Index offset using "each nth point" in PGFPlots

Question

The each nth point = \n option of PGFPlots allows to sample data points in a list, keeping only the points indexed 2n+1 (with n=0,1,...). I would like to be able to extract the points with indices 2n+m (similarily to the option mark phase = m and mark repeat = n).

Here is my unsuccessful attempt, where somehow, the command skip coords between index={0}{\m} seems to be ignored:

\begin{filecontents}{pts.dat}
        x    y
        1    0
        0.5 0.866
        -0.5    0.866
        -1  0
        -0.5    -0.866
        0.5 -0.866
        1   0
    \end{filecontents}
\documentclass[border=5pt]{standalone}
\usepackage{pgfplots}
\begin{document}
\begin{tikzpicture}
\begin{axis}[no marks]
\addplot[ultra thick, dashed, lightgray] table {pts.dat};
\foreach \n in {0,3}
    \foreach \m in {1,\n}
        {
          \addplot[
                skip coords between index={0}{\m},
                each nth point=\n,
                filter discard warning=false,
                unbounded coords=discard
                ] table {pts.dat};
        }
\end{axis}
\end{tikzpicture}
\end{document}

Answer 1

I'm not quite sure what plots you wish to accomplish, but yes currently skip coords between index={<begin>}{<end>} and each nth point={<n>} work independently.

The example below provides a new and more general option each nth point starting from={<n>}{<start>}. each nth point={<n>} is now equivalent to each nth point starting from={<n>}{0}.

For the \edef trick used inside \foreach, see this answer.

\begin{filecontents}{pts.dat}
 x    y
 1    0
 0.5  0.866
-0.5  0.866
-1    0
-0.5 -0.866
 0.5 -0.866
 1    0
\end{filecontents}
\documentclass[border=5pt]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.18}
\makeatletter
\pgfplotsset{
  /pgfplots/each nth point starting from/.style 2 args={
    /pgfplots/each nth point starting from={x}{#1}{#2}
  },
    % #1: the filter name: x, y, z, or something exotic like hist/data
    % #2: the N of 'each nth'
  % #3: the starting coordindex
  % Example:
  %  {x}{3}{0} will leave indices 0, 3, 6, ...
  %  {x}{3}{1} will leave indices 1, 4, 7, ...
    /pgfplots/each nth point starting from/.style n args={3}{
        /pgfplots/#1 filter/.append code={%
            \ifnum\coordindex=0
        \begingroup
          % do not pollute \pgfmathresult
          \pgfkeys{/pgf/fpu=false}%
          \pgfmathsetmacro\c@pgfplots@eachnthpoint@xfilter{int(Mod(-(#3),#2))}%
          \pgfmath@smuggleone\c@pgfplots@eachnthpoint@xfilter
        \endgroup
                \edef\c@pgfplots@eachnthpoint@xfilter@cmp{#2}%
            \else
                \pgfplotsutil@advancestringcounter\c@pgfplots@eachnthpoint@xfilter
            \fi
            \ifx\c@pgfplots@eachnthpoint@xfilter@cmp\c@pgfplots@eachnthpoint@xfilter
                \def\c@pgfplots@eachnthpoint@xfilter{0}%
            \else
                \let\pgfmathresult\pgfutil@empty
            \fi
        }
    },
}
\makeatother
\begin{document}
\begin{tikzpicture}
  \begin{axis}[no marks]
    \addplot[ultra thick, dashed, lightgray] table {pts.dat};
\foreach \m in {1,...,3} {
  \edef\x{
    \noexpand\addplot[
      each nth point starting from={3}{\m},
      filter discard warning=false,
      unbounded coords=discard
    ] table {pts.dat};
  }
  \x
}

\foreach \m in {1,2} {
  \edef\x{
    \noexpand\addplot[blue,
      each nth point starting from={2}{\m},
      filter discard warning=false,
      unbounded coords=discard
    ] table {pts.dat} -- cycle;
  }
  \x
}

\end{axis}
\end{tikzpicture}
\end{document}