%Started May 1996, C.G. van der laan,
[email protected]
%Version June 1996
\newif\ifdraft\drafttrue
\draftfalse
\ifdraft\else\input psfig \fi
%Watch out for double ! in verbatim, especially with %!!PS
\input blue.tex \loadtocmacros\tolerance500\hbadness=499\hfuzz=5pt
\parindent=1pc\everyverbatim{\unmc}
%Needed EPS files: baker.eps, barnwindowii.eps, bentley.eps,
% eschera.eps, escherb.eps, escherknotmf.eps,
% escherknotiii.epsabr, flower.eps,
% gurariabc.eps, gurarisq.eps
% jvr.eps, linebundle.eps, malbork.eps,
% polygon.eps, polygonii.eps, prpie.eps,
% sine.eps, sinedisks.eps, seal.eps,
% textalongarc.eps, textalongspiral.eps.
\bluetitle Paradigms: Just a little bit of PostScript
\blueissue \maps{96}2
\bluepictures\metapostpic\pstexpic
\blueabstract It is all about creating EPS\Dash with graphics\Dash
to be merged with \AllTeX{} scripts.
The emphasis is on creating raw PostScript for simple symmetrical pictures.
Asides, like
incorporating accurate graphs of math functions,
typesetting text along curved paths, or
tables set sideways have been addressed.
A poor man's mftoeps approach is touched upon:
(declarative) METAFONT into (imperative) PostScript.
\bluekeywords Declarative program, education, EPS, Escher, graphics,
imperative code, \AllTeX,
math graphs, METAFONT, merging EPS and \AllTeX,
MetaPost, mftoeps, PostScript,
sideways tables, text along curved paths.
\beginscript
\bluehead BLUe's Design X
Hi folks.
The user's guide which comes with BLUe's format system\Dash
Publishing with \TeX, PWT for short\Dash
is processed {\em completely\/} by \TeX, {\em no\/} other tools such as
\PS{} are needed.\ftn{Nobody knows what the future has in store, but for
the moment I consider it a good thing that the PWT guide can be processed
just by \TeX, well \dots with BLUe's format.}
However, of late I exercised \MF
\Dash well, eventually MetaPost with the help of Jos Winnink\Dash
for graphics to be included in \TeX{} documents, and finally embarked PostScript
straightaway to create EPS pictures.
$$\metapostpic$$
\PS{} is involuntary needed to (electronically) paste up the graphics, and
as resulting file format.\ftn{For exchange the {\tt.tex} and
(hand-coded) {\tt.eps} files are much better suited
because of their conciseness. This can't be beaten, not even by
Adobe's PDF\Dash Portable Document Format.}
If we come to think of graphics as
$$\vbox{\hbox{just doing the `right' strokes or fills}}$$
then \PS{} provides the means for this:
lines, splines and circular arcs,
to be drawn or filled.\ftn{PostScript II also provides for colors and
processing in a network.}
I use the sidestep
$$\vbox{\hbox{\MF{} $\rightarrow $MetaPost $\rightarrow$ EPS}}$$
for general pictures but also for obtaining the right (control) points
explicitly from a decalarative specification in \MF,
as shown by Escher's knot at the end.\ftn{Another way
for arriving at the EPS code is
to use Jackowski's |mftoeps| package or to use MetaPost.}
$$\pstexpic$$
With respect to graphics \PS{} can be seen as a {\em little\/} language
in the UNIX tradition.\ftn{See Bentley's Little languages in
`More programming pearls\Dash\-Confes\-sions from a coder.' Addison-Wesley.}
A little bit of \PS{} adheres the 80\%--20\% adage:
80\% of the effects (or more) with
20\% of the energy (or less).
One can with a little knowledge of \PS{} code graphics immediately
and {\em completely\/} in \PS.
The more so because of the ubiquitous public domain GhostScript
previewers to verify the result,
next to of course the \PS{} laser printers.
Furthermore, text is just a special case of graphics, and merging
just a little bit of text\Dash malenki Russians would say\Dash
with the graphics goes equally simple at first glance.
And to end the lovesong the inclusion of accurate graphs of mathematical functions
goes well via coding these in \PS{} and including these as figures.
(Of course Hobby's graph extension could be used as well, or other advanced
graphics packages.)
This is illustrated by a graph of the sine function to convey the idea.
PStricks is about {\em interfacing}. Not assuming knowledge of \PS.
This note discusses mainly {\em merging}.
Is about extending your \TeX pertise
with just a little\Dash tsjut-tsjut Russians would say\Dash
knowledge of \PS{} rewarded by high returns.
Below I'll summarize what is needed from \PS, and illustrate the use of it
with a few examples, introducing en route the operators we need given the example.
\bluehead PostScript
\bluesubhead Processing
\PS{} comes with a user's guide (cookbook) and reference manual,
the so-called blue and red books in the Adobe \PS{} series.
For processing \PS{} an interpreter is needed, such as
a \PS{} laser printer or a GhostScript previewer.
For inclusion in \AllTeX{} I use the psfig macros.\ftn{Courtesy Trevor J. Darrell.}
Goossens in his PostScript and \AllTeX, \maps{92}1, nicely details about
inclusion of PostScript.\ftn{See also the \LaTeX{} Companion.}
As with PDF I consider the post-processing capability {\em independently\/} from
the tool which created the \PS{} source, very powerful and flexible.
\bluesubhead Subset 0 from the language
\PS{} is stack-oriented.
This means that operations are prescribed in polish-reverse notation,
also known as prefix notation,
similar to the HP pocket calculators.
Addition\Dash use of operator |add|\Dash for example is notated as follows.
\beginverbatim
2 3 add%yields 5 on the stack, 2 3 consumed
!endverbatim
\PS{} is artificially structured via structure information in
comments, double \%-ed comments. Programs which obey the Adobe
structure are called conforming and this is usually needed for inclusion
within \AllTeX, especially the BoundingBox line is required.
\blueexample Conforming EPS structure
\beginverbatim
%!!PS EPS
%%Title: <name>
%%Creator: <name>
%%CreationData: <date>
%%BoundingBox: <llx> <lly> <urx> <ury>
%%DocumentFonts: (atend)
%%EndComments
<prolog>
%%EndProlog
%%Page: 0 1
<page 1>
%%Page: 1 2
<page 2>
%%Trailer
<...>
%%DocumentFonts: Times-Roman ...
%%Pages: 3
%%EOF
!endverbatim
Creating and drawing paths is done by separate operators.
For creating paths operations like
|moveto| are provided while drawing goes via |stroke|.
\beginverbatim
0 0 moveto 0 10 lineto%create path
stroke%draw a v-line of 10pt height
!endverbatim
Variables\Dash names to be associated with their values\Dash
are handled via the so-called dictionaries.
The functionality can also be obtained via procedures.
\beginverbatim
/size {10} def
!endverbatim
The so-called literal name is preceded by a slash to distinguish the declaration
from its invoke. The invoke is done by just the name, also called executable name.
The procedure text is surrounded by curly braces.
Parameters are absent too. The (operand) stack is used.
For graphics we have a CurrentTransformMatrix\Dash CTM\Dash which maps the
user space on the device space, the printer or screen.
Equally powerful is the concept of encapsulating graphics via
|gsave| and |grestore|, that is the graphics state is local\Dash encapsulated\Dash
after |gsave| until |grestore|.
Next to the CTM \PS{} maintains the currentpoint and currentpath.
Batagelj, \maps{95}1\Dash Combining \TeX{} and \PS\Dash
provides an in a nutshell overview.\ftn
{Nice are the hints to remove repeated parts from files which are
generated by CorelDRAW and Mathematica, in order to reduce the size
of the automatically generated and to be included files.
(The idea is to remove duplicate `dictionaries' which are included with each result.)
The example of how to include graphs of math functions in a document is
{\em very\/} useful.
However, with respect to his first picture I would prefer to use the
inherent symmetry in the data as opposed to providing all the data.}
Another introduction is in Fokker en van Oostrum's `Plaatjes in een tekst,'
\maps{94}2, next to a survey of drawing software.
\bluesubhead Summary of (graphics) commands
The following snapshot is borrowed from Gurari, well \dots a little modified.\ftn{%
Gurari E.M (1994):
\TeX{} \& \LaTeX\Dash Drawing \& Literate Programming.
McGraw Hill. ISBN 0-07-025208-4.}
Its main purpose is to show that the number of relevant graphics primitives
is low.
The functionalities will be dealt with along the way in the examples.
For the details of the commands or the list of operators
see the red book.\ftn{A complete list with functional summaries is
in the red book section 6.2 Operator summary.}
$$\everyverbatim{\emc}
\vbox{\halign{\hfil#\cr
\bf Arithmetic and math operators\hfill\cr
|<num>| |<num>| mul $num$ \cr
|<num>| sine $num$ \cr
%
\bf Path construction operators\hfill\cr
currentpoint $x$ $y$ \cr
|<x>| |<y>| moveto \cr
|<dx>| |<dy>| rmoveto \cr
|<x>| |<y>|lineto \cr
|<dx>| |<dy>| rlineto \cr
$\langle q_{1x}\rangle$ $\langle q_{1y}\rangle$ $\langle q_{2x}\rangle$
$\langle q_{2y}\rangle$ $\langle p_{2x}\rangle$ $\langle p_{2y}\rangle$
curveto \cr
$\langle c_x\rangle$ $\langle c_y\rangle$ $\langle r\rangle$
$\langle ang_1\rangle$ $\langle ang_2\rangle$ arc \cr
%
\bf String operators\hfill\cr
|<string>| |<num>| |<num>| getinterval \cr
%
\bf Character and font operators\hfill\cr
{\tt\char92}|<fontname>| findfont \cr
\ |<fontsize>| scalefont setfont \cr
|<string>| show \cr
|{<body>}| |<string>| kshow \cr
%
\bf Graphics state operators\hfill\cr
|<num>| setgray \cr
|<num>| setlinewidth \cr
%
\bf Dictionary operators\hfill\cr
/|<defname> {<body>}| def \cr
%
\bf Coordinate system and matrix operators\hfill\cr
|<num>| |<num>| translate \cr
|<num>| |<num>| scale \cr
|<num>| rotate \cr
%
\bf Relational, boolean, and bitwise operators\hfill\cr
|<num>|\||<string>| |<num>|\||<string>| le $bool$\cr
%
\bf Control operators\hfill\cr
|<bool> {<truepart>} {<falsepart>}| ifelse \cr
|<num> {<body>}| repeat \cr
|<from> <step> <to>{<body>}| for \cr }
}$$
With prefix
$\langle in\rangle\> \langle operator\rangle\>\langle result\rangle$
is elegant.
\bluesubhead What is not allowed as EPS?
I'm not knowledgeable enough to answer that question, nor do I know of
a full-blown definition of EPS.
For the moment it is some subset which works with all interpretors,
with my subset 0 in there.
When one restricts oneself to the basics of graphics, arithmetic and similar
operations then the boundary area between EPS and full \PS\Dash
or its various implementations\Dash is not in sight.
\bluesubhead Documentation
The red book\Dash the reference manual\Dash is generally recommended, though
the blue book\Dash the tutorial and cookbook\Dash is also nice.\ftn{I used the
\PS I red book and this is well-suited to get the flavour.
For \TeX{} and METAFONT %\MF{} %font not available
this is similar. To grasp the basic ideas
Knuth's first book is a more concise survey of the main lines of thought than
\TB{} and {\sl The METAFONTbook}.}
\blueexample Pie chart from the blue book
$$\ifdraft\vbox to3in{\vss\hbox{Pie chart}\vss}
\else\psfig{file=prpie.eps,height=3in}
\fi$$
The invoke is essentially as follows and shows that the codes can be used
straightforwardly.\ftn{It is not standard \PS. We have to construct some kind of
library to use the PostScript programs from.
Maybe the CTAN as global network library?
Copied on the various CD-ROMS?}
It is no longer necessary to mesh around with the picture environment or so,
to achieve the effect.
\beginverbatim
%preliminary matter
(January Pie Sales)
24 12 %... array size
[ [(Blueberry) .12 ]
[(Cherry) .30 ]
[(Apple) .26 ]
[(Boston Cream) .16 ]
[(Other) .04 ]
[(Vanilla Cream) .12 ]
] 306 396%translate center to
140 %size
DrawPieChart
showpage
!endverbatim
There is also a \PS-FAQ, consult
|ftp wilma.cs.brown.edu:|\\
\null\qquad \qquad |pub/comp.lang.postscript|.
It contains an annotated bibliography as well.
The examples from Adobe's blue book are available on the net.
\bluesubhead Proofing
For previewing or printing, {\em as such\/}
I have to include a shift to move the picture away from the lower left corner,
say
\beginverbatim
300 500 translate
!endverbatim
\bluesubhead Inclusion
I usually build a figure symmetrically around the origin and then include
it via
\beginverbatim
$$\psfig{file=<name>,height=<number><unit>}$$
!endverbatim
A unit can be |in|(ch), |cm|, and ilks. \cs{psfig} is very vulnerable to
spaces because of \TeX's parsing. So no spaces in there.
Now and then I forget to inactivate the |translate| needed while previewing.
No real problem.
\bluesubsubhead BoundingBox
Providing the right BoundingBox coordinates has all to do with
proper placement within context, the look-and-feel.
Default \PS{} assumes the origin\Dash in user space\Dash
at the lower left corner of the paper\Dash in device space.
Surround the picture by as-if lines and supply the coordinates, in points as units
in user space coordinates,
of the lower left corner and the upper right corner in the
BoundingBox specification.
Simple is to build a picture around its symmetry point\Dash
and let this coincide with the origin\Dash
with as pleasing result that the horizontal positioning comes out centered,
when used within math display.
Vertically, I add a 10 or so
extra on either side in the BoundingBox specification,
but that depends on the character of the picture.
Some preview systems can measure the BoundingBox and allow adjustment
interactively.\ftn{For a summary of tools to assist finding the BoundingBox
coordinates see, Reckdahl K (1995): Using EPS graphics in \LaTeX{}
documents.
[email protected].}
\bluesubhead Writing PostScript
A line bundle and a variant of it are introduced to
show how to create simple EPS.
\bluesubsubhead A line bundle
$$\ifdraft\vbox to1in{\vss\hbox{Line bundle}\vss}
\else\psfig{file=linebundle.eps,height=1in}
\fi$$
How to do this in \PS? A line as such is simple.
First a |moveto| and then a |lineto|. So a way is to create a loop and repeatedly
draw from the origin to the end of the various lines.
This can be done elegantly by using appropriately the CTM.
\beginverbatim
%!!PS EPS
%%Title: Line bundle
%%Creator: cgl
%%CreationDate: June 4 1996
%%BoundingBox: -40 -45 40 45
%%Pages: 1
%%EndProlog
%%Page: 1 1
/r 36 def
10{0 0 moveto r 0 lineto
36 rotate
}repeat stroke showpage
!endverbatim
Explanation.
The idea is that first a simple line is draw, for example along the x-axes.
What happens if after that we rotate? Right, the mapping is changed.
And what happens if we supply the {\em same\/} line after this?
Indeed, it will show up rotated. Because \PS{} is an interpretive
language we can realize this specification after the rotate via a loop,
which for this simple case reads |10{...}repeat|.\ftn{Do you see the variant
for drawing a polygon? This duality linebundle and polygon has been used
by Gabo and is about what he called stereometry versus perimetry,
the structure versus the surface}
\beginquote
Appropriately maintaining the CTM for symmetrical pictures can yield simple
looking \PS{} programs.
\endquote
\bluesubsubhead A flower
$$\ifdraft\vbox to1in{\vss\hbox{Flower}\vss}
\else\psfig{file=flower.eps,height=1in}
\fi$$
This exercises the use of |arc|.
\beginverbatim
%!!PS EPS
%%Title: Flower
%%Creator: cgl (Courtesy Papert)
%%CreationDate: June 4 1996
%%BoundingBox: -40 -45 40 45
%%Pages: 1
%%EndProlog
%%Page: 1 1
/r 36 def
10{r r moveto%begin drawing point
r 0 r 90 180 arc
currentpoint%origin
0 r r 270 360 arc
36 rotate
}repeat stroke showpage
!endverbatim
Explanation.
We have the same structure as the previous program but the `line' is now
a little more elaborated: two arcs of a circle.
\PS{} provides an operator for drawing circular arcs, called arc.
The arc has $(x,y)$ as centre, r as radius,
$ang_1$ the angle of a vector from $(x,y)$ of length $r$
to the first endpoint of the arc, and
$ang_2$ the angle of a vector from $(x,y)$ of length $r$
to the second endpoint of the arc.\ftn{The arc is drawn counter clockwise.
|arcn| draws clockwise.}
These arguments are expected to be on the stack.
\beginverbatim
x y r ang1 ang2 !bf arc
!endverbatim
Important is to realize that arc {\em counts\/} its angle from (x, 0) and that
the {\em drawing\/} starts from the point on the stack
The specification of the flower in \MF/\MP{} reads essentially as follows.
\beginverbatim
for k:= 1 upto 10:
draw(origin{up}..{right}(up+right){down}..
{left}origin) rotated 36k;
endfor
!endverbatim
Explanantion.
\MF{} allows for specification of the directions\ftn{There is also a
quartercircle which apart from orientation is drawn similarly.}
$up =(0,1), right=(1,0)$.
IMHO, with all respect the \MF{} and \PS{} programs are similar
modulo some syntactic sugar.
However, the extra possibility of specifying the directions is more convenient
than using control points.
But perhaps that is a matter of taste, although the handling of control points
is powerful as B\'ezier himself has shown in the past.
From this I conclude that for these simple kinds of pictures we can as well use
\PS{} straightaway.
\bluehead Some more Graphics
\blueexample Malbork window
This is all about using |curveto|, especially choosing suitable control points.
$$\ifdraft\vbox to1in{\vss\hbox{Malbork window}\vss}
\else\psfig{file=malbork.eps,height=1in}
\fi$$
\beginverbatim
%!!PS EPS
%%Title: Malbork Window
%%Creator: cgl
%%CreationDate: May 21 1996
%%BoundingBox: -40 -40 40 40
%%Pages: 1
%%EndProlog
%%Page: 1 1
45 rotate 10 0 moveto
4{20 0 37.5 12.5 25 25 curveto
12.5 37.5 0 20 0 10 curveto
90 rotate
}repeat%inside lops next
5 0 moveto
4{5 35 35 5 0 5 curveto
90 rotate
}repeat%enclosing circle next
36 0 moveto
0 0 36 0 360 arc
stroke showpage
!endverbatim
Explanation.
|translate| changes the CTM,
with the effect that the device coordinates are shifted. (Useful for
use of \PS{} alone out of context.)
|rotate| changes the CTM, and because of being an interpretive language
the various loop traversals map the {\em same\/} user coordinates on the
rotated device coordinates.
$\langle number\rangle \{\dots\}$ |repeat| is a loop to be traversed
$\langle number\rangle$ of times.
|curveto| adds a spline to the current path
from the currentpoint to the last point on the stack.
The first two points are the so-called control points of the spline.\ftn{Much similar
as in METAFONT. Choosing for the inner lop the control
points in this way is borrowed from
Haralambous Y (1995): Some METAFONT techniques.
\tubissue{16}(1), 46\dash53. It is also supplied in the description
of |curveto| in the red book.}
|arc| adds a circular arc to the current path from the currentpoint.
The details of the arguments for the operators are nicely documented in the
red book.
\blueexample Escher's impossible triangle
This is all about {\em wrong\/} projections.
However, these kinds of pictures are intriguing and fun.
I consider them well-suited to illustrate \PS's drawing capabilities.
$$\ifdraft\vbox to1in{\vss\hbox{Escher's impossible triangle}\vss}
\else\psfig{file=eschera.eps,height=1in}
\fi$$
\beginverbatim
%!!PS EPS
%%Title: Escher's impossible triangle
%%Creator: cgl (inspired by Guy Shaw)
%%CreationDate: May 23 1996
%%BoundingBox: -40 -40 40 40
%%Pages: 1
%%EndProlog
%%Page: 1 1
3{25 34 moveto
25 -34 lineto
17 -38.2 lineto
17 20 lineto
-17.6 0 lineto
120 rotate
}repeat stroke showpage
!endverbatim
\on5{} points, the right stroke and a rotation or two, that's it.
End of story.
However, it is all about finding those \on5{} points.
$$\ifdraft\vbox to1in{\vss\hbox{the 5 points}\vss}
\else\psfig{file=escherb.eps,height=1in}
\fi$$
\beginverbatim
%!!PS EPS
%%Title: Essential stroke
%%Creator: cgl (inspired by Guy Shaw)
%%CreationDate: May 23 1996
%%BoundingBox: -40 -40 40 40
%%Pages: 1
%%EndProlog
%%Page: 0 1
25 34 moveto currentpoint
0 -68 rlineto currentpoint%down
-120 rotate
25 34 lineto%preserve symmetry
120 rotate currentpoint
17 20 lineto currentpoint
-17.6 0 lineto currentpoint
%labels
/Courier findfont 8 scalefont setfont
moveto -5 -3 rmoveto (5) show
moveto 1 1 rmoveto (4) show
moveto 2 -5 rmoveto (3) show
moveto 2 0 rmoveto (2) show
moveto 2 0 rmoveto (1) show
stroke showpage
!endverbatim
Explanation.
The essential stroke figure also illustrates the integration
of text in this case digits.
|currentpoint| pushes the point on the stack.
The last |moveto|-s pop these coordinates up.
|rmoveto| moves {\em relatively.}
\smallbreak
And what about their relationships, and
what about the minimal information to be prescribed?
Looking more closely it turns out that {\em only\/} the first point is all
that is needed.
The rest is implicit to the nature of the figure.\ftn{Of course
one can also think of other equivalent parameters like size and thickness.}
\beginverbatim
%!!PS EPS
%%Title: Escher's Impossible triangle II
%%Creator: cgl
%%CreationDate: May 23 1996
%%BoundingBox: -40 -40 40 40
%%Pages: 1
%%EndProlog
%%Page: 1 1
%Parameterized over p1
/point {25 34} def%note x<y
%
3{point moveto
currentpoint neg lineto%down
-120 rotate
point lineto%preserve symmetry
120 rotate
currentpoint 2 div neg lineto
currentpoint 3 sqrt mul sub 0 lineto
120 rotate
}repeat stroke showpage
!endverbatim
Explanation.
|currentpoint| yields the coordinates of the current point of the path on the stack.
The other operations do what their names suggest.
The temporarily change of the CTM within the loop expresses the
rotation symmetry relation between points \on1{} and \on3.
\blueexample Bentley's polygon
This code is all about a double loop and using the loop variable from the stack,
next to using the |gsave| and |grestore| advantageously.
$$\ifdraft\vbox to1in{\vss\hbox{Bentley's polygon}\vss}
\else\psfig{file=bentley.eps,height=1in}
\fi$$
\beginverbatim
%!!PS EPS
%%Title: Bentley's double loop
%%Creator: cgl
%%CreationDate: May 30 1996
%%BoundingBox: -100 -105 100 105
%%EndProlog
10{1 1 9{100 0 moveto
gsave
36 mul rotate%loopcount*36
100 0 lineto stroke
grestore
} for
36 rotate
}repeat showpage
!endverbatim
Explanantion.
|gsave| and |grestore| are needed to draw locally, that is at the end
the graphics state\Dash currentpoint, currentpath and CTM\Dash
is restored with the values at the beginning.
\on1{} \on1{} \on9{} stand for beginvalue step and endvalue of the |for| counter.
\blueexample Another double loop
A set of nested polygons provide also a double loop situation.
$$\ifdraft\vbox to1in{\vss\hbox{Polygons}\vss}
\else\psfig{file=polygon.eps,height=1in}
\fi$$
\beginverbatim
%!!PS EPS Nested pentagons
%%Title: Pentagons
%%Creator: cgl
%%CreationDate: June 17 1996
%%BoundingBox: -100 -100 100 100
%%Pages: 1
%%EndProlog
%%Page: 1 1
10 10 100{dup 0 moveto
5{72 rotate
dup 0 lineto
}repeat
}for stroke showpage
!endverbatim
\blueexample Polygons with splines as sides
This generalization of polygons was introduced by Jackowski at Euro\TeX{} \on95.
A special case of \MF's interpath functionality is shown en-passant.
$$\ifdraft\vbox to1in{\vss\hbox{flexess}\vss}
\else\psfig{file=polygonii.eps,height=1in}
\fi$$
\beginverbatim
%!!PS EPS Nested `squares'
%%Title: polygon.eps II
%%Creator: cgl
%%CreationDate: June 17 1996
%%BoundingBox: -100 -100 100 100
%%Pages: 1
%%EndProlog
%%Page: 1 1
/r 100 def
/r1 {r .25 mul} def
/r3 {r .75 mul} def
25{r 0 moveto
4{r3 r3 r1 r1 0 r curveto
90 rotate
}repeat
.9 .9 scale
}repeat stroke showpage
!endverbatim
\blueexample Barn window
This is all about playing with circles and circular arcs.\ftn{The first example
in the blue book collection provides a similar picture with gradually
changing scales of grey.}
$$\ifdraft\vbox to1in{\vss\hbox{Barn window}\vss}
\else\psfig{file=barnwindowii.eps,height=1in}
\fi$$
\beginverbatim
%!!PS EPS
%%Title: Barn Window II
%%Creator: cgl
%%CreationDate: May 29 1996
%%BoundingBox: -45 -45 45 45
%%Pages: 1
%%EndProlog
%%Page: 1 1
/l 36 def
/r {l 22.5 sin mul} def
/m {l 22.5 cos mul} def
8{r .5 mul 0 moveto
l 0 lineto
currentpoint %begin circular arc
22.5 rotate m 0%center
r %radius
-90 90 arc
22.5 rotate
}repeat
%inner circle
/rin {r .5 mul} def
rin 0 moveto
0 0 rin 0 360 arc
%outer circle
/rout {r m add} def
rout 0 moveto
0 0 rout 0 360 arc
%extra circles
/rin {r .25 mul} def
22.5 rotate
8{m rin add 0 moveto
m 0 rin 0 360 arc
45 rotate
}repeat stroke showpage
!endverbatim
I'm sure I'll come back some day and look again through this window,
but then pastel colored.
\blueexample Baker's inspiration
$$\ifdraft\vbox to1in{\vss\hbox{Woody Baker's picture}\vss}
\else\psfig{file=baker.eps,height=1in}
\fi$$
This example is similar to Escher's impossible triangle.
Find the essential stroke and rotate.
\beginverbatim
%!!PS EPS
%%Creator: cgl (inspired by Woody Baker)
%%CreationDate: May 1996
%%BoundingBox: -80 -80 80 80
%%Pages: 1
%%EndProlog
%%Page: 1 1
4{-15 25 moveto
0 -10 rlineto
60 0 rlineto
0 -30 rlineto
10 0 rlineto
0 40 rlineto
-70 0 rlineto
0 10 rlineto
80 0 rlineto
0 -60 rlineto
-30 0 rlineto
0 10 rlineto
10 0 rlineto
%
35 -25 moveto
0 -10 rlineto
20 0 rlineto
10 10 rlineto
%
45 15 moveto
10 10 rlineto
90 rotate
}repeat stroke
%
/Courier findfont 10 scalefont setfont
-55 -75 moveto
(Courtesy Woody Baker)show
showpage
!endverbatim
\blueexample Romanovsky's real Escher
$$\ifdraft\vbox to1in{\vss\hbox{JVR's picture}\vss}
\else\psfig{file=jvr.eps,height=1in}
\fi$$
Grey scales can be obtained simply via $\langle number\rangle$ |setgray|,
with $\langle number\rangle \in [0, 1]$.
0 denotes black and 1 is white.
The idea is to construct the essential path\Dash
the stroke denoted by a grey scale\Dash
and to use this \on3{} times.
\bluehead Math graphs
In \AllTeX{} documents it is a problem\ftn{Communicated by Nico Temme.
He solved the problem by doing the calculations in PASCAL.
For advanced manipulations Mathematica or Mapple
are generally used where the resulting EPS is pasted up in the
\AllTeX{} script as usual.}
how to include accurate graphs of mathematical functions.
Because of \PS's arithmetic and graphics capabilities it is
handy to use \PS.
\blueexample Sine function
$$\ifdraft\vbox to1in{\vss\hbox{sine function}\vss}
\else\psfig{file=sine.eps,height=1in}
\fi$$
\beginverbatim
%!!PS EPS
%%Title: Sine function
%%Creator: cgl (inspired by Batagelj)
%%CreationDate: May 27 1996
%%BoundingBox: -200 -110 200 110
%%EndProlog
/Courier findfont 15 scalefont setfont
%figure scaled by 100
%x-axes and label
-200 0 moveto 200 0 lineto
-15 -15 rmoveto (x) show
%y-axes and label
0 -110 moveto 0 110 lineto
-35 -10 rmoveto (sin) show
%function
-180 0 moveto
-180 10 180{%from step to
dup sin 100 mul%(x, 100sin x)
lineto
}for stroke showpage
!endverbatim
The invoke might read as follows.
\beginverbatim
$$\psfig{file=sine.eps,height=1in}$$
!endverbatim
\bluehead Text set along curved paths
A teaser. With the advent of scalable and rotationable outline fonts
this is possible too.
\blueexample Along a circle
$$\ifdraft \vbox to 1in{\vss\hbox{text along an arc}\vss}
\else \psfig{file=textalongarc.eps,height=1in}
\fi$$
\beginverbatim
%!!PS EPS
%%Title: Typesetting along arcs
%%Creator: cgl
%%CreationDate: June 4 1996
%%BoundingBox: -100 50 100 125
%%Pages: 1
%%EndProlog
%%Page: 1 1
/Courier findfont 10 scalefont setfont
/text (happybirthday) def
50 rotate
0 1 12{0 100 moveto
text exch 1 getinterval show
-10 rotate
}for stroke showpage
!endverbatim
Joseph Romanovsky communicated that |kshow|\Dash kerning (and more general
positioning) under user control\Dash
is available which allows a general
def to be executed between two characters of a string.
\blueexample Along a spiral
The blue book provides an example of typesetting along a path\Dash
a quotation of Woody Allen\Dash
where the path accentuates his filmmaker profession.
The example below shows a nice effect with little knowledge of \PS,
essentially the use of |kshow|.
$$\ifdraft \vbox to 2in{\vss\hbox{text along spiral}\vss}
\else \psfig{file=textalongspiral.eps}
\fi$$
\beginverbatim
%!!PS EPS
%%Title: Text along spiral
%%Creator: J.V. Romanovsky
%%BoundingBox: -100 -90 60 70
%%EndProlog
/Courier findfont 20 scalefont setfont
-100 0 moveto 50 rotate
{-10 rotate 3 0 rmoveto .98 .98 scale}
(Olga Grineva my charming
St Peterburg hostess)kshow
showpage
!endverbatim
\blueexample Seals
The problem has been discussed by Hoenig at Euro\TeX{} \on92,
and Zlatu\v{s}ka at Euro\TeX{} \on95, both biased by \MF.
\PS{} alone is suited too with an overall simpler process.
Combining two earlier supplied examples yields Zlatu\v{s}ka's seal
in principle.\ftn{The blue book also provides a seal\Dash
Symphony No.\on9\Dash
but that is more complex and ipso facto requires more knowledge of \PS{}
to understand what is going on, IMHO, with all respect.
To set this poster from the blue book is no more difficult than the
use of |arc|, however. My example gives you the feeling that you
understand what is going on, I hope.}
\beginverbatim
%!!PS EPS
%%Title: Seal, in principle
%%Creator: cgl
%%CreationDate: June 6 1996
%%BoundingBox: -110 -45 110 100
%%Pages: 1
%%EndProlog
%%Page: 1 1
%150 650 translate
/Courier findfont 10 scalefont setfont
/text (happy postscripting to you) def
/r 100 def
gsave
90 rotate %begin orientation
0 r moveto%begin point
{-7.04 rotate 0 r moveto} text kshow
grestore%next the central Escher
3{25 34 moveto
25 -34 lineto
17 -38.2 lineto
17 20 lineto
-17.6 0 lineto
120 rotate
}repeat stroke showpage
!endverbatim
$$\ifdraft \vbox to 1.5in{\vss\hbox{seal}\vss}
\else \psfig{file=seal.eps,height=1.5in}
\fi$$
Remark. The difference of fonts in the main text and that used by \PS{}
is no longer there when \PS{} fonts are used throughout, be it
the \PS{} version of the CM family.
\blueexample Gurari's squares
$$\ifdraft \vbox to 1in{\vss\hbox{Gurari's squares}\vss}
\else \psfig{file=gurarisq.eps,height=1in}
\fi$$
\beginverbatim
%!!PS Gurari squares
%%BoundingBox: -200 -110 200 110
%%Creator: cgl
%%CreationDate: June 20 1996
%%EndProlog
/r 22 def
/square {1 1 4{0 r rlineto
90 rotate}for} def
0 0 moveto 90 rotate
50{r 0 rmoveto square
-30 rotate .9 .9 scale
}repeat stroke showpage
!endverbatim
\blueexample Gurari's ABC
Very nice this suggestion of motion.
$$\ifdraft \vbox to 1.5in{\vss\hbox{Gurari's speedy ABC}\vss}
\else \psfig{file=gurariabc.eps,height=1.5in}
\fi$$
\beginverbatim
%!PS EPS
%%Title: Guarai's ABC
%%BoundingBox: 0 -45 100 75
%%Creator: Gurari
%%CreationDate: copied June 17 1996
%%Pages: 1
%%EndComments
%%EndProlog
%%Page: 1 1
/Times-Bold findfont 45 scalefont setfont
-40 rotate
1 -.03 0{setgray
0 0 moveto
(ABC) show
3 rotate
} for
0 0 moveto -4 rotate
1 setgray (ABC) show
showpage
!endverbatim
\blueexample Walking along the S-curve
In {\sl The METAFONTbook\/} ex\on13.\on10{} is about drawing overlapping
disks along a path, the S-figure.
How to do this in \PS{} straightaway?
There is no `point of' a path operator so the best we can attain is
to walk along a math function.
$$\ifdraft \vbox to 1in{\vss\hbox{S-figure}\vss}
\else \psfig{file=sinedisks.eps,height=1in}
\fi$$
\beginverbatim
%!PS Sine with overlapping disks
%%BoundingBox: -200 -110 200 110
%%Creator: cgl (METAFONTbook ex13.10)
%%CreationDate: June 17 1996
%%EndProlog
newpath
-180 10 180{dup sin 100 mul%(x, 100sin x)
12.5 0 360 arc
gsave 1 setgray fill grestore
stroke
}for showpage
!endverbatim
Explanation. |1 setgray fill| is the erase functionality, encapsulated to
yield what we want.
\bluehead Tables set sideways
Another teaser is to set tables rotated.
Rokicki provided rotate macros along with his |dvips|, among others.
I have borrowed the essence from his rotate macros
and recast into the following.
\beginverbatim
\def\rotate#1%stuff
#2%degrees in PS direction
{\setbox\abox=\hbox{#1}%
\adim\ht\abox\advance\adim by\dp\abox
\hbox to\adim{\vbox to\wd\abox
{\vskip\wd\abox
\special{ps: gsave
currentpoint currentpoint translate
#2 neg rotate
neg exch neg exch translate}%
\box\abox\vss}\hss}%
\special{ps: currentpoint
grestore moveto}%
}%end rotate
!endverbatim
The point is that it is not much.
The |ps:| is dependent on the system still, alas.
\blueexample Rotated table
The example works under UNIX with Rokicky's |dvips|.
%under UNIX
\newdimen\adim
\newbox\abox
%
\def\rotate#1%stuff
#2%degrees in PS direction
{\setbox\abox=\hbox{#1}%
\adim\ht\abox\advance\adim by\dp\abox
\hbox to\adim{\vbox to\wd\abox{\vskip\wd\abox
\special{ps: gsave currentpoint currentpoint
translate #2 neg rotate
neg exch neg exch translate}%
\box\abox\vss}\hss}%
\special{ps: currentpoint grestore moveto}%
}%end rotate
\begindemo
\def\data{1\cs2\rs
3\cs4 }
pre
\rotate{\framed
\btable\data}
{90}
post
!yields
\def\data{1\cs2\rs 3\cs4 }
pre
\rotate{\framed\btable\data}{90}
post
\enddemo
Remark.
Gurari (1994) has provided some more examples of \PS$\leftrightarrow$(Al)Dra\TeX{}
interaction. Real interfacing.
Apart from portability problems it gets quite complicated.
For the moment I refrain and code the `pictures' in raw \PS{}
assisted by \MF{} for prompting control points of those curves
which can be specified elegantly in a declarative way.
\bluehead METAFONT/MetaPost user interface
Sometimes it is more natural to specify points and {\em directions}.
It is true that specifying a control point along the direction
can yield the same effect but the distance between the point
and its control point influences the shape.
\blueexample Escher's knot
This example is all about specifying directions.
$$\ifdraft\vbox to1in{\vss\hbox{Escher knot II}\vss}
\else\psfig{file=escherknotmf.eps,height=1in}
\fi$$
In \MF{} the coding would read as follows.
\beginverbatim
%Escher's Knot. June 96.
[email protected]
def openit = openwindow currentwindow
from origin to (screen_rows,screen_cols)
at (-2r,3r)enddef;
pickup pencircle scaled 1;
tracingstats:=proofing:=1; screenstrokes;
pair p[];
%parameters
r:=100; alfa=90;
%
p2:=(0,.85r); %independent from p1,3,4
p4:=(0,-.5r);
%dependent points because of symmetry
p1:=p4 rotated -120;
p3:=p4 rotated 120;
path q;
q=p1{dir alfa}..{(1,0)}p2..
{dir(-alfa)}p3..{dir(alfa-240)}p4;
draw q;
draw q rotated 120;
draw q rotated-120;
showit;
end
!endverbatim
By the nature of the figure not only points are related but
also their directions.
How to cope with this in \PS?
It can be done but is not so elegant, honestly speaking cumbersome.
But \dots there is a solution or two, hang on.
\beginverbatim
%!!PS EPS
%%Title: Escher knot II
%%Creator: cgl (inspired by Knotplot)
%%CreationDate: June 1996
%%BoundingBox: -95 -95 95 95
%%Pages: 1
%%EndProlog
%%Page: 1 1
%
/angle 90 def
/r 100 def
/point {0 -.5 r mul}def
/p1 {-.25 r mul 3 sqrt mul .25 r mul moveto
currentpoint
angle sin 2 mul add exch
angle cos 2 mul add exch
-20 .85 r mul
0 .85 r mul
curveto stroke} def
/p3 { .25 r mul 3 sqrt mul .25 r mul moveto
%Control point
currentpoint
angle sin -15 mul add exch
angle cos 15 mul add exch
%Control point:
% 58.62 -.5 r mul 5 add%angle 90
0 angle -240 add cos -15 mul add
-.5 r mul angle -240 add sin -15 mul add
0 -.5 r mul
curveto stroke} def
3{p1
gsave -1 1 scale p1 grestore%reflect
p3
120 rotate
}repeat showpage
!endverbatim
Explanation.
The essential curve is split into \on3{} pieces: p$_1$,\dots p$_3$.
The first two are related by reflection.
The third must properly match. In the Columbus's egg paragraph
the straight |.eps| code is given,
biased by the knowledge of the (control) points.
\bluesubhead A teaser
More complicated is when the line is changed into a tube, and
when we have to deal with hidden lines.
In \MF{} the code could read as follows, where use is made of
|intersectiontimes| and of subpaths.\ftn{This code works as such on my Mac
with Bluesky's PD METAFONT. For other environments build a character
from it, or adapt it for use in MetaPost, or even simpler copy the
bread-and-butter EPS code which is appended at the end.}
\blueexample Escher's knot III
This example is all about getting from a {\em declarative\/} specification
in \MF{} to a {\em imperative\/} EPS code.
$$\ifdraft\vbox to1in{\vss\hbox{Escher knot III}\vss}
\else\psfig{file=escherknotiii.epsabr,height=1in}
\fi$$
First the declarative \MF{} code.
\beginverbatim
%Escher Knot III. June 96.
[email protected]
def openit = openwindow currentwindow
from origin to (screen_rows,screen_cols)
at (-2r,3r)enddef;
pickup pencircle scaled 1;
tracingstats:=proofing:=1; screenstrokes;
numeric t, u, v, w;
pair p[]; path q[];
def assignpoints=
p2:=(0,.85r); %independent from p1,3,4
p4:=(0,-.5r);
%dependent points because of symmetry
p1:=p4 rotated -120;
p3:=p4 rotated 120;
enddef;
%
alfa=90;r:=100; assignpoints;
q1:=p1{dir alfa}..{(1,0)}p2..
{dir(-alfa)}p3..{dir(alfa-240)}p4;
%inside
r:=.75r; assignpoints;
q2:=p1{dir alfa}..{(1,0)}p2..
{dir(-alfa)}p3..{dir(alfa-240)}p4;
(t,u)= subpath (2.5,3) of q1
intersectiontimes (q2 rotated -120);
(v,w)= q2 intersectiontimes
(q1 rotated 120);
%showvariable t,u;
draw subpath (0,2.5 + t/2) of q1;
draw subpath (0,2.5 + t/2) of q1
rotated 120;
draw subpath (0,2.5 + t/2) of q1
rotated-120;
%showvariable v,w;
draw subpath (v,3) of q2;
draw subpath (v,3) of q2 rotated 120;
draw subpath (v,3) of q2 rotated-120;
showit;
end
!endverbatim
To give the reader an impression of what \MP{} will yield
|escherknotIII.eps|, the imperative code, is included.\ftn{A white lie. I have edited the file
and reduced the data\Dash and deleted
|dtransform|, |idtransform| and the various |set...|\Dash
for the \on6{} strokes into only \on2{} and rotated these.
METAFONT allowed me to declaratively specify the picture while
MetaPost provided me with the essential path data.
Well\dots even METAFONT can be asked to provide those (control) points.}
\beginverbatim
%!!PS EPS
%%BoundingBox: -40 -31 40 43
%%Creator: MetaPost and JJW, CGL
%%CreationDate: June 17 1996
%%Pages: 1
%%EndProlog
%%Page: 1 1
3{-21.6507 12.5 moveto
-21.6507 27.74551 -13.78212 42.5003
0 42.5003 curveto
13.78212 42.5003 21.6507 27.74551
21.6507 12.5 curveto
21.6507 -0.24506 16.04897 -12.19249
6.58395 -20.3313 curveto
%
-14.3152 15.86746 moveto
-12.43301 23.58928 -7.45113 29.75021
0 29.75021 curveto
9.64748 29.75021 15.15549 19.42186
15.15549 8.75 curveto
15.15549 -2.07904 9.37823 -12.08548
0 -17.5 curveto
120 rotate
}repeat stroke showpage
!endverbatim
As can be seen from the last code it is all about finding the right
(control) points and draw the strokes, as remarked at the beginning of this note.
The difference between the declarative \MF{} specification and
the resulting (unedited) \MP{} code is striking.
When the last code is shown first one would say, ah\dots \PS{}
is easy just data and some strokes.
The resulting code is equivalent to Woody Baker's code:
just the right stroke and a rotation or two.
KnotPlot on the net provides a more complicated version where
the light reflection is emulated by shades of grey.
The gzipped file is \on64KB, however.
A world of difference.
\bluesubhead Columbus' egg
Why not use \MF{} to create `the (control) points' from the descriptive picture
and use these in raw \PS{} straightaway?
After assigning
|precontrol|-s and |postcontrol|-s to pairs and
inserting |show|-s, \MF{} yielded for the simple Escher knot the data
in the transcript file.
A little editing of this log file resulted in the following
imperative EPS code.
\beginverbatim
%!!PS EPS
%%Title: Escher knot (mf prompted)
%%Creator: cgl
%%CreationDate: June 1996
%%BoundingBox: -80 -80 80 80
%%Pages: 1
%%EndProlog
%%Page: 1 1
3{-43.30139 25 moveto
-43.30139 55.49103 -27.56424 85.00061
0 85.00061 curveto
27.56424 85.00061 43.30139 55.49103
43.30139 25 curveto
43.30139 -5.94014 26.79497 -34.5299
0 -50 curveto
120 rotate
}repeat stroke showpage
!endverbatim
I presume the functionality is similar to Jackowski's |mftoeps|.
The above method is my Poor Man's \MF2EPS, with concise, very concise
and intelligible EPS as result.
\bluehead Acknowledgements
First of all Don Knuth and John Hobby thank you.
Thank you Joseph Romanovsky for
showing by example the power of \PS, and for
your cooperation on the \MF$\leftrightarrow$\PS{} duality.
Thank you Bogus\l{}aw Jackowski for your `\PS{} for \TeX ies'
at Bacho\TeX{} \on96, suggesting that \PS{} as such is beneficial
for \TeX ies, next to your mftoeps.
Thank you Eitan Gurari and anonymous \TeX ies of which I borrowed material,
not in the least Adobe for providing \PS{} to start with.
Piet Tutelaers provided me with a copy of the PSFAQ, and
Erik Frambach traced the file with examples from the blue book, next to KnotPlot.
As usual Jos Winnink proofed the paper and lend a helping hand in
procrusting towards MAPS inclusion if not for processing |escherknot.mf|
into |escherknot.eps| via \MP.
\bluehead Conclusion
To code symmetrical and simple curves in raw \PS{} is fun and yields elegant
scripts and concise files.
To merge text with graphics is fun too, and the teaser to set along curved paths
can be done by \PS{} elegantly.
Another teaser of drawing math curves accurately along with \AllTeX{} is solved also
by means of \PS.
Powerful too is to {\em extend\/} the inclusion of .eps files
at the dvi level by a little more interaction between \AllTeX{} and \PS.
Rotating a box, with as applications for example
typesetting tables in landcape, is possible in \PS, at the expense of system
dependency because of the \cs{special}-s.
{\em Merging\/} a little knowledge of \PS{} with \TeX pertise is powerful.
PStricks concentrates on {\em interfacing\/} \AllTeX{} with \PS{} at the expense
of burdening \AllTeX{} too much, IMHO, with all respect.
For \cs{rotate} I interfaced too. However, for typesetting along curved
paths I would not think of interfacing via rotated boxes or so.
Of course, people who do need advanced features or have special wishes
might better use Adobe Illustrator, CorelDRAW, Mathematica, or Adobe Photoshop,
and not to forget the pleasing MetaPost.
To understand and learn \TeX{} did take me a couple of years.
To acqaint myself with \MF{} did cost me a few months.
Learning just a little bit of \PS{} was a matter of weeks, and
when concentrating
on paths and (control) points the |moveto|, |arc| and |curveto|
can be grasped in a late afternoon.
Although the blue book contains also examples of typesetting text,
I consider \TeX{} unsurpassed for this. The best of both worlds is to
combine \AllTeX{} and \PS.
Maybe we should follow Adobe and extend the use of \PS{} by PDF\Dash
or use the alternative HTML\Dash to facilitate WWW surfing.
\bluehead What more?
For pictures I use a \TeX{} controlled database with the beneficial side-effect
that I don't have to worry about file systems when using pictures
(tools, references and ilks) on different machines.
I would welcome a similar functionality for my collection of \PS{}
pictures to be used with \cs{psfig}.
A next step is the manipulation of colors either via \MP{} or \PS{} directly.
Jackowski uses Adobe Illustrator for example to enrich interactively
the systematic EPS pictures created by \MF.
Indeed interesting, very interesting,
but beyond my possibilities for some time to come.
Neither do I have access to color \PS{} printers as yet, alas.
My case rests.
Have fun, and all the best.
\makesignature
\pasteuptoc
\endscript
