[Tex/LaTex] Grid dots in pgfplots

pgfplots

How can I generate a multi-resolution dot grid (see image) in pgfplots? The dot grid does not necessarily coincide with the axis ticks.

multi-resolution dot grid

edit: The above plot was created using

\addplot[only marks,mark=*] plot table[row sep=crcr,]{ high res. coordinates }
\addplot[only marks,mark=*] plot table[row sep=crcr,]{ low res. coordinates }

with huge tables of MATLAB-computed coordinates. What I'm looking for in this question, is a way to algorithmically create the dot grid in pgfplots.

Best Answer

With tikz

\documentclass[tikz,border=10pt]{standalone}
\begin{document}
  \begin{tikzpicture}
    \draw (-2.6,-2.6) rectangle (2.6,2.6);
    \foreach \x in {-2,-1,...,2}{
    \draw (\x,-2.4) -- (\x,-2.6)node[below,font=\footnotesize] {\x};
    \draw (\x,2.4) -- (\x,2.6);
    }
    \foreach \y in {-2,-1,...,2}{
    \draw (-2.4,\y) -- (-2.6,\y)node[left,font=\footnotesize] {\y};
    \draw (2.6,\y) -- (2.4,\y);
    }
    \foreach \x in {-2.4,-2.2,...,2.4}{
    \foreach \y in {-2.4,-2.2,...,2.4}{
    \fill[black!30] (\x,\y) circle[radius=0.5pt];
    }}
    \foreach \x in {-2.4,-1.8,...,2.4}{
    \foreach \y in {-2.4,-1.8,...,2.4}{
    \fill[black!80] (\x,\y) circle[radius=0.8pt];
    }}
  \end{tikzpicture}
\end{document}

enter image description here

Using pgfplots.

I took Tarass's answer and added the fots to the back ground so that plots come front.

\documentclass{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.10}
\usetikzlibrary{backgrounds}

\begin{document}

\begin{tikzpicture}

\begin{axis}[xmin=-2.6,xmax=2.6,
    ymin=-2.6,ymax=2.6,
    after end axis/.code={%
    \begin{scope}[on background layer]
    \foreach \x in {-2.4,-2.2,...,2.4}{
    \foreach \y in {-2.4,-2.2,...,2.4}{
    \fill[black!30] (axis cs:\x,\y) circle[radius=0.5pt];
    }}
    \foreach \x in {-2.4,-1.8,...,2.4}{
    \foreach \y in {-2.4,-1.8,...,2.4}{
    \fill[black!80] (axis cs:\x,\y) circle[radius=0.8pt];
    }}
    \end{scope}
    },]
    \addplot {x^2};
\end{axis}
\end{tikzpicture}
\end{document}

enter image description here

This is some what slower than Christian Feuersänger's approach though.

With \addplot (still slower)

\documentclass[border=10pt]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.10}

\begin{document}

\begin{tikzpicture}

\begin{axis}[xmin=-2.6,xmax=2.6,
    ymin=-2.6,ymax=2.6,
    ]
    \foreach \x in {-2.4,-2.2,...,2.4}{
    \foreach \y in {-2.4,-2.2,...,2.4}{
    \addplot[only marks,mark size=0.5pt,black!30] coordinates {(\x,\y)} ;
    }}
    \foreach \x in {-2.4,-1.8,...,2.4}{
    \foreach \y in {-2.4,-1.8,...,2.4}{
    \addplot[only marks,mark size=0.8pt,black!80] coordinates {(\x,\y)} ;
    }}
    \addplot {x^2};
\end{axis}
\end{tikzpicture}
\end{document}

enter image description here

Related Solutions

[Tex/LaTex] set minor grid values in pgfplots

The incorrect position of the minor ticks for small values stems from the insufficient accuracy of the maths engine. You can increase the accuracy a fair bit by using the fpu library by replacing

y coord trafo/.code=\pgfmathparse{ln(-ln(1-#1)))}

with

y coord trafo/.code={
    \pgfkeys{/pgf/fpu=true}
    \pgfmathparse{ln(-ln(1-#1)))}
    \pgfkeys{/pgf/fpu=false}
}

but this is still not perfect.

If you have the option of compiling your document with lualatex, you can make use \directlua statements to do the calculations:

y coord trafo/.code={
    \edef\pgfmathresult{\directlua{tex.print(math.log(-math.log((1-#1))))}}
}

will give you

Close-up of the bottom left-hand corner:

If using luatex is not an option for you, you might have to write a new pgfmath function that uses precomputed tabulated data (similar to what's done for the trigonometric functions in the math parser).

To change the style of the grid lines defined using the extra y ticks, you have to use extra y tick style={yticklabels={},major grid style={red}}: The grid lines defined by the extra y ticks are major grid lines, so you have to set the major grid style within the context of the extra y tick style.

\documentclass[border=5mm]{standalone}
\usepackage{luaotfload}
\usepackage[EU2]{fontenc}
\usepackage{lmodern}
\usepackage{pgfplots}

\begin{document}
\begin{tikzpicture}
\begin{axis}[scale only axis,
  % plot style
  every axis plot/.append style={line width=1.0pt,blue},
  % labels
  xlabel=Lebensdauer $t$,
  ylabel=Ausfallhäufigkeitssumme $R(t)$,
  % axis limits
  xmin=0,xmax = 20.0,
  ymin=0.001, ymax=0.999,
  % calculate functions only in this domain
  domain=0.1:20,
  % x-axis: log scale with linear numbers
  xmode=log,log ticks with fixed point,
  % grid style
  grid=both, % major and minor for both axis (alt: major, minor, none)
  minor grid style={gray!25},
  major grid style={black!50},
  % -- set weibull plot grid positions --
  % remove tick lines
  major tick length=0pt,
  minor tick length=0pt,
  % yticks (major grid lines)
  ytick      ={0.001,0.002,0.003,0.004,0.005,
               0.01,0.02,0.03,0.04,0.05,
               0.10,0.20,0.30,0.40,0.50,0.60,0.70,0.80,0.90,0.99,0.999},
  % according labels
  yticklabels={0.1,0.2,0.3,0.4,0.5,1,2,3,4,5,10,20,30,40,50,60,70,80,90,99,99.9},
  % 
  extra y tick style={yticklabels={},major grid style={red}}, % color is ignored !
  % position of minor y-grid lines
  extra y ticks=  {0.001,0.0011,0.0012,0.0013,0.0014,0.0015,0.0016,0.0017,0.0018,0.0019,0.002,0.0021,0.0022,0.0023,0.0024,0.0025,0.0026,0.0027,0.0028,0.0029,0.003,0.00325,0.0035,0.00375,0.004,0.00425,0.0045,0.00475,0.005,0.0055,0.006,0.0065,0.007,0.0075,0.008,0.0085,0.009,0.0095,0.01,0.011,0.012,0.013,0.014,0.015,0.016,0.017,0.018,0.019,0.02,0.0225,0.025,0.0275,0.03,0.035,0.04,0.045,0.05,0.055,0.06,0.065,0.07,0.075,0.08,0.085,0.09,0.095,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.22,0.23,0.24,0.25,0.26,0.27,0.28,0.29,0.3,0.32,0.34,0.36,0.38,0.4,0.42,0.44,0.46,0.48,0.5,0.52,0.54,0.56,0.58,0.6,0.62,0.64,0.66,0.68,0.7,0.72,0.74,0.76,0.78,0.8,0.82,0.84,0.86,0.88,0.9,0.909,0.918,0.927,0.936,0.945,0.954,0.963,0.972,0.981,0.99,0.991,0.992,0.993,0.994,0.995,0.996,0.997,0.998,0.999},
  % tic position calculation (coord. transformation)
  % must be below the tick positions !
  y coord trafo/.code={
    \edef\pgfmathresult{\directlua{tex.print(math.log(-math.log((1-#1))))}}
%   \pgfkeys{/pgf/fpu=true}
%   \pgfmathparse{ln(-ln(1-#1)))}
%   \pgfkeys{/pgf/fpu=false}
  }
]
%
\addplot[domain=0.01:100, sharp plot] gnuplot{ 1-exp(-x**2)};
\end{axis} 
\end{tikzpicture}

\end{document}

[Tex/LaTex] pgfplots: Grid Lines below Filling

If you add set layers option the axis environment, it sets a hierarchricrhchaheal(!?) order as the standard layer order, namely axis background, axis grid, axis ticks, axis lines, axis tick labels, main, axis descriptions, axis foreground. This simply switches the order of drawing order. Hence it is feature not a bug. Otherwise you can reorder the layers as a customized layer style

\documentclass{standalone}
\usepackage{tikz,pgfplots}

\pgfplotsset{compat=1.10}
\usepgfplotslibrary{fillbetween}

\begin{document}

\begin{tikzpicture}
\begin{axis}[set layers,
    axis lines = middle,
    smooth,
    no markers,
    xlabel = {$x$},
    ylabel = {$y$},
    minor tick num =1,
    grid=both,
    domain=0:2,]
        \addplot+[domain=0:1,samples=200,name path=A,black] {sqrt(x)};
        \addplot+[domain=0:1,name path=B,black] {x};
        \addplot[blue!50] fill between[of=A and B];
\end{axis}
\end{tikzpicture}
\end{document}

enter image description here

Best Answer

Related Solutions

[Tex/LaTex] set minor grid values in pgfplots

[Tex/LaTex] pgfplots: Grid Lines below Filling

Related Question