# TikZ: Understanding the usage of calc library

For the following MWE, I need to place block (yaw) {C} midway between (1) the middle point between (output) and (integrator) (2) and (sum2).

So, how can I correct this syntax \node [block] (yaw) at ([yshift=-2cm]$(integrator)+0.5*{(output)-(integrator)}!0.5!(sum2)$) {C}; to make it work?

\documentclass{article}
\usepackage{tikz,mathtools,amssymb}
\usetikzlibrary{shapes,arrows,positioning,calc}

\begin{document}

\tikzset{
block/.style = {draw, fill=white, rectangle, minimum height=3em, minimum width=3em},
tmp/.style  = {coordinate},
sum/.style= {draw, fill=white, circle, node distance=1cm},
input/.style = {coordinate},
output/.style= {coordinate},
pinstyle/.style = {pin edge={to-,thin,black}
}
}

\begin{tikzpicture}[auto, node distance=2cm,>=latex',align=center]
\node [sum] (sum2) {};
\node [block, right = 1cm of sum2](ractuator){$\frac{2}{s+2}$};
\node [block, right = 1cm of ractuator,] (vdynamics) {$\frac{-0.125(s+0.437)}{(s+1.29)(s+0.193)}$};
\node [block, right = 1cm of vdynamics,] (integrator) {$\frac{1}{s}$};
\node [output, right = 1.5cm of integrator] (output) {};
\node [block] (yaw) at ([yshift=-2cm]$(integrator)+0.5*{(output)-(integrator)}!0.5!(sum2)$) {C};
%
\draw [->] (ractuator) -- (vdynamics);
\draw [->] (vdynamics) -- (integrator);
\draw [->] (integrator) -- node[name=heading]{$\Psi(s)$} (output);
\end{tikzpicture}

\end{document}


Additionally, is it possible to create a new node using \node [tmp, below = 2cm of ($(output)!0.5!(integrator)$) ] (tmp1) {}; without creating auxiliary nodes/coordinates?

• Hey! Did ($.25*(output)+.25*(integrator)+.5*(sum2)$) work for you? – Vinzza Nov 15 '18 at 10:26
• @Vinzza It does. But, why does my approach not work? – Diaa Nov 15 '18 at 10:33
• Comments do not allow enough characters, so I have replied with an answer! I hope it will help you! :) – Vinzza Nov 15 '18 at 13:27
• Your approach does not work because you try to use { and } where you should use ($ and $). Try ($(0,-2cm)+(integrator)+0.5*($(output)-(integrator)$)!0.5!(sum2)$) to have something that does not throw an error. However, from your description in words I think you want \node [block] (yaw) at ($(0,-2cm)+($(output)!0.5!(integrator)$)!0.5!(sum2)$) {C};, yet this can be done without calc: \node [block] (yaw) at ([yshift=-2cm]barycentric cs:output=1,integrator=1,sum2=2) {C};. – marmot Nov 15 '18 at 14:27

I don't know how complex expression can be understood by calc but instead of trying to understand how to write such expression, I think it's easier to use an auxiliar coordinate and solve the problem:

\documentclass{article}
\usepackage{tikz,mathtools,amssymb}
\usetikzlibrary{shapes,arrows,positioning,calc}

\begin{document}

\tikzset{
block/.style = {draw, fill=white, rectangle, minimum height=3em, minimum width=3em},
tmp/.style  = {coordinate},
sum/.style= {draw, fill=white, circle, node distance=1cm},
input/.style = {coordinate},
output/.style= {coordinate},
pinstyle/.style = {pin edge={to-,thin,black}
}
}

\begin{tikzpicture}[auto, node distance=2cm,>=latex',align=center]
\node [sum] (sum2) {};
\node [block, right = 1cm of sum2](ractuator){$\frac{2}{s+2}$};
\node [block, right = 1cm of ractuator,] (vdynamics) {$\frac{-0.125(s+0.437)}{(s+1.29)(s+0.193)}$};
\node [block, right = 1cm of vdynamics,] (integrator) {$\frac{1}{s}$};
\node [output, right = 1.5cm of integrator] (output) {};
\coordinate (aux) at ($(integrator.east)!.5!(output)$);
\node [block] (yaw) at ([yshift=-2cm]$(aux)!0.5!(sum2)$) {C};
\draw (aux) |- (yaw);
\draw (yaw)-|(sum2);
%
\draw [->] (ractuator) -- (vdynamics);
\draw [->] (vdynamics) -- (integrator);
\draw [->] (integrator) -- node[name=heading]{$\Psi(s)$} (output);
\end{tikzpicture}

\end{document}


• Many thanks. For my question edit, can I make a new node using this syntax \node [tmp, below = 2cm of ($(output)!0.5!(integrator)$) ] (tmp1) {};? – Diaa Nov 15 '18 at 11:13
• @Diaa Something like \node [block, yshift=-2cm] (yaw) at ($(aux)!.5!(sum2)$) {C}; works for me. Instead of yshift you could also use below=2cm but with a different result. The calc expression in positioning option didn't work for me. – Ignasi Nov 15 '18 at 11:24
• @Diaa In any case I don't see the problem in using auxiliary coordinates/nodes. What's wrong with them? – Ignasi Nov 15 '18 at 11:25
• Nothing wrong; I just want to teach myself how to reduce my code :) – Diaa Nov 15 '18 at 11:31

Your approach does not work because you try to use { and } where you should use ($ and $). You can definitely do that without auxiliary coordinates and actually even without calc.

\documentclass{article}
\usepackage{tikz,mathtools,amssymb}
\usetikzlibrary{shapes,arrows,positioning,calc}

\begin{document}

\tikzset{
block/.style = {draw, fill=white, rectangle, minimum height=3em, minimum width=3em},
tmp/.style  = {coordinate},
sum/.style= {draw, fill=white, circle, node distance=1cm},
input/.style = {coordinate},
output/.style= {coordinate},
pinstyle/.style = {pin edge={to-,thin,black}
}
}

\begin{tikzpicture}[auto, node distance=2cm,>=latex',align=center]
\node [sum] (sum2) {};
\node [block, right = 1cm of sum2](ractuator){$\frac{2}{s+2}$};
\node [block, right = 1cm of ractuator,] (vdynamics) {$\frac{-0.125(s+0.437)}{(s+1.29)(s+0.193)}$};
\node [block, right = 1cm of vdynamics,] (integrator) {$\frac{1}{s}$};
\node [output, right = 1.5cm of integrator] (output) {};
\node [block] (yaw) at
($(0,-2cm)+($(output)!0.5!(integrator)$)!0.5!(sum2)$) {C};
%
\draw [->] (ractuator) -- (vdynamics);
\draw [->] (vdynamics) -- (integrator);
\draw [->] (integrator) -- node[name=heading]{$\Psi(s)$} (output)
coordinate[midway] (aux);
\draw (aux) |- (yaw) -| (sum2);
\end{tikzpicture}

\bigskip

\begin{tikzpicture}[auto, node distance=2cm,>=latex',align=center]
\node [sum] (sum2) {};
\node [block, right = 1cm of sum2](ractuator){$\frac{2}{s+2}$};
\node [block, right = 1cm of ractuator,] (vdynamics) {$\frac{-0.125(s+0.437)}{(s+1.29)(s+0.193)}$};
\node [block, right = 1cm of vdynamics,] (integrator) {$\frac{1}{s}$};
\node [output, right = 1.5cm of integrator] (output) {};
\node [block] (yaw) at
([yshift=-2cm]barycentric cs:output=1,integrator=1,sum2=2) {C};
%
\draw [->] (ractuator) -- (vdynamics);
\draw [->] (vdynamics) -- (integrator);
\draw [->] (integrator) -- node[name=heading]{$\Psi(s)$} (output)
coordinate[midway] (aux);
\draw (aux) |- (yaw) -| (sum2);
\end{tikzpicture}

\end{document}


• I am sorry, but could you tell me where I can find more explanation on this line ([yshift=-2cm] barycentric cs:output=1,integrator=1,sum2=2)? – Diaa Nov 15 '18 at 14:45
• @Diaa Section 13.2.2 Barycentric Systems of the pgfmanual. Come on, it only has 1161 pages. (Just kidding! ;-) – marmot Nov 15 '18 at 14:47
• XD. If you don't mind, I have off-topic question: when saying node distance = 2 cm, it measures this distance between the nodes centers. Is it possible to make this distance imply the spacing between (left node.east) and (right node.west) instead? – Diaa Nov 15 '18 at 14:58
• @Diaa I am not sure I agree with your statement. You are already loading positioning, in which case the distances are measured between the node boundaries (modulo a very tiny bit of fine print). Try e.g. \node [block, right=of sum2](ractuator){$\frac{2}{s+2}$}; in your settings. Then you will see that the distance between the node boundaries, and not centers, is 2cm, which is the value of node distance in your code. – marmot Nov 15 '18 at 15:03
• I tried drawing a new node \node [block, above of = yaw, draw=none, node distance=1mm] {Yaw Rate\\Sensor}; and the result is two overlapping nodes as seen here. – Diaa Nov 15 '18 at 15:28

Here, to simplify the code, I'll replace (integrator) with (A), (output) with (B) and (sum2) with (C). There is two things not right with ($(A) + 0.5*{ (B)-(A) }!0.5!(C)$).

• First, I don't think you can use {}, with the calc package, for the coordinate part. For me, it only works for with scalar. So (${2+2}*(A)$) will compute, but not ($2*{(A)+(B)}$) (or am I wrong?)

• The second thing is that this formula doesn't seem to correspond to the point you want. I kind of get that you want to start from (A), "move" to the middle of [AB] and continue like that, but you mix relative (B-A) and absolute positioning (C). One right formula would have been (${ (A) + 0.5*{(B)-(A)} }!0.5!(C)$). But because tikz can't do the computation, you'll have to give the expanded formula: ($.25*(A) + .25*(B) + .5*(C)$).

One other way to do it is ($(A) !.5! (B) !.5! (C)$). Here, we take the middle of (A) and (B), and then the middle of the result and (C).

I hope this will answer your interrogations!

You can test the three solutions here (the last one with temporary coordinate):

\documentclass[tikz,margin=10pt]{standalone}
\usetikzlibrary{calc}

\begin{document}

\begin{tikzpicture}[line width=1]

\draw[black!10] (0,0) grid (4,4);
\node (A) at (1,1) {A};
\node (B) at (3,1) {B};
\node (C) at (2,3) {C};

%% 1
\draw[red] ($(A) !.5! (B) !.5! (C)$) circle (.05);
%% 2
\draw[orange] ($.25*(A) + .25*(B) + .5*(C)$) circle (.1);
%% 3
\coordinate (foo) at ($(A) !.5! (B)$);
\draw[yellow] ($(foo) !.5! (C)$) circle (.15);

\end{tikzpicture}
\end{document}


which gives

• Thanks for the answer, but I didn't interrogate :) – Diaa Nov 15 '18 at 15:29

The calc library allows you to apply Parway Modifiers repeatedly. Thus, the following syntax

($(integrator)!.5!!(output)!0.5!(sum2)$)


does the following:

• pgf calculates the middle of (integrator) and (output)
• then calculates the middle of this last calculated point and the next one (sum2)

We can continue like this as many times as we want.

Here is for example page 144 of the manual 3.0.1a modified by adding two more points.

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

\begin{document}
\begin{tikzpicture}[every node/.style={draw,circle,inner sep=1pt}]
\draw [help lines] (0,0) grid (3,2);
%first node
\draw[densely dotted] (0,0) -- (3,2);
\node[] at ($(0,0)!.3!(3,2)$) {1};
%second node
\draw[densely dotted] ($(0,0)!.3!(3,2)$) -- (3,0);
\node[] at ($(0,0)!.3!(3,2)!.7!(3,0)$){2};

%third node
\draw[densely dotted] ($(0,0)!.3!(3,2)!.7!(3,0)$)--(3,2);
\node[]at ($(0,0)!.3!(3,2)!.7!(3,0)!.6!(3,2)$) {3};

%fourth node
\draw[densely dotted] ($(0,0)!.3!(3,2)!.7!(3,0)!.6!(3,2)$)--(0,2);
\node[]at ($(0,0)!.3!(3,2)!.7!(3,0)!.6!(3,2)!.5!(0,2)$) {4};
\end{tikzpicture}

\end{document}


Unfortunately, this does not simplify the writing of the code. The use of an auxiliary point as @Ignasi did is therefore more elegant.

## Updated just for fun: A complete solution with the calc library

And without using yshift=-2cm and without intermediate point (It's really complicated and unreadable!)

\draw (sum2)|-($(integrator)!.5!(output)!0.5!(sum2)!2cm!90:(sum2)$)node[block]{C}-|($(integrator)!.5!(output)$);


But which places the point in the same place with the syntax indicated in the manual 3.0.1a p143, i quote:

The general meaning of <a>!<factor>!<angle>:<b> is “First, consider the line from <a> to <b>. Then rotate this line by <angle> around the point <a>.

\documentclass{article}
\usepackage{tikz,mathtools,amssymb}
\usetikzlibrary{shapes,arrows,positioning,calc}

\begin{document}

\tikzset{
block/.style = {draw, fill=white, rectangle, minimum height=3em, minimum width=3em},
tmp/.style  = {coordinate},
sum/.style= {draw, fill=white, circle, node distance=1cm},
input/.style = {coordinate},
output/.style= {coordinate},
pinstyle/.style = {pin edge={to-,thin,black}
}
}

\begin{tikzpicture}[auto, node distance=2cm,>=latex',align=center]
\node [sum] (sum2) {};
\node [block, right = 1cm of sum2](ractuator){$\frac{2}{s+2}$};
\node [block, right = 1cm of ractuator,] (vdynamics) {$\frac{-0.125(s+0.437)}{(s+1.29)(s+0.193)}$};
\node [block, right = 1cm of vdynamics,] (integrator) {$\frac{1}{s}$};
\node [output, right = 1.5cm of integrator] (output) {};
\draw (sum2)|-($(integrator)!.5!(output)!0.5!(sum2)!2cm!90:(sum2)$)node[block]{C}-|($(integrator)!.5!(output)$);
\draw [->] (ractuator) -- (vdynamics);
\draw [->] (vdynamics) -- (integrator);
\draw [->] (integrator) -- node[name=heading]{$\Psi(s)$} (output);

\end{tikzpicture}
\end{document}


Nevertheless, here is a solution that includes a series of Parway Modifiers.

\documentclass{article}
\usepackage{tikz,mathtools,amssymb}
\usetikzlibrary{shapes,arrows,positioning,calc}

\begin{document}

\tikzset{
block/.style = {draw, fill=white, rectangle, minimum height=3em, minimum width=3em},
tmp/.style  = {coordinate},
sum/.style= {draw, fill=white, circle, node distance=1cm},
input/.style = {coordinate},
output/.style= {coordinate},
pinstyle/.style = {pin edge={to-,thin,black}
}
}

\begin{tikzpicture}[auto, node distance=2cm,>=latex',align=center]
\node [sum] (sum2) {};
\node [block, right = 1cm of sum2](ractuator){$\frac{2}{s+2}$};
\node [block, right = 1cm of ractuator,] (vdynamics) {$\frac{-0.125(s+0.437)}{(s+1.29)(s+0.193)}$};
\node [block, right = 1cm of vdynamics,] (integrator) {$\frac{1}{s}$};
\node [output, right = 1.5cm of integrator] (output) {};
\draw (sum2)|-([yshift=-2cm]$(integrator)!.5!(output)!0.5!(sum2)$)node[block]{C}-|($(integrator)!.5!(output)$);

\draw [->] (ractuator) -- (vdynamics);
\draw [->] (vdynamics) -- (integrator);
\draw [->] (integrator) -- node[name=heading]{$\Psi(s)$} (output);

\end{tikzpicture}
\end{document}


Translated with www.DeepL.com/Translator

one way how to reduce your code:

• use tikz librarychains placement nodes in chain and draw lines between them by macro join
• node "c" in feedback simple pace below of node vdynamics
• put coordinates in image directly and not via nodes
• coordinates can contain labels, exploit this for label $\Psi$
• define nodes distance only ones and than use it all all nodes positioning

\documentclass{article}
\usepackage{tikz,nccmath,amssymb}
\usetikzlibrary{arrows,
calc, chains,
positioning,
shapes}

\begin{document}

\tikzset{
block/.style  = {draw, fill=white, rectangle, minimum size=3em,
on chain, join=by ->},
sum/.style  = {draw, fill=white, circle},
}
\makeatletter
\tikzset{suspend join/.code={\def\tikz@after@path{}}}   % <--- for dicountinue of jon macro
\makeatother

\begin{tikzpicture}[
node distance = 0.5cm and 1cm,
start chain = going right,
> = latex']
\coordinate (in);
\node [sum,right=of in, on chain] (sum2)    {};
\node [block]   (ractuator)     {$\mfrac{2}{s+2}$};
\node [block]   (vdynamics)     {$\mfrac{-0.125(s+0.437)}{(s+1.29)(s+0.193)}$};
\node [block]   (integrator)    {$\mfrac{1}{s}$};
\coordinate[right=of integrator] (out)      {};
\node [block, suspend join,
below = of vdynamics]  (yaw) {C};
%
\draw[->]   (in) -- (sum2);
\draw[->]   (integrator) -- coordinate[label=$\Psi(s)$] (psi) (out);
\draw[->]   (psi) |- (yaw);
\draw[->]   (yaw) -| (sum2);
\end{tikzpicture}
\end{document}


off-topic: for fraction is used \mfrac (medium sized fraction) defined in the nccmath package