"Stroke" a predefined path

Question

I would like to use the name of a previous defined path to draw it later on in my code. I have included an example below, where I define two paths, "D1" and "S1", and then later on, draw these very sames paths. In the example, I draw the paths, using essentially the same code, which is redundant. Is there a way to recall the name of the path and draw a line using the previously defined path?

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

\begin{document}

\begin{tikzpicture}[yscale=3,xscale=3]

%Pre-Define Paths

\path[name path=D1] (0,1.8) -- (1.8,0);
\path[name path=S1] (0,0) -- (1.8,1.8);
\path[name intersections={of=D1 and S1,by=EQ}];

%axis

\draw[->,thick] (0,0) -- (3,0) node[right,fontscale=0] {Quantity};
\draw[->,thick] (0,0) -- (0,2) node[left,fontscale=0] {Price};

%Initial Equilibrium

\fill[black] (EQ) circle (.5pt) node[right] {$EQ$};
\draw[blue] (0,1.8) -- (1.8,0);
\draw[red] (0,0) -- (1.8,1.8);


\end{tikzpicture}

\end{document}

Answer 1

You can use the undocumented save path key that saves the whole path on a very low level in a macro. You can use this path again with the use path key defined as

\makeatletter
\tikzset{use path/.code=\tikz@addmode{\pgfsyssoftpath@setcurrentpath#1}}
\makeatother

Any path operators shouldn’t be used here.

If you want to save part of a path and want to use them later (maybe also only as a part), you can use the saveuse path key from another answer of mine defined as

\tikzset{
  saveuse path/.code 2 args={
    \pgfkeysalso{#1/.estyle={insert path={#2}}}%
    \global\expandafter\let\csname pgfk@\pgfkeyscurrentpath/.@cmd\expandafter\endcsname % not optimal as it is now global through out the document
                           \csname pgfk@\pgfkeyscurrentpath/.@cmd\endcsname
    \pgfkeysalso{#1}%
  }
}

The saveuse path key saves a path as an insert path key (and uses it also) which can be used later for the same path (as long as you don’t change the transformation matrix).

Code A

\documentclass[tikz,convert=false]{standalone}
\usetikzlibrary{intersections}
\makeatletter
\tikzset{use path/.code=\tikz@addmode{\pgfsyssoftpath@setcurrentpath#1}}
\makeatother
\begin{document}
\begin{tikzpicture}[yscale=3,xscale=3]

%Pre-Define Paths
\path[save path=\pathA,name path=D1] (0,1.8) -- (1.8,0);
\path[save path=\pathB,name path=S1] (0,0) -- (1.8,1.8);
\path[name intersections={of=D1 and S1,by=EQ}];

%axis
\draw[->,thick] (0,0) -- (3,0) node[right] {Quantity};
\draw[->,thick] (0,0) -- (0,2) node[left] {Price};

%Initial Equilibrium
\fill[black] (EQ) circle (.5pt) node[right] {$EQ$};
\draw[blue][use path=\pathA];
\draw[red] [use path=\pathB];
\end{tikzpicture}
\end{document}

Code B

\documentclass[tikz,convert=false]{standalone}
\usetikzlibrary{intersections}
\tikzset{
  saveuse path/.code 2 args={
    \pgfkeysalso{#1/.estyle={insert path={#2}}}%
    \global\expandafter\let\csname pgfk@\pgfkeyscurrentpath/.@cmd\expandafter\endcsname % not optimal as it is now global through out the document
                           \csname pgfk@\pgfkeyscurrentpath/.@cmd\endcsname
    \pgfkeysalso{#1}%
  }
}
\begin{document}
\begin{tikzpicture}[yscale=3,xscale=3]

%Pre-Define Paths
\path[name path=D1] [saveuse path={pathA}{(0,1.8) -- (1.8,0)}];
\path[name path=S1] [saveuse path={pathB}{(0,0) -- (1.8,1.8)}];
\path[name intersections={of=D1 and S1,by=EQ}];

%axis
\draw[->,thick] (0,0) -- (3,0) node[right] {Quantity};
\draw[->,thick] (0,0) -- (0,2) node[left] {Price};

%Initial Equilibrium
\fill[black] (EQ) circle (.5pt) node[right] {$EQ$};
\draw[blue][pathA];
\draw[red] [pathB];
\end{tikzpicture}
\end{document}

Answer 2

A simple solution is to store the path D1 in a variable \D1, and so for S1. Then use this variable as many times as needed. Here is an example:

\documentclass[12pt]{article}
\usepackage{amsmath}
\usepackage{enumerate}
\usepackage{tikz}
\usepackage{xcolor}
\usepackage{tikz-3dplot}
\usepackage{hyperref}
\usepackage{ifthen}
\usepackage{pgfplots}

\usetikzlibrary{calc,3d,shapes, pgfplots.external, intersections}
\pgfplotsset{compat=1.11} 

\begin{document}
\begin{tikzpicture}[yscale=3,xscale=3]

%Pre-Define Paths

  \def\D1{(0,1.8) -- (1.8,0)}
  \def\S1{(0,0) -- (1.8,1.8)}

\path[name path=D1] \D1;
\path[name path=S1] \S1;
\path[name intersections={of=D1 and S1,by=EQ}];

%axis

\draw[->,thick] (0,0) -- (3,0) node[right] {Quantity};
\draw[->,thick] (0,0) -- (0,2) node[left] {Price};

%Initial Equilibrium

\fill[black] (EQ) circle (.5pt) node[right] {$EQ$};
\draw[blue] \D1;
\draw[red] \S1;

\end{tikzpicture}
\end{document}

Here is the figure: