TikZ doesn't find all intersections between plot and a line

Question

Why doesn't TikZ find all intersections. They are obviously there …

\documentclass[border=10mm]{standalone}

\usepackage{tikz}
\usetikzlibrary{intersections}

\begin{document}
\begin{tikzpicture}[point/.style={fill=blue,minimum size=1mm,inner sep=0pt,circle}]
    % Zoom (to prevent oveflow)
    \def\yzoom{100}
    % Plots
    \foreach \T/\xmin/\a in {%
        0.27/1.538/a,
        0.28/1.590/b,
        0.29/1.649/c
    } {
        \draw [thin,name path global/.expanded={kurve \a}]
            plot [raw gnuplot] function {%
                set xrange [\xmin:10];
                set yrange [0:0.08*\yzoom];
                set samples 1000;
                f(x) = \yzoom*(\T/(x-1) - 1/(x**2));
                plot f(x);
            };
    }
    % Lines
    \foreach \p/\a in {%
        %% T = 0.27
        0.0231/a,
        %% T = 0.28
        0.02855/b,
        %% T = 0.29
        0.0338/c
    }{
        \draw [red,thin,name path global/.expanded={linie \a}]
            (0,\p*\yzoom) -- (10,\p*\yzoom) node [fill=white,pos=0.1] {\a};
    }
    % Intersections points
    \path [name intersections={of=kurve a and linie a,by={P1,P2,P3}}]
        (P1) node [point] {} (P2) node [point] {} (P3) node [point] {};
    \path [name intersections={of=kurve b and linie b,by={P1,P2,P3}}]
        (P1) node [point] {} (P2) node [point] {} (P3) node [point] {};
    \path [name intersections={of=kurve c and linie c,by={P1,P2,P3}}]
        (P1) node [point] {} (P2) node [point] {} (P3) node [point] {};
\end{tikzpicture}
\end{document}

There seems to be no problem with the names of the paths but TikZ is missing four intersection points.

Bonus question: Is it possible to solve the last part (adding blue points) with the second \foreach? I tried it but I get the error File ended while scanning use of \tikz@intersect@path@names@parse..

Answer 1

I don’t know why PGF doesn’t find these intersections, it probably has do to something with how the path is built internally from the points of the table of values gnuplot creates.

It works if you either

• set set samples 100 or
• use—with the original samples setting—the smooth option.

All intersections are found now.

---

The of key (\tikz@intersect@path@names@parse) expects spaces around and which is obviously stripped if you use of=kurve \a and linie \a, so you will need to do of/.expanded=kurve \a\space and linie \a or of={kurve \a} and linie \a.

You also might introduce spurious spaces with \foreach in:

\foreach \p/\a in {%
    %% T = 0.27
    0.0231/a,
    %% T = 0.28
    0.02855/b,
    %% T = 0.29
    0.0338/c             % <- there’s a space!
}{

This space actually may help if you .expanded with the of key but is usually trouble so avoiding this is reccomended.

(That space is also present in the other \foreach loop but as it is used with an .expanded before PGFkeys processes it, it is stripped.)

Code

\documentclass[convert=false,tikz]{standalone}
\usetikzlibrary{intersections}
\begin{document}
\begin{tikzpicture}[point/.style={fill=blue,minimum size=1mm,inner sep=0pt,circle}]
    % Zoom (to prevent oveflow)
    \def\yzoom{100}
    % Plots
    \foreach \T/\xmin/\a in {
        0.27/1.538/a,
        0.28/1.590/b,
        0.29/1.649/c
    } {
        \draw [thin,smooth,name path global/.expanded={kurve \a}]
            plot [raw gnuplot] function {%
                set xrange [\xmin:10];
                set yrange [0:0.08*\yzoom];
                set samples 1000;
                f(x) = \yzoom*(\T/(x-1) - 1/(x**2));
                plot f(x);
            };
    }
    % Lines
    \foreach \p/\a in {%
        %% T = 0.27
        0.0231/a,
        %% T = 0.28
        0.02855/b,
        %% T = 0.29
        0.0338/c%
    }{
        \draw [red,thin,name path global/.expanded={linie \a}]
            (0,\p*\yzoom) -- (10,\p*\yzoom) node [fill=white,pos=0.1] {\a};
        \path [name intersections={of={kurve \a} and linie \a, total=\t}] \foreach \s in {1,...,\t} {(intersection-\s) node[point]{}};
    }
\end{tikzpicture}
\end{document}

Output