Optimal arrangement of pictures/boxes in a page

Question

Does anybody come up with a way to automatically arrange a few figures or boxes in a larger rectangle or page?

Here it is a real world example: One is producing a beamer presentation. One has 4 or 5 ready made figures, of different aspect ratios. And wants to distribute the figures regardless of any special order but want the slide to more or less fill up and the height or width of each figure to adjust "nicely" and not necessarily regular or rectangular.

The idea is to minimize the unused space and/or make the pictures align/resize nicely. But Doing this manually requires a lot of error and trial and keeping track of similar forced width or height of nearby images.

For example, Google Images and Google+ uses this technique to optimize the space taken by images and posts:

Fake code (will display 5 things automatically arranged, sequential order may be lost):

\begin{frame}
\begin{arrangedfigure}[5] %five boxes/images
\includegraphics{fig1} &
\includegraphics{fig2} &
\includegraphics{fig3} &
\minipage{text} &
\includegraphics{fig4}
\end{arrangedfigure}
\end{frame}

Related questions, dealing with this but not in an automatic way:

Special arrangement of subfigures

What is the best way of arranging multiple minipages on a page?

How to arrange a figure consisting of four subfigures?

Answer 1

I'm using the method developed in Making the text fit in a specific space in Latex to explore various aspects to this question. I am not rearranging any items, but am assuming that I have a string of N images that I am being asked to stuff into a certain size rectangle.

I am treating each image as text, and allowing line breaking to create the rows. So far, I've tried three version.

1) The raw version, relative figure sizes stay as given

2) make all figures same height

3) manually tweak the scaling, in an informal effort to avoid vast disparities in figure height and width, and to not leave last line largely un-full.

I have drawn a box around the image to help us gauge whether the boxes are overfull. REVISED to use \raggedright and \hfill to successfully avoid overrunning margins.

\documentclass{article}
\usepackage{scalerel}
\usepackage{fp}
\usepackage{xcolor}
\usepackage{fancyhdr}
\pagestyle{fancy}
\newcount\boxheight
\newcount\boxwidth
\newlength\constrainedwidth
\newsavebox\testbox
\newlength\currentwidth

\newcommand\aspect[1]{%
  \boxheight=\ht#1\relax%
  \boxwidth=\wd#1\relax%
  \FPdiv\testaspect{\the\boxheight}{\the\boxwidth}%
%\testaspect\\%                  COMMENT THIS LINE TO REMOVE ASPECT-RATIO PRINTS
}
% TARGET-HEIGHT, TARGET-WIDTH, CONTENT, GUESS>NATURAL-WIDTH, dWIDTH
\newcommand\constraintext[5]{%
  \def\svfboxsep{\the\fboxsep}%
  \setlength\fboxsep{0pt}%
  \setlength\constrainedwidth{#2}%
  \sbox\testbox{\rule{#2}{#1}}%
%TARGET ASPECT RATIO\\%          COMMENT THIS LINE TO REMOVE COMMENT
%V\\%                            COMMENT THIS LINE TO REMOVE COMMENT
  \aspect{\testbox}%
  \edef\aspectratio{\testaspect}%
  \constrainsize{#1}{\aspectratio}{#3}{#4}{#5}%
  \setlength\fboxsep{\svfboxsep}%
}
\newcommand\constrainsize[5]{%
  \sbox{\testbox}{\fbox{\begin{minipage}[b]{#4}{#3}\end{minipage}}}%
  \aspect{\testbox}%
  \FPiflt{\testaspect}{#2}%
    \setlength{\currentwidth}{#4}%
    \addtolength{\currentwidth}{-#5}%
    \constrainsize{#1}{#2}{#3}{\currentwidth}{#5}%
  \else
    \setlength\constrainedwidth{#1}%
    \FPdiv\result{1.0}{#2}%
%RESET ANY OTHER COUNTERS, TO AVOID ITERATION CREEP
   \setcounter{section}{0}%
   \setcounter{figure}{0}%
%                               CHANGE \framebox TO \makebox TO REMOVE FRAME
    \framebox[\result\constrainedwidth]{\hfill%
      \scaleto{\begin{minipage}[b]{\currentwidth}\raggedright #3\end{minipage}}{#1}%
      \hfill%
    }%
  \fi%
}

\newsavebox\Ab
\newsavebox\Bb
\newsavebox\Cb
\newsavebox\Db
\newsavebox\Eb
\newsavebox\Fb

\def\A{\usebox{\Ab}\hfill}
\def\B{\usebox{\Bb}\hfill}
\def\C{\usebox{\Cb}\hfill}
\def\D{\usebox{\Db}\hfill}
\def\E{\usebox{\Eb}\hfill}
\def\F{\usebox{\Fb}\hfill}

\def\AA{\textcolor{green}{\rule{3in}{2in}}}
\def\BB{\textcolor{red}{\rule{2in}{1in}}}
\def\CC{\textcolor{cyan!50}{\rule{1.75in}{2in}}}
\def\DD{\textcolor{blue!40}{\rule{1.5in}{2in}}}
\def\EE{\textcolor{blue}{\rule{2.25in}{2.25in}}}
\def\FF{\textcolor{red!20}{\rule{2.5in}{1.5in}}}

\def\testcase{%
  \centering\constraintext{.999\textheight}{.999\textwidth}{%
  \A\B\C\F\D\E%
  \B\C\A\E\D\F%
  \D\B\F\C\A\E%
  \E\F\D\C\A\B%
  \F\C\B\D\E\A%
  }{3\textheight}{1ex}%May have to increase next-to-last argument if divide by 0
  \clearpage
}
\begin{document}
\fancyhead[c]{Method 1: All images remain the same relative size}
\savebox{\Ab}{\AA}
\savebox{\Bb}{\BB}
\savebox{\Cb}{\CC}
\savebox{\Db}{\DD}
\savebox{\Eb}{\EE}
\savebox{\Fb}{\FF}
\testcase

\fancyhead[c]{Method 2: All images scaled to the same height}
\savebox{\Ab}{\AA}
\savebox{\Bb}{\scalerel*{\BB}{\AA}}
\savebox{\Cb}{\scalerel*{\CC}{\AA}}
\savebox{\Db}{\scalerel*{\DD}{\AA}}
\savebox{\Eb}{\scalerel*{\EE}{\AA}}
\savebox{\Fb}{\scalerel*{\FF}{\AA}}
\testcase

\fancyhead[c]{Method 3: Manually Scale images}
\savebox{\Ab}{\scalebox{.98}{\AA}}
\savebox{\Bb}{\scalebox{1.8}{\BB}}
\savebox{\Cb}{\scalebox{1.0}{\CC}}
\savebox{\Db}{\scalebox{1.0}{\DD}}
\savebox{\Eb}{\scalebox{.95}{\EE}}
\savebox{\Fb}{\scalebox{1.05}{\FF}}
\testcase
\end{document}

---

EDIT: To answer the OP's question about vertical centering of the figures, it can be done by defining the images as centered about the baseline. In the case of \includegraphics, it would require a \raisebox of minus 1/2 the image height. In the case of my MWE, the down shift of \rules can be obtained with the optional argument.

\def\AA{\textcolor{green}{\rule[-1in]{3in}{2in}}}
\def\BB{\textcolor{red}{\rule[-.5in]{2in}{1in}}}
\def\CC{\textcolor{cyan!50}{\rule[-1in]{1.75in}{2in}}}
\def\DD{\textcolor{blue!40}{\rule[-1in]{1.5in}{2in}}}
\def\EE{\textcolor{blue}{\rule[-1.125in]{2.25in}{2.25in}}}
\def\FF{\textcolor{red!20}{\rule[-.75in]{2.5in}{1.5in}}}