hobby: TeX capacity exceeded (parameter stack size?) error, when using tangency information at a point to draw a path

Question

I am getting a TeX capacity exceeded error when running the following example code (which comes from the answer to this question:

\documentclass{article}

\usepackage{lmodern}
\usepackage[T1]{fontenc}

\usepackage{tikz}
\usetikzlibrary{calc, hobby}
\tikzset{tangent/.style = \tikzset{
        tangent/.style = {
            in angle={(180+#1)},
            Hobby finish,
            designated Hobby path=next,
            out angle=#1
        }
    }}

\begin{document}
    \begin{figure}[htbp]
        \centering
        \begin{tikzpicture}

        \coordinate (y) at (0,3);
        \coordinate (x) at (5,0);

        \coordinate (sp0) at (1.5, 0);
        \coordinate (ep0) at (3.5, 2);
        \coordinate (csp0) at (2.5, 1);
        \coordinate (cep0) at (2.75, 0);

        \coordinate (sp1) at (ep0);
        \coordinate (ep1) at (4.5, 3);
        \coordinate (csp1) at (4.25, 4);
        \coordinate (cep1) at (4.25, 2);

        \coordinate (sp2) at (sp0);
        \coordinate (ep2) at (0, -1);
        \coordinate (csp2) at (0.5, -1);
        \coordinate (cep2) at (0.5, -1);

        \draw[<->] (y) node[left] {$f(x)$} -- (0,0) --  (x) node[below] {$x$};

        % Using \pgfmathanglebetweenpoints to calculate the angle for tangent
        % tangent takes a degree unit angle
        \pgfmathanglebetweenpoints{\pgfpointanchor{cep0}{center}}{\pgfpointanchor{ep0}{center}}
        \let\angle=\pgfmathresult
        \draw (ep2) to [curve through ={(sp0) .. ([tangent=\angle]ep0)}] (ep1) ;

        \draw[dashed] (cep0) -- (csp1);
        \draw[dotted] let \p1 = (ep0) in (ep0) -- (0, \y1);
        \draw[dotted] let \p1 = (ep0) in (ep0)-- (\x1, 0);

        \draw let \p1 = (ep0) in (\x1,1pt) -- (\x1,-3pt) node[anchor=north] {$x_0$};
        \draw let \p1 = (cep0) in (\x1,1pt) -- (\x1,-3pt) node[anchor=north] {$x_1$};
        \draw let \p1 = (ep0) in (1pt, \y1) -- (-3pt, \y1) node [anchor=east] {$f(x_0)$};
        \end{tikzpicture}
        \caption{Newton's method in action: diagram drawn using the \texttt{hobby} package.}
        \label{fig:newton_method_2}
    \end{figure}
\end{document}

The full error from the log being:

! TeX capacity exceeded, sorry [parameter stack size=10000].
\pgfkeys@@qset #1#2#3->
                       \def \pgfkeysdefaultpath {#2/}\pgfkeys@parse #3,\pgfk...
l.85 ...h ={(sp0) .. ([tangent=\angle]ep0)}] (ep1)
                                                   ;
If you really absolutely need more capacity,
you can ask a wizard to enlarge me.

Searches for this error have revealed to me that the solutions are sometimes pretty arcane...so I am not sure where the issue with this lies at all. Could I simply "increase capacity" as suggested by the error message?

Answer 1

You are trying to set a style as part of the definition of that style. So TiKZ ties itself in knots as the settings are viciously recursive.

\documentclass{article}

\usepackage{lmodern}
\usepackage[T1]{fontenc}

\usepackage{tikz}
\usetikzlibrary{calc, hobby}
\tikzset{
        tangent/.style = {
            in angle={(180+#1)},
            Hobby finish,
            designated Hobby path=next,
            out angle=#1
        }
    }

\begin{document}
    \begin{figure}[htbp]
        \centering
        \begin{tikzpicture}

        \coordinate (y) at (0,3);
        \coordinate (x) at (5,0);

        \coordinate (sp0) at (1.5,0);
        \coordinate (ep0) at (3.5,2);
        \coordinate (csp0) at (2.5,1);
        \coordinate (cep0) at (2.75,0);

        \coordinate (sp1) at (ep0);
        \coordinate (ep1) at (4.5,3);
        \coordinate (csp1) at (4.25,4);
        \coordinate (cep1) at (4.25,2);

        \coordinate (sp2) at (sp0);
        \coordinate (ep2) at (0,-1);
        \coordinate (csp2) at (0.5,-1);
        \coordinate (cep2) at (0.5,-1);

        \draw[<->] (y) node[left] {$f(x)$} -- (0,0) --  (x) node[below] {$x$};

        % Using \pgfmathanglebetweenpoints to calculate the angle for tangent
        % tangent takes a degree unit angle
        \pgfmathanglebetweenpoints{\pgfpointanchor{cep0}{center}}{\pgfpointanchor{ep0}{center}}
        \let\angle=\pgfmathresult
        \draw (ep2) to [curve through ={(sp0) .. ([tangent=\angle]ep0)}] (ep1) ;

        \draw[dashed] (cep0) -- (csp1);
        \draw[dotted] let \p1 = (ep0) in (ep0) -- (0,\y1);
        \draw[dotted] let \p1 = (ep0) in (ep0)-- (\x1,0);

        \draw let \p1 = (ep0) in (\x1,1pt) -- (\x1,-3pt) node[anchor=north] {$x_0$};
        \draw let \p1 = (cep0) in (\x1,1pt) -- (\x1,-3pt) node[anchor=north] {$x_1$};
        \draw let \p1 = (ep0) in (1pt,\y1) -- (-3pt,\y1) node [anchor=east] {$f(x_0)$};
        \end{tikzpicture}
        \caption{Newton's method in action: diagram drawn using the \texttt{hobby} package.}
        \label{fig:newton_method_2}
    \end{figure}
\end{document}

I don't know if they caused problems here, but note that TiKZ/PGF can also be sensitive to spaces, so be consistent in your usage.