TeX typesetting

Orphans and widows. On this subject Tschichold wrote:

"Doubtless all textbooks of typesetting warn that the exit line of a paragraph at the head of a book page must be avoided at all cost. /.../ Is there really nothing we can tighten a little, or space out perhaps? Possibly we can save a line at the beginning of the chapter by moving the first paragraph up? The best method is to simply shorten the preceding page by a line."

Bringhurst wrote:

"Balance facing pages not by adding extra lead or puffing up the word space, but by exporting or importing single lines to and from the preceding or following spreads. The same technique is used to avoid widows, and to extend or shorten any chapters that would otherwise end with a meager few lines on the final page."

In TeX we can set \widowpenalty (and \clubpenalty) to 10000 and if we have vertically stretchable material on the page the type area will get it's height, but lines will not match across the spread. Without strechable material that page will be a line shorter but the spread will be unbalanced in height instead.

So if we want this hands-on method of dealing with widows, we need a macro to carefully extend or shorten pages, preferably without being too intrusive and spread out in the code.

Luckily, Petr Olsak has a macro like this for OpTeX: https://petr.olsak.net/optex/optex-tricks.html#widows

For my purposes, I like the page number to be at a set distance from the type area instead of a set distance from the page bottom, so I could remove some code, and ended up with this example for plain:

% For this example, the document normally has 5 lines per page
\vsize=\topskip \advance\vsize by 4\baselineskip

% Backup original vsize 
\newdimen\originalvsize \originalvsize=\vsize

% Macro that defines another macro on the form \ap:<pageno>, 
% which expands to how many lines should be adjusted.
% Example: \adjustpage{15}{+1} defines \ap:15 which expands to +1.
\def\adjustpage#1#2{%
	\expandafter\xdef\csname ap:#1\endcsname{#2}
	\ifnum #1=1
		\setvsize
	\fi
}

% For use in the output routine
\def\setvsize{%
	\global\vsize=\originalvsize
	\ifcsname ap:\the\pageno\endcsname
		\global\advance \vsize by \csname ap:\the\pageno\endcsname \baselineskip
	\fi
}

% \setvsize needs to be expanded after page number has been incremented, but before the next typeset material.
\output{\plainoutput \setvsize}

%%%%%%%%%%%%%%%%%%%

% No penalty since we're dealing with widows manually now
\widowpenalty=0
\clubpenalty=0

% This adjusts the 2-3 spread to have one extra line on each page
\adjustpage{2}{+1} \adjustpage{3}{+1}

% Test text, some paragraphs of Lorem ipsum
\input lipsum

\bye