Xrfgtjtk

Here's what I currently have to type:

documentclass{standalone}



usepackage{tikz}



begin{document}

begin{tikzpicture}

  coordinate (a) at (90:3cm);

  coordinate (b) at (210:3cm);

  coordinate (c) at (-30:3cm);



  node [above] at (a) {$a$};

  node [below left] at (b) {$b$};

  node [below right] at (c) {$c$};



  draw [thick,green, fill=green,opacity=0.5]

  (barycentric cs:a=1,b=0,c=0) --

  (barycentric cs:a=1,b=0,c=1) --

  (barycentric cs:a=1,b=1,c=0) -- cycle;



  draw [ultra thick] (a) -- (b) -- (c) --cycle;

end{tikzpicture}

end{document}

This is a little tedious. Since I'll want to draw lots of shapes using the same a,b,c-based barycentric coordinates. Is there a way to pass an option to scope for example that would allow me to have (1,0,1) evaluate as (barycentric cs:a=1,b=0,c=1)?

If it is ok for you to use normalized barycentric coordinates, ie (x,y,z) such that x+y+z=1, then you can simply set x=(a),y=(b),z=(c). So in place of (1,1,0) you should use (.5,.5,0).

documentclass{standalone}

usepackage{tikz}



begin{document}

  begin{tikzpicture}

    path

      (90:3cm) coordinate (a) node[above] {$a$}

      (210:3cm) coordinate (b) node[below left] {$b$}

      (-30:3cm) coordinate (c) node[below right] {$c$};



    draw [thick,green, fill=green,opacity=0.5]

      (barycentric cs:a=1,b=0,c=0) --

      (barycentric cs:a=1,b=0,c=1) --

      (barycentric cs:a=1,b=1,c=0) -- cycle;



    draw [ultra thick] (a) -- (b) -- (c) --cycle;



    % set x=(a),y=(b),z=(c) and use normalized barycentric coordinates

    draw[ultra thick, red, dashed, x=(a),y=(b),z=(c)]

    (1,0,0)  -- (.5,0,.5) -- (.5,.5,0) --cycle;

  end{tikzpicture}

end{document}

You can define

newcommand{foo}[3]{(barycentric cs:a=#1,b=#2,c=#3)}

and then use it as

  draw [thick,green, fill=green,opacity=0.5]

  foo{1}{0}{0} --

  foo{1}{0}{1} --

  foo{1}{1}{0} -- cycle;

or combine with another command with 9 parameters

newcommand{faa}[9]{

  draw [thick,green, fill=green,opacity=0.5]

  foo{#1}{#2}{#3} --

  foo{#4}{#5}{#6} --

  foo{#7}{#8}{#9} -- cycle;

}

and use as

faa{1}{0}{0}{1}{0}{1}{1}{1}{1}

MWE

documentclass{standalone}



usepackage{tikz}

newcommand{foo}[3]{(barycentric cs:a=#1,b=#2,c=#3)}

newcommand{faa}[9]{

  draw [thick,green, fill=green,opacity=0.5]

  foo{#1}{#2}{#3} --

  foo{#4}{#5}{#6} --

  foo{#7}{#8}{#9} -- cycle;

}

begin{document}

begin{tikzpicture}

  coordinate (a) at (90:3cm);

  coordinate (b) at (210:3cm);

  coordinate (c) at (-30:3cm);



  node [above] at (a) {$a$};

  node [below left] at (b) {$b$};

  node [below right] at (c) {$c$};



  draw [thick,green, fill=green,opacity=0.5]

  foo{1}{0}{0} --

  foo{1}{0}{1} --

  foo{1}{1}{0} -- cycle;



  faa{1}{0}{0}{1}{0}{1}{1}{1}{1}



  draw [ultra thick] (a) -- (b) -- (c) --cycle;

end{tikzpicture}

end{document}

You can also use insert path to abbreviate the coordinates.

documentclass{standalone}



usepackage{tikz}



begin{document}

begin{tikzpicture}[bcs/.style args={#1|#2|#3}{insert path={--(barycentric

cs:a=#1,b=#2,c=#3)}}]

  coordinate (a) at (90:3cm);

  coordinate (b) at (210:3cm);

  coordinate (c) at (-30:3cm);



  node [above] at (a) {$a$};

  node [below left] at (b) {$b$};

  node [below right] at (c) {$c$};



  draw [thick,green, fill=green,opacity=0.5] (a)

  [bcs={1|0|1},bcs={1|1|0}] -- cycle;



  draw [ultra thick] (a) -- (b) -- (c) --cycle;

end{tikzpicture}

end{document}

Another thing you could do is to locally change the TikZ parser. Then the whole path really boils down to

  begin{scope}[bary={a}{b}{c}]

   draw [thick,green, fill=green,opacity=0.5] 

    (1,0,0) -- (1,0,1) -- (1,1,0) -- cycle;

  end{scope}

where bary={a}{b}{c} install the barycentric coordinate system in the scope (we don't want it everywhere) and you really just have to specify the three numbers.

documentclass[tikz,border=3.14mm]{standalone}



makeatletter % https://tex.stackexchange.com/a/365418/121799

tikzset{bary/.code n args={3}{

  deftikz@parse@splitxyz##1##2##3,##4,{%

    def@next{tikz@scan@one@point##1(barycentric cs:#1=##2,#2=##3,#3=##4)}%

    }}}

makeatother



begin{document}

begin{tikzpicture}

  coordinate (a) at (90:3cm);

  coordinate (b) at (210:3cm);

  coordinate (c) at (-30:3cm);



  node [above] at (a) {$a$};

  node [below left] at (b) {$b$};

  node [below right] at (c) {$c$};

  begin{scope}[bary={a}{b}{c}]

  draw [thick,green, fill=green,opacity=0.5] 

  (1,0,0) -- (1,0,1) -- (1,1,0) -- cycle;

  end{scope}   

  draw [ultra thick] (a) -- (b) -- (c) --cycle;

end{tikzpicture}

end{document}