%% 
%% FMP Tutorial (English)
%% Copyright (C) 1998 Joachim Korittky
%% Copyright (C) 2002 Meik Hellmund
%% 
%% This file is part of Functional MetaPost.
%% 
%% Functional MetaPost is free software; you can redistribute it
%% and/or modify it under the terms of the GNU General Public License
%% as published by the Free Software Foundation; either version 2 of
%% the License, or (at your option) any later version.
%% 
%% Functional MetaPost is distributed in the hope that it will be
%% useful, but WITHOUT ANY WARRANTY; without even the implied warranty
%% of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
%% GNU General Public License for more details.
%% 
%% You should have received a copy of the GNU General Public License
%% along with Functional MetaPost; if not, write to the
%% Free Software Foundation, Inc., 59 Temple Place, Suite 330,
%% Boston, MA 02111-1307 USA
%% 

\documentclass[fleqn]{article}

%options hugs -h1m -P:/home/wferi/FuncMP-1.2
%align 33

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\begin{document}

\makeatother
\title{\texttt{\FMP} \\
       Tutorial}
\author{Joachim Korittky}


%\selectlanguage{german}

\begin{hide}

> module Tutorial where
> import FMPTurtle
> import FMPTree
> import FMPCanvas
> import FMPMatrix
> import FMPFrames

\end{hide}

\maketitle


\tableofcontents
\newpage
\enlargethispage{3cm}

> dbs                           =  draw [arrow ("Information"<+C) ("Query"<+C),
>                                       arrow ("Spec"<+C) ("Query"<+C),
>                                       arrow ("Proc"<+C) ("Querying"<+C),
>                                       arrow ("Output"<+C) ("Querying"<+C),
>                                       arrow ("Querying"<+C) ("Bib"<+C),
>                                       arrow ("Query"<+C) (xy (ref("Servers"<+C))(ref("Query"<+C)))
>                                               #setEndCut"Servers",
>                                       line (xy (ref ("Center"<+W)-vec(10,0)) (ref ("Information" <+N)))
>                                               (xy (ref ("Center"<+W)-vec(10,0)) (ref ("Warehouse"<+S)))
>                                               # setPattern dotted,
>                                       line (xy (ref ("Center"<+E)+vec(10,0)) (ref ("Information" <+N)))
>                                               (xy (ref ("Center"<+E)+vec(10,0)) (ref ("Warehouse"<+S)))
>                                               # setPattern dotted
>                                       ]
>                                 (cdrop (0,0) frontEnd & cdrop (200,0) backEnd
>                               &  cdrop (440,30) servers)
>       where
>       frontEnd                =  (oval (texCol "specification\\\\Component") # setName "Spec")
>                               |=|(oval (texCol "Data Processing\\\\Component") # setName "Proc")
>                               |=|(oval (texCol "Output\\\\Component") # setName "Output")
>       backEnd                 =   setTrueBoundingBox(drum (texCol "Information\\\\Servers\\\\Descriptions") 
>                                              # setName "Information")
>                               |=|(box ((box ("\\parbox{150pt}{\\begin{itemize}\\item Query Generation" ++  
>                                      "\\item Information Server Selection\\item Query Translation" ++ 
>                                      "\\item$\\ldots$\\end{itemize}}")  #setName "Query")
>                               |=| (box ("\\parbox{95pt}{\\begin{itemize}\\item Querying\\item Browsing" ++ 
>                                   "\\item Reorganization\\item Ranking\\item$\\ldots$\\end{itemize}}") 
>                                   # setName "Querying"))#setName"Center" # setDX 16 # setDY 16)
>                               |=|(setTrueBoundingBox(drum (texCol "Bibliographic\\\\Data\\\\Records") 
>                                   # setName"Bib")
>                               |=|"Warehouse" #setBGColor 0.9#setName"Warehouse")
>       servers                 =  fuzzy 1 2 (tex "Library Catalogues"  |=| vspace 30
>                                       |=| tex "Electronic Journals"   |=| vspace 30
>                                       |=| tex "FTP Servers") # setName "Servers"
>       texCol c                =  tex ("\\begin{tabular}{c}"++c++"\\end{tabular}")

\begin{center}
%if recalc
\perform{ generate "DataBases" 1 dbs }
%else
\epsfig{file=DataBases.1,width=12cm}
%endif
\end{center}


\newpage


\subsection{Introduction}


> conc259                       =  draw [arrow ("1" <+ C) (dk!!0,0),
>                                       arrow ("2" <+ C) (dk!!1,-5),
>                                       arrow ("n" <+ C) (dk!!8,-40)]
>                                  (cards
>                               &  cdraw (darrow (100+dk!!1,-20) (0,-20) "d_2")
>                               &  cdraw (darrow (100+dk!!2,-30) (0,-30) "d_3")
>                               &  cdraw (darrow (100-100*d 11,-55) (0,-55) "d_{n+1}")
>                               &  cdraw ((-330,-45).-.(100-100*d 11,-45)
>                                               .-.(100-100*d 11,-70))
>                               &  cdrop (-230,-60) "table"
>                               &  cdrop (-120,20) (tex "card $1$" # setName "1")
>                               &  cdrop (-175,15) (tex "card $2$" # setName "2")
>                               &  cdrop (-310,-20) (tex "card $n$"# setName "n"))
>       where
>       cards                   =  foldl (&) relax [cdraw ((x,y).-.(x+100,y)
>                                       .-.(x+100,y-5).-.(x,y-5).-.cycle')
>                                               |(x,y)<-zip dk [0,-5..]]
>       dk                      = [-100*d i|i<-[2..10]]
>       d 1                     = 0
>       d n                     = (n-1+sum [d i|i<-[1..(n-1)]])/(n-1)
>       darrow a b s            = a .-. b # setArrowHead (arrowHeadSize 4 180)
>                                         # setStartArrowHead (arrowHeadSize 4 180)
>                                         # setLabel 0.5 C (math s # setBGColor white)

\begin{center}
%if recalc
\perform{ generate "Concrete" 259 conc259 }
%else
\epsfig{file=Concrete.259}
%endif
\end{center}

\newpage

> conc66                        =  box (0,0) (50,100) (\i->(0,200-i*1.5))
>                                                       (\i->(i*1.5,200))
>                               &  box(50,0) (100,33.3) (\i->(0,i)) (\i->(i,-50))
>                               &  box(75,33.3) (100,66.6) (\i->(0,100-i)) (\i->(i,100))
>                               &  box(50,33.3) (75,53.3) (\i->(0,i)) (\i->(i,0))
>                               &  cdraw (vec(50,100).-.vec(100,100).-.vec(100,50))
>                               &  frac (-10,50) 1
>                               &  frac (25,-12) 2
>                               &  frac (75,-12) 2
>                               &  frac (110,17) 3
>                               &  frac (110,50) 3
>                               &  frac (62,65) 4
>                               &  frac (88,78) 4
>                               &  frac (40,42) 5
>                               &  cdrop (65,90) "etc."
>       where
>       frac p n                =  cdrop p (math ("\\frac{\\textstyle 1}{\\textstyle "
>                                               ++show n ++"}") # setBGColor white)
>       box (ax,ay)(bx,by)fa fb =  cdrop (0.5*(ax+bx),0.5*(ay+by))
>                                       (cdraws [fa i.-.fb i|i<-[-50,-40..200]]
>                                       & cclip p
>                                       & cdraw p)
>               where
>               p               =  vec(ax,ay) .-.vec(bx,ay) .-.vec(bx,by)
>                                  .-.vec(ax,by) .-. cycle'

\begin{center}
%if recalc
\perform{ generate "Concrete" 66 conc66 }
%else
\epsfig{file=Concrete.66}
%endif
\end{center}

\newpage

> hamilton                      =  arrows (matrix [[empty,empty,k 1,empty,k 4],
>                                                  [i ||| hspace 20,empty,empty,empty,
>                                                   empty,empty,hspace 20|||ip1],
>                                                  [empty,k 2,empty,k 5,empty,
>                                                   k 6 # setName "6"]])
>       where
>       i                       =  circle (math "i") # setName "i"
>       ip1                     =  oval (math "i+1") # setName "ip1"
>       k s                     =  boxArrows s (box (math ("K_"++show s))
>                                  # setDX 8
>                                  # setDY 8)
>       arrows                  =  draw [("i"<+C) ... (2<*1<*C)  # setEndAngle 0,
>                                       ("i"<+C) ... (1<*2<*C)  # setEndAngle 0,
>                                       curve (1<*5<*C) 0 0 (4<*3<*C),
>                                       curve (2<*4<*C) 0 0 (5<*3<*C),
>                                       curve (5<*6<*C) 0 0 (6<*2<*C),
>                                       arrow (4<*6<*C) ("ip1"<+C) # setStartAngle 0,
>                                       arrow (6<*5<*C) ("ip1"<+C) # setStartAngle 0]
>       curve x a1 a2 y         =  x ... y # setStartAngle a1 # setEndAngle a2
>       boxArrows               :: Int -> Frame -> Picture
>       boxArrows s             =  setName s . draw [   out 4 0.2, out 5 0.5, out 6 0.8,
>                                                       to 1 0.2, to 2 0.5, to 3 0.8]
>               where
>               out m n         =  arrow (med n (ref NE) (ref SE))
>                                        (med n (ref NE) (ref SE)+vec(10,0))
>                                  # setLabel 1 C (empty # setName (m::Int))
>               to m n          =  arrow (med n (ref NW) (ref SW)-vec(10,0))
>                                        (med n (ref NW) (ref SW))
>                                  # setLabel 0 C (empty # setName (m::Int))

\begin{center}
%if recalc
\perform{ generate "Schoening" 165 hamilton }
%else
\epsfig{file=Schoening.165}
%endif
\end{center}

\newpage

> torte = cake [(30,blue),(15,red),(10,green),(10,yellow)]
>       where
>       cake as = drawBack (toAngles as)
>               & drawCake (toAngles as)
>       toAngles as = ad (map (\(a,c)-> (a/(sum (map fst as)/360),c)) as)
>       ad []           = [(0,black)]
>       ad ((a,c):as)   = (a+fst (head (ad as)),c):ad as
>       drawBack []     = relax
>       drawBack [_]    = relax
>       drawBack ((a,c):(b,c2):as)
>                       = cfill (toArea (carc' (vec(0,-10)) 100 60 a b .-. carc' (vec(0,0)) 100 40 b a .-. cycle')
>                               #setColor (c-grey 0.3)) & drawBack ((b,c2):as)
>       drawCake []     = relax
>       drawCake [_]    = relax
>       drawCake ((a,c):(b,c2):as)
>                       =  cfill (toArea (vec (0,0) .-. carc' (vec(0,0)) 100 60 a b .-. cycle')
>                               #setColor c) & drawCake ((b,c2):as)


> carc'         :: Point -> Numeric -> Numeric -> Numeric -> Numeric -> Path
> carc' p rx ry w1 w2           =  (p + vec (rx*cos a1, - ry*sin a1)
>                               ... p + vec (rx*cos a2, - ry*sin a2)
>                               ... p + vec (rx*cos a2b, - ry*sin a2b)
>                               ... p + vec (rx*cos a3, - ry*sin a3)
>                               ... p + vec (rx*cos a4b, - ry*sin a4b)
>                               ... p + vec (rx*cos a4, - ry*sin a4)
>                               ... p + vec (rx*cos a5, - ry*sin a5))
>               where
>               a1              =  w1
>               a2              =  w1 + 0.05*(w2 - w1)
>               a2b             =  w1 + 0.25*(w2 - w1)
>               a3              =  w1 + 0.5 *(w2 - w1)
>               a4b             =  w1 + 0.75*(w2 - w1)
>               a4              =  w1 + 0.95*(w2 - w1)
>               a5              =  w2


\begin{center}
%if recalc
\perform{ generate "Torte" 1 torte }
%else
\epsfig{file=Torte.1}
%endif
\end{center}

\newpage


\subsection{Atomic pictures}

The basic data type of the \FMP\ language is
|Picture| or shorter, |Pic|. Expressions of this type describe pictures,
which can be copiled to  \MP--code or combined to new more complex pictures.

Atomic pictures are those not generated by combination or modification of
other pictures.

Two such atomic expressions are the embedding of arbitrary \LaTeX\
expressions  and the generation of an empty rectangle of given size:

< tex                           :: String -> Picture

< space                         :: Numeric -> Numeric -> Picture

Every picture in \FMP\ has a surrounding bounding box.\footnote{A bounding box
  in \FMP\ is not necessarily rectangular. Triangular and circular bounding
  boxes are also possible.} Bounding boxes allow the combination of pictures
without accidental overlaps.

The two atomar functions  |tex| and |space|
can be extended easily. The following function allows the use of
the \TeX\ math mode

< math                          :: String -> Picture
< math p                        =  tex ("$" ++ p ++ "$")

Also defined are functions for horizontal or vertical space (with names
borrowed from \LaTeX)

< hspace, vspace                :: Numeric -> Picture
< hspace n                      =  space n 0
< vspace n                      =  space 0 n

This will be useful, too:

< empty                         :: Picture
< empty                         =  space 0 0

\subsection{Colors}

Every visible object in \FMP\ has a color. The default is |black|.
Colors are described by their RGB values, i.e. by additive mixing of the basic
colors red, green and blue:


< color                         :: Double -> Double -> Double -> Color

Some colors are predefined:

< white                         =  color 1 1 1
< black                         =  color 0 0 0
< red                           =  color 1 0 0
< green                         =  color 0 1 0
< blue                          =  color 0 0 1
< yellow                        =  color 1 1 0
< cyan                          =  color 0 1 1
< magenta                       =  color 1 0 1
< grey n                        =  color n n n

The type |Color| is an instance of |Num| and |Fractional|. We can
add, subtract and multiply colors. This happens componentwise.
Therefore, |red + green| gives |yellow| and
|cyan - blue| denotes the color |green|.
The function  |fromRational| is implemented, too:
 |0.5 * magenta| is interpreted as |grey 0.5 * magenta|,
giving |color 0.5 0 0.5|.

The color of a picture is changed by

< setColor                      :: Color -> Picture -> Picture

Properties of pictures, like |Color|, are called attributes and
modified by attribute functions.
One such attribute function, setting the background color, is

< setBGColor                    :: Color -> Picture -> Picture

Attribute functions are more readable using a postfix notation and the
|#| operator.

< (#)                           :: a -> (a -> b) -> b
< a # f                         =  f a

\Abbildung{Color attribute functions}{
\beside{0.75}{

> color1                        = tex "colors"
>                                 # setColor green
>                                 # setBGColor 0.2

}
\VRule{30pt}

\beside{0.16}{
\begin{center}
%if recalc
\perform{ generate "TutColor" 1 color1 }
%else
\epsfig{file=TutColor.1}
%endif
\end{center}
}}


\subsection{Frames}

< box, circle, oval             :: Picture -> Picture

%if recalc
\perform{ generate "TutDrum" 1 newshapes }
%else
\epsfig{file=TutDrum.1}
%endif

> newshapes                     = shape (setDX 10.triangle)
>                                   |||| shape (triangle)
>                                       |||| cloud 345 67 (tex "joe")

> shape                         :: (IsPicture a, HasBGColor a)
>                               => (Picture -> a) -> Picture
> shape f                       =  setTrueBoundingBox
>                                       (draw   [ ref C .-. ref C + 60 .* dir a
>                                               | a <- [0,  10.. 360] ]
>                                               (f (tex "joe") # setBGColor 0.7))

%erw"ahne automatische Gr"o"senanpassung
%Attributierung; dx
%Boxen fester Gr"o"se

\subsection{Combination of pictures}

Up to now, we created atomic pictures and added frames. Let us now
combine two pictures to a new one.
The most common combinators set two pictures side by side or on top of the
other.

< (|||)                         :: Picture -> Picture -> Picture

< (|-|)                         :: Picture -> Picture -> Picture

Sometimes we want a small distance between the pictures:


< (||||)                        :: Picture -> Picture -> Picture
< a |||| b                      =  a ||| hspace 8 ||| b

< (|=|)                         :: Picture -> Picture -> Picture
< a |=| b                       =  a |-| vspace 8 |-| b


Now it is  time to discuss units. \MP\  uses as basic unit PostScript
points which correspond to $1/72$ inch. We use them in \FMP, too.
|hspace 8| defines a horizontal distance of $1/9$ inch or approximately
$2.82$ mm.
Some predefined constants allow the
use of other units


< mm, pt, bp, cm, pc, cc, inch  :: Numeric
< mm                            =  2.83464
< pt                            =  0.99626
< dd                            =  1.06601
< bp                            =  1
< cm                            =  28.34645
< pc                            =  11.95517
< cc                            =  12.79213
< inch                          =  72

|hspace (2*cm)| generates a distance of two centimeters.


\Abbildung{Placements}{
\beside{0.9}{

> bsp30                         =    tree1
>                               |||| hspace 10
>                               |||| ("$\\Longrightarrow$" |=| "right rotation")
>                               |||| hspace 10
>                               |||| tree2

\begin{hide}

> tree1 = node (circle "y" # label E "-1") [enode (circle "x" # label E "-1") [
>                       enode tri1 [],
>                       enode tri2 []],
>               enode tri3 []] # setDistH 16
> tree2 = node (circle "x" # label E "0") [enode tri1 [],edge (node (circle "y" # label E "0") [
>                       edge (node tri2 [] # setDistV (distCenter 30)),
>                       edge (node tri3 [] # setDistV (distCenter 30))] # setDistH 20)] # setDistH 26
> tri1 = triangle "1" # setDY 1 # setHeight 60 # setWidth 20 # label S (math "h")
> tri2 = triangle "2" # setDY 1 # setHeight 30 # setWidth 10 # label S (math "h-1")
> tri3 = triangle "3" # setDY 1 # setHeight 30 # setWidth 10 # label S (math "h-1")

\end{hide}

\HRule

\begin{center}
%if recalc
\perform{ generate "TutArrange" 30 bsp30 }
%else
\epsfig{file=TutArrange.30}
%endif
\end{center}
}}

\Abbildung{Combinations of frames and placements}{
\beside{0.9}{

> bsp40                         = box2 (tex "set of all languages"
>                               |=| box2 (tex"rec. enum. languages or typ 0"
>                               |=| box2 (tex "decideable languages"
>                               |=| box2 (tex "contextsensitive or typ 1"
>                               |=| box2 (tex "contextfree or typ 2"
>                               |=| box2 "regular or typ 3--languages")))))
>               where
>               box2 a          = rbox 20 a
>                               # setDX 8
>                               # setDY 8

\HRule

\begin{center}
%if recalc
\perform{ generate "TutArrange" 40 bsp40 }
%else
\epsfig{file=TutArrange.40}
%endif
\end{center}
}}

The combinators have generalizations  for more than two pictures:


< row                           :: [Picture] -> Picture

< column                        :: [Picture] -> Picture

Fig.~\ref{fig:traffic} shows a variant with
additional space between the pictures

< rowSepBy                      :: Numeric -> [Picture] -> Picture

< columnSepBy                   :: Numeric -> [Picture] -> Picture

\Abbildung{\label{fig:traffic}A traffic light}{
\beside{0.75}{

> bsp60                         = box ( columnSepBy 10
>                                       [circle "R"
>                                        # setDX 10
>                                        # setBGColor red,
>                                        circle "O"
>                                        # setDX 10
>                                        # setBGColor yellow,
>                                        circle "G"
>                                        # setDX 10
>                                        # setBGColor green ] )
>                                 # setBGColor black
>                                 # setDX 10
>                                 # setDY 10

}\VRule{150pt}
\beside{0.16}{
\begin{center}
%if recalc
\perform{ generate "TutArrange" 60 bsp60 }
%else
\epsfig{file=TutArrange.60}
%endif
\end{center}
}}

Sometimes we need a two dimensional alignment of pictures, as
in Fig.~\ref{fig:matrix1}.

< matrix                        :: [[Picture]] -> Picture

The function |matrix| generates columns and rows. Every column has the
width of the picture with the largest width in it. Analogously, every row has
the height of the highest picture in it. Then the pictures are centered in the
so-defined rectangular cells.

There is also a variant with additional space:

< matrixSepBy                   :: Numeric -> Numeric -> [[Picture]] -> Picture

\Abbildung{Alignment with the |matrix| function\label{fig:matrix1}}{
\beside{0.75}{

> matrix1                       = matrix [      [tex "a", tex "b" ],
>                                               [empty,   tex "c", tex "d"]]

}\VRule{40pt}
\beside{0.16}{
\begin{center}
%if recalc
\perform{ generate "TutMatrix" 1 matrix1 }
%else
\epsfig{file=TutMatrix.1}
%endif
\end{center}
}}


\subsection{Paths}

type Point,

< vec                           :: (Numeric, Numeric) -> Point

< med                           :: Numeric -> Point -> Point -> Point

type Numeric

< xpart                         :: Point -> Numeric

< ypart                         :: Point -> Numeric

< angle                         :: Point -> Numeric

< dist                          :: Point -> Point -> Numeric

< med                           :: Numeric -> Numeric -> Numeric -> Numeric

composite functions:

< dir                           :: Numeric -> Point
< dir a                         =  vec (cos a, sin a)

< xy                            :: Point -> Point -> Point
< xy p1 p2                      =  vec (xpart p1, ypart p2)

< xdist                         :: Point -> Point -> Numeric
< xdist p1 p2                   =  xpart p1 - xpart p2

< ydist                         :: Point -> Point -> Numeric
< ydist p1 p2                   =  ypart p1 - ypart p2

Syntax for paths:

< (.-.)                         :: (IsPath a, IsPath b) => a -> b -> Path

< (...)                         :: (IsPath a, IsPath b) => a -> b -> Path

< (.--.)                        :: (IsPath a, IsPath b) => a -> b -> Path

< (....)                        :: (IsPath a, IsPath b) => a -> b -> Path

< (.&.)                         :: (IsPath a, IsPath b) => a -> b -> Path

< cycle'                        :: Path

\Abbildung{A simple path of line segments}{
\beside{0.9}{

> path1                         =  vec (20,20) .-. vec (0,0) .-. vec (0,30)
>                               .-.vec (30,0) .-. vec (0,0)

\begin{hide}

> dot'          = toPicture bullet

> path1'        = path1
>               # setLabel 0 C dot'
>               # setLabel 0.25 C dot'
>               # setLabel 0.5 C dot'
>               # setLabel 0.75 C dot'
>               # setLabel 1 C dot'

\end{hide}

\HRule

\begin{center}
%if recalc
\perform{ generate "TutPath" 1 path1' }
%else
\epsfig{file=TutPath.1}
%endif
\end{center}
}}

\begin{hide}

> mark5                         :: (IsPicture a) => a -> Picture
> mark5 p                       = overlay' [
>                                       ref ((0::Int) <+ C) .= ref (global "z0"),
>                                       ref ((1::Int) <+ C) .= ref (global "z1"),
>                                       ref ((2::Int) <+ C) .= ref (global "z2"),
>                                       ref ((3::Int) <+ C) .= ref (global "z3"),
>                                       ref ((4::Int) <+ C) .= ref (global "z4")]
>                                       (Just 1) [dot', dot', dot', dot',
>                                                       dot', toPicture p]

> fig4a                         =  define [     ref "z0" .= vec (0,0),
>                                               ref "z1" .= vec (60,40),
>                                               ref "z2" .= vec (40,90),
>                                               ref "z3" .= vec (10,70),
>                                               ref "z4" .= vec (30,50)]
>                                  (column [
>                               setTrueBoundingBox (mark5 ("z0" ... "z1" ... "z2" ... "z3" ... "z4"))
>                               ])

> fig4b                         =  define [     ref "z0" .= vec (0,0),
>                                               ref "z1" .= vec (60,40),
>                                               ref "z2" .= vec (40,90),
>                                               ref "z3" .= vec (10,70),
>                                               ref "z4" .= vec (30,50)]
>                                  (column [
>                               setTrueBoundingBox (mark5 ("z0" ... "z1" ... "z2" ... "z3" ... "z4" ... cycle'))
>                               ])

> fig4c                         =  define [     ref "z0" .= vec (0,0),
>                                               ref "z1" .= vec (60,40),
>                                               ref "z2" .= vec (40,90),
>                                               ref "z3" .= vec (10,70),
>                                               ref "z4" .= vec (30,50)]
>                                  (column [
>                               setTrueBoundingBox (mark5 ("z0" ... "z1" ... "z2" ... "z3" .-. "z4" .-. cycle'))
>                               ])

\end{hide}

\Abbildung{Different path connectors}{
\begin{tabular}{ccc}
|z0 ... z1 ... z2 ... z3 ... z4| &
|z0 ... z1 ... z2 ... z3 ... z4 ... cycle'| &
|z0 ... z1 ... z2 ... z3 .-. z4 .-. cycle'| \\[2em]
\hline\\[1em]

%if recalc
\perform{ generate "TutFigureA" 4 fig4a }
%else
\epsfig{file=TutFigureA.4}
%endif

&

%if recalc
\perform{ generate "TutFigureB" 4 fig4b }
%else
\epsfig{file=TutFigureB.4}
%endif

&

%if recalc
\perform{ generate "TutFigureC" 4 fig4c }
%else
\epsfig{file=TutFigureC.4}
%endif
\end{tabular}
}



\Abbildung{Start and end angle of path segments can be set}{
\beside{0.70}{
\beside{0.5}{

> fig7                          = [ vec (0, 0) ... vec (3*cm, 0)
>                                   # setStartAngle 45
>                                   # setEndAngle (-10*a)
>                                 | a <- [0..9] ]

}\VRule{60pt}
\beside{0.35}{
%if recalc
\perform{ generate "TutPath" 7 fig7 }
%else
\epsfig{file=TutPath.7}
%endif
}\\
\beside{0.5}{

> fig8                          = [ vec (0, 0) ... vec (3*cm, 0)
>                                   # setStartAngle 45
>                                   # setEndAngle (10*a)
>                                 | a <- [0..7] ]

}\VRule{60pt}
\beside{0.35}{
%if recalc
\perform{ generate "TutPath" 8 fig8 }
%else
\epsfig{file=TutPath.8}
%endif
}}}

\Abbildung{The difference between the path connectors  |(...)| and |(....)|.}{
\beside{0.9}{

> fig9                          = rowSepBy 20 [ (z0...z1
>                                               # setStartVector up
>                                               # setEndVector right)...z2
>                                               # setEndVector down,
>                                               (z0....z1
>                                               # setStartVector up
>                                               # setEndVector right)....z2
>                                               # setEndVector down ]

\begin{hide}

>       where
>       z0 = vec(-50,0)
>       z1 = vec(  0,8)
>       z2 = vec( 50,0)

> fig9'                         = rowSepBy 20 [ mark3 ((z0...z1
>                                               # setStartVector up
>                                               # setEndVector right)...z2
>                                               # setEndVector down),
>                                               mark3 ((z0....z1
>                                               # setStartVector up
>                                               # setEndVector right)....z2
>                                               # setEndVector down) ]
>       where
>       mark3                   :: (IsPicture a) => a -> Picture
>       mark3 p                 = setTrueBoundingBox (overlay' [
>                                       ref ((0::Int) <+ C) .= z0,
>                                       ref ((1::Int) <+ C) .= z1,
>                                       ref ((2::Int) <+ C) .= z2]
>                                       (Just 1) [dot', dot',
>                                                       dot', toPicture p])
>       z0 = vec(-50,0)
>       z1 = vec(  0,8)
>       z2 = vec( 50,0)

\end{hide}

\HRule

\begin{center}
%if recalc
\perform{ generate "TutPath" 9 fig9' }
%else
\epsfig{file=TutPath.9}
%endif
\end{center}
}}

\Abbildung{The tension ``pulling'' a path segments can be set}{
\beside{0.9}{

> fig10                         = rowSepBy 20 [
>                                       z0...(  z1...z2
>                                               # setJoin (joinTension (tension 1)) )
>                                       ...z3,
>                                       z0...(  z1...z2
>                                               # setJoin (joinTension (tension 2.3)) )
>                                       ...z3,
>                                       z0...(  z1...z2
>                                               # setJoin (joinTensions (tension 2.5)
>                                                                       (tension 0.8)) )
>                                       ...z3 ]

\begin{hide}

>       where
>       z0 = vec(  0,0)
>       z1 = vec( 15,15)
>       z2 = vec( 75,15)
>       z3 = vec( 90,0)

> fig10'                                = rowSepBy 20 [
>                                       mark4 (z0...(z1...z2
>                                               # setJoin (joinTension (tension 1)))
>                                       ...z3),
>                                       mark4 (z0...(   z1...z2
>                                               # setJoin (joinTension (tension 2.3)))
>                                       ...z3),
>                                       mark4 (z0...(   z1...z2
>                                               # setJoin (joinTensions (tension 2.5)
>                                                                       (tension 0.8)))
>                                       ...z3) ]
>       where
>       mark4                   :: (IsPicture a) => a -> Picture
>       mark4 p                 = setTrueBoundingBox (overlay' [
>                                       ref ((0::Int) <+ C) .= z0,
>                                       ref ((1::Int) <+ C) .= z1,
>                                       ref ((2::Int) <+ C) .= z2,
>                                       ref ((3::Int) <+ C) .= z3]
>                                       (Just 1) [dot', dot', dot',
>                                                       dot', toPicture p])
>       z0 = vec(  0,0)
>       z1 = vec( 15,15)
>       z2 = vec( 75,15)
>       z3 = vec( 90,0)


\end{hide}

\HRule

\begin{center}
%if recalc
\perform{ generate "TutPath" 10 fig10' }
%else
\epsfig{file=TutPath.10}
%endif
\end{center}
}}

< draw                          :: [Path] -> Picture -> Picture

\subsection{Dash patterns}

< dashPattern                   :: [Double] -> Pattern

derived functions:

< dashed                        :: Pattern
< dashed                        =  dashPattern [3, 3]

< dotted                        :: Pattern
< dotted                        =  dashPattern [-1, 2.5, 0, 2.5]


\subsection{Pencils}

< penSquare                     :: (Numeric, Numeric) -> Numeric -> Pen

< penCircle                     :: (Numeric, Numeric) -> Numeric -> Pen


\Abbildung{Calligraphic effects}{
\beside{0.9}{

> calligraphic                  = (transformPath (scaled 40) fullcircle
>                                       # setPen (penCircle (0.1, 5) 20))
>                               |||| (transformPath (scaled 40) halfcircle
>                                       # setPen (penSquare (5, 5) 45))
>                               |||| (transformPath (scaled 40) quartercircle
>                                       # setPen 5)

\HRule

\begin{center}
%if recalc
\perform{ generate "TutPen" 1 calligraphic }
%else
\epsfig{file=TutPen.1}
%endif
\end{center}
}}


\Abbildung{A horizontal bracket}{
\beside{0.9}{

> hBrack                        = hBracket (vec(0,0)) (vec(100,0))
>               where
>               hBracket pl pr  =       pl
>                                  .... pl + vec(5, 5)
>                                  .--. med 0.5 pl pr + vec(-5, 5)
>                                  .... med 0.5 pl pr + vec( 0, 10)
>                                  .&.  med 0.5 pl pr + vec( 0, 10)
>                                  .... med 0.5 pl pr + vec( 5, 5)
>                                  .--. pr + vec(-5, 5)
>                                  .... pr
>                                       # setPen (penCircle (0.001, 1) 0)

\HRule

\begin{center}
%if recalc
\perform{ generate "TutPen" 2 hBrack }
%else
\epsfig{file=TutPen.2}
%endif
\end{center}
}}

\subsection{Arrows}

< defaultArrowHead              :: PathArrowHead
< arrowHeadSize                 :: Double -> Double -> PathArrowHead

derived functions:

< arrowHeadBig                  :: PathArrowHead
< arrowHeadBig                  =  pathArrowHeadSize 8 4
< default'                      =  defaultArrowHead

different arrow styles

< ahFilled, ahLine              :: ArrowHeadStyle
< ahFilled                      =  AHFilled
< ahLine                        =  AHLine

< setArrowHeadStyle             :: ArrowHeadStyle -> ArrowHead -> ArrowHead
< getArrowHeadStyle             :: ArrowHead -> ArrowHeadStyle

\Abbildung{A linked list}{
\beside{0.9}{

> bsp50                         = pointerChain 25 ["12", "2", "2", "103"]
>       where
>       pointerChain dx ps      = draw (backarrow :chainarrows)
>                                 (rowSepBy dx [ b # setName (i::Int)
>                                              | (b, i) <- zip (map recBox ps) [0..]])
>               where
>               n               = length ps
>               backarrow       = arrow (ref (n-1 <* "bullet" <+ C))
>                                       (ref (n-1 <* "bullet" <+ C) + vec(0,20))
>                                    .--. arrow (ref (0 <* W) + vec(0,20))
>                                               (ref (0 <* W))
>               chainarrows     = [ arrow (ref (i <* "bullet" <+ C))
>                                         (ref (i+1 <* W))
>                                 | i <- [0..n-2] ]
>               recBox a        =   (box a # setHeight (16*pt))
>                               ||| (box (toPicture bullet # setName "bullet")
>                                    # setHeight (16*pt) # setWidth (16*pt))

\HRule

\begin{center}
%if recalc
\perform{ generate "TutArrow" 50 bsp50 }
%else
\epsfig{file=TutArrow.50}
%endif
\end{center}
}}

%-------------------------------

\subsection{Names}

< data Dir                      =  C | N | NE | E | SE | S | SW | W | NW

Reference points: C,S,N,W,E.., ref

< setName                       :: Name -> Picture -> Picture

< (<+)                          :: Name -> Name -> Name
< (<*)                          :: Int -> Name -> Name

%type Name + Operationen


%----------------------

\subsection{Areas}

type Area

< fill                          :: [Area] -> Picture -> Picture

\Abbildung{Arbitrary cyclic paths can be filled.}{

\beside{0.6}{

> bsp4                          = let p = vec(-1*cm, 0)
>                                       ... vec(0, -1*cm)
>                                       ... vec(1*cm, 0)
>                                       # setStartVector down
>                                       # setEndVector up
>                                 in
>                                 fill [ (p ...vec(0, 0)
>                                         # setEndVector (vec(-1, -2)))
>                                      ...cycle'
>                                         # setEndVector up ]
>                                 (p ... vec(0, 1*cm) ... cycle')

}\VRule{140pt}
\beside{0.15}{
%if recalc
\perform{generate "TutArea" 4 bsp4}
%else
\epsfig{file=TutArea.4}
%endif
}}

\Abbildung{Another Example}{

\beside{0.9}{

> bsp5                          = box ( math "U"
>                                   ||| ooalign
>                                       [ toPicture [   toArea a  # setColor 0.7,
>                                                       toArea b  # setColor 0.7,
>                                                       toArea ab # setColor 0.4 ],
>                                         aOverB ] )
>               where
>               aOverB          = column [ math "B" # setBGColor white,
>                                          vspace 50,
>                                          math "A" # setBGColor white ]
>               a               = transformPath (scaled 30) fullcircle
>               aa              = transformPath (scaled 30) halfcircle
>               b               = transformPath (scaled 30 & shifted (0,-30))
>                                               fullcircle
>               ab              = buildCycle aa b

\HRule

\begin{center}
%if recalc
\perform{generate "TutArea" 5 bsp5}
%else
\epsfig{file=TutArea.5}
%endif
\end{center}
}}


\subsection{Clipping}

< clip                          :: Path -> Picture -> Picture

\subsection{Symbolic equations}

< define                        :: [Equations] -> Picture -> Picture
< define                        :: [Equations] -> Path -> Path
< define                        :: [Equations] -> Area -> Area

type Equation

<       (.=)                    :: a -> a -> Equation
<       equal                   :: [a] -> Equation

<       (.==)                   :: a -> a -> Boolean
<       (./=)                   :: a -> a -> Boolean
<       (.<)                    :: a -> a -> Boolean
<       (.<=)                   :: a -> a -> Boolean

< whatever                      :: Point

< whatever                      :: Numeric

\Abbildung{Unknown values are derived automatically by equation solving.}{
\beside{0.65}{\small

> bsp3                          =  define [
>               equal [ref "z1", -ref "z2", vec(0.2*inch,0)],
>               equal [ xpart (ref "z3"), - xpart (ref "z6"), 0.3*inch ],
>               equal [ xpart (ref "z3")+ypart (ref "z3"),
>                       xpart (ref "z6")+ypart (ref "z6"), 1.1*inch],
>               ref "z4"        .= med (1/3) (ref "z3") (ref "z6"),
>               ref "z5"        .= med (2/3) (ref "z3") (ref "z6"),
>               equal [ ref "z20",
>                       med whatever (ref "z1") (ref "z3"),
>                       med whatever (ref "z2") (ref "z4")],
>               equal [ ref "z30",
>                       med whatever (ref "z1") (ref "z4"),
>                       med whatever (ref "z2") (ref "z5")],
>               equal [ ref "z40",
>                       med whatever (ref "z1") (ref "z5"),
>                       med whatever (ref "z2") (ref "z6")]]
>                                  (toPicture ["z1" .-. "z20"
>                                          .-. "z2" .-. "z30"
>                                          .-. "z1" .-. "z40"
>                                          .-. "z2",
>                                              "z1" .-. "z2"
>                                              # setPen 1,
>                                              "z3" .-. "z6"
>                                              # setPen 1])

}
\VRule{280pt}

\beside{0.15}{
%if recalc
\perform{ generate "TutDefine" 1 bsp3 }
%else
\epsfig{file=TutDefine.1}
%endif

}}

\Beispiel{Brackets}{
\beside{0.9}{

> brack                         =  [ bracket ((5+x/14) .* dir x, (10+x/8) .* dir x)
>                                  | x <- [0, 23 .. 720] ]

> bracket                       :: (Point, Point) -> Path
> bracket (pl, pr)              =  define [
>               ref "start"     .= pl,
>               ref "end"       .= pr,
>               var "ang"       .= angle (ref "start"-ref "end"),
>               var "d"         .= cond (dist (ref "start") (ref "end") .< 20)
>                                       (dist (ref "start") (ref "end")/4)
>                                       5,
>               ref "vecl"      .= var "d" .* dir (var "ang"-135),
>               ref "vecr"      .= var "d" .* dir (var "ang"-45),
>               ref "start2"    .= ref "start" + ref "vecl",
>               ref "end2"      .= ref "end" + ref "vecr",
>               ref "mid"       .= med 0.5 (ref "start") (ref "end")
>                                       + (1.41 * var "d")
>                                       .* dir (var "ang"-90),
>               ref "midl"      .= ref "mid" - ref "vecl",
>               ref "midr"      .= ref "mid" - ref "vecr" ]
>                         (pl .... ref "start2" .--. ref "midl" .... ref "mid"
>                      .&. ref "mid" .... ref "midr" .--. ref "end2" .... pr
>                          # setPen (penCircle (0.001, var "d"/5) (var "ang")))

\HRule

\begin{center}
%if recalc
\perform{ generate "TutDefine" 2 brack }
%else
\epsfig{file=TutDefine.2}
%endif
\end{center}
}}

< overlay                       :: [Equations] -> [Picture] -> Picture

\Beispiel{Brackets with ``intelligent'' labels}{
\beside{0.9}{

> brackLabel                    =  [ bracket' x
>                                       ((5+x/14) .* dir x, (10+x/8) .* dir x)
>                                  | x <- [0, 67 .. 720] ]

> bracket'                      :: IsPicture a => a -> (Point, Point) -> Path
> bracket' l (pl, pr)           =  bracket (pl, pr)
>                                  # setLabel 0.5 C label
>       where
>       label                   =  overlay' [
>               var "ang"       .= angle (pl-pr),
>               ref (0 <* C)    .= cond (var "ang" .< (-175.5)
>                                                + 175.5 .< var "ang")
>                                                       (ref (1 <* S))
>                       (cond (var "ang" .< (-112.5))   (ref (1 <* SE))
>                         (cond (var "ang" .< (-67.5))  (ref (1 <* E))
>                          (cond (var "ang" .< (-22.5)) (ref (1 <* NE))
>                           (cond (var "ang" .< 22.5)   (ref (1 <* N))
>                            (cond (var "ang" .< 67.5)  (ref (1 <* NW))
>                             (cond (var "ang" .< 112.5)(ref (1 <* W))
>                                                       (ref (1 <* SW))
>                               ))))))] (Just 0)
>                                       [empty, toPicture l]

\HRule

\begin{center}
%if recalc
\perform{ generate "TutDefine" 3 brackLabel }
%else
\epsfig{file=TutDefine.3}
%endif
\end{center}
}}



%-------


\subsection{Transformations}

< scale                         :: Double -> Picture -> Picture
< rotate                        :: Double -> Picture -> Picture

\Abbildung{A recursive picture.}{
\beside{0.9}{

> fig28                         = rek 4 empty
>               where
>               rek 0 pic       = pic
>               rek n pic       = ooalign [draw [p] [ toArea a # setColor 0.6,
>                                                     toArea p # setColor white ],
>                                       rotate 90 (scale (1/3) (rek (n-1) pic)) ]
>               p               = transformPath (scaled 30) fullcircle
>               a               = (vec(90, 0) ... vec(0, 30) ... vec(-90, 0)
>                                  # setEndCurl 1)
>                                  ... vec(0, -30) ... cycle'
>                                      # setEndCurl 1

\HRule

\begin{center}
%if recalc
\perform{ generate "TutTransform" 1 fig28 }
%else
\epsfig{file=TutTransform.1}
%endif
\end{center}
}}

\Abbildung{Another recursive picture.}{
\beside{0.9}{

> inverse [] = []
> inverse (b:bs) = inv b:inverse bs
>       where
>       inv '0' = 'f'
>       inv '1' = 'e'
>       inv '2' = 'd'
>       inv '3' = 'c'
>       inv '4' = 'b'
>       inv '5' = 'a'
>       inv '6' = '9'
>       inv '7' = '8'
>       inv '8' = '7'
>       inv '9' = '6'
>       inv 'a' = '5'
>       inv 'b' = '4'
>       inv 'c' = '3'
>       inv 'd' = '2'
>       inv 'e' = '1'
>       inv 'f' = '0'
>       inv _   = '0'
>
> figBit0 = image Depth1  figBit'
> figBit1 = image Depth1 (map inverse figBit')
> -- The image is defined as an array of hex strings:
> -- figBit' = [
> --      "00000000000000000000000000000000000000000000000000000000000000",
> --      "00001000000000000200000000000000000000000000000000000000000000",
> --  ... 300 more such lines ... ]
>
> figBitc = image Depth24 colorBit
> -- colorBit =[
> --        "edcfb1ffe2bbf7e2b1ffe2bbffedcfe2c59effe2bbffe2bbffedcfedcfb1f",
> --        "fa7ffe2bbf7d9b1edcfa7e2c59ee2c59eedcfb1a79e80bba7899e89769380",
> -- ... etc. ... ]

\begin{hide}

> figBit2 = image Depth1 (map inverse figBit'')
> figBit'' = [
>       "ffffffffffffffffffffffffffffffffffffffff", "ffffffffffffffffffffffffffffffffffffffff",
>       "ffffffffffffffffffffffffffffffffffffffff", "ffffffffffffffffffffffffffffffffffffffff",
>       "ffffffffffffffffffffffffffffffffffffffff", "ffffffffffffffffffffffffffffffffffffffff",
>       "ffffffffffffffffffffffffffffffffffffffff", "ffffffffffffffffffffffffffffffffffffffff",
>       "ffffffffffffffffffffffffffffffffffffffff", "ffffffffffffffffffffffffffffffffffffffff",
>       "ffffffffffffffffffffffffffffffffffffffff", "ffffffffffffffffffffffffffffffffffffffff",
>       "ffffffffffffffffffffffffffffffffffffffff", "ffffffffff9fffffffffffffffffffffffffffff",
>       "ffffffffffbfffffffffffffffffffffffffffff", "ffffffffffbfffffffffffffffffffffffffffff",
>       "ffffffffffbfffffffffffffffffffffffffffff", "ffffffffff0fffffffffffffffffffffffffffff",
>       "ffffffffffafffffffffffffffffffffffffffff", "ffffffffff0fffffffffffffffffffffffffffff",
>       "ffffffffff2fffffffffffffffffffffffffffff", "fffffffffb0fffffffffffffffffffffffffffff",
>       "fffffffffa17ffffffffffffffffffffffffffff", "fffffffffecfffffffffffffffffffffffffffff",
>       "fffffffff907ffffffffffffffffffffffffffff", "fffffffffd13ffffffffffffffffffffffffffff",
>       "fffffffffd11ffffffffffffffffffffffffffff", "fffffffff843ffffffffffffffffffffffffffff",
>       "fffffffffc10ffffffffffffffffffffffffffff", "fffffffff8c2ffffffffffffffffffffffffffff",
>       "fffffffff880ffffffffffffffffffffffffffff", "fffffffffa883fffffffffffffffffffffffffff",
>       "fffffffff8463fffffffffffffffffffffffffff", "fffffffff9053fffffffffffffffffffffffffff",
>       "fffffffff88407ffffffffffffffffffffffffff", "fffffffffb246fffffffffffffffffffffffffff",
>       "fffffffff00807ffffffffffffffffffffffffff", "fffffffff00927ffffffffffffffffffffffffff",
>       "ffffffffd10057ffffffffffffffffffffffffff", "ffffffffe44811ffffffffffffffffffffffffff",
>       "ffffffffe820500fffffffffffffffffffffffff", "fffffffff21000801e0c3fffffffffffffffffff",
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>       "ffffffffff8b23ffff800015492e2931ffffffff", "ffffffffff9e4bffffc002426f9dc084ffffffff",
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>       "ffffffffff1d47fffff00012db60f884ffffffff", "ffffffffff9683fffff82106dec07f127fffffff",
>       "ffffffffffaa97fffffc042b57a03ff23fffffff", "fffffffffff687fffffe014a81508f50ffffffff",
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>       "ffffffffffdb47ffffffd260780848f7ffffffff", "ffffffffffb697ffffffe0021a00567fffffffff",
>       "ffffffffffd5477ffffff4000680171f7fffffff", "fffffffffff4c77ffffff80000002c0dffffffff",
>       "ffffffffffe94fffffffff8000001e87bfffffff", "ffffffffffd557fffffffffc00001da0ffffffff",
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>       "fffffffffff587ffffffffff80fc03f83bffffff", "ffffffffffd6afffffefffffc0ffe25a1effffff",
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>       "fffffffffff687ffffffffd4248ffcfb204fffff", "ffffffffffed97fffffffe28401ffe3a9001ffff",
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>       "fffffffffffaaffffffe20bffff7ffc6fb0003bf", "fffffffffff525f7fffebfffffffffeafd1000ff",
>       "ffffffffffff95effffffffffffffff9760001ff", "fffffffffffa45fffffffffffffffffc3844003f",
>       "ffffeffffff597efffffffffffffffff1e08400f", "fffffffffffb57ffffffffffffffffffef81c1ff",
>       "fffffffffffecdffffffffffffffffffffe07fff", "fffffffffffd43fffff7fffffffffffffff83fff",
>       "fdfffffffffdd7fbefefffffffffffffffffdfff", "fffffffffffb4793ffdfffffff7fffffffffffff",
>       "ffffffffdffed7ffffbfffffffdfffffffffffff", "ffffbffffefaa6ffffffffffffffffffffffffff",
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>       "fffffffdfeeeaffffffe5fffffffffffffffffff", "fffffffdffffefffeb9effffffffffffffffffff",
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>       "fffffff7ffffaeef51f7cff7ffffffffffffffff", "ffffbffbfe7dec7d1d1cffffffffffffffffffff",
>       "fffffffffffb6fff9f1beffdffffffffffffffff", "fffbff7bfff5c98d1fffefffffffffffffffffff",
>       "fffffffffe7ae989deffffffffffffffffffffff", "fffffffbfff3cfffefff7ff7ffffffffffffffff",
>       "fffbff5bffffcfdfffffffffffffffffffffffff", "fffffffbfffbcf8fc69fefffffffffffffffffff",
>       "fffffcfcffefcbaebffbffefffffffffffffffff", "ffebffffbfe9cbf767f5fffdffffffffffffffff",
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>       "fffffedffff5cfbeffb7ff7fffffffffffffffff", "fffffdf7ffd96b9ff3cf79fbffffffffffffffff",
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>       "fffffff7fff7dff7fffddf7fffffffffffffffff", "fffffff9bdffffffffff7f3fffffffffffffffff",
>       "fffffffffeffefffdfffffffffffffffffffffff", "fffffffd6fdffffdffeddfffffff5fffffffffff",
>       "ffffffdecffffefff76bfffffffffdffffffffff", "fffffffbd7fffcfffbe77fffffffffffffffffff",
>       "ffffffbff7ffffffbfebffffffffffffffffffff", "ffffff7ff7fff7efff7d7fffefffffffffffffff",
>       "fffffefcbffff7f5ffcdfffffbfffbffffffffff", "ffffffffffeff6fbefcffffff7ffffffffffffff",
>       "fffffffffefef3fbfbfbffffffffffffffffffff", "ffff7feffffffffffdfffefdffffffffffffffff",
>       "ffffffffffbfffffffffffffffffffffffffffff", "fffffefffbfffffffffffffeffffffffffffffff",
>       "ffdffdfff7ffffffffbfffffffffffffffffffff", "ffeffffffdfe7b7fffffffffddefffffffffffff",
>       "ffffffffdbffffbfffffffffffffffffffffffff", "ffefdfffffebffbfffffffffffffffffffffffff",
>       "ffffffffffffffffbff9fffdfdffffffffffffff", "fffffffefffffffffffbffffffffffffffffffff",
>       "ffff7fffffffbcfdfffcffffffffffffffffffff", "fffffdf7fffe2fffdfffffffffffffffffffffff",
>       "fbfffbffffffffffffffffffffffffffffffffff", "ffffffffffffffffffffffffffffffffffffffff",
>       "ff7dfffffffffdf7dffffffffdffffffffffffff", "ffffffeffffffdf4fff7ffffffffffffffffffff",
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>       "ffffffbffffffbffffffffffffffffffffffffff", "fffffffff7fffffffffdffffffffffffffffffff",
>       "ffffffffffffffffffffffffffffffffffffffff", "fffffffffbfff7fffffdffffffffffffffffffff",
>       "ffffffffffffffffffffffffffffffffffffffff", "fffff7ffffffffffffff7fffffffffffffffffff",
>       "fffffffffffdffffffffffffffffffffffffffff", "ffffffffffffffffffffffffffffffffffffffff",
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>       "ffffffffffffffffefffffffffffffffffffffff", "ffffffffffffffffefffffffffffffffffffffff",
>       "ffffffffffffffffefffffffffffffffffffffff", "ffffffffffffffffefffffffffffffffffffffff",
>       "ffffffffffffffffffffffffffffffffffffffff"
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>       "00000000000974a2d576aed55adfb6abfbb55aaba551768000000000000000",
>       "0000810001f74aafabff555ef7baedaaaeeff5545b55dc0000000000000000",
>       "00000000015a5559557aadb55aefbaab7bb5555556a57c8000000008000000",
>       "0000000008b75556d5feab6befb6f6d5aefefaaaadaaf50110000000000000",
>       "00800000f7ad52bbb5bf6d5eb57b5bbeebabadad5b52bc0000080000000000",
>       "000020002f6b556ead7edaeadbadf7eb5edf7f55b6d5748001021000000000",
>       "0000005ff9aaaad575bfd6ad6d7ebd5fd36aeaff5daada0000000000000000",
>       "0000001b56d55dbfaabeb55bbbabfffab6bebfaaf755748000000000000000",
>       "00002776ddb56b695d6fabf6d776ad576de9557faed2ddb500000200000000",
>       "000009adb6aaaed6eabfdaadb6ed7ffdd556b7eb5b6aaaa400000004000000",
>       "00000b7b6b555ab559bfebbb6b5bad6b75f56d5ef6d576a920000000200000",
>       "002ff6d6def6f56fb57ff555def577deeeaeab52adf5d55555000000020000",
>       "000adbedb5adafb56d5ff56fbb56defbb5daae955bbabc9548400000008000",
>       "17ff6ebb6aaab56edbfffe9d76ddbbd6feaaa96ad576d155555a9000002000",
>       "25aadd6ddb556eddaabffc5bddb6efbbdb755694aff5b6aaaaa40000000000",
>       "0777ebb776b6db6b6dfff5ad776dbef77dad6aa55aad545555514000000000",
>       "fdaebedaadadb6ddb53fffaaeedb6bedef6aad5ab7f6d5aaaaad5f64000000",
>       "eeddeb6dfb556b6bdaf7fed3b5b6deb77bd6abadaffd8a5555555040000800",
>       "5b6b5ef6aebbdeed7b3ffff4ded56ffdff7ddd777df6b5aaaaab6dbda80000",
>       "6dddb5ddfdd6b5dbd6bfffe4b5b55d57ddeb6bdd57ff45555aad5a55200000",
>       "b6b76f6baaad6f6ababfffeadb7577fd7f5edebbdf755adad55aaab5480000",
>       "efedfadeff7bdadeeaaefffe5edbaeb7f7f5b56d7fdd56b5b6b76febb7d200",
>       "dabb5775a9d6b76b5abffffcabbd6dfdddffebdbdbf255aeaaaad55d5d5000",
>       "b7d6fdeefebdeddeedafbfff5577b6afff6d5ebeffedb555b6adbeebb6ff80",
>       "ed7db75babab5bb5b56fffff56dddb7bb7ffebf7f7b5556d6d6b535d6dae00",
>       "dbebfdf6fd76ed7edb5fefffd5af6eeefdef5d5dbdeb555bab5aedb6dbdf80",
>       "b75f575b57adb7d5beebffffeb75fb5fef7ef7ffffaab5555ad75ad5b6b578",
>       "6dfaedfdfd76dd6f755ffefffadedefbbfdbdaab6ed5ab76b5bad7eadaefd0",
>       "bbafb75757ddb7badbadfffffd25b7aef7feb7fffbd56aab6ed6ba3f775d6c",
>       "eefdfdfdfebb6d6fb6afeffffeaeaddbdff7fb6fff555ad5a9bd6aeadaebb4",
>       "bdd7db5755f6dfdaed6ffffffa4adf77777d57fbb5d5ab5b5776dd5bb75f6c",
>       "f77d7efbfead6abdb6adfbffffdb6bdefddffd7fed5576b6eccaaab6daeaf4",
>       "bfefebd76bbbbdd6ddafff7fffd6db75dff7abfff555556db5b76edb77bb5c",
>       "7abebebdded6eb7bb755ffdffff8b6df777ddfadb556adaad6aaadb6ed6ee8",
>       "effbf7ebbbbdddaf6eeffffffff55d5aefefaaff6ab5755b6d6f5b5b5db5dc",
>       "bdaf5dbf76d6b77adb55ffffffe976efbafedfadeaaaaad6db5aadb6eadeb4",
>       "f7fdf7eaedbbedd7b6d5fff7fffe4b94afd5f7e0156edeb4b6d7776ddfb5ec",
>       "5d6fbd5fdf6d5b7eefabfffffffeabeb5ebb5be95ad575aaaaaadadeb56eb4",
>       "f7db77f56af7efab5aeafffdffffaa5ad2afffe0175baf6dad56b56b6ab5dc",
>       "db7eed5fdf5ab5def755ffffffffd5b6b4ab57e0ad555adb5b6dd55ddf6f74",
>       "ffdbbff575efff6b5df5dfffdffffc00013dfee80aafeb55555abb776ab5dc",
>       "d5feeadfefbaaaf6eb55fffffffff6aa802b5be016d55eafb757f56edddb74",
>       "ffbbbff55af7ff5d5fb57fff7ffffc84215df7e89dadf5daaaaaaaddb6b6dc",
>       "5aeef55ff7aed5ebeaebfffff7fffd9144b77faa135b2eb55777756b6d6fb4",
>       "f7fffffb6efb7fbeb75dffffffffff45293adff40eb6d5ab6adadb5edadd6c",
>       "fed55b6fb5afd575eed37dfffdfffc9401df7d8b25edab6aedb6b6b5b7abb4",
>       "dbfff7feef7dbfef5deddffffffffd290577efba8b2aaed55b5b6d6edd76dc",
>       "ffaadedbb5ebd55aeb5bfffffdfffc5201bebfd50aefaaaaeaf6b55b76bb74",
>       "56fffbbefabf7ff7bdd4ffffffbff501206fee9757556d7db6addbb6ededac",
>       "ffeaaeebadf5eadad771fbfffefffc0200bbffad0aaedbab6aaaad6db6aba8",
>       "aadfffbef75edfbf7fad3fffffefd090402fad4ba5e9b576dab6b6db6f6eb4",
>       "f7faaafddafbbaf5d5eaffffffffd204002eff9b5556aaad6d5b6badb5daa8",
>       "dad7ffd7bfadf75f6fb57fbfffffb040800fae9725b5addbb5aead7edb56d4",
>       "fffd757d7577adf5baeaafffffde8292280dfd9ba55576b56f69dbab6eef58",
>       "aab7ffefdfdedbdfedda7fffffff8120900bbe97a955adeb5a5b56ddb5d5b4",
>       "fffd557abb75ef7ab76aaffffffd52540601fd1b46f6db5edbaab5b6ef5ad4",
>       "f7b7ffdf6ddfbaeffdb57ffffffe90a81405fc9751adb5b5ad56ab6bbab5b4",
>       "dd7daaf6df75efdeabdaafeffff7a5641509fd17a6d5576b76aaaddd6dead4",
>       "bfefff7dabdfbd75ff6b7ffffff45ab48a017c9fa576dadead55db6bdb5bbc",
>       "f6daadef7ff577bfbadaaffffffd75d41281fe2b65daabb5db6d56deb6aad4",
>       "6fbfff7db6bbeeed6fb66ffbfff05fa0a4017c9fa9b57edb56d56db5edddb4",
>       "faf5fbf7dfeebb5bf57a5fffffd07fa50a00fd17e2d7556d55555ad6ab6b6c",
>       "dfafb6dd757deeff5baa6ffffff02b885201f45f556cdbb6abd56bbb76b574",
>       "76f5fff7fff75baafef69bffffe17fa2bec07d5fe5dbb56d6ab6dd6dadd6ac",
>       "efbf6d7f5b5ff6ffd5fa2fff7fd06ec8de80fd5feb6aaedbd56dabd6b6baa8",
>       "dd75ffd5fdfadfd6bebe4efffec5552afb417abfb55f6b6ab6db7d6ddb65dc",
>       "bbefb5ef6f6fbabdebb62fffffaab54aeec1765fe5555db6d5b6abdab6dab4",
>       "f75edfb5fbfaf7f7bf7e8bbffeaa4d55b9107d7f55b5ab6dbaabb6adadab6c",
>       "5af5effbdfbfaead6ad62ffffb552aab6e417e5ff56b56d5555eedbb5576d8",
>       "ef5fbd5776f6fd7bbfbe8ffffe925592dd447577a5b6ed5b6aeb5b6d5dad54",
>       "bdf577ddffdfabeeeaf60adffa6e855502b57e7ff56d9bb55aadd6db5b5b6c",
>       "eb5fdd7bad75fd5bbfbe8fbffe9a5aaa553574bf65ab756b55aab556d6d558",
>       "bff6f7eeffff6ff6d6f703fffab6854285feed7feadaabdd6eb7dbf55ab6b4",
>       "ed5fbebbb5effb5fbdde8fdffd2ead9525b7745feb75b6b7596ab6ab57ad6c",
>       "fbf5edeeffbbaef5777602fffa5a8b5542fefd7ff5ad6aedabaded6d5aaaa8",
>       "aeafbfbbaaeefbdfaddf8bdbedaf555b15efd57f6aeb5fb56d5b5bdb556dac",
>       "fb7aeadfffbbdeb6ff7e03fffabf4d57477ffa7ff5dd6aaedb76ed56aed6a8",
>       "add77daad5ef77dfaaef83b776adaadd21dfb2dfe56bd6d5b5adb6b575bb54",
>       "ff7ddf57ef7add75dfbb02fbeeaf96ab87f7f57ff5deadbb6f7b6daed6d6d4",
>       "55d776dbddeff7df757e83ef6aaea55721ffa97fe5b5d556dad6db5555b554",
>       "ff7ddfa57bbabd75efef817fbf5bdadd0fdfeb7ff96ebaddb5b5b6b6db6ea8",
>       "add776c9eeffebdf5abe837dfb6e96aa57ffb2fff5db56b76f6d6dadb6d5b4",
>       "ff7dffb2bfb6beedf7efd07fdedfa5f696efebdfeab6eddad55b5b55555aa8",
>       "d5d7dbe4eddffbfeddbd817fffefaaad57bfd37ffadddb6dbdb6b6b6abb554",
>       "7f7d7fd2bffaaeab77efd17f7ebb4bb517efb5ffeab6b6b6ab6d6dad6d5768",
>       "dbd7eb7d376ffbffeeb5b07fffff956aaffbab7ffdefaddafedbea55ab7554",
>       "7efd5df4affb57ad5befd25fffefabaa5bdfd3dfeabadbb75bb6b55556ad54",
>       "abb7f7af55aefd7bfebdf07ffffe8af48effd7fffd776d6af76dd4b6aadae8",
>       "fdfebefb4bfbb7ef6bf7785fffffabaa5fefabfff5ddbed6daf6b55555b754",
>       "576bebd797777d7dbeafd03fefbe857517dfd6fbf56b6bbdb75b756ad56ad8",
>       "fdbebd7f69ded6d7edfdf45ffbff03805fffafffeabedd6b6dddc556955ab4",
>       "d7ebf7db45fbffbf77abf81ffff602b40eefabfffaab6b56df77595aaab2ac",
>       "7d7f5d7ff92f5afddd77745bffdd49015ffeeffffaf6defd69dd556d55ad68",
>       "d7daf7eb4adff7577fddf41ffff680441fff9bfffdbdb5abb76b555b5576d4",
>       "feffdebfe8adbdffd6ebfc1ffffd2a9157dfaffffabb6b5d6dfd5576aaadb4",
>       "55d57deb7ebff75b7fbd5c17fec154009fffefbffab7b6ebfaababaaa95554",
>       "ff6ff7bfdb2b5dffeaf7fc9fffd455245ffeaffffabedabd576e555aaa2db4",
>       "55faaeeafefff76adfad7d13ff6154009fef5bfffaab6d56fab5abaaaadb54",
>       "ffaffdbfdbaabfbff6fedd17fec8a9505fffafddfebdb6df5f6eab6aaa96b4",
>       "d57d6bf6beffeaf5adab7e8bfb3614001ffb6ffffd6b6d6aead92add556d54",
>       "bfd7febff7ab7feffbfddd93fea948485fff5ffffabedadbbdb6ad554aab54",
>       "f57d55ed5dfdd6bad7577f0bfa5612009ffed7ffff55b76d6b752b5a952ad4",
>       "6fd7ff7fb76f7deffdfd6f83fa14845017feaffffabedabbddaed6d6a95558",
>       "bd7d55d5eddbd75eabb7bda3fa2a08005ff75fffff57756d76da95b4aa4ab4",
>       "ebefff7fb77f7df5fefedf82fc1602a01ffeefeffebdafb7edf57b6aaa9554",
>       "bf5db6d6efead7bfb5dbffa3f8260a885ffabbfffed76add5b5b56d554aad4",
>       "eaf77dbfbadfbeeadf7ead83fa0a00801ff75fffffaed6befdead56aa92ab4",
>       "bfadd7eaefb5ebbff5d5ffa2e80a842457fa7ffbff75bdebabb52ed5555554",
>       "eafbfabf5eff7ef76ffeafa1f00100489ffaaffffeafd336ded56daa554ad4",
>       "bfaf5f7bebd7dbadfab77fe2e40441245ffa7ffffffabeedb5badb56a92aa8",
>       "d57af5af5f7efef6dffd6fa3e88190489ff57fffffafeadb6bd56dbaaa5554",
>       "7bafbf7df5ebdbddf577dfc9620001105ffa5ffffefab7b6dd6b5ed5549554",
>       "befef5d7af5f7f775fdebfe2594950041ff0ffffff57ed6df6daab6eaaaaa8",
>       "fbdbef7efbf5d5fdf575d7a0a48050095ff57ffffeecbadb5b6aabdaa924b4",
>       "af6f5dd5aedf7f57bfdf7fe85a00040017f27fffffdb776eefb56e6daa5528",
>       "fafdeb7ffbf5ebfaf576dfe0940200105fd97feffeb6dadbbaedd5db6a9554",
>       "6fd75dd557dfbededfdf7ff45d0048049ff57fffffdb77b6d7dabeb6d4aab4",
>       "dabfb77ffd7aebbbbd75afe00000000017f17ffffff6dd7b7ab5a5adb54a6c",
>       "77eaeeead7d7ffeeebdf7ff4aa0000001ffa7ffffedb75adaf76debb692d58",
>       "dd5f5bb77dfeaabdff756fe0280000489ff17ffffffeef76f5d5b56d5a4b54"
>       ]

> colorBit =[
>  "edcfb1ffe2bbf7e2b1ffe2bbffedcfe2c59effe2bbffe2bbffedcfedcfb1ffe2bbedcfa7ffe2bbf7d9b1edcfa7e2c59ee2c59eedcfb1a79e80bba7899e897693806b9e8976a79e80271c00584e3030300030300008080027270093806b9e8980806b62806b626b6b586b6b5862625858584e58584e626258",
>  "f7d9b1edcfb1edcfa7edcfb1edcfb1edcfb1edcfa7ffe2bbf7e2b1c5bb899ebb4effff80c5d94e89a7439ebb4eedcfa7c5b193edcfb1bba7899e898093806b89766276766293806bcfa7804e3000624e00080800302708584e309e89809e8980898076806b626b6b5858584e6b6b5858584e58584e58584e",
>  "cfb193edcfb1ffe2bbedcfb1edcfb1edcfb1edcfb1ffff89a7c562c5d94e93b1629ebb4effff8093b16293b16289a7439ebb4ec5b19393806b93806b93806b806b62767662bb9e43898030806b00080800080800433a1c624e006b6b2793806b6b6b58766b62766b62766b6258584e58584e58584e626258",
>  "edcfb1edcfb1ffedcfedcfb1ffe2bbffe2bb93b1626b8927ffff80b1c56bb1cf4ed9e24effff80edf79ee2f780ffff80d9e24e9eb14393806b767662806b62806b6289803089a743a780276b6212896b126b3000272700623a126b62126b6b58767662766b626b6b5858584e58584e58584e4e4e4358584e",
>  "edcfb1ffedcfffedcfcfb193edcfb1ffff8076933af7f74eb1c56bffffa7ffffa7ffffa7ffffa7ffff89d9ed9389a74376933a6b6b58584e30806b62806b6293806b898030d9d96b6b6212896b00a780270808004e3000c589271c1200271c006b6b586b6b586b6b586b6b586b6b586262584e584e4e584e",
>  "edcfb1ffedcfffe2bbedcfb1e2cf9e76933af7f74e6b892789a743ffff80a7bb08f7ff6b9ebb4ed9ed80a79e8076933a4e763a89a743899e126b80128076587676629eb1436b6212bb9e2776933ad9e24ea776086b6212896b27433a003a4300807658806b626b6b58766b6258584e6b6b5858584e4e4e43",
>  "cfb193ffe2bbedcfb1edcfb1e2f7809ebb4e4e62004e763affff80ffff8076933a89a74376933a76933a6b8927ffffa7ffff80c5d94e6b89274e6b12806b627676629ebb4e303000a78043624e00896b126b62124e6b12fff727624e12cfb16b6b6b586b6b586b6b586b6b586b6b5858584e58584e4e4e43",
>  "c5b193edcfb1edcfb1f7d9b1cfe26bd9d96b4e6b1c4e6208e2ed6b809e274e6b1c6b89279ebb4eedf76bb1cf4e93b13089a7433a4e1c4e763a4e763a3030088076586b6212433a004e6b1c9eb143272700e29e126b6b27a78027272700121200271c0058584e766b6262625858584e58584e58584e626258",
>  "c5b193edcfb1f7d9b19e8062d9cf43c5d94ed9e24e6b89274e6b1cb1cf4e4e763ae2ed6b9eb1434e6b1c3a4e08ffff8993b1309ebb4e4e763a4e6b123a4e0827301c4e3000c58927624e121c1200624e00a78027a77608896b274e3000303000303008766b62766b62766b626b6b5862625858584e58584e",
>  "bba789d9bb93edcfb1898030b1cf4e4e6b126b89274e763a6b6b27c5d94ec5d94ed9e24e4e6b1cedf76b93b130cfe26b4e763a4e763a4e763a9ebb4e3a4e08271c00271c00bb9e43624e00a78043f793001c12001c1200eda727624e12433a00896b27ffffcfffffc5ffffcfffffcfd9bb9362625858584e",
>  "d9bb93cfb193e2c59e6b6b27b1cf4eb1c5274e6b1289a743cfe26bb1cf4e4e6b1c4e6b124e6b1c4e6b1c6b6b273a4e1c4e763aedf79e4e763a8980303a4e080000000000006b6b27e28027303008303008ffbb08624e00896b00ffffe2ffffcfffffcfffffc5ffffcfffffc5ffffc5ffffa7ffffa7fff79e",
>  "bba789cfb193f7d9b14e6b1c809e274e62004e6b126b8927b1c56b93b1624e6b1c3a4e1c4e6b1c3a4e0876933a6b892776933a4e763a3a4e1c3a43003a43003a3a1c080800624e00271c00896b004e6208894e006b6212ffffe2ffffe2ffff80ffffcfffffc5ffffc5ffffcffff780d99e27fff79effffa7",
>  "cfb189cfb193edcfb19ebb4e6b892789a743809e276b6b274e763a8076584e6b1c3a43003a4e084e6b1c3a43006b80126b89273030083a43003a4300272700767662000000624e00ffc527d99e27896b27303000ffffe2ffffc5ffffe2ffffc5f7c54effd962f7c54effd962ffffa7fff79ebb9e27fff79e",
>  "e2c59ed9bb93edcfa7ffffc59eb143b1c527809e273a43004e6b1c6b89273a43004e6b123a4e08271c00271c00434e00433a004e6b123a4300272700271c00766b62080800ffff80e29e12272700433a00c58927ffffe2ffffe2ffffcfffff80fff76bffffa7ffd962fff780f7c54efff79effffa7a78043",
>  "ffffcfffffcfffffe2ffffcf9eb1436b80126b89274e62084e62004e62083a43003a4e084e62086b6b273a4300433a004e62083a4300434e00121200303000ffedcfbbcf301c1200080800a78027121200ffffcfffffe2fff79effcf43ffffa7ffffa7ffffa7ffffa7ffff89ffffa7ffffc5623a12a79376",
>  "ffffcfffffe2ffffe2ffffe2ffd980d9e24ef7f74e809e27b1c527b1c5276b89274e6b126b8012303000623a122727001212002727000000001c1200ffff4ed9d96b1212002727003a4300303000272700ffffcffff780ffffc5ffffc5fff76bfff76bffffc5ffa743edc56bfff79ebba789433a00b19e76",
>  "ffedcfffedcfffedcfffffcfffedcfffff80fff76ba7bb08e2e2276b80004e6b123a4e086b3000ff5827b12700cf4308cf3a12272700ffed12ffff80623a12272700ffffe2ffffcf898030ffffc5ffffa7fff79effffc5ffff80ffff80cf8008ffd962896b12bb9e43edc56b934e1c8980306b6b27626258",
>  "ffffcff7d9a7f7d9b1ffe2bbffff4effff4eeded27eded27fff727586200272700a74e12cf1c00ff5827f71c00ffffcfcf1c00b11c006b6b00898000624e00ffffcfffff80ffffa7ffff80ffffa7ffffa7272700ffffa7fff780cf8008e29e12ffd962c58927584e30584e30806b6227270827301c3a3a1c",
>  "ffe2bbedcfb1ffe2bbcfc508ffff27ffff80ffffa7ffffa7ffffa7ffff27271c00cf3a00b11c00cf3a12b11c00b11c00891200b12700624e00433a00fff76beded27ffff00ffff27d9d900fff76bffff00fff780ffa743a74e12edc56bffd962a77608623a123a3a1c3a3a1c43431c271c002727123a3a1c",
>  "a78043d98062f7d9a7a7bb08ffff4efff727c5cf08e2e227b1c527a7bb006b8012a73a08e25830b127008912006212006212004308004e3000ffed00ffff12ffffa7ffff80939300ffffc5806b00ff8962ff8962ffa743ffff4effff27ff9e27623a12433a00433a1c584e30584e30272708272712271c00",
>  "bb9e27bb9e27e2c59e896b00ffcf43c55830434e006b80126b80124e6200434e006212008912008912006212006212004e30006b1c00896b12899e00ffffcfffffe2e2e227586200ffff80ff9e27ff763aff763aff9e27ffffa7fff727ff9e27cf4e123027083030083a3a1c27301c121208121208271c00",
>  "cf6b4343080030300093431cc5623a6b1c002727002727003a43003030000808003a00006212003a0000430800430800d9cf43fff76bffff4effffc5ffff80eded27ffffc5ffff803a4300ffed12ff5827ff5827ff761cfff727ffc527f77600893008303008303008271c00272712080800080800080800",
>  "8927006b1c00430800893008621200d980621c12002727001c1200080800121200ff4308ff5827ff43083a4300ffffa7f77600f77600a77608bb9e43ffffa7434e00bb9e27898000ffa743ffbb12ff761cff6b08ff6b08ff9308cf7600894e00303000271c00271c003a3a1c271c00080800000000121208",
>  "a78043d98062272700430800a780439358306b30003a4300271c00623a12ffb189cf1c00ff5827f71c00fff76bfff727ff761cff761cff3000cf8008cfc508d9cf43303000080800a78027ff8012ff9312ff761cff6b08cf6b00cf6b006b3000272700121200121200272708080800121200000000121208",
>  "c55830623a12d9cf43303000271c00ff89620808000808000000006b1c00a74e12621200cf1c008912006b8012a77608fff79eff3000cf27006b1c006b6b006b6b00b1a7891212003a3a1cff763aff761cff6b08ff6b08ed8008cf4e12624e001c1200080800271c00271c00080800080800000000121208",
>  "3a000027270058584e1c1200623a128927006b3000121200f79e766b1c00584e303a0000621200ff3000ff5827430800f71c00ff3000a73a083030003a3a1c27301c0000004e4e43271c00a74e12f74308ff6b08ff8012e28027894e00433a00000000000000080800121200080800000000000000000000",
>  "934e276b3000cf6b43935830000000430800623a12935830430800430800272712272700f74308ff761cff4308934e27ed4312b11c0030300008080027301c76767627301c121208272712121200623a12894e08cf4308a74e126b3000000000271c00080800080800121208080800000000000000000000",
>  "893008621200b14e27893008433a1c271c00584e3000000000000058584e3a3a1c3a3a1cf71c00ff4308cf1c00623a12584e30edcfb10808004e584e584e304e584e4e584e0000009393934e584e0000003a0000271c00433a1c433a1c3a3a1c584e30584e3027301c080800080800000000000000000000",
>  "584e306b6b586b6b58433a1c000000c5b1930000001212000000000000000808000808004308006b1c00121200271c006b6b58807658807658806b6293939327301c93939327271276767627301c121200807658584e30584e3043431c4e4e438976623a3a1c3a3a1c3a3a1c27301c272712080800121208",
>  "584e30584e306b6b273a3a1c0000003a3a1c0808003a3a1c0808000000006262580000008076589e8976f7d9b1cfa780f7d9b1d9bb93ffe2bbffedcf93806b8076588076584e4e434e584e121208e2c59ee2c59eedcfa7f7d9b1d9bb93cfb193f7e2b1e2c59e807658767662806b623a3a1c2727123a3a1c"]



\end{hide}

\HRule

%\epsfig{file=Wirth.ps}

%%\begin{center}
%%%if recalc
%%\perform{ generate "TutBit" 1 (scale 5 figBit ||| box "test mit Text") }
%%%else
%%\epsfig{file=TutBit.1}
%%%endif
%%\end{center}

\hspace{\stretch{1}}
%if recalc
\perform{ generate "TutBit" 2 (scale 2 figBit0 |=| box "figbit0") }
%else
\epsfig{file=TutBit.2}
%endif
\hspace{\stretch{1}}
%if recalc
\perform{ generate "TutBit" 3 (scale 2 figBit1 |=| box "figbit1") }
%else
\epsfig{file=TutBit.3}
%endif
\hspace{\stretch{1}}
%if recalc
\perform{ generate "TutBit" 1 (scale 5 figBitc |=|  box "figBitc") }
%else
\epsfig{file=TutBit.1}
%endif
\hspace{\stretch{1}}

}}


\end{document}