[Tex/LaTex] Automatically avoid more than one node when drawing a path

automationtikz-pgf

Background

Andrew Stacey's answer to Automatically connect nodes without overlapping other nodes or connections presents code to make a path avoid a node by going through a corner of that node (instead of through the node itself). In it's current state it only lets you specify one point to go through. I would like to be able to specify several points to be able to avoid several nodes. (In chat I was advised to make a new question for this issue since it's a different question.)

Note that I will also be happy with answers not building on Andrew's code.

Problem

Tree diagrams may contain many nodes and it may be hard to draw them so that no path crosses no node. Andrew's code helps to avoid one node but not several.

Here follows a minimal example to illustrate what I mean (note that there may be many more nodes in a tree digrams). Given these nodes

\node(a) {\(A\)};
\node(b1) at ($(a)+(1,-0.5)$){\(B_1\)};
\node(b2) at ($(b1)+(0,0.5)$){\(B_2\)};
\node(b3) at ($(b2)+(0,0.5)$){\(B_3\)};
\node(c1) at ($(b1)+(2,0)$){\(C_1\)};
\node(c2) at ($(c1)+(0,0.5)$){\(C_2\)};
\node(c3) at ($(c2)+(0,0.5)$){\(C_3\)};
\node(d) at ($(c2)+(1,0)$){\(D\)};

is there a method to draw a path from (a) to (d) and specify that the path should avoid (b2) but also any other node without manually specifying angles for the path?

With Andrew's code I can specify only one node to avoid and although it helps to avoid the node I specify, (b2), the path ends up crossing other nodes (the red paths in the image). I would like to be able to also specify it to avoid (b1), (b3), (c1), (c2) and (c3) (so that I get a result such as the green paths in the image).

Example of correct and incorrect paths

The code to produce the image:

\documentclass{article}

\usepackage{tikz}
\usetikzlibrary{calc}

\makeatletter
\tikzset{
  through point/.style={
    to path={%
      \pgfextra{%
        \tikz@scan@one@point\pgfutil@firstofone(\tikztostart)\relax
        \pgfmathsetmacro{\pt@sx}{\pgf@x * 0.03514598035}%
        \pgfmathsetmacro{\pt@sy}{\pgf@y * 0.03514598035}%
        \tikz@scan@one@point\pgfutil@firstofone#1\relax
        \pgfmathsetmacro{\pt@ax}{\pgf@x * 0.03514598035 - \pt@sx}%
        \pgfmathsetmacro{\pt@ay}{\pgf@y * 0.03514598035 - \pt@sy}%
        \tikz@scan@one@point\pgfutil@firstofone(\tikztotarget)\relax
        \pgfmathsetmacro{\pt@ex}{\pgf@x * 0.03514598035 - \pt@sx}%
        \pgfmathsetmacro{\pt@ey}{\pgf@y * 0.03514598035 - \pt@sy}%
        \pgfmathsetmacro{\pt@len}{\pt@ex * \pt@ex + \pt@ey * \pt@ey}%
        \pgfmathsetmacro{\pt@t}{(\pt@ax * \pt@ex + \pt@ay * \pt@ey)/\pt@len}%
        \pgfmathsetmacro{\pt@t}{(\pt@t > .5 ? 1 - \pt@t : \pt@t)}%
        \pgfmathsetmacro{\pt@h}{(\pt@ax * \pt@ey - \pt@ay * \pt@ex)/\pt@len}%
        \pgfmathsetmacro{\pt@y}{\pt@h/(3 * \pt@t * (1 - \pt@t))}%
      }
      (\tikztostart) .. controls +(\pt@t * \pt@ex + \pt@y * \pt@ey, \pt@t * \pt@ey - \pt@y * \pt@ex) and +(-\pt@t * \pt@ex + \pt@y * \pt@ey, -\pt@t * \pt@ey - \pt@y * \pt@ex) .. (\tikztotarget)
    }
  }
}
\makeatother

\begin{document}

\begin{tikzpicture}
% Nodes
\node(a) {\(A\)};
\node(b1) at ($(a)+(1,-0.5)$){\(B_1\)};
\node(b2) at ($(b1)+(0,0.5)$){\(B_2\)};
\node(b3) at ($(b2)+(0,0.5)$){\(B_3\)};
\node(c1) at ($(b1)+(2,0)$){\(C_1\)};
\node(c2) at ($(c1)+(0,0.5)$){\(C_2\)};
\node(c3) at ($(c2)+(0,0.5)$){\(C_3\)};
\node(d) at ($(c2)+(1,0)$){\(D\)};
% Boundaries
\draw[thick] ($(a)+(-0.2,0.9)$) to ($(d)+(0.2,0.9)$);
\draw[thick] ($(a)+(-0.2,-0.9)$) to ($(d)+(0.2,-0.9)$);
% Andrew's code ends up crossing a node
\draw[->,red] (a) to[through point={(b2.north east)}] (d);
\draw[->,red] (a) to[through point={(b2.north west)}] (d);
\draw[->,red] (a) to[through point={(b2.south west)}] (d);
\draw[->,red] (a) to[through point={(b2.south east)}] (d);
\draw[->,red] (a) to[through point={(b2.north)}] (d);
\draw[->,red] (a) to[through point={(b2.south)}] (d);
% Manually specifying angles to show acceptable results
\draw[->,green] (a) to[out=10,in=120] (d);
\draw[->,green] (a) to[out=15,in=163] (d);
\draw[->,green] (a) to[out=-12,in=196] (d);
\draw[->,green] (a) to[out=-10,in=240] (d);
\end{tikzpicture}

\end{document}

Best Answer

By using one of Jake's previous answers, I tried to fit the points in an ellipse and the result is not so bad. Also it reduces the manual labor. But there are a few issues which can be improved but I am not able to type \pgfmathparse stuff as others do. (I wish I have time!) Anyway, here is the code and some explanation after it.

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{calc,fit,shapes}
\makeatletter
\tikzset{
  through point/.style={
    to path={%
      \pgfextra{%
        \tikz@scan@one@point\pgfutil@firstofone(\tikztostart)\relax
        \pgfmathsetmacro{\pt@sx}{\pgf@x * 0.03514598035}%
        \pgfmathsetmacro{\pt@sy}{\pgf@y * 0.03514598035}%
        \tikz@scan@one@point\pgfutil@firstofone#1\relax
        \pgfmathsetmacro{\pt@ax}{\pgf@x * 0.03514598035 - \pt@sx}%
        \pgfmathsetmacro{\pt@ay}{\pgf@y * 0.03514598035 - \pt@sy}%
        \tikz@scan@one@point\pgfutil@firstofone(\tikztotarget)\relax
        \pgfmathsetmacro{\pt@ex}{\pgf@x * 0.03514598035 - \pt@sx}%
        \pgfmathsetmacro{\pt@ey}{\pgf@y * 0.03514598035 - \pt@sy}%
        \pgfmathsetmacro{\pt@len}{\pt@ex * \pt@ex + \pt@ey * \pt@ey}%
        \pgfmathsetmacro{\pt@t}{(\pt@ax * \pt@ex + \pt@ay * \pt@ey)/\pt@len}%
        \pgfmathsetmacro{\pt@t}{(\pt@t > .5 ? 1 - \pt@t : \pt@t)}%
        \pgfmathsetmacro{\pt@h}{(\pt@ax * \pt@ey - \pt@ay * \pt@ex)/\pt@len}%
        \pgfmathsetmacro{\pt@y}{\pt@h/(3 * \pt@t * (1 - \pt@t))}%
      }
      (\tikztostart) .. controls +(\pt@t * \pt@ex + \pt@y * \pt@ey, \pt@t * \pt@ey - \pt@y * \pt@ex) and +(-\pt@t * \pt@ex + \pt@y * \pt@ey, -\pt@t * \pt@ey - \pt@y * \pt@ex) .. (\tikztotarget)
    }
  }
}
\makeatother
\begin{document}
\begin{tikzpicture}
\node(a) {\(A\)};
\node(b1) at ($(a)+(1,-0.5)$){\(B_1\)};
\node(b2) at ($(b1)+(0,0.5)$){\(B_2\)};
\node(b3) at ($(b2)+(0,0.5)$){\(B_3\)};
\node(c1) at ($(b1)+(2,0)$){\(C_1\)};
\node(c2) at ($(c1)+(0,0.5)$){\(C_2\)};
\node(c3) at ($(c2)+(0,0.5)$){\(C_3\)};
\node(d) at ($(c2)+(1,0)$){\(D\)};
%all the points
\node [draw,ellipse,thick,inner sep=0,fit={(b1) (b2) (b3) (c1) (c2) (c3)}] (avoid1) {};
\draw[->,thick] (a) to[through point={(avoid1.north west) (avoid1.north east)}] (d);
%just the c group
\node [draw,ellipse,blue,inner sep=0,fit={(c1) (c2) (c3)}] (avoid2) {};
\draw[->,blue] (a) to[through point={(avoid2.north)}] (d);
%just the b group
\node [draw,ellipse,yellow,thick,inner sep=1,fit={(b1) (b2) (b3)}] (avoid3) {};
\draw[->,yellow,thick] (a) to[through point={(avoid3.north)}] (d);
\end{tikzpicture}
\end{document}

enter image description here

This is drawing the bounding ellipses and trying to avoid them. The resulting curves grouped by color. As you can see Andrew's code is still doing a fine job. What is needed is to select the north or the south of the dummy nodes avoid which define the curve to pass from below or above. Also I had to define two control nodes to pass through when all obstacles were included see the avoid1 case. (I am really surprised that it accepted two nodes, superb!). If you think that the resulting curve is overshooting you can decrease the inner sep of the ellipse node.

I think TikZ needs this kind of a, say around, library. I tried to get the control points of a Beziér curve and other angle computation stuff but I can't understand the math syntax of pgf yet. So hope this can help a bit.

EDIT : I have tried to simplify the whole fitting process then I realized that the fit is not necessary if we can smoothen the path. I checked the manual and only thing that is almost what we want is the smooth option with the extra freedom of tension parameter.

I have tried it out with the following

\begin{tikzpicture}
\matrix (o) [matrix of nodes, column sep=2cm,nodes=draw,draw=red]{
$A_1$&$B_1$ &$C_1$ &$D_1$\\
$A_2$&$B_2$ &$C_2$ &$D_2$\\
$A_3$&$B_3$ &$C_3$ &$D_3$\\
};
\node (s) at (-6,0) {S};
\node (f) at (6,0) {F};

\draw[blue] plot [smooth, tension=0.5] coordinates{%
(s.east)  (o-2-1.south) (o-2-2.north) (o-1-3.north) (o-1-4.south) (f.west)};
\draw plot [smooth, tension=0.8] coordinates{%
(s.east)  (o-2-1.north) (o-1-2.north) (o-1-4.north) (f.west)};
\draw[yellow,thick] plot [smooth, tension=0.5] coordinates{%
(s.east)  (o-3-1.south) (o-3-4.south) (f.west)};
\end{tikzpicture}

This gives the following result: enter image description here

The tension parameter adjusts how smooth the corners should be rendered. Default is reported as 0.55. So one can still fit some nodes into a bigger shape and use it to avoid but this node-by-node connection seems easier. Also, this introduces new issues such as the out and in angles are slightly awkward and I couldn't make the arrows look normal. I would be glad if someone teaches me how to do it properly.

Related Solutions

[Tex/LaTex] Tikz node labels more below than below

In the first case the one node is placed below the point with content $b_1$ . In the second case a node without content (but still with positive height) is placed at the point and a second node with $b_1$ is placed below it.

Maybe a picture helps:

\begin{tikzpicture}
    \fill (0,0) circle (0.05) node[below,draw]{$b_1$};
    \fill (1,0) circle (0.05) node[label=below:$b_1$,draw]{};
\end{tikzpicture}

example

[Tex/LaTex] How to draw points in TikZ

Method I (using node)

\tikzset{
  every point/.style = {circle, inner sep={.75\pgflinewidth}, opacity=1, draw, solid, fill=white},
  point/.style={insert path={node[every point, #1]{}}}, point/.default={},
  point name/.style = {insert path={coordinate (#1)}},
}

and some extra stuff :

\tikzset{
  colored point/.style = {point={fill=#1}},
  inherit/.style = {point/.style={insert path={node[circle, inner sep={.75\pgflinewidth}, draw, fill, #1]{}}}}
}

Satisfies 1.
Satisfies 2 with styling like this [point={fill=red, very thick}]
Partially satisfies 3. I don't know how to define draw opacity=inherit or fill=inherit. I define new style inherit which will redefine the entire point by removing the opacity=1 and fill=white, but this is ugly ;).
Partially satisfy 4 : you can use point name=A. I would like to be able to use quotes for saying something like [point={red, "A"}] but I don't know how to do this.
Almost satisfy 5 : we can put [point] almost anywhere, like (A) [point], or node[point, above]{A}, or coordinate[point](A). But can't be used with \coordinate at or \node at (except if you repeat yourself like this \coordinate (A) at (1,1) (A) [point];)
FAILS on 6. I know that there is a hacky solution to put node on layer, but this is in contradiction with 7).
Satisfies 7.

The full code of all tests and the result

\documentclass[varwidth,border=50]{standalone}
\usepackage{tikz}

% not clear how to use layers with this method
\pgfdeclarelayer{background}
\pgfdeclarelayer{foreground}
\pgfsetlayers{background,main,foreground}

\tikzset{
  every point/.style = {circle, inner sep={.75\pgflinewidth}, opacity=1, draw, solid, fill=white},
  point/.style={insert path={node[every point, #1]{}}}, point/.default={},
  colored point/.style = {point={fill=#1}},
  point name/.style = {insert path={coordinate (#1)}},
  inherit/.style = {point/.style={insert path={node[circle, inner sep={.75\pgflinewidth}, draw, fill, #1]{}}}}
}

\begin{document}
  \begin{itemize}

    % ---------------------------------
    \item Test 1 : ok.\\[1em]
    \begin{tikzpicture}
      \foreach[count=\i] \w in {ultra thin, thin, ultra thick} {
      \draw[yshift=-\i em, \w] (0,0) -- (.5,0) [point] -- (1,0);
      }
      \foreach[count=\i] \s in {.2, .5, 1} {
      \draw[xshift=1.5cm, yshift=-\i em, scale=\s] (0,0) -- (.5,0) [point] -- (1,0);
      }
    \end{tikzpicture}

    % ---------------------------------
    \item Test 2 : ok.

    % ---------------------------------
    \item Test 3 : partialy ok, there is no good \texttt{inherit}.\\
    \begin{tikzpicture}[scale=2, very thick]
      \filldraw[draw opacity=.5, draw=red, fill opacity=.3, densely dotted]
        (0,0) [point] -- (.5,0) [point={ultra thick, fill=green}] -- (.5,.5) [inherit, point] -- cycle;
    \end{tikzpicture}

    % ---------------------------------
    \item Test 4 : almost ok (using \texttt{point name})\\
    \begin{tikzpicture}
      \draw[very thick] (0,1) [point] -- (1,0) [point={thick, fill=green, point name=A}];
      \draw[ultra thick, purple] (0,0) [point] -- (A);
    \end{tikzpicture}

    % ---------------------------------
    \item Test 5 : almost ok.

    % ---------------------------------
    \item Test 6 : fails ! (visible in test 4 too)\\
    \begin{tikzpicture}
      \coordinate (A) at (0,1) (A) node[point=ultra thick, left] {A};
      \coordinate (B) at (1,0) (B) [thick, point];
      \draw (A) -- (B);
    \end{tikzpicture}

  \end{itemize}
\end{document}

enter image description here

Method II (using pic)

\pgfdeclarelayer{background}
\pgfdeclarelayer{foreground}
\pgfsetlayers{background,main,foreground}

\tikzset{
  every point/.style = {radius={\pgflinewidth}, opacity=1, draw, solid, fill=white},
  pt/.pic = {
    \begin{pgfonlayer}{foreground}
      \path[every point, #1] circle;
    \end{pgfonlayer}
  },
  point/.style={insert path={pic{pt={#1}}}}, point/.default={},
  point name/.style = {insert path={coordinate (#1)}}
}

FAILS on 1. I don't know how to inherit styles from path to pic. Is there some style like current path style ?
Satisfies 2. Same as method I.
FAILS on 3. We can style as in method I, but because (1) fails, (3) fails.
Partially satisfies 4. Same as method I.
FAILS on 5 : as there is a bug in 'pic' we can't use node after it in PGF 3.0. When this bug will be fixed, this method will be equivalent to the first one at this test.
Satisfies 6. This is the main interest of this method.
Satisfies 7.

The full code of all tests and the result

\documentclass[varwidth,border=50]{standalone}
\usepackage{tikz}

\pgfdeclarelayer{background}
\pgfdeclarelayer{foreground}
\pgfsetlayers{background,main,foreground}

\tikzset{
  every point/.style = {radius={\pgflinewidth}, opacity=1, draw, solid, fill=white},
  pt/.pic = {
    \begin{pgfonlayer}{foreground}
      \path[every point, #1] circle;
    \end{pgfonlayer}
  },
  point/.style={insert path={pic{pt={#1}}}}, point/.default={},
  colored point/.style = {point={fill=#1}},
  point name/.style = {insert path={coordinate (#1)}}
}

\begin{document}
\begin{itemize}
\item Test 1 : fails for sizing from path width, scale is ok.\\[1em]
\begin{tikzpicture}
  \foreach[count=\i] \w in {ultra thin, thin, ultra thick} {
  \draw[yshift=-\i em, \w] (0,0) -- (.5,0) [point] -- (1,0);
  }
  \foreach[count=\i] \s in {.2, .5, 1} {
  \draw[xshift=1.5cm, yshift=-\i em, scale=\s] (0,0) -- (.5,0) [point] -- (1,0);
  }
\end{tikzpicture}

\item Test 2 : partialy ok, there is no \texttt{inherit} (at all).

\item Test 3 : fails ! Can't inherit style from path.\\
\begin{tikzpicture}[scale=2, very thick, densely dotted]
  \filldraw[draw opacity=.5, draw=red, fill opacity=.3]
    (0,0) [point] -- (.5,0) [point={ultra thick, fill=green}] -- (.5,.5) [point] -- cycle;
\end{tikzpicture}

\item Test 4 : almost ok (using \texttt{point name})\\
\begin{tikzpicture}
  \draw[very thick] (0,1) [point] -- (1,0) [point={thick, fill=green, point name=A}];
  \draw[ultra thick, purple] (0,0) [point] -- (A);
\end{tikzpicture}

\item Test 5 : fails ! (can't put node after [point] )

\item Test 6 : ok.\\
\begin{tikzpicture}
  \path (0,1) node[left] {A} coordinate (A) [point=ultra thick];
  \coordinate (B) at (1,0) (B) [thick, point];
  \draw (A) -- (B);
\end{tikzpicture}
\end{itemize}
\end{document}

enter image description here

Background

Problem

Best Answer

Related Solutions

[Tex/LaTex] Tikz node labels more below than below

[Tex/LaTex] How to draw points in TikZ

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