Tikz: Add text to lines using `\draw` and connect lines

Question

I have a box and two additional lines. Now I want to add some text horizontally aligned to the lines halfway. I did not find any useful examples which were not too complicated.

Another problem I am trying to solve is that I want to connect the vertical line with the box. Why is there a small distance? How can I get rid of it? And why do the two lines not connect in the middle of the box? How can I solve this?

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{trees}
\begin{document}
\begin{figure}[h]
\begin{center}
\begin{tikzpicture}
\draw (0,0) -- (4,0) -- (4,4) -- (0,4) -- (0,0);
\node at (-4,3) (nodeXi) {$x_i$};
\node at (2,2) (nodeXj) {$x_j$};
\node at (2,4) (nodeD) {};
\draw (nodeXi) -- (nodeXj);
\draw (nodeXj) -- (nodeD);
\end{tikzpicture}
\end{center}
\caption{A meaningful caption}
\end{figure}
\end{document}

Answer 1

When you create a node, it has a rectangular shape by default and a positive inner sep which pads the contents. Even if the node is empty, it therefore has size.

When you draw from or to a node, TikZ calculates the nearest point on the node's border and draws to or from that. You can see what is going on by adding a drawing command to all the nodes in the picture:

There are various ways to avoid this effect when it is unwanted. One is to specify that the node have the coordinate shape so that it has no size.

\node [coordinate] ...;
\coordinate ...;

Another is to specify the anchor you want the drawing command to begin or end at.

\draw ... (<node>.<anchor>) ...;

For example,

  \draw (nodeXi.center) -- (nodeXj.center);
  \draw (nodeXj.center) -- (nodeD.center);

\documentclass[border=10pt,tikz]{standalone}
\begin{document}
\begin{tikzpicture}[every node/.append style={draw=red}]
  \draw (0,0) rectangle (4,4);
  \node at (-4,3) (nodeXi) {$x_i$};
  \node at (2,2) (nodeXj) {$x_j$};
  \node at (2,4) (nodeD) {};
  \draw (nodeXi.center) -- (nodeXj.center);
  \draw (nodeXj.center) -- (nodeD.center);
  \begin{scope}[yshift=50mm]
    \draw (0,0) -- (4,0) -- (4,4) -- (0,4) -- cycle;
    \coordinate [label=below:$x_i$] (nodeXi') at (-4,3);
    \coordinate [label=below:$x_j$] (nodeXj') at (2,2);
    \node [coordinate] at (2,4) (nodeD') {};
    \draw (nodeXi') -- (nodeXj');
    \draw (nodeXj') -- (nodeD');
  \end{scope}
\end{tikzpicture}
\end{document}

If I understood the other question, I'd try to answer it. But I don't, so I can't.

Answer 2

It is not very clear what you mean with "... text horizontally aligned to the lines halfway ...". See if the following solution is what you're looking for:

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{trees}
\begin{document}
\begin{figure}[h]
\begin{center}
\begin{tikzpicture}
\node (box) [draw, minimum size=4cm] at (2,2) {};
\node at (-4,3) (nodeXi) {$x_i$};
\node at (box)  (nodeXj) {$x_j$};
\draw (nodeXi) -- node[above=3mm] {horizontal text} (nodeXj);
\draw (nodeXj) -- node[right] {horizontal text}  (box.north);
\end{tikzpicture}
\end{center}
\caption{A meaningful caption}
\end{figure}
\end{document}

Addendum: according to your comment, I guess that you'd like to obtain something like this:

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{trees}
\begin{document}
\begin{figure}[h]
\begin{center}
\begin{tikzpicture}
\node (box) [draw, minimum size=4cm] at (2,2) {};
\node  (nodeXi) at (-4,3){$x_i$};
\draw (nodeXi)  -- node[above=3mm] {horizontal text} (box.center) 
                   node[right] {$x_j$}  
                -- node[right] {horizontal text}  (box.north);
\end{tikzpicture}
\end{center}
\caption{A meaningful caption}
\end{figure}
\end{document}