Getting the page breaks right for a \beginsection macro

Question

I've found this code in the question No indent in the first paragraph in a section in Plain TeX

\def\mysection#1{%
  \goodbreak
  \vskip2\baselineskip
  \noindent #1\par
  \nobreak
  \vskip\baselineskip
  \everypar={{\setbox0\lastbox}\everypar={}}}

but it doesn't stretch the bottom of the page when the page breaks on a new paragraph (here the stretching was found in the skips around the section title).

$The skips around the title are stretched when the page breaks around a \mysection$

So I tried

\def\mysection#1{%
  \filbreak
  \vskip2\baselineskip
  \noindent #1\par
  \nobreak
  \vskip\baselineskip
  \everypar={{\setbox0\lastbox}\everypar={}}}

which now encourages page breaks a bit too much... (The 2nd page was broken before the 3d section) $with \filbreak, the page breaks too easily around a \mysection$

Here is my question: how can I define a \mysection that

breaks the page if (and only if) there is no space for the section title and the first line of the first paragraph of the section;
ends the page with a \hfil if the page is broken on a section title?

Test file:

\def\mysection#1{%
    \filbreak
    %\goodbreak
    \vskip2\baselineskip
    \noindent #1\par
    \nobreak
    \vskip\baselineskip
    \everypar={{\setbox0\lastbox}\everypar={}}}

some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text 

\mysection{Hello world!}
some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text 

\mysection{Nice title!}
some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text 

some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text 

some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text 

\mysection{This one too}
some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text 

some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text 
\bye

@egreg It's a good start but it has some bugs (I reformulated the question) — lvaneesbeeck, Dec 26 '13 at 16:14

egreg · Answer 1 · 2013-12-26T17:37:14.677

Use the same idea as \filbreak, but with a finite plus component:

\def\mysection#1{%
    \par
    \vskip2\baselineskip plus 3\baselineskip
    \penalty-500
    \vskip 0pt plus -3\baselineskip
    \noindent #1\par
    \nobreak
    \vskip\baselineskip
    \everypar={{\setbox0\lastbox}\everypar={}}}

some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text 

\mysection{Hello world!}
some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text 

\mysection{Nice title!}
some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text 

some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text 

some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text 

\mysection{This one too}
some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text 

some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text some text 

\bye

enter image description here

What's the idea of \filbreak? The command issues two \vskip commands with a \penalty in between:

\vskip<specs-a>
\penalty<amount>
\vskip<specs-b>

There are three cases:

No page break is taken at those items
A page break is taken at the first glue
A page break is taken at the penalty

Notice that the second glue is not a feasible page break point, because it's preceded by a penalty, which is a discardable item.

In case 1 the two glues will appear on the page; in case 2 the three items will disappear at the page break; in case 3 the second glue item will disappear.

Now, what does \filbreak do? Its definition is

\par\vfil\penalty-200\vfilneg

where \vfil and \vfilneg are primitives equivalent to

\vskip 0pt plus 1fil

and

\vskip 0pt plus -1fil

respectively. So, in case 1, no vertical space will result, because the infinite components cancel each other. In case 2, nothing will be “seen”. In case 3 only the plus 1fil will act, adding infinite stretchability to the page.

In my variation I use the same penalty as \goodbreak (-500), but the first glue item is 2\baselineskip plus 3\baselineskip and the second glue item is 0pt plus -3\baselineskip. The idea is the same: in case 1 the net amount of glue is 2\baselineskip; in case 2 nothing is seen; in case 3 the amount of stretching is 3\baselineskip, so TeX will be invited not to leave more space than needed for accommodating three lines: the section title, the empty line after it and the first line of the following paragraph. I'd try with two lines, to be honest, in order to avoid a club line.

Can you explain how and why it works? When I do \vskip2\baselineskip plus \vsize \penalty-500 \vskip 0pt plus -\vsize I have the same problem of breaking the 2nd page in the middle. Does it have to do with the fact that 3\baselineskip is the size of "the title + the following white space + the first line of the next paragraph"? — lvaneesbeeck, Dec 26 '13 at 17:16
@lvaneesbeeck With plus \vsize is just the same as plus 1fil, isn't it? With plus 3\baselineskip you add a finite amount of stretchability, so TeX won't be keen into leaving too much text in the next page. — egreg, Dec 26 '13 at 17:18
\the\vsize prints 643.20255pt. If I change plus 3\baselineskip with 100\baselineskip I also have the same problem. — lvaneesbeeck, Dec 26 '13 at 17:22
well you said "let's add a finite stretchability". Okay so if I change the spacing after the title (e.g. for a subsection) the plus component has to be changed accordingly. I was thinking maybe there would be a "clean" way of doing.
I don't think it's strictly necessary to add space for the two first lines of the 1st paragraph since TeX will add a \clubpenalty. But it's safer anyway — lvaneesbeeck, Dec 26 '13 at 18:02
I still don't get why adding too much stretchability breaks pages even when there is space for the section title. Does TeX first try to add skip of the natural with + the natural stretch before analyzing what comes next? — lvaneesbeeck, Dec 26 '13 at 18:48
@lvaneesbeeck No, it doesn't, but makes more desirable to push contents in the next page. — egreg, Dec 26 '13 at 18:51

Getting the page breaks right for a \beginsection macro

1 Answers1