[Programming] Relative coordinates

[Denis Girou]

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  Talking recently with somebody from Italy, I show him the simplification
that using relative coordinates can introduce in some cases.

  Unfortunately relative coordinates are not available in PSTricks!
During some old discussion with Timothy in 1994, he tell me that he absolutely 
agree that this functionality was useful and that he will think to that for a
future version.

  But as we have not this one, I can propose the minimal implementation
I write at this time (I clean it up recently) for people interested. It works
only for cartesian and polar coordinates, but it is the most common cases.

  I think that usage is straightforward looking at these examples.

\documentclass{article}

\usepackage{pstricks}

\newpsobject{showgrid}{psgrid}{subgriddiv=0,gridlabels=6pt}

\makeatletter

% Minimal implementation of relative cartesian and polar coordinates
% (n:m) means add n units in X direction and m in Y direction
% (n!m) means add n units in X direction and b degrees of angle
% Denis Girou (CNRS/IDRIS - France) <Denis.Girou at idris.fr> - 1994/1997
%
% New functions
\def\psaddtoxlength#1#2{%
\let\@psunit\psxunit
\afterassignment\pstunit at off
\advance#1 #2\@psunit}
%
\def\psaddtoylength#1#2{%
\let\@psunit\psyunit
\afterassignment\pstunit at off
\advance#1 #2\@psunit}
%
\def\psaddtoangle#1{\edef\pst at angle{\pst at angle #1 \pst at angleunit add }}
%
\def\RelativeCartesian at coor#1#2{%
\psaddtoxlength\pst at dimg{#1}%
\psaddtoylength\pst at dimh{#2}%
\edef\pst at coor{\pst at number\pst at dimg \pst at number\pst at dimh}}
%
\def\RelativePolar at coor#1#2{%
\psaddtoxlength\pst at dimg{#1}%
\psaddtoangle{#2}%
\edef\pst at coor{\pst at number\pst at dimg \pst at angle \tx at PtoC}}
%
\def\special@@@coor#1;#2;#3\@nil{%
\ifx#3;\relax
\polar at coor{#1}{#2}%
\else
% DG modification begin - 1994
\special@@@@coor#1::\@nil
\fi}
\def\special@@@@coor#1:#2:#3\@nil{%
\ifx#3:\relax
\RelativeCartesian at coor{#1}{#2}%
\else
\special@@@@@coor#1!!\@nil
\fi}
\def\special@@@@@coor#1!#2!#3\@nil{%
\ifx#3!\relax
\RelativePolar at coor{#1}{#2}%
\else
% DG modification end
\cartesian at coor#1,\relax,\@nil
\fi}

\makeatother

\begin{document}

\begin{pspicture}(4,4)
  \showgrid
  \SpecialCoor
  \psline[linecolor=blue]{->}(2,3)(3,2)(2,0)
  \psline[linecolor=red]{->}(0,2)(2:-1)(4,4)(-2:0)
  \psline[linecolor=green]{->}(2,2)(-1:-2)(3:2)(-1:1)
  \psframe[linewidth=1mm](2,2)(1:1)
\end{pspicture}
\hspace{1cm}
\begin{pspicture}(4,4)
  \showgrid
  \SpecialCoor
  \psset{xunit=2}
  \pspolygon[linecolor=blue](1,3)(1.5,2)(0.5,1)
  \pspolygon[linecolor=green](1,2)(-0.5:-2)(1.5:2)(-0.5:1)
\end{pspicture}

\vspace{1cm}
\begin{pspicture}(4,4)
  \showgrid
  \SpecialCoor
  \pscurve[linecolor=blue]{->}(2,3)(3,2)(1,1)
  \pscurve[linecolor=green]{->}(2,2)(-1:-2)(3:2)(-1:1)
\end{pspicture}
\hspace{1cm}
\begin{pspicture}(4,4)
  \showgrid
  \SpecialCoor
  \psline[linecolor=blue]{->}(2;30)(3;60)(1;30)
  \pscurve[linecolor=green]{->}(2;30)(1!30)(-2!-30)
  \psline[linecolor=red]{->}(0;0)(3!90)(0!-90)(2!45)
\end{pspicture}

\vspace{1cm}
\begin{pspicture}(4,4)
  \showgrid
  \SpecialCoor
  \psline[linecolor=blue]{->}(2;30)(4;60)(1;30)
  \psline[linestyle=dotted,dotsep=2mm]{->}(2;30)(2!30)(-3!-30)
\end{pspicture}
\hspace{1cm}
\begin{pspicture}(4,4)
  \showgrid
  \SpecialCoor
  \degrees[4]
  \psline[linecolor=blue]{->}(3;0)(4;1)(0;2)
  \psline[linestyle=dotted,dotsep=2mm]{->}(3;0)(1!1)(-4!1)
\end{pspicture}

\end{document}

D.G.

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