Non-rectangular body geometry

Question

I'd love to typeset a document where the inner margin follows a sinuous path. For example, like the one below (done in Scribus).

I tried wrapping the text around a curvy image set at the appropriate location, but that didn't work, obviously, since images are always rectangular, right?

I checked in the documentation of package geometry if one could define a \rightmargin that would be dependent on some other variable (like line-number), but I didn't find anything.

Google and tex.stackexchange searches for any number of combinations of relevant-sounding terms yielded nothing.

I'm ready to use luatex or whatever (ideally, I'd like to use microtype too). Any help much appreciated!

EDIT: Ideally the solution wouldn't require manual tuning, apart from giving the initial shape of the "curvy" margin. Indeed, I'd like to use it for a little book of about 60 pages. The problem with \shapepar (or \cutout, or even \parshape for that matter) is that it has to be fine-tuned for each individual paragraph, knowing beforehand the length of the text and the paragraph's position on the page (also, a paragraph split over two pages seems to be pretty tough to handle).

Answer 1

This version tries to take into account the vertical spaces taken up by sections; might even work with figures, tables, etc... (untested).

\documentclass[a4paper]{article}

\def\LINESPERPAGE{45}
\usepackage[textheight=\LINESPERPAGE\baselineskip]{geometry}

\usepackage{lipsum}
\usepackage{xinttools}% requires version 1.09m or later

% \edef\MOCKSINE {%
% {0pt \the\dimexpr\textwidth-3em}%
% {0pt \the\dimexpr\textwidth-4em}%
% {0pt \the\dimexpr\textwidth-5em}%
% {0pt \the\dimexpr\textwidth-5.75em}%
% {0pt \the\dimexpr\textwidth-6em}%
% {0pt \the\dimexpr\textwidth-5.75em}%
% {0pt \the\dimexpr\textwidth-5em}%
% {0pt \the\dimexpr\textwidth-4em}%
% {0pt \the\dimexpr\textwidth-3em}%
% {0pt \the\dimexpr\textwidth-2em}%
% {0pt \the\dimexpr\textwidth-1em}%
% {0pt \the\dimexpr\textwidth-0.25em}%
% {0pt \the\dimexpr\textwidth-0em}%
% {0pt \the\dimexpr\textwidth-0.25em}%
% {0pt \the\dimexpr\textwidth-1em}%
% {0pt \the\dimexpr\textwidth-2em}%
% }

% let's divide by two the sizes of the undulation.
\edef\MOCKSINE {%
{0pt \the\dimexpr\textwidth-1.5em}%
{0pt \the\dimexpr\textwidth-2em}%
{0pt \the\dimexpr\textwidth-2.5em}%
{0pt \the\dimexpr\textwidth-2.875em}%
{0pt \the\dimexpr\textwidth-3em}%
{0pt \the\dimexpr\textwidth-2.875em}%
{0pt \the\dimexpr\textwidth-2.5em}%
{0pt \the\dimexpr\textwidth-2em}%
{0pt \the\dimexpr\textwidth-1.5em}%
{0pt \the\dimexpr\textwidth-1em}%
{0pt \the\dimexpr\textwidth-.5em}%
{0pt \the\dimexpr\textwidth-0.125em}%
{0pt \the\dimexpr\textwidth-0em}%
{0pt \the\dimexpr\textwidth-0.125em}%
{0pt \the\dimexpr\textwidth-.5em}%
{0pt \the\dimexpr\textwidth-1em}%
}


\makeatletter

\edef\MCK@LINESPERPAGE {\the\numexpr \LINESPERPAGE\relax }

\def\MCK@LINECOUNT {0}

\def\SETUPPARSHAPE {%
  \xdef\MCK@tmpB {\the\numexpr \pagetotal/\baselineskip}%
  \ifnum\MCK@tmpA>\MCK@tmpB
  % assume we are on a new page. !!!Something more robust should be done here!!!
  \xdef\MCK@LINECOUNT
   {\the\numexpr\MCK@LINECOUNT+\MCK@tmpB-\MCK@tmpA+\MCK@LINESPERPAGE}%
  \else
  \xdef\MCK@LINECOUNT {\the\numexpr\MCK@LINECOUNT+\MCK@tmpB-\MCK@tmpA}%
  \fi
  \global\let\MCK@tmpA\MCK@tmpB   
  \edef\STARTINDEX {\the\numexpr\MCK@LINECOUNT+16-16*((\MCK@LINECOUNT+8)/16)}%
  \parshape 16 \xintListWithSep { }{\xintTrim \STARTINDEX\MOCKSINE}
               \xintListWithSep { }{\xintKeep \STARTINDEX\MOCKSINE} \relax
}

\def\STARTUNDULATIONS {\def\MCK@LINECOUNT {0}\def\MCK@tmpA {0}%
    \def\par {\oldpar \SETUPPARSHAPE }\SETUPPARSHAPE }
\def\STOPUNDULATIONS {\let\par\oldpar }
\makeatother

\let\oldpar\par
\AtBeginDocument {\STARTUNDULATIONS }

\begin{document}

\newcount\cnta
\cnta1
\loop

\section{This is a section}
\lipsum [\cnta-\numexpr\cnta+3\relax]
\section{This is another section}
\lipsum [\numexpr\cnta+3\relax-\numexpr\cnta+7\relax]

\advance\cnta 8
\ifnum\cnta < 50
\repeat
\end{document}

---

FIRST ANSWER

First two pages:

This will be broken by almost anything I guess. And \everypar is un-usable as it will also be often overwritten I am afraid.

\documentclass{article}
% \usepackage[english]{babel}
% \usepackage{blindtext}
\usepackage{lipsum}
\usepackage{xinttools}% requires version 1.09m or later

\edef\MOCKSINE {%
{0pt \the\dimexpr\textwidth-3em\relax}%
{0pt \the\dimexpr\textwidth-4em\relax}%
{0pt \the\dimexpr\textwidth-5em\relax}%
{0pt \the\dimexpr\textwidth-5.75em\relax}%
{0pt \the\dimexpr\textwidth-6em\relax}%
{0pt \the\dimexpr\textwidth-5.75em\relax}%
{0pt \the\dimexpr\textwidth-5em\relax}%
{0pt \the\dimexpr\textwidth-4em\relax}%
{0pt \the\dimexpr\textwidth-3em\relax}%
{0pt \the\dimexpr\textwidth-2em\relax}%
{0pt \the\dimexpr\textwidth-1em\relax}%
{0pt \the\dimexpr\textwidth-0.25em\relax}%
{0pt \the\dimexpr\textwidth-0em\relax}%
{0pt \the\dimexpr\textwidth-0.25em\relax}%
{0pt \the\dimexpr\textwidth-1em\relax}%
{0pt \the\dimexpr\textwidth-2em\relax}%
}

\def\LINECOUNT {0}

\def\SETUPPARSHAPE {%
 \xdef\LINECOUNT  {\the\numexpr\LINECOUNT+\prevgraf}%
 \edef\STARTINDEX {\the\numexpr\LINECOUNT+16-16*((\LINECOUNT+8)/16)}%
 \parshape 16 \xintListWithSep { }{\xintTrim \STARTINDEX\MOCKSINE}
              \xintListWithSep { }{\xintKeep \STARTINDEX\MOCKSINE} \relax
}


\let\oldpar\par
\AtBeginDocument {\def\par {\oldpar \SETUPPARSHAPE }

\begin{document}
\SETUPPARSHAPE 
\lipsum [1-20]
\end{document}

% problems with \blindtext
% \blindtext [10]
% I don't know why.