\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}