Random decoration of plot axis messes up direction of axis arrow

Question

I've been experimenting with "xkcdifying" a plot I want to make, based on the information found here and some pasting from other sources (this is my first time using pgfplots). Everything worked fine so far, until I wanted to give the axes arrows. But it seems that the random steps decoration always turns up the arrow head on the x axis:

If the marked line in the below code is commented out, the arrow is displayed correctly again, but of course the nice random effect is gone:

\documentclass{article}
\usepackage{pgfplots}

\begin{document}
\begin{tikzpicture}
\pgfplotsset{every axis/.append style={line width=1pt}}

\begin{axis}[%
  axis lines=middle,
  decoration={%
    random steps, % CRITICAL LINE
    segment length=1mm,
    amplitude=0.2pt
  }, 
  every tick/.style={thick,black,decorate},
  enlarge x limits=true,
  y tick style={draw=none},
  yticklabel=\empty,
  every inner x axis line/.append style={->},
  every inner y axis line/.append style={->},
]
\begin{scope}[decoration={random steps,segment length=3pt,amplitude=0.5pt},decorate]
\addplot [blue,samples=50, domain=0:120] {(2479*x^6)/5513508000000-(13697*x^5)/61261200000+(7935509*x^4)/220540320000-(1889983*x^3)/816816000+(2038007*x^2)/40840800+(335201*x)/1021020};
\end{scope}
\end{axis}

\end{tikzpicture}
\end{document}

Now, am I right in my guess that this is an error due to the randomization? And how can it be fixed?

Answer 1

I think this is due to how axis lines are drawn and seems to me a candidate as a bug. Consider the following;

\documentclass{article}
\usepackage{pgfplots}
\begin{document}
\begin{tikzpicture}[mydeco/.style={
  decoration={%
    random steps, % CRITICAL LINE
    segment length=1mm,
    amplitude=1pt,#1,
    post length=10mm,
    post= lineto % Change to " moveto "!
  },
  decorate,
}
]
\begin{axis}[%
  line width=1pt,
  axis lines*=middle,
  every inner x axis line/.style={->,mydeco},
  every inner y axis line/.style={->,mydeco},
]
\begin{scope}[mydeco={segment length=3pt,amplitude=0.5pt},decorate]
\addplot [blue,samples=50, domain=0:120,->] {(2479*x^6)/5513508000000-(13697*x^5)/61261200000+(7935509*x^4)/220540320000-(1889983*x^3)/816816000+(2038007*x^2)/40840800+(335201*x)/1021020};
\end{scope}
\end{axis}

\draw[mydeco,->,red,ultra thick] (0,0) -- (5,6);
\end{tikzpicture}
\end{document}

Here I tried to stop the decoration 10mm before the path end. It is OK for paths but not for axis lines. This means there is a move operation somewhere that changes the current path such that post length and post path drawing mechanism is not applied to the axis line. As an example change lineto to moveto and we can replicate that behavior on other paths too.

I will attempt to have a look but that part of the code is really involved due to 3D/2D settings. Maybe Christian can help here. Otherwise we can open a ticket. Then randomized paths would have the arrow head automatically without any post=... tweak.

---

It turns out that this behaviour is due to a missing expansion in an internal PGFPlots macro. PGFPlots uses a decoration to place axis discontinuity marks, which requires setting pre length and post length values for the decoration. PGFPlots sets pre length and post length using macros (called \xdisstart, \xdisend, etc.). If no discontinuity is used, these macros are set to 0pt. However, for some reason, arrow tips aren't placed correctly when the pre length and post length values contain unexpanded macros. So in order to fix the behaviour, you can redefine an internal PGFPlots macro by placing the following code in your preamble:

\makeatletter
\def\pgfplots@drawaxis@innerlines@onorientedsurf#1#2#3{%
    \if2\csname pgfplots@#1axislinesnum\endcsname
        \draw[/pgfplots/every inner #1 axis line,%
            decorate,%
            #1discont,%
            decoration={% Expand the macros before setting the values
                pre length/.expand twice=\csname #1disstart\endcsname,
                post length/.expand twice=\csname #1disend\endcsname
            }
            ]
        \pgfextra
        \csname pgfplotspointonorientedsurfaceabsetupforset#3\endcsname{\csname pgfplots@logical@ZERO@#3\endcsname}{2}%
        \pgfpathmoveto{\pgfplotspointonorientedsurfaceab{\csname pgfplots@#1min\endcsname}{\csname pgfplots@logical@ZERO@#2\endcsname}}%
        \pgfpathlineto{\pgfplotspointonorientedsurfaceab{\csname pgfplots@#1max\endcsname}{\csname pgfplots@logical@ZERO@#2\endcsname}}%
        \endpgfextra
        ;
    \fi
}%
\makeatother