Coordinate problem in connection with command "use"

Question

In the MWE the points P and M are the same although they are defined by different coordinates (by (0,0) and (0,3) respectively). (My aim is to define a point M on the blue polar and should be different from the touching point P and lying inside the ellipse.)

It seems that \coordinate[use tangent] (M) at (0,3); does not work properly, but it does with (0,0).

The tangent definition is from How do I make tangents to ellipses and lines parallel to these?

\documentclass{standalone}
\usepackage{tikz}
\usetikzlibrary{calc}
\usetikzlibrary{decorations.markings}
\usetikzlibrary{intersections}
\usepackage{pgfplots}
\pgfplotsset{compat=1.15}
\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
  ]
  \def\a{4} % major half axis
  \def\b{2} % minor half axis
  \draw[thick, tangent=0.35] (0,0) ellipse ({\a} and {\b});
  %polar
  \draw [blue, thick, use tangent] (0,3) -- (0,-2);
  \coordinate[use tangent] (P) at (0,0);
  \coordinate[use tangent] (M) at (0,3);
  \filldraw (P) circle (2pt);
  \node[left] at (P) {$P$};
  \node[right] at (M) {$M$};
 \end{tikzpicture}
\end{document}

score 1 · Accepted Answer · answered Jun 05 '21 at 11:29

You need to invoke use tangent each time when you want to draw something in the tangent frame (the correct name should be Frenet frame). I rewrote your code using a scope; I think it's easier to follow.

The code

\documentclass[margin=.5cm]{standalone}
\usepackage{tikz}
\usetikzlibrary{calc}
\usetikzlibrary{decorations.markings}
\usetikzlibrary{intersections}
\begin{document}
\tikzset{
  tangent/.style={
    decoration={
      markings,% switch on markings
      mark=at position #1 with {
        \coordinate (tangent point-%
        \pgfkeysvalueof{/pgf/decoration/mark info/sequence number})
        at (0, 0);
        \coordinate (tangent vector-%
        \pgfkeysvalueof{/pgf/decoration/mark info/sequence number})
        at (1, 0);
        \coordinate (normal vector-%
        \pgfkeysvalueof{/pgf/decoration/mark info/sequence number})
        at (0, 1);
      }
    },
    postaction=decorate
  },
  use tangent/.style={
    shift=(tangent point-#1),
    x=(tangent vector-#1),
    y=(normal vector-#1)
  },
  use tangent/.default=1
}
\def\a{4} % major half axis
\def\b{2} % minor half axis
\begin{tikzpicture}
  \draw[thick, tangent=0.3] (0, 0) ellipse ({\a} and {\b});
% polar
  \begin{scope}[use tangent]
    \draw [blue, thick] (0, 3) -- (0, -1);
    \draw[fill=white]
    (0, 0) coordinate (P) circle (2pt) node[above left] {$P$}
    (0, 3) coordinate (M) circle (2pt) node[below right] {$M$};
  \end{scope}
\end{tikzpicture}
\end{document}

Coordinate problem in connection with command "use"

1 Answers1