Line through two points with offset in TikZ

Question

I could not find a native command in TikZ allowing to draw a line going through two specified points where an offset can be controlled. So far, I'm using the calc extension to perform what I need but there may be something better:

\documentclass[12pt]{book}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{tikz}
\usetikzlibrary{calc}
\begin{document}
\begin{tikzpicture}
\coordinate (V1) at (0.5,2.25); % initial point 1
\coordinate (V2) at (1.5,3.25); % initial point 2
\coordinate (V3) at ($1.2*(V1)-0.2*(V2)$); % offset 1
\coordinate (V4) at ($-0.2*(V1)+1.2*(V2)$); % offset 2
\draw (V3)--(V4); % line with offset
\end{tikzpicture}
\end{document}

Answer 1

It's defined in tkz-base. You need to give % of the line added at the right and at the left. It's useful to get 2*AB; 3*AB etc.

\documentclass[12pt]{scrartcl}
\usepackage{tikz}
\usetikzlibrary{calc}
\begin{document}

\tikzset{%
    add/.style args={#1 and #2}{
        to path={%
 ($(\tikztostart)!-#1!(\tikztotarget)$)--($(\tikztotarget)!-#2!(\tikztostart)$)%
  \tikztonodes},add/.default={.2 and .2}}
}  

\begin{tikzpicture}
\coordinate (A) at (0,0);
\coordinate (B) at (4,2);
\node at (A) {$\bullet$};
\node at (B) {$\bullet$};
\draw [add= 1 and .5, red, ultra thick] (A) to (B);
\end{tikzpicture}   

\end{document} 

Application

\begin{tikzpicture}
\coordinate (A) at (0,0);
\coordinate (B) at (1,0);
\foreach \t in {-0.25,0,...,4}
{\draw [add= {\t} and {\t}, 
       red,
       ultra thick] ([yshift=1.5*\t cm]A) to  ([yshift=1.5*\t cm]B) ;}
\end{tikzpicture}

Answer 2

If all you want to do is to extend the line in both directions you can use shorten >=<length> and shorten <=<length> and provide a negative length:

\draw [shorten >= -0.25cm, shorten <=-0.30cm] (V1)--(V2);

To be able to see this, I have defined new coordinate (V1') and (V2') which are offset horizontally from the original. The black line is your manually extended line from (V1) to (V2) (ie, (V3)--(V4)), and the red is a line from (V1') -- (V2') extended using the shorten specification. The location of each these coordinate is shown by the blue circle.

Code:

\documentclass[12pt]{book}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{tikz}
\usetikzlibrary{calc}
\begin{document}
\begin{tikzpicture}
\coordinate (V1) at (0.5,2.25); % initial point 1
\coordinate (V2) at (1.5,3.25); % initial point 2
\coordinate (V3) at ($1.2*(V1)-0.2*(V2)$); % offset 1
\coordinate (V4) at ($-0.2*(V1)+1.2*(V2)$); % offset 2

\draw [black, thick] (V3)--(V4); % line with offset (manually extended)


%% Shift the coordinate to be able to see the result
\coordinate (V1') at ($(V1) + (0.50cm,0)$);
\coordinate (V2') at ($(V2) + (0.50cm,0)$);

%% Draw line but extend it in either direction (extended via shorten)
\draw [red, thick, shorten >= -0.25cm, shorten <=-0.30cm] (V1')--(V2');

%% Show the location of the coordinates -- useful for debugging
\draw [thin, gray,-latex]  (V1) -- (V1');
\draw [thin, gray,-latex]  (V2) -- (V2') ;
\foreach \name/\placement in {V1/left, V2/left, V3/left, V4/left, V1'/right, V2'/right} {%
    \node [fill=blue!50,shape=circle,inner sep=1pt] at (\name) {};
    \node [gray, \placement] at (\name) {\tiny $\name$};
}
\end{tikzpicture}
\end{document}

Answer 3

Another solution using [pos =] in the path.

\begin{tikzpicture}
\coordinate (A) at (0,0);
\coordinate (B) at (4,2);
\path (A) -- (B) coordinate[pos=-1](dd) coordinate[pos=1.5](ff);
\draw (dd) -- (A)node{$\bullet$}-- (B) node {$\bullet$}--(ff);
\end{tikzpicture}