[Tex/LaTex] Tikz – intersections between curve and line

intersectionstikz-pgf

I am trying to plot the intersection between a line and two curves.
I tried using path but I get the following errors: "I do not know the path named 'curve'. Maybe you misspelt it". And I also get "No shape named intersection-1 is known". Any ideas what is going on? Thanks.

\usetikzlibrary{intersections}
\begin{center}
\begin{tikzpicture}
\begin{axis}[
domain=0.1:6,
axis lines = left,
xlabel = $x$,
ylabel = {$y$},
xmin=0.1, xmax=6,
ymin=0.1, ymax=1,
minor tick num=0,
scaled ticks=false,
xticklabel=\empty,
yticklabel=\empty,
xtick=\empty,
ytick=\empty,
]
\addplot[smooth,thick,black, name path=curve] {(3*x-2+0.4*4.4)/(3*x+0.4*4.4)}node[pos=0.8,sloped,yshift=6pt]{$y_{0}$};
\addplot[smooth,thick,blue] {(3*x-2)/(3*x)}node[pos=0.95,sloped,yshift=-6pt]{$y_{1}$};
\addplot[smooth,red, dashed, name path=line] coordinates {(2,0)(2,0.75)};
\path [draw,name intersections={of={curve and line}}]
 (intersection-1) circle[radius=2pt];
\end{axis}
\end{tikzpicture}

Best Answer

Your path line is to short, it doesn't cross path curve but only touch it. It seems that this make at older version of pgfplots your problem, however with recent version (1.14) I can't reproduce your problem. Anyway, to be on safe side, I suggest some changes in your MWE. They are indicated by % <-- in code:

\documentclass[tikz,
               border=3mm,
               ]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.14, set layers}
\usetikzlibrary{intersections}

\begin{document}
    \begin{tikzpicture}
\begin{axis}[
domain=0.1:6,
axis lines = left,
xlabel = $x$,
ylabel = {$y$},
xmin=0.1, xmax=6,
ymin=0.1, ymax=1,
scaled ticks=false,
xticklabel=\empty, yticklabel=\empty,
xtick=\empty, ytick=\empty,
every axis plot post/.append style={very thick, smooth,}
]
\addplot[name path=A,black] {(3*x-2+0.4*4.4)/(3*x+0.4*4.4)}
            node[pos=0.8,sloped,yshift=6pt]{$y_{0}$};
\addplot[blue] {(3*x-2)/(3*x)}
            node[pos=0.95,sloped,yshift=-6pt]{$y_{1}$};
\path[name path=B] (2,0) -- (2,2); % <-- added, this path cross pat A
\draw[draw,name intersections={of=A and B, by={a}},fill=white]% <-- intersection i named by "a"
    (a) circle (2pt);
\pgfonlayer{pre main}
\coordinate (b) at (0.1,0.1);
\draw[red, densely dashed]  (a) -- (a |- b) node[below,text=black] {$x_i$};% <-- instead of addplot for path "line"
\endpgfonlayer
\end{axis}
    \end{tikzpicture}
\end{document}

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

enter image description here

[Tex/LaTex] TikZ: Drawing an arc from an intersection to an intersection

A solution which allows to draw intersection segments of any two intersections is available as tikz library fillbetween.

This library works as general purpose tikz library, but it is shipped with pgfplots and you need to load pgfplots in order to make it work:

\documentclass{standalone}

\usepackage{tikz}
\usepackage{pgfplots}
\usetikzlibrary{fillbetween}

\begin{document}

\begin{tikzpicture}

\draw [name path=red,red] (120:1.06) circle (1.9);
%\draw [name path=yellow,yellow] (0:1.06) circle (2.12);
\draw [name path=green,green!50!black] (0:0.77) circle (2.41);
\draw [name path=blue,blue] (0:0) circle (1.06);

% substitute this temp path by `\path` to make it invisible:
\draw[name path=temp1, intersection segments={of=red and blue,sequence=L1}];
\draw[red,-stealth,ultra thick, intersection segments={of=temp1 and green,sequence=L3}];

\end{tikzpicture}

\end{document}

enter image description here

The key intersection segments is described in all detail in the pgfplots reference manual section "5.6.6 Intersection Segment Recombination"; the key idea in this case is to

create a temporary path temp1 which is the first intersection segment of red and blue, more precisely, it is the first intersection segment in the Left argument in red and blue : red. This path is drawn as thin black path. Substitute its \draw statement by \path to make it invisible.
Compute the desired intersection segment by intersecting temp1 and green and use the correct intersection segment. By trial and error I figured that it is the third segment of path temp1 which is written as L3 (L = left argument in temp1 and green and 3 means third segment of that path).

The argument involves some trial and error because fillbetween is unaware of the fact that end and startpoint are connected -- and we as end users do not see start and end point.

Note that you can connect these path segments with other paths. If such an intersection segment should be the continuation of another path, use -- as before the first argument in sequence. This allows to fill paths segments:

\documentclass{standalone}

\usepackage{tikz}
\usepackage{pgfplots}
\usetikzlibrary{fillbetween}

\begin{document}

\begin{tikzpicture}

\draw [name path=red,red] (120:1.06) circle (1.9);
%\draw [name path=yellow,yellow] (0:1.06) circle (2.12);
\draw [name path=green,green!50!black] (0:0.77) circle (2.41);
\draw [name path=blue,blue] (0:0) circle (1.06);

% substitute this temp path by `\path` to make it invisible:
\draw[name path=temp1, intersection segments={of=red and blue,sequence=L1}];
\draw[red,fill=blue,-stealth,ultra thick, intersection segments={of=temp1 and green,sequence=L3}]  
    [intersection segments={of=temp1 and green, sequence={--R2}}]
;

\end{tikzpicture}

\end{document}

enter image description here

Best Answer

Related Solutions

[Tex/LaTex] TikZ doesn’t find all intersections between plot and a line

Code

Output

[Tex/LaTex] TikZ: Drawing an arc from an intersection to an intersection

Related Question