to define them in a quicker and at the same
time clearer way. What is the relationship between points 1 and 3? As we’ve
seen when we defined them for the character E, they are vertically aligned, at
a distance h from each other, and point 3 is above point 1. In other words, z3
− z1 is a vertical vector, pointing upwards, and of length h. We already know
a vertical vector pointing upwards: up. And we know its length is 1. So to get
a vertical vector pointing upwards of length h, we just need to multiply up by
h (you can check by writing “length(h*up)” that we indeed get a vector of the
desired length). And we can finally write the full relationship between points 1
and 3 as:
z 3 − z 1 = h*up
or (identical equation but written a little differently):
z 1 = z 3 − h*up
But we also know easily how to position point 1 with a simple equation: we want
to put it at coordinates (0, 0), which happen to be the coordinates of origin. So it’s
enough to write “z1 = origin” to know exactly where point 1 is positioned, and
by virtue of the relationship it shares with point 3, point 3’s position is now also
fully known. And since we can concatenate equations, we can write the whole
positioning of points 1 and 3 in a single, short, but also self-explanatory line:
z1=z3-h*up=origin;
See how using METAFONT’s predefined pair values shortens our program and
clears it up?8
Now we only need to define point 2, and all our construction points will have
been defined. Since point 2 doesn’t share any specific feature with the two other
construction points, we will simply define it through its coordinates. Since we
want to use this point to make sure that the D will have the same width as the
already defined characters, it is obvious what its x coordinate will be:
x2=w;
As for its y coordinate, we are rather free here. But to keep the same look and
feel for all our characters, we are going to place point 2 at the same height as the
synonymous to a bad design.
You could make the line look even more explicit by using a transformation instead of simple algebra, since
as we’ve seen it “shifted” is equivalent to a simple addition for pairs. However, using transformations when
simple algebra would be enough slows METAFONT down slightly, and the added explicitness is
minimal is this case.
249
bars of the E and the A. And at this point the originally strange choice of point
numerotation we made becomes fully justified, as it means we can simply copy
the necessary line from the definition of E (or A):
(y3-y2)=Phi*(y2-y1);
without any change, and have our point 2 correctly placed!9
Now that the points are defined, we can draw the D shape. First, we need to
choose the pen we want to draw it. We use the one we already defined in terms
of the golden number:
Next, we begin with the simple part, which is to draw the straight line of the D:
draw z1..z3;
Finally, we need to draw the curve that will close the shape of our D. We could
of course simply write “draw z1..z2..z3;”. You can check the result in Figure .22, where you can immediately see that the resulting character is both taller
and wider than the E we defined. Once again, that’s because of METAFONT’s
idea of a “good” curve passing through defined points, and that idea doesn’t necessarily take into account considerations like the width and height of the character we want to make. So if we want a character following our specifications,
we are going to need to give METAFONT some more information. Since we
said (and we keep it that way) that 3 points would be enough to define our D,
the only information we can add is in terms of directions at those points. To keep
our character to the height we want, we need to make sure that METAFONT
starts and ends the curve horizontally. We can do that using the predefined right
and left, as such: “draw z1 {right}..z2 ..{left}z3 ;” (don’t forget that a curve has
also a sense of drawing. From z1 to z2 it goes to the right, and from z2 to z3
it goes to the left. This explain why right and left are used as they are. If you
switched them, the resulting curve would be very different). The result is shown
in Figure .23. It is better, but still not exactly what we want: METAFONT likes
curves to be as symmetric as possible, even when the points that define them are
not symmetrically positioned, which is why the resulting curve overruns point 2
on the right. If we want our D to be w wide, we need to ensure that point 2 is the
farthest to the right that the curve will get. You can simply do that by specifying
that when the curve passes by point 2, it should do so in a vertical direction,
using up. So that finally the correct line we need to write to draw our curve is:
draw z1{right}..z2{up}..{left}z3;
Just add a line to label our three points and another one to show up the character
and end the program:
Remember, by defining z 1 and z 3 , we also automatically define their coordinates, and thus also y 1 and
y3.
250
showit; shipit; end
And we’re done! Once again, just transform the resulting output file into a DVI
file and you should get Figure .24. Well done!
Let’s now sum it up by putting together all the instructions necessary to define
our D character, and we’re ready for another exercise! ^
đ
1
2
3
4
5
6
7
8
9
10
11
Phi=(1+sqrt5)/2;
w=100;
h=Phi*w;
z1=z3-h*up=origin;
x2=w;
(y3-y2)=Phi*(y2-y1);
draw z1..z3;
draw z1{right}..z2{up}..{left}z3;
showit; shipit; end
xEXERCISE .17:
Once again, let’s check that you have understood this lesson by creating another character by yourself, this time a C as in Figure .25.
Once again, it will be based on the golden number:
• the ratio of its height by its width is equal to the golden number;
• its leftmost point is at the same height as the horizontal bar of
the E and A characters (or at the same height as the rightmost
point of the D character we just drew);
• its topmost and bottommost points are not horizontally centered. Rather, their horizontal position is simply the character
width divided by the golden number;
• its bottom end is vertically lower than its leftmost point, by a
ratio of twice the golden number;10
• its endpoints are symmetrically positioned;
• it is drawn with the pen we defined earlier in this section.
Once again, just make the character 100 pixels wide to make it
comparable to the other characters we already defined.
Once again, we first need to choose our construction points. To
draw the C character as we want it, we need of course to define
Why such a ratio? Well, with other ratios the resulting character just didn’t look right to me. Your aesthetic
sense may be different, and that’s not a problem. But here I want you to reproduce the same character
as the one on the figure. ^
¨
251
its end points. And since we also need to position correctly its topmost, bottommost and leftmost points, we take them as construction
points too. This adds up to five points, that we will label as in Figure .26.
I will not insult your intelligence by repeating the reason for the
first three lines of this program:
Phi=(1+sqrt5)/2;
w=100;
h=Phi*w;
Then, against all common sense, we are going to define point 3
first! ^
đ Being the leftmost point of our character, defining its x
coordinate is obvious:
x3=0;
The next part may seem a little difficult: how can we define point
3 to be at the same height as the bars on the E and A characters,
when no other point has been defined yet? If you think that, it means
that you forgot that METAFONT has no problem working with
unknown quantities! Although points 2 and 4 haven’t been defined
yet, you can already use them in equations. As long as they are
finally defined before we try to draw anything, METAFONT will
be perfectly happy. So we can now take the line from the definition
of point 2 in the E, A and D characters, adapt it to the point labels
we have chosen here, and end up with:
y4-y3=Phi*(y3-y2);
Now let’s define point 1, which is defined to be below point 3 by a
ratio of twice the golden number. It simply means that its y coordinate is equal to the y coordinate of point 3 divided by such a value.
And since we want our C to be w wide, we can simply define both
coordinates with one equation:
z1=(w,y3/2Phi);
People who know a little about programming languages may be
surprised that writing y3/2Phi works as intended. Well, it does. ^
¨
If you don’t trust it or are unsure, you can always put parentheses:
y3/(2Phi).11 We can then define point 2, the bottommost point of
Incidentally, although the meanings of the expressions “2Phi” and “2*Phi” are equivalent, if you had used
the second one parentheses would have mandatory. That’s because “y 3 /2*Phi” corresponds mathematy
y3
ically to 23 Φ, while “y 3 /(2*Phi)” (and “y 3 /2Phi”) corresponds to 2Φ
. You can always try to remember
that omitting the multiplication sign is like putting parentheses around its operands. We will see all this in
more detail in a future lesson.
252
the character. This makes its y coordinate easy to define. As for its x
coordinate, it is already completely described in the exercise as the
width of the character divided by the golden number. We can thus
now write:
z2=(w/Phi,0);
We now define point 5, the other end of our C. The exercise asks
for both endpoints to be symmetrically positioned. Since it wasn’t
explained further, we can take it to mean that point 5 should be
the reflection of point 1. If you look at Figure .26, you can easily
understand where the reflecting line is positioned: it’s a horizontal line cutting the character exactly in half (in other words, at h/2
height). Once you know that, you can easily define the transformation that will transform point 1 into point 5, using the “reflectedabout” transformation with two points defined to be at h/2 height.
We could put them (horizontally) anywhere, but it’s just as simple
to put them at horizontal position 0 and w. So we can now write:
z5=z1 reflectedabout ((0,h/2),(w,h/2));
But the funny thing here is that if you look carefully at the figure and
at the definition of point 4, you will see that it is the result of applying that same reflection to point 2, so that you can immediately
write:
and have point 4 correctly defined.12 Now the y coordinate of point
3 was defined in terms of points 2 and 4. Now that they are completely defined, point 3 is also completely defined, so that our point
definitions are finished.
We can now add the line that will choose the pen we use to draw
our character:
Of course, you could have strictly followed the definition and written “z 4 = (w/Phi,h);”, but keeping point
2 and 4 vertically aligned is a good idea, aesthetically speaking, and if you decided to move them a little
you would have to change two lines in the program, while when using the reflection you need to change
only one line: point 4 always follows point 2. In such a simple case it seems hardly worth the effort, but
as your designs will get more complex so will your point definitions, and having as many point definitions
be relative to other points rather than absolute will help you when you need to change things. It’s one of
the things that define meta-ness, so let’s get used to it already. ^
đ
253
Once this is done, the only thing left to do is to actually draw it.
Since the whole C character is made of one smooth curve, we need
a single “draw” command, going from point 1 to point 5 in order
(and explaining thus the numbering we chose here). Of course, in
order to keep the curve from overrunning the limits we defined for
our character, we do as we did with the D character and we specify
the direction of drawing at points 2, 3 and 4 (it is not needed for
points 1 and 5). I trust you understood how we did it with the D
character and thus understand the following line:
draw z1..z2{left}..z3{up}..z4{right}..z5;
We can now end up with the usual lines of labelling and ending the
file:
showit; shipit; end
and the result you will find in mfput.2062gf should be identical
to the one in Figure .26.
To sum up the whole exercise, here’s the whole list of instructions
we used to define our C character:
1
2
3
4
5
6
7
8
9
10
11
12
13
Phi=(1+sqrt5)/2;
w=100;
h=Phi*w;
x3=0;
y4-y3=Phi*(y3-y2);
z1=(w,y3/2Phi);
z2=(w/Phi,0);
draw z1..z2{left}..z3{up}..z4{right}..z5;
showit; shipit; end
6 We’re done!
Here we are! Lesson 2 has finally come to an end. OK, I might have lied a little
in Section 11 when I said that lessons would be lighter from then on. You will
probably have found this lesson rather heavy. However, it focussed strongly on
contents and didn’t contain that many different topics, so it should be easier to
understand than the previous one. However, I must insist once again that you
must have truly understood the concepts presented in this lesson before carrying
on with the next lesson. Next lesson we will finally see how to make true font
files that can be used with TEX and LATEX , so it is really important that you
254
understand what has been explained until now. So don’t hesitate to try and make
your own characters (now that you can make curves, you shouldn’t be limited
anymore. You can even try numbers! ^
¨ ), play with pens, and if you still don’t
get something, you can always contact me at metafont.tutorial@free.fr, or
via the (La)TeX/METAFONT-for-Conlangers13 mailing list. But right now, go and
do something else! Enough METAFONTing for today! ^
¨
255
pencircle scaled 20;
(a)
pencircle xscaled 20 yscaled 5;
(b)
pencircle xscaled 5 yscaled 20;
(c)
pensquare scaled 20;
(d)
pensquare xscaled 20 yscaled 5;
(e)
pensquare xscaled 5 yscaled 20;
(f)
256
Figure .18: Examples of the same loop drawn with different pens.
pencircle xscaled 20
yscaled 5 rotated 30;
(a)
(b)
(d)
(e)
pencircle x
yscaled 5 r
(c
257
Figure .19: Again the same loop drawn with pens of identical shape but tilted at
pencircle x
yscaled 5 ro
(f
Figure .20: A simple E character drawn with a calligraphic pen
Figure .21: A simple A character drawn with a calligraphic pen
258
Figure .22: A simple but incorrect D character
Figure .23: A better but still incorrect D character
259
Figure .24: The correct simple D character
Figure .25: A simple C character
260
Figure .26: A simple C character, with labels
261
Index
METAFONT, 168
TEX , 168
Adobe, 5, 165
Apple Inc., 165, 166
Appropriation, 161
Carson, David, 164
Code, 6
Design Education, 5
Designer, 5
Emigre, 164
Graphic Design Software, 6
GUI, 6
Gutenberg, 161, 162
Kittler, Friedrich, 6
Knuth, Donald E., 168
Lafuente, Ricardo, 161
Learning, 5
Linotype, 161, 162
Macromedia, 5, 165
Microsoft, 165
PostScript, 165
Truetype, 165
Typography, 161
Unix, 168
van Schaik, Michael, 5
Workspace, 5, 6
263
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2
The Linux Information Project. Pipes: A Brief Introduction, 2010. [Online; accessed 21-February-2010].
3
Friedrich Kittler. There is No Software, 1995. [Online; accessed 27January-2010].
4
Wikipedia. Jodi (art collective) — Wikipedia, The Free Encyclopedia,
2009. [Online; accessed 27-January-2010].
5
Microsoft Corporation. Windows Vista Features, 2010. [Online; accessed 27-January-2010].
6
Free Software Foundation. BadVista, 2010. [Online; accessed 27January-2010].
7
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Boxes and Glue

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