% Copyright 2019 by Till Tantau
%
% This file may be distributed and/or modified
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% 2. under the GNU Free Documentation License.
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\section{To Path Library}
\label{library-to-paths}

\begin{tikzlibrary}{topaths}
    This library provides predefined to paths for use with the |to| path
    operation. After loading this package, you can say for instance |to [loop]|
    to add a loop to a node.

    This library is loaded automatically by \tikzname, so you do not need to
    load it yourself.
\end{tikzlibrary}


\subsection{Straight Lines}

The following style installs a to path that is simply a straight line from the
start coordinate to the target coordinate.

\begin{key}{/tikz/line to}
    Causes a straight line to be added to the path upon a |to| or an |edge|
    operation.
    %
\begin{codeexample}[]
\tikz {\draw (0,0) to[line to] (1,0);}
\end{codeexample}
    %
\end{key}


\subsection{Move-Tos}

The following style installs a to path that simply ``jumps'' to the target
coordinate.

\begin{key}{/tikz/move to}
    Causes a move to be added to the path upon a |to| or an |edge| operation.
    %
\begin{codeexample}[]
\tikz \draw (0,0) to[line to] (1,0)
                  to[move to] (2,0) to[line to] (3,0);
\end{codeexample}
    %
\end{key}


\subsection{Curves}

The |curve to| style causes the to path to be set to a curve. The exact way
this curve looks can be influenced via a number of options.

\begin{key}{/tikz/curve to}
    Specifies that the |to path| should be a curve. This curve will leave the
    start coordinate at a certain angle, which can be specified using the |out|
    option. It reaches the target coordinate also at a certain angle, which is
    specified using the |in| option. The control points of the curve are at a
    certain distance that is computed in different ways, depending on which
    options are set.

    All of the following options implicitly cause the |curve to| style to be
    installed.

    \begin{key}{/tikz/out=\meta{angle}}
        The angle at which the curve leaves the start coordinate. If the start
        coordinate is a node, the start coordinate is the point on the border
        of the node at the given \meta{angle}. The control point will, thus,
        lie at a certain distance in the direction \meta{angle} from the start
        coordinate.
        %
\begin{codeexample}[]
\begin{tikzpicture}[out=45,in=135]
  \draw (0,0) to (1,0)
        (0,0) to (2,0)
        (0,0) to (3,0);
\end{tikzpicture}
\end{codeexample}
    \end{key}
    %
    \begin{key}{/tikz/in=\meta{angle}}
        The angle at which the curve reaches the target coordinate.
    \end{key}

    \begin{key}{/tikz/relative=\meta{true or false} (default true)}
        This option tells \tikzname\ whether the |in| and |out| angles should
        be considered absolute or relative. Absolute means that an |out| angle
        of 30$^\circ$ means that the curve leaves the start coordinate at an
        angle of 30$^\circ$ relative to the paper (unless, of course, further
        transformations have been installed). A \emph{relative} angle is, by
        comparison, measured relative to a straight line from the start
        coordinate to the target coordinate. Thus, a relative angle of
        30$^\circ$ means that the curve will bend to the left from the line
        going straight from the start to the target. For the target, the
        relative coordinate is measured in the same manner, namely relative to
        the line going from the start to the target. Thus, an angle of
        150$^\circ$ means that the curve will reach target coming slightly from
        the left.
        %
\begin{codeexample}[]
\begin{tikzpicture}[out=45,in=135,relative]
  \draw (0,0) to (1,0)
              to (2,1)
              to (2,2);
\end{tikzpicture}
\end{codeexample}

\begin{codeexample}[]
\begin{tikzpicture}[out=90,in=90,relative]
  \node [circle,draw] (a) at (0,0) {a};
  \node [circle,draw] (b) at (1,1) {b};
  \node [circle,draw] (c) at (2,2) {c};

  \path (a) edge (b)
            edge (c);
\end{tikzpicture}
\end{codeexample}
    \end{key}

    \begin{key}{/tikz/bend left=\meta{angle} (default \normalfont last value)}
        This option sets |out=|\meta{angle}|,in=|$180-\meta{angle}$|,relative|.
        If no \meta{angle} is given, the last given |bend left| or |bend right|
        angle is used.
        %
\begin{codeexample}[preamble={\usetikzlibrary{automata,positioning}}]
\begin{tikzpicture}[shorten >=1pt,node distance=2cm,on grid]
  \node[state,initial]  (q_0)                {$q_0$};
  \node[state]          (q_1) [right=of q_0] {$q_1$};
  \node[state,accepting](q_2) [right=of q_1] {$q_2$};

  \path[->] (q_0) edge              node [above]  {0} (q_1)
                  edge [loop above] node          {1} ()
                  edge [bend left]  node [above]  {1} (q_2)
                  edge [bend right] node [below]  {0} (q_2)
            (q_1) edge              node [above]  {1} (q_2);
\end{tikzpicture}
\end{codeexample}

\begin{codeexample}[]
\begin{tikzpicture}
  \foreach \angle in {0,45,...,315}
    \node[rectangle,draw=black!50] (\angle) at (\angle:2) {\angle};

  \foreach \from/\to in {0/45,45/90,90/135,135/180,
                         180/225,225/270,270/315,315/0}
    \path (\from) edge [->,bend right=22,looseness=0.8] (\to)
                  edge [<-,bend left=22,looseness=0.8] (\to);
\end{tikzpicture}
\end{codeexample}
    \end{key}

    \begin{key}{/tikz/bend right=\meta{angle} (default \normalfont last  value)}
        Works like the |bend left| option, only the bend is to the other side.
    \end{key}

    \begin{key}{/tikz/bend angle=\meta{angle}}
        Sets the angle to be used by the |bend left| or |bend right|, but
        without actually selecting the |curve to| or the |relative| option.
        This is useful for globally specifying a |bend angle| for a whole
        picture.
    \end{key}

    \begin{key}{/tikz/looseness=\meta{number} (initially 1)}
        This number specifies how ``loose'' the curve will be. In detail, the
        following happens: \tikzname\ computes the distance between the start
        and the target coordinate (if the start and/or target coordinate are
        nodes, the distance is computed between the points on their border).
        This distance is then multiplied by a fixed factor and also by the
        factor \meta{number}. The resulting distance, let us call it $d$, is
        then used as the distance of the control points from the start and
        target coordinates.

        The fixed factor has been chosen in such a way that if \meta{number} is
        |1|, if the |in| and |out| angles differ by 90$^\circ$, then a quarter
        circle results:
        %
\begin{codeexample}[]
\tikz \draw (0,0) to [out=0,in=-90]               (1,1);
\tikz \draw (0,0) to [out=0,in=-90,looseness=0.5] (1,1);
\end{codeexample}
    \end{key}

    \begin{key}{/tikz/out looseness=\meta{number}}
        Specifies the looseness factor for the out distance only.
    \end{key}

    \begin{key}{/tikz/in looseness=\meta{number}}
        Specifies the looseness factor for the in distance only.
    \end{key}
    %
    \begin{key}{/tikz/min distance=\meta{distance}}
        If the computed distance for the start and target coordinates are below
        \meta{distance}, then \meta{distance} is used instead.
    \end{key}
    %
    \begin{key}{/tikz/max distance=\meta{distance}}
        If the computed distance for the start and target coordinates are above
        \meta{distance}, then \meta{distance} is used instead.
    \end{key}
    %
    \begin{key}{/tikz/out min distance=\meta{distance}}
        The minimum distance set only for the start coordinate.
    \end{key}
    %
    \begin{key}{/tikz/out max distance=\meta{distance}}
        The maximum distance set only for the start coordinate.
    \end{key}
    %
    \begin{key}{/tikz/in min distance=\meta{distance}}
        The minimum distance set only for the target coordinate.
    \end{key}
    %
    \begin{key}{/tikz/in max distance=\meta{distance}}
        The maximum distance set only for the target coordinate.
    \end{key}
    %
    \begin{key}{/tikz/distance=\meta{distance}}
        Set the minimum and maximum distance to the same value \meta{distance}.
        Note that this causes any computed distance $d$ to be ignored and
        \meta{distance} to be used instead.
        %
\begin{codeexample}[]
\begin{tikzpicture}[out=45,in=135,distance=1cm]
  \draw (0,0) to (1,0)
        (0,0) to (2,0)
        (0,0) to (3,0);
\end{tikzpicture}
\end{codeexample}
        %
    \end{key}
    %
    \begin{key}{/tikz/out distance=\meta{distance}}
        Sets the minimum and maximum out distance.
    \end{key}
    %
    \begin{key}{/tikz/in distance=\meta{distance}}
        Sets the minimum and maximum in distance.
    \end{key}
    %
    \begin{key}{/tikz/out control=\meta{coordinate}}
        This option causes the \meta{coordinate} to be used as the start
        control point. All computations of $d$ are ignored. You can use a
        coordinate like |+(1,0)| to specify a point relative to the start
        coordinate.
    \end{key}
    %
    \begin{key}{/tikz/in control=\meta{coordinate}}
        This option causes the \meta{coordinate} to be used as the target
        control point. You can use a coordinate like |+(1,0)| to specify
        a point relative to the \emph{end} coordinate.
    \end{key}
    %
    \begin{key}{/tikz/controls=\meta{coordinate}| and |\meta{coordinate}}
        This option causes the \meta{coordinate}s to be used as control points.
        %
\begin{codeexample}[]
\tikz \draw (0,0) to [controls=+(90:1) and +(90:1)] (3,0);
\end{codeexample}
    \end{key}
\end{key}


\subsection{Loops}

\begin{key}{/tikz/loop}
    This key is similar to the |curve to| key, but differs in the following
    ways: First, the actual target coordinate is ignored and the start
    coordinate is used as the target coordinate. Thus, it is allowed not to
    provide any target coordinate, which can be useful with unnamed nodes.
    Second, the |looseness| is set to |8| and the |min distance| to |5mm|.
    These settings result in rather nice loops when the opening angle
    (difference between |in| and |out|) is 30$^\circ$.
    %
\begin{codeexample}[]
\begin{tikzpicture}
  \node [circle,draw] {a} edge [in=30,out=60,loop] ();
\end{tikzpicture}
\end{codeexample}
    %
\end{key}

\begin{stylekey}{/tikz/loop above}
    Sets the |loop| style and sets in and out angles such that loop is above
    the node. Furthermore, the |above| option is set, which causes a node label
    to be placed at the correct position.
    %
\begin{codeexample}[]
\begin{tikzpicture}
  \node [circle,draw] {a} edge [loop above] node {x} ();
\end{tikzpicture}
\end{codeexample}
    %
\end{stylekey}

\begin{stylekey}{/tikz/loop below}
    Works like the previous option.
\end{stylekey}
%
\begin{stylekey}{/tikz/loop left}
    Works like the previous option.
\end{stylekey}
%
\begin{stylekey}{/tikz/loop right}
    Works like the previous option.
\end{stylekey}
%
\begin{stylekey}{/tikz/every loop (initially {->,shorten >=1pt})}
    This style is installed at the beginning of every loop.
    %
\begin{codeexample}[]
\begin{tikzpicture}[every loop/.style={}]
  \draw (0,0) to [loop above] () to [loop right] ()
              to [loop below] () to [loop left]  ();
\end{tikzpicture}
\end{codeexample}
    %
\end{stylekey}


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