How can I create an angled grid in a 2D PGFPlots plot?

Question

Is it possible to make PGFPlots display 45° height lines in an axis? Basically, what I am looking for is a grid defined by y=-x + k*1000, k being a natural number. My numbers are rather large, e.g. y is between 54,000 and 59,000 and x between 0 and 5000 for one of my plots, which causes dimension too large errors when employing Jake's solution. Is there a way to achieve this without plotting the grid lines as functions? The respective plot is axis equal.

Answer 1

Update: Now works with large numbers

Here's a macro (and accompanying pgfplots style) which draws a diagonal grid with a gradient of -1. It works regardless of the unit lengths of the plot and regardless of whether the axis limits are set explicitly or not. It will work with large numbers, but care must be taken to select an adequate diagonal grid spacing, as the \foreach loop cannot handle more than 45000 entries (then again, that many grid lines probably wouldn't make much sense).

What it does first is to determine the width and height of the plot in plot dimensions by querying the key /pgfplots/xmin, /pgfplots/xmax etc. This has to happen after all the plots have been defined, as otherwise the values could still change. That's why the macro uses \pgfplotsextra{}, which tells pgfplots to execute the code at the end of the so called "surveying phase', i.e. after everything has been defined, but before it has actually been drawn.

After the number of required grid lines have been determined from the width and height of the plot, a \foreach loop is executed which draws the lines. It uses the every axis grid style, so that you can influence the appearance of the diagonal grid lines in the same way as you would with normal grid lines.

To activate the diagonal grid in an axis, just use the key diagonal grid in the axis options.

Here's an example of the output:

And here's the implementation. The option execute at begin plot is only available in the development version of PGFPlots. For earlier versions, just call \diagonalgrid before the first plot. The spacing of the lines can be adjusted using the key diagonal grid spacing:

\documentclass{article}

\usepackage{pgfplots}

\newcommand{\diagonalgrid}{
    \pgfplotsextra{
        \pgfkeys{/pgf/fpu}
        \pgfmathparse{\pgfkeysvalueof{/pgfplots/diagonal grid spacing}}
        \let\spacing=\pgfmathresult
        \pgfmathparse{\pgfkeysvalueof{/pgfplots/xmin}}
        \let\xmin=\pgfmathresult
        \pgfmathparse{\pgfkeysvalueof{/pgfplots/xmax}}
        \let\xmax=\pgfmathresult
        \pgfmathparse{\pgfkeysvalueof{/pgfplots/ymin}}
        \let\ymin=\pgfmathresult
        \pgfmathparse{\pgfkeysvalueof{/pgfplots/ymax}}
        \let\ymax=\pgfmathresult
        \pgfmathparse{round((\pgfkeysvalueof{/pgfplots/xmin}-\spacing)/\spacing)*\spacing}
        \let\roundxmin=\pgfmathresult
        \pgfmathfloattofixed{\pgfmathresult}
        \let\fixedxmin=\pgfmathresult\fixedxmin
        \pgfmathparse{round((\pgfkeysvalueof{/pgfplots/xmax}+\spacing)/\spacing)*\spacing}
        \let\roundxmax=\pgfmathresult
        \pgfmathparse{round((\pgfkeysvalueof{/pgfplots/ymin}-\spacing)/\spacing)*\spacing}
        \let\roundymin=\pgfmathresult
        \pgfmathfloattofixed{\pgfmathresult}
        \let\fixedymin=\pgfmathresult
        \pgfmathparse{round((\pgfkeysvalueof{/pgfplots/ymax}+\spacing)/\spacing)*\spacing}
        \let\roundymax=\pgfmathresult
        \pgfmathparse{(\roundxmax-\roundxmin + \roundymax-\roundymin)/\spacing}
        \pgfmathfloattofixed{\pgfmathresult}
        \let\totalnumber=\pgfmathresult
        \foreach \n in {0,...,\totalnumber}{
            \pgfmathparse{(\n * \spacing+ \roundxmin)}
            \pgfmathfloattofixed{\pgfmathresult}
            \let\currentxmin=\pgfmathresult
            \pgfmathparse{(\n * \spacing+ \roundymin)}
            \pgfmathfloattofixed{\pgfmathresult}
            \let\currentymin=\pgfmathresult
            \pgfkeys{/pgf/fpu=false}
            \draw [/pgfplots/every axis grid] (axis cs:\fixedxmin,\currentymin) -- (axis cs:\currentxmin,\fixedymin);
        }
    }
}
\pgfkeys{/pgfplots/diagonal grid/.style={execute at begin axis={\diagonalgrid}}}
\pgfkeys{/pgfplots/diagonal grid spacing/.initial={1}}

\begin{document}

\begin{tikzpicture}
\begin{axis}[axis equal,grid=both,diagonal grid,diagonal grid spacing=1000]
\addplot [domain={10000:15000}]{-0.2*x+50000};
\end{axis}
\end{tikzpicture}


\end{document}