drawing a line without coordinates

Question

I want to draw a line that goes through a point A en B but does not stop at A nor at B. Can anybody help. I want to use it for constructions in optics.

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{intersections}
\begin{document}
\begin{tikzpicture}
  \draw[very thin, dotted, color=gray,step= 0.5 cm] (-12.1,-5.1) grid (12.1,5.1);
  \draw (-12.1,0) -- (12.1,0) ;
  \draw [<->, ultra thick] (0,-3.2) -- (0,3.2) ;
  \coordinate (L1) at (0,3);
  \coordinate (L2) at (0,-3);
  \coordinate (L3) at (0,1.5); %evenwijdig met hoofdas
  \coordinate (V1) at (9,0);
  \coordinate (V2) at (9,1.5);
  \coordinate (F1) at (4,0);
  \coordinate (F2) at (-4,0);
  \draw [->, thick] (V1) -- (V2) node[right] {voorwerp};
  \fill (F1) circle (2pt) node[below] {$f_1$};
  \fill (F2) circle (2pt) node[below] {$f_2$};
  \draw [name path=A--B] (V2) -- (L3);
  \draw [name path=C--D] (L1) -- (L2);
  \path [name intersections={of=A--B and C--D,by=E}];
  \node [fill=red,inner sep=1pt,label=-90:$E$] at (E) {};
  \draw [name path=K--L] (E) -- (F2);
  \line(4,2){6};
\end{tikzpicture}
\end{document}

Answer 1

Here's one possibility using the <coord>!<number>!<coord> syntax; the line will extend past both coordinates by 1cm:

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

\begin{document}

\begin{tikzpicture}
\node[circle,fill=green,label=left:a] (a) at (1,0) {};
\node[circle,fill=green,label=left:b] (b) at (3,2) {};
\draw[blue] ($ (a)!-1cm!(b) $) -- ($ (b)!-1cm!(a) $);
\end{tikzpicture}

\end{document}

Sections 13.5.3 The Syntax of Partway Modifiers and 13.5.4 The Syntax of Distance Modifiers of the pgfmanual contain the description of useful operations involving coordinates.

The shorten option gives another simpler alternative:

\documentclass{article}
\usepackage{tikz}

\begin{document}

\begin{tikzpicture}
\node[circle,fill=green,label=left:a] (a) at (1,0) {};
\node[circle,fill=green,label=left:b] (b) at (3,2) {};
\node[circle,fill=green,label=left:c] (c) at (5,2) {};
\node[circle,fill=green,label=left:d] (d) at (7,0) {};
\draw[blue,shorten >=-1cm,shorten <=-1cm] (a) -- (b);
\draw[red,shorten >=-2cm,shorten <=-1cm] (c) -- (d);
\end{tikzpicture}

\end{document}

Answer 2

an alternative that I like to use

\documentclass{article}
\usepackage{tikz}

\begin{document}

\begin{tikzpicture}
\path (1,0) node[label=above:a,circle,fill=green,](a){} -- 
      (3,2)node[label=above:b,circle,fill=green,](b){} 
      coordinate[pos=1.5](ff) 
      coordinate[pos=-0.5](dd);
\draw (dd) -- (ff);
\end{tikzpicture}    
\end{document}

Using [pos = xx] to place a point ( node or coordinates) as well as between the two points at the segment beyond. Negative values ​​are used to place the point before the first.

Answer 3

A PSTricks solution just for comparison purpose.

\documentclass[pstricks,border=12pt]{standalone}
\usepackage{pst-eucl}

\begin{document}
\begin{pspicture}[showgrid](5,5)
    \pstGeonode[PosAngle={90}]
        (2,2){A}
        (3,3){B}
    \pstLineAB[nodesep=-1,linecolor=red]{A}{B}
\end{pspicture}
\end{document}

We can use nodesepA and nodesepB instead of nodesep if we want to have asymmetric line extension.