The best way to debug this sort of stuff is to first change the \path to a \draw so you can see what intersections you are looking for. Using \draw for the horizontal line:
\draw [name path=A] (1E-12, 50) -- (1E-4, 50);
you don't see the line on the graph. Hence, no intersections. Within pgfplots's axis environment you need to use the axis cs coordinate system. So, changing this to:
\draw [name path=A] (axis cs: 1E-12, 50) -- (axis cs: 1E-4, 50);
you can see the horizontal line. Changing the above back to \path you obtain:
Code:
\documentclass{memoir}
\usepackage{tikz}
\usepackage{pgfplots}
\usetikzlibrary{intersections}
\begin{document}
\begin{figure}
\begin{tikzpicture}
\begin{axis}[ymin=0,ymax=100,xmin=5E-13,xmax=3E-4,
xlabel=Concentration,
ylabel=Effect (\%),
axis lines=left,
width=2\marginparwidth,
height=1.4\marginparwidth,
ytick={0,25,50,75,100},
xmode = log,
tick label style = {font=\footnotesize},
]
\addplot [color=black, name path=P] coordinates {
(1E-4, 0)
(1E-5, 0)
(1E-6, 2)
(1E-7, 21)
(1E-8, 66)
(1E-9, 88)
(1E-10, 94)
(1E-11, 95)
(1E-12, 96)
};
\addplot [only marks] coordinates {
(1E-4, 0)
(1E-5, 0)
(1E-6, 2)
(1E-7, 21)
(1E-8, 66)
(1E-9, 88)
(1E-10, 94)
(1E-11, 95)
(1E-12, 96)
};
\path [name path=A] (axis cs: 1E-12, 50) -- (axis cs: 1E-4, 50);
\path [name intersections={of=A and P}];
\draw[-latex, thick, red] (1E-12, 50) -- (intersection-1);
\end{axis}
\end{tikzpicture}
\end{figure}
\end{document}
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}
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}
Best Answer
In order to get the corner right, the path should be drawn in a single
\drawcommand. You can still use theintersection ofin this: