Is it possible to place floats some lines from top (or bottom) of page?

Question

Question: I wonder if it is possible to kindly tell LaTeX to put floats (automatically) either 1) some lines from the top of the page or 2) some lines from bottom of the page?

To clarify:

• I know about the htbpH options of floats, none of them do what I'm asking for.
• I still want the floats to float.
• I don't have anything against if the floats appear in the middle of a paragraph, otherwise the H option would have been OK.
• I am aware of this question, where it is asked where to put floats for a high typographic standard (but not how to do that in TeX).
• I am somewhat aware of that TeX works very much with paragraphs, and that it might be a reason this is not possible. If so, that is an acceptable answer.

Background

In the nice typographical guide (in Swedish) "Sättningsregler" by W. N. Lansburgh (1961) it is suggested to place images like described above. Also, this is something one happens to find in older (pre TeX) books. Below, you find two example images I scanned from a book from 1904 where this placement is in action. (Hopefully with sufficiently low resolution, so that I do not violate some copyright law.)

Example images

Answer 1

So.. this just redefines b doing t as well would just be twice as much work (but too much for tonight:-) adding new "variant b" , say B while leaving the original b untouched would be possible but quite a bit more work as you'd need to find all the places where latex thinks it "knows" about the possible float areas and make it know about two more.

It basically lets the standard algorithm work, so leaving space for a float at the bottom of the page, then it vsplits the page arbitrarily 5 baselines up from the bottom, this may not actually split at that point, as it may be an equation or image or anything, but it will split somewhere and the figure is slotted in, note it uses half \textfloatsep above and below the figure (so the space adds up without having to make too many changes to latex, so you might want to increase that value....

three new "almost b" floats and one t

\documentclass[a4paper]{article}
\renewcommand\bottomfraction{.7}
\setcounter{bottomnumber}{1}% article default but don't change it:-)

\makeatletter
\def \@cflb {%
    \let\@elt\@comflelt
    \setbox\@tempboxa \vbox{}%
    \@botlist
    \setbox\@outputbox \vbox{%
%start of change
\setbox\tw@\vsplit\@outputbox to\dimexpr\ht\@outputbox-5\normalbaselineskip\relax
\unvbox\tw@
\vskip .5\textfloatsep
\unvbox\@tempboxa
\vskip -\floatsep
\vskip .5\textfloatsep
\unvbox\@outputbox
%end of change
                             }%
    \let\@elt\relax
    \xdef\@freelist{\@freelist\@botlist}%
    \global \let \@botlist\@empty
}
\makeatother



\errorcontextlines1000
\def\a{One \refstepcounter{enumi}\theenumi\ two \Roman{enumi}, three four chicken dug dog elephant penguin,\ifnum\value{enumi}<27\ \alph{enumi}\fi. }
\def\b{\a\a\a\a\begin{equation}\theenumi+1=\refstepcounter{enumi}\theenumi\end{equation}\a\a\a\ifodd\value{enumi}\a\a\fi\par}
\def\c{\a\a\b\a\a\b\b\a}
\newcommand\f[2][b]{\begin{figure}[#1]\centering\rule{5cm}{\ifodd\value{figure} 3cm\else6cm\fi}\caption{#2}\end{figure}}
\begin{document}

\a
\f[b]{zz}
\c
\c

\f{qq}
\a
\f{jj}
\f[tp]{ttt}
\b

\c\c
\end{document}