How does a figure's height influence its positioning?

Question

Sometimes a figure I want to place at the bottom of a page is placed on the next page regardless of the available space. I, finally, did some testing and realized that the height of a figure may not be more than 25% of the \textheight for it to be placed at the bottom. And, at least in my tests, it may not exceed 65% of the \textheight to be placed at the top.

UPDATE: As described by the comments and the linked explanation of the placing algorithm in most cases adding ! to the positioning parameters should solve the problem. Following a working example with bottom positioning and a page of follow-up text:

\documentclass{article}
\usepackage{graphicx}
\usepackage{lipsum}
\begin{document}
Some text here.
\begin{figure}[!b]%
\includegraphics[draft, height=0.40\textheight, width=0.6\columnwidth]{example-image}%
\centering
\caption{Relaxing constraints with !, this figure (40% textheight) 
    will be placed at the bottom, too.}%
\label{}%
\end{figure}
\lipsum[1-5]
\end{document}

However, in my original document, the text and figure is followed by a minipage which does not fit into the same page and needs to be placed on the next page (in fact, it is a rather lengthy lstlisting which I don't want to break up). Adding such a minipage to the above code yields strange behavior. The figure is placed on the first page but not at the bottom. Instead it seems to behave as if the h positioning has been used:

\documentclass{article}
\usepackage{graphicx}
\usepackage{lipsum}
\begin{document}
Some text here.
\begin{figure}[!b]%
\includegraphics[draft, height=0.40\textheight, width=0.6\columnwidth]{example-image}%
\centering
\caption{Relaxing constraints with !, this figure (40% textheight) 
    will be placed at the bottom, too.}%
\end{figure}
\begin{minipage}{\linewidth}
\lipsum[1-5]
\end{minipage}
\end{document}

The same behavior can be observed when I add the text without a minipage but trigger a pagebreak before the lipsum. I assume minipage may introduce a pagebreak or equivalent if it doesn't fit onto a page.

Last but not least, a clearpage before the minipage solves the problem and places the figure at the bottom while, as far as I understand the algorithm, a figure may only be placed on subsequent pages when the layouter reaches a clearpage:

\documentclass{article}
\usepackage{graphicx}
\usepackage{lipsum}
\begin{document}
Some text here.
\begin{figure}[!b]%
\includegraphics[draft, height=0.40\textheight, width=0.6\columnwidth]{example-image}%
\centering
\caption{Relaxing constraints with !, this figure (40% textheight) 
    will be placed at the bottom, too.}%
\label{}%
\end{figure}
\clearpage
\begin{minipage}{\linewidth}
\lipsum[1-5]
\end{minipage}
\end{document}

I love such corner cases as I constantly seem to run into them in every aspect of my life. Maybe someone can explain what happens here and how to deal with the situation in a way which does not fall back on you ten pages later in the document ;)

Best wishes, Stefan

Answer 1

Adding such a minipage to the above code yields strange behavior. The figure is placed on the first page but not at the bottom. Instead it seems to behave as if the h positioning has been used:

This is a misunderstanding of b which does not imply flush to bottom of the page, but rather "place below the text" so as the page is short, the image, even using b, is relatively high on the page.

if you add \flushbottom to the preamble you get

Although as there is no available stretchy space on that page you are warned

Underfull \vbox (badness 10000) has occurred while \output is active

Note you should not routinely use ! as in [!b] as ! means "ignore user-set constraints on this instance" It is better to set more suitable constraints, eg set \bottomfraction to 0.7 rather than 0.3, then use [bp]

I assume minipage may introduce a pagebreak or equivalent if it doesn't fit onto a page.

minipage has no positioning or spacing code at all, it simply works like a large letter. If a minipage does not fit then the page break may be needed but as in the example here, no special glue or penalties are added so the spacing depends on any other glue that may be on the page.