PgfPlots Vertical Asymptotes Are Cut Short

Question

The following MWE

\documentclass{standalone}
\usepackage{pgfplots}

\begin{document}

    \begin{tikzpicture}[scale=0.75]
        \begin{axis}[ylabel=Y-Axis, xlabel=X-Axis, xmin=0.000, xmax=0.9, ymin=0, ymax=12, clip=false, yticklabel pos=right, ylabel near ticks]
        \pgfplotsinvokeforeach{2,3,5,10}{
            \addplot[mark=none, domain=0.000:0.9, thick] {-ln(x/#1^2)/ln(#1)}; %Varying R values
        }
        \end{axis}
    \end{tikzpicture}

\end{document}

yields the following graph

Mathematically, these lines should extend to infinity when they reach x=0 at the left-hand side of the box.

What is the "best way" to get these lines close to the edge of the box or otherwise fill them in so they are not cut-off?

Answer 1

You will need to use the samples option to addplot and increase the number:

\addplot[mark=none, domain=0.000:0.9, thick,samples=40] {-ln(x/#1^2)/ln(#1)} node [pos=0,left] {$R=#1$}; %Varying R values

here 40 is just a wild guess.

Edit, actually a sample value of 500 is probably more what you want as 40 doesn't give you anything that different.

with a sample value of 500 you get this:

Edit2: Following @Jake suggestion, you can indeed use the samples at option to addplot to specify the intervals in x values which need more definition/samples. In this particular case, samples at={0.001,0.002,...,0.01,0.02,...,0.9} gives you a sample every 0.001 between 0.001 and 0.01 and a sample of 0.01 between 0.01 and 0.9. This is of course a manual setting and will have to be adapted to your different plots but in this case it works particularly well. In addition the smooth option with get rid of most of the raggedness of the plot:

The advantage of the samples=500 solution is that it is fairly generic across plots but it does require a lot more calculations which add to compilation time but may be the best solution if you are plotting things which varies a lot across the entire x range (tan(x) for example).