%% $Id: pst-news09.tex 62 2008-11-25 19:52:07Z herbert $
\documentclass[11pt,english,BCOR10mm,DIV12,bibliography=totoc,parskip=false,smallheadings
    headexclude,footexclude,oneside]{pst-doc}
\listfiles
\let\Lfile\LFile
\usepackage[utf8]{inputenc}
\usepackage{pstricks,pst-plot,xkvview}
\let\pstplotFV\fileversion
\let\pstplotFD\filedate
\usepackage{pst-eucl,pst-func}
\renewcommand\bgImage{\psscalebox{15}{\color{blue!20}2010}}
\def\textat{\char064}
\lstset{explpreset={pos=l,width=-99pt,overhang=0pt,hsep=\columnsep,vsep=\bigskipamount,rframe={}},
    escapechar=?}
\begin{document}

%\psset{PstDebug=1}
\title{\texttt{News -- 2010}\\ \Large new macros and bugfixes for the
basic package \nxLFile{pstricks}}
\author{Herbert Voß}
\date{\today}

\maketitle

\clearpage
\tableofcontents

\clearpage
\part{\texttt{pstricks} -- package}

\section{General}
There exists a new document class \LClass{pst-doc} for writing PSTricks documentations,
like this news document. It depends on the KOMA-Script document class \LClass{scrartcl}.
\LClass{pst-doc} defines a lot of special macros to create a good index. Take one of
the already existing package documentation and look into the source file. Then it will be
easy to understand, how all these macros have to be used.

When running \Lprog{pdflatex} the title page is created with boxes and inserted 
with the macro \Lcs{AddToShipoutPicture} from the package \LPack{eso-pic}. It
inserts the background title page image \Lfile{pst-doc-pdf} to use directly
\Lprog{pdflatex}.
When running \Lprog{latex} the title page
 is created with \PST\ macros.This allows to use the Perl script \Lprog{pst2pdf} or
the package \LPack{pst-pdf} or \LPack{auto-pst-pdf} or any other program/package which
supports \PS\ code in the document.


%--------------------------------------------------------------------------------------
\section{\texttt{pstricks.sty}}
%--------------------------------------------------------------------------------------
\subsection{New optional argument}

With the setting of the optional argument \Loption{pdf} the package \LPack{auto-pst-pdf} will be loaded
by PSTricks. This requires that you run \Lprog{pdflatex} as 

\begin{BDef}
\Lprog{pdflatex} \texttt{-{}-}\Loption{shell-escape} \texttt{<file>} & \% \TeX\,Live users\\
\Lprog{pdflatex} \texttt{-{}-}\Loption{enable-write18} \texttt{<file>} & \% MiK\TeX\ users
\end{BDef}

The package exports the \Lenv{pspicture} environments into single images which are collected in
a created file \texttt{<file>-pics.pdf} and inserted automatically in the last \Lprog{pdflatex}
run.



%--------------------------------------------------------------------------------------
\section{\texttt{pstricks.tex} (\pstricksFV -- \pstricksFD)}
%--------------------------------------------------------------------------------------

\subsection{Coordinates}
With the setting \Lcs{SpecialCoor} the package allows different kinds of coordinates.
The macro \Lcs{uput} can now be used in a different way. 
The default behaviour for nodes with a relative point puts its argument \emph{without} rotation
on the line $\overline{AB}$. When using the prefix > before the node or the $x$-value for
cartesian coordinates, the behaviour is different. Now the angle between the line $\overline{OB}$
and the horizontal line
is taken into account and the placement of the argument of \Lcs{uput} is different to
the default behaviour. 

\begin{LTXexample}[width=6cm,wide=true]
\begin{pspicture}[showgrid](5,6)
\pnode(0,4){A}\psdot(A)
\pnode(3,2){B}\psdot(B)
\psline(A)(B)
\psline[linestyle=dashed](A)(3,4)
\psline[linestyle=dashed](A)(3,6)
\psline[linestyle=dashed](B)
\uput{1cm}[(B)](A){foo}
\uput{1cm}[(B)](>A){bar}
\end{pspicture}
\end{LTXexample}


\subsection{New optional arguments}
The new arguments are only valid for the macros \Lcs{psellipse}, \Lcs{pscircle}, \Lcs{psarc}.
\Lcs{psellipticarc}, \Lcs{pscurve}, \Lcs{psplot}, and \Lcs{psparametricplot}.

\medskip
\begin{tabular}{@{} l >{\em}l l l @{}}\toprule
\emph{name} & type & \emph{default} & \emph{description}\\\midrule
\Lkeyword{dashcolor} & color & \nxLcs{relax} & for colored dashed lines \\
\Lkeyword{startLW} & length & \Lcs{pslinewidth} & starting linewidth \\
\Lkeyword{endLW}   & length & \Lcs{pslinewidth} & ending linewidth \\
\Lkeyword{startWL} & integer& 380               & starting wave length\\
\Lkeyword{endWL}   & integer& 780               & ending wave length \\
\Lkeyword{variableLW} & boolean & \false       & use variable linewidth\\
\Lkeyword{variableColor} & boolean & \false       & use variable color\\\bottomrule
\end{tabular}

\bigskip
\begingroup
\psset{linewidth=2mm,linestyle=dashed}
\begin{pspicture}(4,-4)
\psline[linecolor=blue,dashcolor=red,linearc=0.5](0,0)(4,0)(4,-4)
\psline[linecolor=blue,dashcolor=cyan,linearc=0.5](0,0)(0,-4)(4,-4)
\end{pspicture}\quad
\begin{pspicture}(4,4)
\psframe[linecolor=blue,dashcolor=green,framearc=0.5](0,0)(4,4)
\end{pspicture}
\quad \psset{linecap=2,dash=5mm 5mm }
\begin{pspicture}(4,-4)
\psline[linecolor=black,dashcolor=black!40,linecap=0](0,0)(4,-4)
\psline[linecolor=blue,dashcolor=red,linearc=0.5](0,0)(4,0)(4,-4)
\psline[linecolor=blue,dashcolor=cyan,linearc=0.5](0,0)(0,-4)(4,-4)
\end{pspicture}
\endgroup

\begin{lstlisting}
\psset{linewidth=2mm,linestyle=dashed}
\begin{pspicture}(4,-4)
\psline[linecolor=blue,dashcolor=red,linearc=0.5](0,0)(4,0)(4,-4)
\psline[linecolor=blue,dashcolor=cyan,linearc=0.5](0,0)(0,-4)(4,-4)
\end{pspicture}\quad
\begin{pspicture}(4,4)
\psframe[linecolor=blue,dashcolor=green,framearc=0.5](0,0)(4,4)
\end{pspicture}
\quad \psset{linecap=2,dash=5mm 5mm }
\begin{pspicture}(4,-4)
\psline[linecolor=black,dashcolor=black!40,linecap=0](0,0)(4,-4)
\psline[linecolor=blue,dashcolor=red,linearc=0.5](0,0)(4,0)(4,-4)
\psline[linecolor=blue,dashcolor=cyan,linearc=0.5](0,0)(0,-4)(4,-4)
\end{pspicture}
\end{lstlisting}


\begin{LTXexample}[width=7cm,wide=true]
\psset{endLW=15pt}
\begin{pspicture}(-3.5,-2.5)(3.5,2.5)
\psellipse[linejoin=2,variableLW,startLW=1pt,
  linecolor=green!40](0,0)(3,1)
\end{pspicture}
\end{LTXexample}


\begin{LTXexample}[width=7cm,wide=true]
\psset{endLW=15pt}
\begin{pspicture}(-2.5,-2.5)(2.5,2.5)
\pscircle[variableLW,startLW=1pt,
  linecolor=blue!40]{2}
\end{pspicture}
\end{LTXexample}

%
\begin{LTXexample}[width=7cm,wide=true]
\psset{endLW=15pt}
\begin{pspicture}(-2.5,-2.5)(2.5,2.5)
\psarc[variableLW,startLW=1pt,
  linecolor=red!40](0,0){2}{10}{300}
\end{pspicture}
\end{LTXexample}

% 
\begin{LTXexample}[width=7cm,wide=true]
\psset{endLW=15pt}
\begin{pspicture}(-3.5,-2.5)(3.5,2.5)
\psellipticarc[variableLW,startLW=1pt,
  linecolor=black!40](0,0)(3,1){90}{30}
\end{pspicture}
\end{LTXexample}

\begin{LTXexample}[width=7cm,wide=true]
\begin{pspicture}(-2.5,-2.5)(2.5,2.5)
\pscurve[variableLW,startLW=1pt,endLW=20pt,
  variableColor](-1,0.5)(-2,1)(2,2)(-1,-2)(2,-2)
\end{pspicture}
\end{LTXexample}

\begin{LTXexample}[width=7cm,wide=true]
\begin{pspicture}(-2.5,-2.5)(2.5,2.5)
\pscurve[variableLW,startLW=1pt,endLW=20pt]%
  (-1,0.5)(-2,1)(2,2)(-1,-2)(2,-2)
\end{pspicture}
\end{LTXexample}

\begin{LTXexample}[pos=t]
\begin{pspicture}(-5,-3)(5,3)
\psplot[variableLW,startLW=1pt,endLW=20pt,
  linecolor=magenta!60,variableColor,
  algebraic,plotpoints=3000,startWL=500,
  endWL=700]{-5}{5}{2*sin(2*x)+cos(x)}
\end{pspicture}
\end{LTXexample}

\begin{LTXexample}[pos=t]
\psset{endLW=24pt}
\begin{pspicture}(-5,-5)(5,5)
\psparametricplot[variableLW,startLW=1pt,
  endLW=60pt,linecolor=red,variableColor,
  algebraic,plotpoints=3000,plotstyle=curve,
  opacity=0.4,strokeopacity=0.4,
  endWL=600]{-5}{5}{t*sin(t) | t*cos(t)}
\end{pspicture}
\end{LTXexample}


\clearpage


\subsection{Macro \nxLcs{psellipse}}

To rotate an ellipse the already existing keyword \Lkeyword{rot} can be
used. This is easier than using the \Lcs{rput} command and its optional
argument for rotating.
\xLkeyword{rot}\xLkeyword{vlines}\xLkeyword{linecolor}
\begin{LTXexample}[width=6cm,wide=true]
\psset{unit=0.25}
\begin{pspicture}(-1,5)(20,18)
\psclip{\psellipse[linecolor=red,
  rot=-12.606](5.821,10.04)(6.633,5.103)}
  \psellipse[linecolor=blue,fillstyle=vlines,
    rot=39.29](13.141,11.721)(6.8,5.4)
\endpsclip
\psellipse[linecolor=blue,rot=39.29](13.1,11.7)(6.8,5.4)
\end{pspicture}

\begin{pspicture}(-1,5)(20,18)
\psellipse[linecolor=blue,rot=-39.29,
  fillstyle=vlines](13.1,11.7)(6.8,5.4)
\psclip{\psellipse[linecolor=red,rot=12.6,
  fillstyle=vlines](5.8,10)(6.6,5.1)}
  \psellipse*[linecolor=white,rot=-39.29](13.1,11.7)(6.8,5.4)
\endpsclip
\psellipse[linecolor=blue,rot=-39.29](13.1,11.7)(6.8,5.4)
\psellipse[linecolor=red,rot=12.6](5.8,10)(6.6,5.1)
\end{pspicture}
\end{LTXexample}

\subsection{Macro \nxLcs{psellipticarc}}\xLcs{psellipticarc}
In a circle the angle is proportional to the bow: $b=r\alpha$. In an
elliptic arc this is no more the case, which is the reason why angles are
internally corrected by PSTricks, to get the same arc lengthts for
different radii:

\xLcs{psellipticarc}
\begin{LTXexample}[width=6cm]
\psset{unit=0.5cm}
\begin{pspicture}(-5.5,-5.5)(5.5,5.5)%
\psset{linewidth=0.4pt,linejoin=1}
\psline(5,0)(0,0)(5,-5)
\psellipticarc(0,0)(3,3){0}{315}
\end{pspicture}%
\end{LTXexample}

\begin{LTXexample}[width=6cm]
\psset{unit=0.5cm}
\begin{pspicture}(-5.5,-5.5)(5.5,5.5)%
\psset{linewidth=0.4pt,linejoin=1}
\psline(5,0)(0,0)(5,-5)
\psellipticarc(0,0)(1,3){0}{315}%
\psset{linecolor=red}
\psellipticarc(0,0)(3,1){22}{222}%
\psline(3;22)\psline(3;222)
\end{pspicture}%
\end{LTXexample}

\begin{LTXexample}[width=6cm]
\psset{unit=0.5cm}
\begin{pspicture}(-5.5,-5.5)(5.5,5.5)%
\psset{linewidth=0.4pt,linejoin=1}
\psline(5,0)(0,0)(5,-5)
\psellipticarc*(0,0)(1,3){0}{315}%
\psset{linecolor=red}
\psellipticarc*(0,0)(3,1){22}{222}%
\psline(3;22)\psline(3;222)
\end{pspicture}%
\end{LTXexample}

\psset{unit=1cm}


If you do not want the angle correction, then use the keyword setting \Lkeyword{correctAngle}=\false:

\begin{LTXexample}[width=6cm]
\psset{unit=0.5cm}
\begin{pspicture}(-5.5,-5.5)(5.5,5.5)%
\psset{linewidth=0.4pt,linejoin=1,
  correctAngle=false}
\psline(5,0)(0,0)(5,-5)
\psellipticarc(0,0)(1,3){0}{315}%
\psset{linecolor=red}
\psellipticarc(0,0)(3,1){22}{222}%
\psline(3;22)\psline(3;222)
\end{pspicture}%
\end{LTXexample}

\begin{LTXexample}[width=6cm]
\psset{unit=0.5cm}
\begin{pspicture}(-5.5,-5.5)(5.5,5.5)%
\psset{linewidth=0.4pt,linejoin=1,
  correctAngle=false}
\psline(5,0)(0,0)(5,-5)
\psellipticarc*(0,0)(1,3){0}{315}%
\psset{linecolor=red}
\psellipticarc*(0,0)(3,1){22}{222}%
\psline(3;22)\psline(3;222)
\end{pspicture}%
\end{LTXexample}




\subsection{Option \texttt{algebraic}}
The option \Lkeyword{algebraic} moved from the other packages into
the main package \LPack{pstricks} to get rid of the dependencies.

By default the function in \Lcs{psplot} has to be described in
Reversed Polish Notation. The option \Lkeyword{algebraic} allows you
to do this in the common algebraic notation. E.g.:

\begin{tabular}{l|l}
RPN & algebraic\\\hline
\verb+x ln+ & \verb+ln(x)+\\
\verb+x cos 2.71 x neg 10 div exp mul+ & \verb+cos(x)*2.71^(-x/10)+\\
\verb+1 x div cos 4 mul+ & \verb+4*cos(1/x)+\\
\verb+t cos t sin+ & \verb+cos(t)|sin(t)+
\end{tabular}

Setting the option \Lkeyword{algebraic}, allow the user
to describe all expression to be written in the classical
algebraic notation (infix notation). The four arithmetic
operations are obviously defined \verb$+-*/$, and also the
exponential operator \verb$^$. The natural priorities are used :
$3+4\times 5^5=3+(4\times (5^5))$, and by default the computation
is done from left to right. The following functions are defined :

\medskip
\begin{tabular}{ll}
\verb$sin$, \verb$cos$, \verb$tan$, \verb$acos$, \verb$asin$ & in radians\\
\verb$log$, \verb$ln$\\
\verb$ceiling$, \verb$floor$, \verb$truncate$, \verb$round$\\
\verb$sqrt$ & square root\\
\verb$abs$ & absolute value\\
\verb$fact$ & for the factorial\\
\verb$Sum$ & for building sums\\
\verb$IfTE$ & for an easy case structure
\end{tabular}

\medskip
These options can be used with \textbf{all} plot macros.

{\bfseries Using the option \Lkeyword{algebraic} implies that all
angles have to be in radians! }

For the \Lcs{parametricplot} the two parts must be divided by the \Lnotation{|} character:

\begin{LTXexample}[width=2cm]
\begin{pspicture}(-0.5,-0.5)(0.5,0.5)
\parametricplot[algebraic,linecolor=red]{-3.14}{3.14}{cos(t)|sin(t)}
\end{pspicture}
\end{LTXexample}

\bigskip
\begingroup
\psset{lly=-0.5cm}
\psgraph[trigLabels,dx=\psPi,dy=0.5,Dy=0.5]{->}(0,0)(-10,-1)(10,1){\linewidth}{6cm}
  \psset{algebraic,plotpoints=1000}
  \psplot[linecolor=yellow,linewidth=2pt]{-10}{10}{0.75*sin(x)*cos(x/2)}
  \psplot[linecolor=red,showpoints=true,plotpoints=101]{-10}{10}{0.75*sin(x)*cos(x/2)}
\endpsgraph
\endgroup

\bigskip
\begin{lstlisting}
\psset{lly=-0.5cm}
\psgraph[trigLabels,dx=\psPi,dy=0.5,Dy=0.5]{->}(0,0)(-10,-1)(10,1){\linewidth}{6cm}
  \psset{algebraic,plotpoints=1000}
  \psplot[linecolor=yellow,linewidth=2pt]{-10}{10}{0.75*sin(x)*cos(x/2)}
  \psplot[linecolor=red,showpoints=true,plotpoints=101]{-10}{10}{0.75*sin(x)*cos(x/2)}
\endpsgraph
\end{lstlisting}


\bigskip
%\begin{LTXexample}[pos=t]
\bgroup
\psset{lly=-0.5cm,unit=1cm}
\psgraph(0,-5)(18,3){0.9\linewidth}{5cm}
  \psset{algebraic,plotpoints=501}
  \psplot[linecolor=yellow, linewidth=4\pslinewidth]{0.01}{18}{ln(x)}
  \psplot[linecolor=red]{0.01}{18}{ln(x)}
  \psplot[linecolor=green,linewidth=4\pslinewidth]{0}{18}{3*cos(x)*2.71^(-x/10)}
  \psplot[linecolor=blue,showpoints=true,plotpoints=51]{0}{18}{3*cos(x)*2.71^(-x/10)}
\endpsgraph
\egroup
%\end{LTXexample}


\bigskip
\begin{lstlisting}
\psset{lly=-0.5cm}
\psgraph(0,-5)(18,3){0.9\linewidth}{5cm}
  \psset{algebraic,plotpoints=501}
  \psplot[linecolor=yellow, linewidth=4\pslinewidth]{0.01}{18}{ln(x)}
  \psplot[linecolor=red]{0.01}{18}{ln(x)}
  \psplot[linecolor=yellow,linewidth=4\pslinewidth]{0}{18}{3*cos(x)*2.71^(-x/10)}
  \psplot[linecolor=blue,showpoints=true,plotpoints=51]{0}{18}{3*cos(x)*2.71^(-x/10)}
\endpsgraph
\end{lstlisting}

\section{New linestyle \nxLkeyval{symbol}}

Instead of drawing a continous line or curve for a series of coordinates, one
can now out a symbol in a given size, direction, and step. This works only
for the line style \Lkeyval{symbol}. It takes the symbol defined by the optional
argument \Lkeyword{symbol}, which can have a single character or a octal number
of three digits. The font is specified by the key \Lkeyword{symbolFont}, which can take
as argument one of the valid \PS fonts or the internal \Lkeyval{PSTricksDotFont}.
If the symbol is given by a single character then the equivilant character in
the given font is used. The difference between two symbols is set by \Lkeyword{symbolStep}
and the symbol rotation by \Lkeyword{rotateSymbol}. For the first symbol there
is an additional keyword \Lkeyword{startAngle}. 
The default values for these new
optional keywords are:

\begin{Xverbatim}{}
\psset[pstricks]{symbolStep=20pt}
\psset[pstricks]{symbolWidth=10pt}
\psset[pstricks]{symbolFont=Dingbats}
\psset[pstricks]{rotateSymbol=false}
\psset[pstricks]{startAngle=0}
\end{Xverbatim}

\begin{LTXexample}[pos=t,preset=\centering]
\pspicture(-1,-1)(8,6)
\psline[linestyle=symbol](0,0)(5,0)(8,4)
\psline[linestyle=symbol,symbol=T](0,1)(5,1)(8,4)
\psline[linestyle=symbol,symbol=u,symbolFont=PSTricksDotFont](0,2)(5,2)(8,4)
\psline[linestyle=symbol,symbol=u,symbolStep=25pt,linecolor=red](0,3)(5,3)(8,2)
\psline[linestyle=symbol,symbol=A,symbolStep=25pt,
  symbolWidth=20pt,linecolor=blue](0,4)(5,4)(8,1)
\psline[linestyle=symbol,symbol=342,rotateSymbol=true,symbolStep=12pt](0,5)(5,5)(8,0)
\endpspicture
\end{LTXexample}

\begin{LTXexample}[pos=t,preset=\centering]
\pspicture(-1,-1)(8,6)
\pscurve[linestyle=symbol](0,0)(5,0)(8,4)
\pscurve[linestyle=symbol](0,1)(5,1)(8,4)
\pscurve[linestyle=symbol,symbol=u,symbolFont=PSTricksDotFont](0,2)(5,2)(8,4)
\pscurve[linestyle=symbol,symbol=u,symbolStep=25pt,linecolor=red](0,3)(5,3)(8,2)
\pscurve[linestyle=symbol,symbol=A,symbolStep=25pt,
  symbolWidth=20pt,linecolor=blue](0,4)(5,4)(8,1)
\pscurve[linestyle=symbol,symbol=342,rotateSymbol=true,
  startAngle=190,symbolStep=12pt](0,5)(5,5)(8,0)
\endpspicture
\end{LTXexample}

\begin{LTXexample}[pos=t,preset=\centering]
\pspicture(-1,-1)(8,6)
\psccurve[linestyle=symbol](0,0)(5,0)(8,4)
\psccurve[linestyle=symbol](0,1)(5,1)(8,4)
\psccurve[linestyle=symbol,symbol=u,symbolFont=PSTricksDotFont](0,2)(5,2)(8,4)
\psccurve[linestyle=symbol,symbol=u,symbolStep=25pt,linecolor=red](0,3)(5,3)(8,2)
\psccurve[linestyle=symbol,symbol=A,symbolStep=25pt,
  symbolWidth=20pt,linecolor=blue](0,4)(5,4)(8,1)
\psccurve[linestyle=symbol,symbol=342,rotateSymbol=true,
  startAngle=190,symbolStep=12pt](0,5)(5,5)(8,0)
\endpspicture
\end{LTXexample}

\begin{LTXexample}[pos=t,preset=\centering]
\pspicture(-1,-1)(5,4)
\pscurve[rotateSymbol=true,linestyle=symbol,
  rot=180,startAngle=100,symbol=",
    symbolWidth=20pt](0,0)(1,4)(3,0)(5,2)
\endpspicture
\end{LTXexample}

\begin{LTXexample}[pos=t,preset=\centering]
\pspicture(-1,-1)(6,4)
\psbezier[rotateSymbol=true,linestyle=symbol,symbol=u,
 symbolFont=PSTricksDotFont,rot=-90,startAngle=0](0,0)(0,4)(6,4)(6,0)
\endpspicture
\end{LTXexample}

\begin{LTXexample}[pos=t,preset=\centering]
\psset{unit=0.5cm}
\pspicture(-1,-4)(6,4)
\pscbezier[rotateSymbol=true,linestyle=symbol,symbol=u,
 symbolFont=PSTricksDotFont](0,4)(4,4)(4,-4)(0,-4)
\pscbezier[linestyle=dashed](0,4)(4,4)(4,-4)(0,-4)
\endpspicture
\end{LTXexample}

\psset{unit=1cm}
\begin{LTXexample}[pos=t,preset=\centering]
\pspicture(-1,-1)(6,4)
\psbezier[rotateSymbol=true,linestyle=symbol,symbol=u,
 symbolFont=PSTricksDotFont](0,0)(0,4)(6,4)(6,0)
\endpspicture
\end{LTXexample}

\begin{LTXexample}[pos=t,preset=\centering]
\pspicture(-1,-1)(6,4)
\pspolygon[rotateSymbol=true,linestyle=symbol,symbol=u,
 symbolFont=PSTricksDotFont](0,0)(0,4)(6,4)(6,0)(1,3)
\endpspicture
\end{LTXexample}

\begin{LTXexample}[pos=t,preset=\centering]
\pspicture(-3,-1)(6,6)
\psccurve[linestyle=symbol,symbol=u, rot=-90,rotateSymbol,
   symbolFont=PSTricksDotFont, symbolWidth=5pt, symbolStep=10pt
](-3,-1)(0,0)(0,4)(6,4)(6,0)(0,4)(-1,5)
\endpspicture
\end{LTXexample}

\begin{LTXexample}[pos=t,preset=\centering]
\pspicture(-1,-1)(6,6)
\pscurve[linestyle=dashed,linecolor=black!30](0,0)(0,4)(6,4)(6,0)(0,4)
\pscurve[rotateSymbol=true,linestyle=symbol,symbol=k,
   symbolFont=PSTricksDotFont, symbolWidth=5pt, symbolStep=10pt,linecolor=blue
](0,0)(0,4)(6,4)(6,0)(0,4)
\endpspicture
\end{LTXexample}


%--------------------------------------------------------------------------------------
\section{Numeric functions}
%--------------------------------------------------------------------------------------

All macros have a \textat{} in their name, because they are
only for internal use, but it is no problem to use them like other
macros. One can define another name without a \textat{}:
\begin{lstlisting}[style=syntax]
\makeatletter
\let\pstdivide\pst@divide
\makeatother
\end{lstlisting}

or put the macro inside the \Lcs{makeatletter} -- \Lcs{makeatother} sequence.


%--------------------------------------------------------------------------------------
\section{Numeric functions}
%--------------------------------------------------------------------------------------

By default \PST\ loads the file \Lfile{pst-fp} which is derived from the
\LPack{fp} package. It supports the following macros:

%--------------------------------------------------------------------------------------
\subsection{\nxLcs{pstFPadd}, \nxLcs{pstFPsub}, \nxLcs{pstFPmul}, and \nxLcs{pstFPdiv}}
%--------------------------------------------------------------------------------------
Multiplication and division:

\begin{BDef}
\Lcs{pstFPadd}\Largb{result}\Largb{number}\Largb{number}\\
\Lcs{pstFPsub}\Largb{result}\Largb{number}\Largb{number}\\
\Lcs{pstFPmul}\Largb{result}\Largb{number}\Largb{number}\\
\Lcs{pstFPdiv}\Largb{result}\Largb{number}\Largb{number}
\end{BDef}

\begin{LTXexample}[width=5cm]
\pstFPmul\Result{-3.405}{0.02345} \Result\quad
\pstFPdiv\Result{-3.405}{0.02345} \Result\\
\pstFPmul\Result{0.02345}{-3.405} \Result\quad
\pstFPdiv\Result{0.02345}{-3.405} \Result\\
\pstFPmul\Result{234.123}{33} \Result\quad
\pstFPdiv\Result{234.123}{33} \Result\\
\pstFPadd\Result{234.123}{33} \Result\quad
\pstFPadd\Result{234.123}{-33} \Result\\
\pstFPsub\Result{234.123}{33} \Result\quad
\pstFPsub\Result{-234.123}{33} \Result
\end{LTXexample}

The zeros can be stripped with the macro \Lcs{pstFPstripZeros}. Expect 
always rounding errors, \TeX\ was not made for calculations \ldots
The value is converted into a length and then reconverted to a 
number by stripping the unit. Which also strips the zeros.

\begin{LTXexample}[width=5cm]
\pstFPmul\Result{-3.405}{0.02345} 
\pstFPstripZeros{\Result}{\Result}\Result\quad
\pstFPdiv\Result{-3.405}{0.02345} 
\pstFPstripZeros{\Result}{\Result}\Result\\
\pstFPmul\Result{0.02345}{-3.405} 
\pstFPstripZeros{\Result}{\Result}\Result\quad
\pstFPdiv\Result{0.02345}{-3.405} 
\pstFPstripZeros{\Result}{\Result}\Result
\end{LTXexample}

%--------------------------------------------------------------------------------------
\subsection{\nxLcs{pstFPMul} and \nxLcs{pstFPDiv}}
%--------------------------------------------------------------------------------------
Integer multiplication and division:

\begin{BDef}
\Lcs{pstFPMul}\Largb{result as a truncated integer}\Largb{number}\Largb{number}\\
\Lcs{pstFPDiv}\Largb{result as a truncated integer}\Largb{number}\Largb{number}
\end{BDef}

\begin{LTXexample}[width=5cm]
\makeatletter
\pstFPMul\Result{-34.05}{0.02345} \Result\quad
\pstFPDiv\Result{-3.405}{0.02345} \Result\\
\pstFPMul\Result{23.45}{-3.405} \Result\quad
\pstFPDiv\Result{0.2345}{-0.03405} \Result\\
\pstFPMul\Result{234.123}{33} \Result\quad
\pstFPDiv\Result{234.123}{33} \Result
\makeatother
\end{LTXexample}

%--------------------------------------------------------------------------------------
\section{The PostScript header files}
\subsection{\nxLFile{pstricks.pro}}
%--------------------------------------------------------------------------------------
It contains now most of the stuff from \LPack{pstricks-add} and the new routines
for plotting lines/curves with symbols.

%--------------------------------------------------------------------------------------
\subsection{\nxLFile{pst-algparser.pro}}
\subsubsection{Using the \texttt{Sum} function}
%--------------------------------------------------------------------------------------

\begin{BDef}
\Lcs{Sum}\Largr{<index name>,<start>,<step>,<end>,<function>}
\end{BDef}

Let's plot the first development of cosine with polynomials:
$\displaystyle\sum_{n=0}^{+\infty}\frac{(-1)^nx^{2n}}{n!}$.

\begin{center}
\bgroup
\psset{algebraic=true, plotpoints=501, yunit=3}
\def\getColor#1{\ifcase#1 black\or red\or magenta\or yellow\or green\or Orange\or blue\or
  DarkOrchid\or BrickRed\or Rhodamine\or OliveGreen\fi}
\begin{pspicture}(-7,-1.5)(7,1.5)
  \psclip{\psframe(-7,-1.5)(7,1.5)}
    \psplot{-7}{7}{cos(x)}
    \multido{\n=1+1}{10}{%
      \psplot[linewidth=1pt,linecolor=\getColor{\n}]{-7}{7}{%
         Sum(ijk,0,1,\n,(-1)^ijk*x^(2*ijk)/fact(2*ijk))}}
   \endpsclip
  \psaxes(0,0)(-7,-1.5)(7,1.5)
\end{pspicture}
\egroup
\end{center}
\begin{lstlisting}
\psset{algebraic=true, plotpoints=501, yunit=3}
\def\getColor#1{\ifcase#1 black\or red\or magenta\or yellow\or green\or Orange\or blue\or
  DarkOrchid\or BrickRed\or Rhodamine\or OliveGreen\fi}
\begin{pspicture}(-7,-1.5)(7,1.5)
  \psclip{\psframe(-7,-1.5)(7,1.5)}
    \psplot{-7}{7}{cos(x)}
    \multido{\n=1+1}{10}{%
      \psplot[linewidth=1pt,linecolor=\getColor{\n}]{-7}{7}{%
         Sum(ijk,0,1,\n,(-1)^ijk*x^(2*ijk)/fact(2*ijk))}}
   \endpsclip
  \psaxes(0,0)(-7,-1.5)(7,1.5)
\end{pspicture}
\end{lstlisting}

\clearpage
%--------------------------------------------------------------------------------------
\subsection[\nxLps{IfTE}]{The variable step algorithm together with the PostScript function \nxLps{IfTE}}
%--------------------------------------------------------------------------------------
\xLps{IfTE}\xLkeyword{VarStep}\xLkeyword{VarStepEpsilon}

\begin{BDef}
\Lps{IfTE}\Largr{<condition>,<true part>,<false part>}
\end{BDef}

Nesting of several \Lps{IfTE} is possible and seen in the
following examples. A classic example is a piece-wise linear
function.

\begin{center}
\psset{unit=0.7cm}
\begin{pspicture}(-7.5,-2.5)(7.5,6)
  \psaxes{->}(0,0)(-7,-2)(7.5,6)[x,-90][y,0]
  \psset{algebraic=true, plotpoints=21,linewidth=2pt}
  \psplot[linecolor=blue]{-7.5}{7.5}{IfTE(x<-6,8+x,IfTE(x<0,-x/3,IfTE(x<3,2*x,9-x)))}
  \psplot[linecolor=red, plotpoints=101]{-7.5}{7.5}{%
      IfTE(2*x<-2^2*sqrt(9),7+x,IfTE(x<0,x^2/18-1,IfTE(x<3,2*x^2/3-1,8-x)))}%
\end{pspicture}
\end{center}
\psset{unit=1cm}

\begin{lstlisting}
\psset{unit=1.5, algebraic, ?\ON?VarStep?\OFF?, showpoints, ?\ON?VarStepEpsilon?\OFF?=.001}
\begin{pspicture}[showgrid=true](-7,-2)(2,4)
  \psplot{-7}{2}{?\ON?IfTE?\OFF?(x<-5,-(x+5)^3/2,?\ON?IfTE?\OFF?(x<0,0,x^2))}
  \psplot{-7}{2}{5*x/9+26/9}
  \psplot[linecolor=blue]{-7}{2}{(x+7)^30/9^30*4.5-1/2}
  \psplot[linecolor=red]{-6.9}{2}
      {?\ON?IfTE?\OFF?(x<-6,ln(x+7),?\ON?IfTE?\OFF?(x<-3,x+6,?\ON?IfTE?\OFF?(x<0.1415926,sin(x+3)+3,3.1415926-x)))}
\end{pspicture}
\end{lstlisting}

When you program a piece-wise defined function you must take care
that a plotting point must be put at each point where the
description changes. Use \Lkeyword{showpoints}=true to see what's
going on when there is a problem. You are on the safe side when
you choose a big number for \Lkeyword{plotpoints}.


\begin{center}
\psset{unit=0.75}
\begin{pspicture}(-8,-8)(8,8)
  \psaxes{->}(0,0)(-8,-8)(8,8)[x,-90][y,0]
  \psset{plotpoints=1000,linewidth=1pt}
  \psplot[algebraic=true]{-8}{8}{ceiling(x)}
  \psplot[algebraic=true, linecolor=yellow]{-8}{8}{rand/(2^31-1)+x}
  \psplot[algebraic=true, linecolor=red]{-8}{8}{floor(x)}
  \psplot[algebraic=true, linecolor=blue]{-8}{8}{round(x)}
  \psplot[algebraic=true, linecolor=green]{-8}{8}{truncate(x)}
  \psplot[algebraic=true, linecolor=cyan]{-8}{8}{div(mul(4,x),7)}
  \psplot[algebraic=true, linecolor=gray]{-8}{8}{abs(x)+abs(x-3)-abs(5-5*x/7)}
  \psplot[algebraic=true, linecolor=gray]{-8}{8}{abs(3*cos(x)+1)}
  \psplot[algebraic=true, linecolor=magenta]{-8}{8}{floor(8*cos(x))}
\end{pspicture}
\end{center}

\begin{lstlisting}
\psset{unit=0.75}
\begin{pspicture}(-8,-8)(8,8)
  \psaxes{->}(0,0)(-8,-8)(8,8)[x,-90][y,0]
  \psset{plotpoints=1000,linewidth=1pt}
  \psplot[algebraic=true, linecolor=yellow]{-8}{8}{rand/(2^31-1)+x}
  \psplot[algebraic=true]{-8}{8}{ceiling(x)}
  \psplot[algebraic=true, linecolor=red]{-8}{8}{floor(x)}
  \psplot[algebraic=true, linecolor=blue]{-8}{8}{round(x)}
  \psplot[algebraic=true, linecolor=green]{-8}{8}{truncate(x)}
  \psplot[algebraic=true, linecolor=cyan]{-8}{8}{div(mul(4,x),7)}
  \psplot[algebraic=true, linecolor=gray]{-8}{8}{abs(x)+abs(x-3)-abs(5-5*x/7)}
  \psplot[algebraic=true, linecolor=gray]{-8}{8}{abs(3*cos(x)+1)}
  \psplot[algebraic=true, linecolor=magenta]{-8}{8}{floor(8*cos(x))}
\end{pspicture}
\end{lstlisting}


\subsection[\nxLps{Derive} function]{Successive derivatives of a polynomial with the PostScript function \nxLps{Derive}}

\begin{center}
\bgroup
\psset{unit=2, algebraic=true, VarStep=true, showpoints=true, VarStepEpsilon=.001}
\def\getColor#1{\ifcase#1 Tan\or RedOrange\or magenta\or yellow\or green\or Orange\or blue\or
  DarkOrchid\or BrickRed\or Rhodamine\or OliveGreen\or Goldenrod\or Mahogany\or
  OrangeRed\or CarnationPink\or RoyalPurple\or Lavender\fi}
\begin{pspicture}[showgrid=true](0,-1.2)(7,1.5)
  \psclip{\psframe[linestyle=none](0,-1.1)(7,1.1)}
  \multido{\in=0+1}{16}{%
    \psplot[algebraic=true, linecolor=\getColor{\in}]{0.1}{7}
    {Derive(\in,Sum(i,0,1,7,(-1)^i*x^(2*i)/Fact(2*i)))}}
  \endpsclip
\end{pspicture}
\egroup
\end{center}

\begin{lstlisting}
\psset{unit=2, algebraic=true, VarStep=true, showpoints=true, VarStepEpsilon=.001}
\def\getColor#1{\ifcase#1 Tan\or RedOrange\or magenta\or yellow\or green\or Orange\or blue\or
  DarkOrchid\or BrickRed\or Rhodamine\or OliveGreen\or Goldenrod\or Mahogany\or
  OrangeRed\or CarnationPink\or RoyalPurple\or Lavender\fi}
\begin{pspicture}[showgrid=true](0,-1.2)(7,1.5)
  \psclip{\psframe[linestyle=none](0,-1.1)(7,1.1)}
  \multido{\in=0+1}{16}{%
    \psplot[algebraic=true, linecolor=\getColor{\in}]{0.1}{7}
    {Derive(\in,Sum(i,0,1,7,(-1)^i*x^(2*i)/Fact(2*i)))}}
  \endpsclip
\end{pspicture}
\end{lstlisting}


\subsection{Special arrow option \texttt{arrowLW}}

Only for the arrowtype \Lnotation{o}, \Lnotation{oo}, \Lnotation{*}, and \Lnotation{**} it is possible to
set the arrowlinewidth with the optional keyword \Lkeyword{arrowLW}.
When scaling an arrow by the keyword \Lkeyword{arrowscale} the width
of the borderline is also scaled. With the optional argument
\Lkeyword{arrowLW} the line width can be set separately and is not
taken into account by the scaling value.

\begin{LTXexample}[width=4cm]
\begin{pspicture}(4,6)
\psline[arrowscale=3,arrows=*-o](0,5)(4,5)
\psline[arrowscale=3,arrows=*-o,
  arrowLW=0.5pt](0,3)(4,3)
\psline[arrowscale=3,arrows=*-o,
  arrowLW=0.3333\pslinewidth](0,1)(4,1)
\end{pspicture}
\end{LTXexample}

\begin{LTXexample}[width=4cm]
\begin{pspicture}(4,6)
\psline[arrowscale=3,arrows=**-oo](0,5)(4,5)
\psline[arrowscale=3,arrows=**-oo,
  arrowLW=0.5pt](0,3)(4,3)
\psline[arrowscale=3,arrows=**-oo,
  arrowLW=0.3333\pslinewidth](0,1)(4,1)
\end{pspicture}
\end{LTXexample}



%--------------------------------------------------------------------------------------
\clearpage
\section{\nxLcs{psforeach} and \nxLcs{psForeach}}
%--------------------------------------------------------------------------------------

The macro \Lcs{psforeach} allows a loop with an individual increment.

\begin{BDef}
\Lcs{psforeach}\Largb{variable}\Largb{value list}\Largb{action}\\
\Lcs{psForeach}\Largb{variable}\Largb{value list}\Largb{action}
\end{BDef}

With \Lcs{psforeach} the \Larg{action} is done inside a group and for \Lcs{psForeach} not.
This maybe useful when using the macro to create tabular cells, which are
alread grouped itself.

\begin{LTXexample}[width=6cm]
\begin{pspicture}[showgrid=true](5,5)
  \psforeach{\nA}{0, 1, 1.5, 3, 5}{%
    \psdot[dotscale=3](\nA,\nA)}
\end{pspicture}
\end{LTXexample}

\begin{LTXexample}[pos=t]
%\usepackage{pst-func}
\makeatletter
\newcommand*\InitToks{\toks@={}}
\newcommand\AddToks[1]{\toks@=\expandafter{\the\toks@ #1}}
\newcommand*\PrintToks{\the\toks@}
\newcommand*{\makeTable}[4][5mm]{%
  \begingroup
    \InitToks%
    \AddToks{\begin{tabular}{|*{#2}{>{\RaggedLeft}p{#1}|}@{}l@{}}\cline{1-#2}}
    \psForeach{\iA}{#3}{\expandafter\AddToks\expandafter{\iA & }}
    \AddToks{\\\cline{1-#2}}%
    \psForeach{\iA}{#3}{\expandafter\AddToks\expandafter{\expandafter%
      \psPrintValue\expandafter{\iA\space /x ED #4} & }}
    \AddToks{\\\cline{1-#2}\end{tabular}}%
    \PrintToks
  \endgroup
}
\makeatother

\sffamily
\psset{decimals=2,valuewidth=7,xShift=-20}
$y=2^x$\\
\makeTable[1cm]{6}{2,4,6,8,10,12}{2 x exp}
\end{LTXexample}

The value List can also be given by the first two and the last value, e.\,g. \verb=1,4,..,31=,
then \PST calculates all values with the distance given by the first two values.

\begin{LTXexample}[pos=t]
\psset{xunit=0.55cm,yunit=2cm}
\begin{pspicture}[showgrid](0,-5mm)(25,1)
  \psforeach{\nA}{0, 3.14,..,25}{\psline(\nA,0)(\nA,1)}
\end{pspicture}
\end{LTXexample}

The internal counter for the steps is named \LCtr{psLoopIndex} and can be used for own purposes.

\begin{LTXexample}[pos=l,width=6cm]
\begin{pspicture}[showgrid=true](5,5)
\psforeach{\nA}{0, 1, 1.5, 2.25, 5}{%
  \psdot[dotscale=3](\the\psLoopIndex,\nA)}
\end{pspicture}
\end{LTXexample}




\part{\nxLPack{pst-node} -- package}

\section{\nxLFile{pst-node.tex}}

The package \LPack{pst-node} now uses the advanced key handling from \LPack{xkeyval}. The reason
why it moved from the base into the contrib sections, where all packages uses \LPack{xkeyval}.

\part{\nxLPack{pst-plot} -- package}

\section{\nxLFile{pst-plot.tex}}

The package \LPack{pst-plot} now uses the advanced key handling from \LPack{xkeyval}. The reason
why it moved from the base into the contrib sections, where all packages uses \LPack{xkeyval}.


\clearpage
\section{List of all optional arguments for \texttt{pstricks}}

\xkvview{family=pstricks,columns={key,type,default}}



\nocite{*}
\bibliographystyle{plain}
\bibliography{PSTricks}

\printindex


\end{document}
