# Tangent line of an arbitrary point on a path \documentclass{article}
\usepackage{tikz}
\usetikzlibrary{decorations.markings}

\begin{document}

\begin{tikzpicture}[
tangent/.style={
decoration={
markings,% switch on markings
mark=
at position #1
with
{
\coordinate (tangent point-\pgfkeysvalueof{/pgf/decoration/mark info/sequence number}) at (0pt,0pt);
\coordinate (tangent unit vector-\pgfkeysvalueof{/pgf/decoration/mark info/sequence number}) at (1,0pt);
\coordinate (tangent orthogonal unit vector-\pgfkeysvalueof{/pgf/decoration/mark info/sequence number}) at (0pt,1);
}
},
postaction=decorate
},
use tangent/.style={
shift=(tangent point-#1),
x=(tangent unit vector-#1),
y=(tangent orthogonal unit vector-#1)
},
use tangent/.default=1
]
\draw [
tangent=0.4,
tangent=0.56
] (0,0)
to [out=20,in=120] (5,2)
to [out=-60, in=110] (9,1);
\draw [blue, thick, use tangent] (-3,0) -- (3,0);
\draw [orange, thick, use tangent=2] (-2,0) -- (2,0) (0,0) -- (0,1);
\end{tikzpicture}
\end{document}

## One Reply to “Tangent line of an arbitrary point on a path”

1. Jili Feng says:

Dear Prof,

why does not it work as your codes where only a curve is replaced by plot? Thanks for your help.

Best regards,

Jili

\documentclass[tikz,border=0.5mm]{standalone}
\usepackage{tikz}
\usetikzlibrary{decorations.markings}

\begin{document}
%Tangent line of an arbitrary point on a path
\begin{tikzpicture}[
tangent/.style={
decoration={
markings,% switch on markings
mark=
at position #1
with
{
\coordinate (tangent point-\pgfkeysvalueof{/pgf/decoration/mark info/sequence number}) at (0pt,0pt);
\coordinate (tangent unit vector-\pgfkeysvalueof{/pgf/decoration/mark info/sequence number}) at (1,0pt);
\coordinate (tangent orthogonal unit vector-\pgfkeysvalueof{/pgf/decoration/mark info/sequence number}) at (0pt,1);
}
},
postaction=decorate
},
use tangent/.style={
shift=(tangent point-#1),
x=(tangent unit vector-#1),
y=(tangent orthogonal unit vector-#1)
},
use tangent/.default=1
]
\draw[help lines] (0,0)grid (10,4);
\draw [
tangent=0.1,
tangent=0.4
]
plot[smooth,tension=0.6] coordinates{ (0,0) (5,2) (10,0) };
%(0,0)
%to [out=20,in=120] (5,2)
%to [out=-60, in=110] (9,1);
\draw [blue, thick, use tangent] (0,0) — (1,0);
\draw [orange, thick, use tangent=2] (-1,0) — (1,0) (0,0) — (0,0.5);
\end{tikzpicture}
\end{document}