Idea: `each nth point={<n>}` with non-zero shift

[Yukai Chou]

The downsampling option each nth point={<n>} always keeps points 0, n, 2n, ..., but users may want to keep points k, n-k, 2n-k, ... (0 <= k < n). Hence a more general option is required and will be helpful.

In https://tex.stackexchange.com/q/649944 I gave an attempt that provides each nth point starting from={<n>}{<k>} which makes each nth point={<n>} equivalent to each nth point starting from={<n>}{0}.

Another approach, letting skip coords between index={<begin>}{<end>} alter \coordindex, seems dangerous and will cause backwards compatibility problems.

Example copied from my tex-sx answer. Sorry it's a bit lengthy.

\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}