Formula for spiral for chapter decoration.

[Denis Girou]

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The following message is a courtesy copy of an article
that has been posted to comp.text.tex as well.

>>>>> "John.Culleton" == John Culleton <john at ccpl.carr.org> writes:

    John.Culleton> I am fooling with "bookends" for chapter titles in fiction.
    John.Culleton> I wonder if any math-literate person out there has the formula
    John.Culleton> for an increasing spiral around a point. I have in mind a symbolic
    John.Culleton> representation of a roll of paper, viewed from the end of the
    John.Culleton> roll.

    John.Culleton> Given the formula I can then crank it into pstricks or some other
    John.Culleton> graphics package to generate the figure.

  With PSTricks, you can play with the following code and adapt it.

  P.S. * You can easily found solutions using other tools, like Metafont or
MetaPost (Alan Hoenig for instance had published some similar examples in
Metafont).
       * For PSTricks, this code is notably cleaner and more powerful than the
one I show in "Les Cahiers GUTenberg" in 1994.

\documentclass{article}

\usepackage{pst-plot}
\usepackage{pst-text}

\makeatletter

% D.G. addition - Jun.  9, 1998 - Polar plots using the \psplot macro
% Code added according the way suggested by Ulrich Dirr <udirr at das-team.com>

% For polar plots
\newif\ifpolarplot
\def\psset at polarplot#1{\@nameuse{polarplot#1}}
\psset at polarplot{false}

\def\psplot at i#1#2#3{%
  \pst at killglue
  \begingroup
    \use at par
    \@nameuse{beginplot@\psplotstyle}%
% D.G. modification begin - Jun.  9, 1998
    \ifpolarplot
      \addto at pscode{%
        \psplot at init
        /x #1 def
        /x1 #2 def
        /dx x1 x sub \psk at plotpoints div def
        /xy {% Adapted from \parametricplot at i
          #3 dup x cos mul exch x sin mul
          \pst at number\psxunit mul exch
          \pst at number\psyunit mul exch
        } def}%
    \else
% D.G. modification end
      \addto at pscode{%
        \psplot at init
        /x #1 def
        /x1 #2 def
        /dx x1 x sub \psk at plotpoints div def
        /xy {
          x \pst at number\psxunit mul
          #3 \pst at number\psyunit mul
        } def}%
% D.G. modification begin - Jun.  9, 1998
    \fi
% D.G. modification end
    \gdef\psplot at init{}%
    \@pstfalse
    \@nameuse{testqp@\psplotstyle}%
    \if at pst
      \psplot at ii
    \else
      \psplot at iii
    \fi
  \endgroup
  \ignorespaces}

% A \doPerChar style macro adapted from Juergen Schlegelmilch
% (<schlegel at Informatik.Uni-Rostock.de> - posted on c.t.t. Jan. 27, 1998)
\def\doPerChar#1#2#3\@nil{%
#1#2%
\edef\@tempa{#3}%
\ifx\@tempa\empty
\else
\doPerChar#1#3\@nil
\fi}

\def\perChar#1#2{\doPerChar#1#2\@nil}

\newdimen\MyDim
\MyDim=0.7pt

\def\CharacterAction#1{%
\pst at dimtonum{\MyDim}{\@tempa}%
\scalebox{1 \@tempa}{#1}
\advance\MyDim by 0.04pt}

\makeatother

\pagestyle{empty}

\begin{document}

\LARGE

\begin{pspicture}(-3.8,-5)(4.5,4.5)
  \pstextpath{\psplot[linestyle=none,polarplot=true,plotpoints=300,unit=5]
                     {500}{-500}{1 2.7182818 x 200 div exp 1 add div}}% Spiral
             {\perChar{\CharacterAction}{3,14159265358979323846264338327950288%
                                         419716939937510582097494459230781640}}
\end{pspicture}

\end{document}


Denis Girou
-- 
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Centre National de la Recherche Scientifique                             |
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