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+%Started May 1996, C.G. van der laan, cgl@rc.service.rug.nl
+%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. reckdahl@leland.stanford.edu.}
+
+\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. cgl@rc.service.rug.nl
+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. cgl@rc.service.rug.nl
+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