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

With my paths.ortho library that contains of

• tikzlibrarypaths.ortho.code.tex and
• tikzlibrarypaths.ortho.tex,

this is possible.

This works by re-writing and intercepting the main TikZ parser. (Which is also the reason this may break with an TikZ update.)

This library introduces six path operators:

• in the hvvh family:
  • |-| and
  • -|-;
• in the udlr family:
  • r-ud,
  • r-du,
  • r-lr and
  • r-rl.

For the hvvh family exist the following keys:

• hvvh/spacing=<n>,

  • hvvh/middle 0 to 1 and hvvh/0 to 1 which are a short-cut (?) for hvvh/spacing=0

  This key affects the timer (that is the function that places nodes along the path).
  The two kinks on the path are the positions 1/<n> and (<n>-1)/<n>. (With |- and -| the kink is at .5.)

  The default is <n> = 4.

  If <n> = 0 (see also the middle 0 to 1 key above), then a special timer is installed that makes the kinks at pos=0 and pos=1. The start of the three-parted line is pos=-1 and the end is pos=2 then.

  The position .5 is always in the middle of the second part of the path.

  These timer settings are valid for the udlr family, too!

• hvvh/ratio sets the ratio of the middle part in relation to the start and the end. Its default is .5. The values 0 and 1 will result in the well-known |- and -| paths.

• hvvh/distance sets—similar to the ratio—the distance between the start and the middle. If this distance is set greater then the orthogonal distance of the to-be-connected coordinates (or less then zero), you will end up with something that also could have been produced with one of the udlr paths.

The udlr family is explained on my answer to How to draw a return arrow from node-3 to node-1.

Negative distances will result in paths that resemble the |-|/-|- paths.

Code (Question)

\documentclass[tikz,border=5pt]{standalone}
\usetikzlibrary{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, hvvh/ratio=.2]
    \draw[red]    (2.1,1.1) |-| (1.1,0.1);
    \draw[orange] (2,1) -|- (1,0);

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

Output (Question)

Examples of the usages of this library …

… can be found in paths.ortho-hvvh.tex and paths.ortho-udlr.tex. Animations created from these examples are hidden behind the following links:

• Output (-|-/|-|)
• Output (udlr/distance)

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}