Vertical and horizontal lines in pgf-tikz

Question

It is easy to produce a path between two nodes consisting of a single horizontal and a single vertical line (from the manual):

\begin{tikzpicture}
  \draw (0,0) node(a) [draw] {A}  (1,1) node(b) [draw] {B};
  \draw (a.north) |- (b.west);
  \draw[color=red] (a.east) -| (2,1.5) -| (b.north);
\end{tikzpicture}

However, what if I wanted the same short syntax to produce a path between (a) and (b) using a horizontal line, a vertical line, and a second horizontal line. It isn't to difficult to calculate the intermediate points, but how could the following syntax be defined?

\begin{tikzpicture}
  \draw (0,0) node(a) [draw] {A}  (3,1) node(b) [draw] {B};
  \draw (a.east) -|- (b.west);
\end{tikzpicture}

Answer 1

This answer extends Marc van Dongen's anwser.

The two styles are -|- and |-| with default value 0.5 to position the intermediate point (so, default is middle point).

\documentclass[margin=2mm]{standalone}
\usepackage{tikz}
\usetikzlibrary{calc}
\tikzset{
  -|-/.style={
    to path={
      (\tikztostart) -| ($(\tikztostart)!#1!(\tikztotarget)$) |- (\tikztotarget)
      \tikztonodes
    }
  },
  -|-/.default=0.5,
  |-|/.style={
    to path={
      (\tikztostart) |- ($(\tikztostart)!#1!(\tikztotarget)$) -| (\tikztotarget)
      \tikztonodes
    }
  },
  |-|/.default=0.5,
}
\begin{document}
\begin{tikzpicture}[thick]
  \draw[->,blue] (2.1,1.1) to[|-|] (1.1,0.1);
  \draw[->] (2,1) to[-|-] (1,0);

  \draw[->,blue] (3.1,0.1) to[|-|] (4.1,1.1);
  \draw[->] (3,0) to[-|-] (4,1);

  \begin{scope}[yshift=-1.5cm]
    \draw[->,red] (2.1,1.1) to[|-|=.2] (1.1,0.1);
    \draw[->,orange] (2,1) to[-|-=.2] (1,0);

    \draw[->,red] (3.1,0.1) to[|-|=.8] (4.1,1.1);
    \draw[->,orange] (3,0) to[-|-=.8] (4,1);
  \end{scope}
\end{tikzpicture}
\end{document}

Answer 2

A previous version of this answer explained the paths.ortho library that was published in my pgf repo on GitHub. The library is now part of my tikz-ext package which should be used instead (and has a proper manual).

With the ext.paths.ortho library that is possible. It works by re-writing and intercepting the main TikZ parser. (Which is also the reason this may possibly break with an TikZ update or another library but I hope it won't.)

This library introduces six path operators:

• Zig-Zag
  • |-| and
  • -|-;
• Zig-Zig
  • r-ud,
  • r-du,
  • r-lr and
  • r-rl.

The following keys exist (when these are used directly with the path operation, the prefix ortho/ should be dropped, e.g. -|-[ratio=.3]).

• ortho/spacing=<ratio>

  This sets the ratio for the middle part part of the Zig-Zag connection. Values under 0 and over 1 will lead to lines that look more like the Zig-Zig paths.

• ortho/distance=<distance>

  Instead of ratio an absolute distance can be used instead, this will be measured from the starting point when <distance> ≥ 0 and from the targeting point otherwise.

• ortho/from center=<true or false> (default true)

  When nodes get connected the placement of the middle part of the Zig-Zag and the Zig-Zig (see below) connections will be calculated from the border of these nodes. The middle part of the connections will be calculated from the nodes’ center if this key is set to true.

New timers are setup for both the Zig-Zag and the Zig-Zig connections, these can be configured through the following keys.

• ortho/spacing=<number> (default 4)

  This affects the the position of the kinks that will be at 1/<number> (default 0.25) and <number>−1/<number> (default 0.75). The position 0.5 will always be at the center of the middle part. Positions 0.0 and 1.0 will be at the start and at the end respectively.

  When <number> is set to 0 the position

  • -1 will be at the start,
  • 0 will be at the first kink,
  • 1 will be at the second kink,
  • 2 will be at the end and
  • 0.5 will still be the center of the middle part.

• ortho/middle 0 to 1 is an alternative to ortho/spacing=0.

The Zig-Zig connections are explained on my answer to How to draw a return arrow from node-3 to node-1.

---

For to and edge connections the keys

• horizontal vertical horizontal for -|- and
• vertical horizontal vertical for |-|

amongst others are defined. Previously, I've used |-| and -|- for these shortcuts but they conflict with arrows specification which is why these are not defined by default anymore. However, they can easily be defined by

\tikzset{ortho/install shortcuts}

amongst others.

Code (Question)

\documentclass[tikz,border=5pt]{standalone}
\usetikzlibrary{ext.paths.ortho}
\begin{document}
\begin{tikzpicture}[thick, ->]
\draw[blue] (2.1, 1.1) |-| (1.1, 0.1);
\draw       (2  , 1  ) -|- (1  , 0  );

\draw[blue] (3.1, 0.1) |-| (4.1, 1.1);
\draw       (3  , 0  ) -|- (4  , 1  );

\begin{scope}[yshift=-1.5cm, ortho/ratio=.2]
  \draw[red]    (2.1, 1.1) |-| (1.1, 0.1);
  \draw[orange] (2  , 1  ) -|- (1  , 0  );

  \draw[red]    (3.1, 0.1) |-|[ratio=.8] (4.1, 1.1);
  \draw[orange] (3  , 0  ) -|-[ratio=.8] (4  , 1  );
\end{scope}
\end{tikzpicture}
\end{document}

Output (Question)

Answer 3

You can do this with a to path. The following solution is intended to highlight the steps that are needed. The solution can draw connections in any direction, not just vertical/horizontal connections, and therefore generalises all other solutions presented thus far.

Also note the solution doesn't include an animated picture, so you can focus on the provided output without any risk of being distracted by the animation:-).

The solution shows a nice application of the not-too-frequently used projection modifier ($(a)!(b)!(c)$), which projects the point (b) onto the infinite line through (a) and (c).

The reader may add their own favourite auxiliary keys for drawing a horizontal-vertical-horizontal connection, or a vertical-horizontal-vertical connection.

\documentclass{scrartcl}
\usepackage{tikz}
\usetikzlibrary{calc}

\makeatletter
% The parsing is done relative to the key "/my connection/,
% which is not part of the user-defined API
\pgfkeys{/my connection/.cd,
         % Save the angle value.
         angle/.store in=\mycon@angle,
         % Save the ratio value.
         ratio/.store in=\mycon@ratio,
         % The draw key triggers the drawing. Should be last.
         draw/.style={/tikz/to path={
         let % \n{a} is the angle.
             \n{a}=\mycon@angle,
             % \n{r} is the ratio.
             \n{r}=\mycon@ratio,
             % \p{s} is the start of the connection.
             \p{s}=(\tikztostart),
             % \p{t} is the target of the connection.
             \p{t}=(\tikztotarget),
             % \p{sa} is some point on the line from \p{s} in direction \n{a}.
             \p{sa}=($(\p{s})+(\n{a}:1)$),
             % \p{st} is some point on the line from \p{t} in direction \n{a}.
             \p{st}=($(\p{t})+(\n{a}:1)$),
             % \p{proj s} is the projection of \p{s} on the line through \p{t} and \p{st}.
             \p{proj s}=($(\p{t})!(\p{s})!(\p{st})$),
             % \p{proj t} is the projection of \p{t} on the line through \p{s} and \p{sa}.
             \p{proj t}=($(\p{s})!(\p{t})!(\p{sa})$)
         in    % Second point of connection.
               -- ($(\p{s})!\n{r}!(\p{proj t})$)
               % Third point of connection.
               -- ($(\p{proj s})!\n{r}!(\p{t})$)
               % Last point of connection.
               -- (\p{t})
            \tikztonodes}}}
% The "connection" key is part of the user-defined API key.
% It has two sub-keys: ratio and angle, with default values 0.5
% and 0 respectively. We use the connection key to set the defaults,
% override the user-provided values for the keys (if any), and then
% draw the connection.
\tikzset{connection/.style={/my connection/.cd,ratio=0.5,angle=0,#1,draw}}
\makeatother

\begin{document}

\begin{tikzpicture}
\draw (0,0) coordinate(a) node[anchor=north]{$a$}
      (6,3) coordinate(b) node[anchor=south]{$b$};
\draw[->]      (a) to[connection] (b);
\draw[blue,->] (b) to[connection={ratio=0.25,angle=30}] (a);
\draw[red,->]  (a) to[connection={ratio=0.25,angle=90}] (b);
\end{tikzpicture}
\end{document}

Answer 4

Try this:

\begin{tikzpicture}
\path (0,0) node(a) [draw] {A} -- (3,1) node(b) [draw] {B} coordinate[pos=0.5](inter);
\draw (a) -| (inter) |- (b) ;
\end{tikzpicture}