Difficulty finding the vertical distances between two lines of content

Question

I'm trying to determine the vertical distance between boxes and a line of text in the immediately following paragraph. Depending on the content of the top box I'm getting a discrepancy of \lineskip.

Here's my not so minimal MWE. I put a lot of colored lines in to help illustrate baselines (blue), struts (orange), depths (purple), and distances between lines (black).

\documentclass{article}
\usepackage{xcolor}
%% set `\parskip` to non-trivial value
\setlength{\parskip}{2ex}
%% --- CREATING A STRUT ---
%% strut to equalize line heights of the two boxes designed to be variable
%% if `\aestrutht` is set to `0.7\baselineskip` there's a `\lineskip` discrepency
%% if `\aestrutht` is set to `0.8\baselineskip` there's no apparent discrpency
\newlength{\aestrutht}
\setlength{\aestrutht}{0.7\baselineskip}
\newlength{\aestrutdp}
\setlength{\aestrutdp}{0.3\baselineskip}
%% first rule is to prevent `\color` from screwing things up!
\newcommand{\aestrut}{%%'
  \rule{0pt}{0pt}%%'
  {%%'
    \color{orange}%%'
    \rule[-\aestrutdp]{2pt}{\dimexpr\aestrutdp+\aestrutht\relax}%%'
  }}
%% --- MAKING THE BASELINES VISIBLE ---
\newcommand{\aeshowbaseline}
  {%%'
    \bgroup
      \color{blue}%%'
      \raisebox{0pt}[0pt][0pt]{%%'
        \makebox[0pt][l]{%%'
          \rule{0.1pt}{\aestrutht}%%'
          \rule{2in}{0.1pt}%%'
        }%%'
      }%%'
    \egroup
  }
%% --- CREATING BOX FOR TOP MATTER ---
%% placed in a box so I can measure its height and depth
\newsavebox{\aebox}
\newcommand{\aeTopMatter}[1]{%%'
  \begin{lrbox}{\aebox}
    \begin{minipage}[t]{1in}
      \raggedright
      \aestrut
      \aeshowbaseline #1
      %%\par\rule{0pt}{0pt}
    \end{minipage}
  \end{lrbox}\usebox{\aebox}}%%'
%%---------------------------------------------------------------------------------
%% --- CREATING BOTTOM MATTER ---
\newcommand{\aeBottomMatter}{%%'
  \hspace*{0.95in}%%'
  \aestrut
  \aeshowbaseline
  \hspace*{1em}%%'
  More text}
%% --- MACRO TO SHOW DEPTH OF TOP BOX ---
\newcommand{\aeShowDepthOfTopMatter}{%%'
  \llap{\color{purple}%%'
    \rule[-\dp\aebox]{1in}{0.1pt}%%'
    \rule[-\dp\aebox]{0.1pt}{\dp\aebox}}}
%% --- MACRO TO SHOW DISTANCE BETWEEN TWO LINES ---
\newcommand{\aeShowDistanceBetweenLines}{%%'
  \raisebox{0pt}[0pt][0pt]{%%'
    \rule{2pt}{\dimexpr\parskip+\dp\aebox+\lineskip+\aestrutht}}}
\begin{document}

\aeTopMatter{Hello World}\aeShowDepthOfTopMatter

\aeBottomMatter\aeShowDistanceBetweenLines

\vspace{0.25cm}

\aeTopMatter{Hello My World}\aeShowDepthOfTopMatter

\aeBottomMatter\aeShowDistanceBetweenLines

\vspace{0.25cm}

\aeTopMatter{Hello World to this hardy world}\aeShowDepthOfTopMatter

\aeBottomMatter\aeShowDistanceBetweenLines

\end{document}

I know two possible ways of fixing thing:

1. I could set the height of \aestrutht a bit bigger
2. I could uncomment the line \par\rule{0pt}{0pt}

I don't understand why either of these work. In the case of the first, my difficulty revolves around the fact that, given how the height of my strut is already set, it is well above the height of any content on the line. So it seems to me I shouldn't need any more boost.

What I would appreciate knowing is why these two fixes work and why there's only a \lineskip in the third case but not the first two.

For a while I thought this might be related to measuring \prevdepth such as using

\par\xdef\tpd{\theprevdepth}

But that gets convoluted with the depth of the top box and generally doesn't seem useful.

Answer 1

This is a case of the same situation that was asked in How to keep a constant baselineskip when using minipages (or \parboxes)? and answered by egreg:

Basically, since minipages with t alignment are used, in the third case, the value of the sum of the depth and the height of the box is responsible for the insertion of the \lineskip glue; in the first two cases, the value of the sum doesn't force the insertion of the glue (for the details of the calculations involved, refer to egreg's excellent answer).

Let's have a look at the height and depth of the boxes involved and let's kill \lineskip:

\documentclass{article}
\usepackage{xcolor}


\newlength\BoxDp
\newlength\BoxHt
%% set `\parskip` to non-trivial value
\setlength{\parskip}{2ex}
%% --- CREATING A STRUT ---
%% strut to equalize line heights of the two boxes designed to be variable
%% if `\aestrutht` is set to `0.7\baselineskip` there's a `\lineskip` discrepency
%% if `\aestrutht` is set to `0.8\baselineskip` there's no apparent discrpency
\newlength{\aestrutht}
\setlength{\aestrutht}{0.7\baselineskip}
\newlength{\aestrutdp}
\setlength{\aestrutdp}{0.3\baselineskip}
%% first rule is to prevent `\color` from screwing things up!
\newcommand{\aestrut}{%%'
  \rule{0pt}{0pt}%%'
  {%%'
    \color{orange}%%'
    \rule[-\aestrutdp]{2pt}{\dimexpr\aestrutdp+\aestrutht\relax}%%'
  }}
%% --- MAKING THE BASELINES VISIBLE ---
\newcommand{\aeshowbaseline}
  {%%'
    \bgroup
      \color{blue}%%'
      \raisebox{0pt}[0pt][0pt]{%%'
        \makebox[0pt][l]{%%'
          \rule{0.1pt}{\aestrutht}%%'
          \rule{2in}{0.1pt}%%'
        }%%'
      }%%'
    \egroup
  }
%% --- CREATING BOX FOR TOP MATTER ---
%% placed in a box so I can measure its height and depth
\newsavebox{\aebox}
\newcommand{\aeTopMatter}[1]{%%'
  \begin{lrbox}{\aebox}
    \begin{minipage}[t]{1in}
      \raggedright
      \aestrut
      \aeshowbaseline #1
      %%\par\rule{0pt}{0pt}
    \end{minipage}
  \end{lrbox}\usebox{\aebox}%
\settoheight\BoxHt{\usebox{\aebox}}%
\settodepth\BoxDp{\usebox{\aebox}}%
Box ht: \the\BoxHt~%
Box dt: \the\BoxDp%
}%%'
%%---------------------------------------------------------------------------------
%% --- CREATING BOTTOM MATTER ---
\newcommand{\aeBottomMatter}{%%'
  \hspace*{0.95in}%%'
  \aestrut
  \aeshowbaseline
  \hspace*{1em}%%'
  More text}
%% --- MACRO TO SHOW DEPTH OF TOP BOX ---
\newcommand{\aeShowDepthOfTopMatter}{%%'
  \llap{\color{purple}%%'
    \rule[-\dp\aebox]{1in}{0.1pt}%%'
    \rule[-\dp\aebox]{0.1pt}{\dp\aebox}}}
%% --- MACRO TO SHOW DISTANCE BETWEEN TWO LINES ---
\newcommand{\aeShowDistanceBetweenLines}{%%'
  \raisebox{0pt}[0pt][0pt]{%%'
    \rule{2pt}{\dimexpr\parskip+\dp\aebox+\lineskip+\aestrutht}}}
\begin{document}

\offinterlineskip
\aeTopMatter{Hello World}\aeShowDepthOfTopMatter

\aeBottomMatter\aeShowDistanceBetweenLines

\vspace{0.25cm}

\aeTopMatter{Hello My World}\aeShowDepthOfTopMatter

\aeBottomMatter\aeShowDistanceBetweenLines

\vspace{0.25cm}

\aeTopMatter{Hello World to this hardy world}\aeShowDepthOfTopMatter

\aeBottomMatter\aeShowDistanceBetweenLines

\end{document}

In the example I used \offinterlineskip to prevent interline glue globally, but one could use \nointerlineskip instead, where appropriate, to prevent interline glue insertion once.