How to “simplify” the syntax of a particular coordinate system in TikZ?

I am writing a document in which I use coordinate system barycentric very many times. So a MWE looks like this

\documentclass[tikz]{standalone}
\begin{document}
\begin{tikzpicture}
\fill (1,4) circle (1pt) coordinate (a) node[above] {$A$}
(0,0) circle (1pt) coordinate (b) node[below] {$B$}
(5,0) circle (1pt) coordinate (c) node[below] {$C$};
\draw (a) -- (b) -- (c) -- cycle;
\fill[red] (barycentric cs:a=1/3,b=1/3,c=1/3) circle (1pt) node[below] {$G$};
\end{tikzpicture}
\end{document}


But it doesn't look so short and concise, does it? When I need to use barycentric a lot, this is really inconvenient.

I want to have something like this:

\tikzset{barycentric coordinates={(a),(b),(c)}}
...
\path[barycentric] (1/3,1/3,1/3) coordinate (x);


being equivalent to

\path (barycentric cs:a=1/3,b=1/3,c=1/3) coordinate (x);


Is it possible?

Of course I can define a macro for this (and I am using this way), but I think the above is much more flexible.

If you have always three (or less) coordinates, there is no problem. TikZ has this out of the box. You only need

\begin{scope}[x={(a)},y={(b)},z={(c)}]
<in this scope your syntax works>
\end{scope}


Full MWE:

\documentclass[tikz]{standalone}
\begin{document}
\begin{tikzpicture}
\fill (1,4) circle (1pt) coordinate (a) node[above] {$A$}
(0,0) circle (1pt) coordinate (b) node[below] {$B$}
(5,0) circle (1pt) coordinate (c) node[below] {$C$};
\draw (a) -- (b) -- (c) -- cycle;
\fill[red] (barycentric cs:a=1/3,b=1/3,c=1/3) circle (1pt) node[below] {$G$};
\begin{scope}[x={(a)},y={(b)},z={(c)}]
\end{scope}
\end{tikzpicture}
\end{document}


This is, however, not a true barycentric coordinate system because it does not do the normalization. In your example where the components add up to one this is fine, though.

If you want to use something that resembles your syntax, allows for an arbitrary number of coordinates and normalizes the coordinates, then consider this:

\documentclass[tikz]{standalone}
\makeatletter
\tikzdeclarecoordinatesystem{b}
{%
{%
\pgf@xa=0pt% point
\pgf@ya=0pt%
\pgf@xb=0pt% sum
\pgfutil@tempcnta=0%
\tikz@b@dolist#1,,%
\pgfmathparse{1/\the\pgf@xb}%
\global\pgf@x=\pgfmathresult\pgf@xa%
\global\pgf@y=\pgfmathresult\pgf@ya%
}%
}%

\def\tikz@b@dolist#1,{%
\def\tikz@temp{#1}%
\ifx\tikz@temp\pgfutil@empty%
\else
\pgf@process{\pgfpointanchor{\csname tikz@bcoord@\the\pgfutil@tempcnta\endcsname}{center}}%
\pgfmathparse{#1}%
\expandafter\tikz@b@dolist%
\fi%
}%
\tikzset{barycentric coordinates/.code={
\pgfutil@tempcnta=0%
\tikz@bc@dolist#1,,%
}}
\def\tikz@bc@dolist#1,{%
\def\tikz@temp{#1}%
\ifx\tikz@temp\pgfutil@empty%
\else
\expandafter\edef\csname tikz@bcoord@\the\pgfutil@tempcnta\endcsname{#1}%
\expandafter\tikz@bc@dolist%
\fi%
}%
\makeatother
\begin{document}
\begin{tikzpicture}
\fill (1,4) circle (1pt) coordinate (a) node[above] {$A$}
(0,0) circle (1pt) coordinate (b) node[below] {$B$}
(5,0) circle (1pt) coordinate (c) node[below] {$C$}
(4,3) circle (1pt) coordinate (d) node[below] {$D$}     ;
\draw (a) -- (b) -- (c) -- (d) -- cycle;
\fill[red] (barycentric cs:a=1/3,b=1/3,c=1/3) circle (1pt) node[below] {$G$};
\begin{scope}[barycentric coordinates={a,b,c}]
\draw (b cs:1,1,1) circle[radius=2pt];
\end{scope}
\fill[red] (barycentric cs:a=1/4,b=1/4,c=1/4,d=1/4) circle (1pt) node[below] {$H$};
\begin{scope}[barycentric coordinates={a,b,c,d}]
\draw (b cs:1,1,1,1) circle[radius=2pt];
\end{scope}
\end{tikzpicture}
\end{document}


You still have to write b cs: but other than it is the syntax you are proposing. (One could eliminate the need to add b cs:, see here, but this will make this code even more hacky, and this will AFAIK only work for 2 or 3 coordinates anyway.)

Since this is not infinitely well known, let me also mention ternary axes that can be loaded with \usepgfplotslibrary{ternary} in pgfplots. They, too, parse coordinates in the way you want.

• Oh, I did not know that TikZ's 3d has this feature! Thanks! – Someone Dec 22 '19 at 13:49

I prefer the notation A=1/3,B=1/3,C=1/3 [More concise, more readable] but it's a matter of taste. Here how I proceed with tkz-euclide

\documentclass[border=.25cm]{standalone}
\usepackage{tkz-euclide}

\begin{document}
\begin{tikzpicture}
\tkzDefPoints{1/4/A,0/0/B,5/0/C,4/3/D}
\tkzDefBarycentricPoint(A=1/3,B=1/3,C=1/3) \tkzGetPoint{G}
\tkzDefBarycentricPoint(A=1/4,B=1/4,C=1/4,D=1/4) \tkzGetPoint{H}

\tkzDrawPolygon(A,...,D)
\tkzDrawPoints[red](G,H)
\tkzDrawPoints(A,B,C,D)

\tkzLabelPoints(A,B,C,D,G,H)
\end{tikzpicture}
\end{document}

% why not
%  \tkzDefBarycentricPoint(A=1,B=1,C=1) \tkzGetPoint{G}
%  \tkzDefBarycentricPoint(A=1,B=1,C=1,D=1) \tkzGetPoint{H}


• Thanks for your answer! – Someone Dec 23 '19 at 9:45