节点如何记住它之前的位置？

Question

考虑以下 MWE：

\documentclass[border=5pt,tikz]{standalone}
\begin{document}
\foreach \n in {2,3,...,20}
{
    \begin{tikzpicture}
        \useasboundingbox (-6,-4) rectangle (2,1);
            \pgfmathsetmacro{\number}{2*\n}
                \node at (1.5,.5) {$n = \pgfmathprintnumber{\number}$};
            \pgfmathsetmacro{\samples}{360/\n}
            \pgfmathsetmacro{\sampleslimit}{360-\samples}
                \pgfmathsetmacro{\pii}{3.14}
                    \pgfmathsetmacro{\limit}{360/\samples-1}
                \pgfmathsetmacro{\current}{(\pii/\n)*\limit}
                    \node[left] at (-1.5,.5) {\tiny
                        \begin{tabular}{lll}
                            $A_{\mathrm{real}}$ &=& 3.14 \\
                            $A_{\mathrm{current}}$ &=& \pgfmathprintnumber{\current}
                        \end{tabular}
                    };
                \foreach \x in {0,\samples,...,\sampleslimit}
                {
                    \pgfmathsetmacro{\arcangle}{\samples/2}
                        \fill[red] (\x:1) arc(\x:\x+\arcangle:1) -- (0,0) -- cycle;
                        \fill[blue] (\x+\arcangle:1) arc(\x+\arcangle:\x+2*\arcangle:1) -- (0,0) -- cycle;
                }
            \pgfmathsetmacro{\limit}{360/\samples-1}
                \foreach \x in {0,1,...,\limit}
                {
                    \pgfmathsetmacro{\shift}{\x*2*sin(\samples/4)}
                    \pgfmathsetmacro{\hshift}{\limit*sin(\samples/4)}
                        \fill[xshift=-\hshift cm,red,xshift=\shift cm,yshift=-1.5cm] (-90-\samples/4:1) arc(-90-\samples/4:-90+\samples/4:1) -- (0,0) -- cycle;
                            \fill[blue,yshift=-1.5cm,xshift=-\hshift cm,xshift=\shift cm] (-90-\samples/4:1) -- (0,0) arc(90-\samples/4:90+\samples/4:1) -- cycle;
                }
        \draw[xshift=-6cm,yshift=-4cm,<->] (0,3.5) -- (0,0) -- (4,0);
        \pgfmathsetmacro{\newnumber}{\n/5}
            \node[xshift=-6cm,yshift=-4cm,fill=green,circle,inner sep=1pt] at (\newnumber,\current) {};
        \draw[xshift=-6cm,yshift=-4cm,red,dashed] (0,\pii) --+ (3.7,0) node[above left] {$A_\mathrm{real} = \pi$};
    \end{tikzpicture}
}
\end{document}

输出如下：

我的问题是：绿色节点如何记住它之前的位置，以便所需的结果看起来像一条绿色虚线？

Answer 1

只需依次建立一个列表即可。

\documentclass[border=5pt,tikz]{standalone}
\begin{document}
\foreach \n in {2,3,...,20}
{
    \begin{tikzpicture}
        \useasboundingbox (-6,-4) rectangle (2,1);
            \pgfmathsetmacro{\number}{2*\n}
                \node at (1.5,.5) {$n = \pgfmathprintnumber{\number}$};
            \pgfmathsetmacro{\samples}{360/\n}
            \pgfmathsetmacro{\sampleslimit}{360-\samples}
                \pgfmathsetmacro{\pii}{3.14}
                    \pgfmathsetmacro{\limit}{360/\samples-1}
                \pgfmathsetmacro{\current}{(\pii/\n)*\limit}
                    \node[left] at (-1.5,.5) {\tiny
                        \begin{tabular}{lll}
                            $A_{\mathrm{real}}$ &=& 3.14 \\
                            $A_{\mathrm{current}}$ &=& \pgfmathprintnumber{\current}
                        \end{tabular}
                    };
                \foreach \x in {0,\samples,...,\sampleslimit}
                {
                    \pgfmathsetmacro{\arcangle}{\samples/2}
                        \fill[red] (\x:1) arc(\x:\x+\arcangle:1) -- (0,0) -- cycle;
                        \fill[blue] (\x+\arcangle:1) arc(\x+\arcangle:\x+2*\arcangle:1) -- (0,0) -- cycle;
                }
            \pgfmathsetmacro{\limit}{360/\samples-1}
                \foreach \x in {0,1,...,\limit}
                {
                    \pgfmathsetmacro{\shift}{\x*2*sin(\samples/4)}
                    \pgfmathsetmacro{\hshift}{\limit*sin(\samples/4)}
                        \fill[xshift=-\hshift cm,red,xshift=\shift cm,yshift=-1.5cm] (-90-\samples/4:1) arc(-90-\samples/4:-90+\samples/4:1) -- (0,0) -- cycle;
                            \fill[blue,yshift=-1.5cm,xshift=-\hshift cm,xshift=\shift cm] (-90-\samples/4:1) -- (0,0) arc(90-\samples/4:90+\samples/4:1) -- cycle;
                }
        \draw[xshift=-6cm,yshift=-4cm,<->] (0,3.5) -- (0,0) -- (4,0);
        \pgfmathsetmacro{\newnumber}{\n/5}
        \ifnum\n=2
            \xdef\Lst{\newnumber/\current}
        \else
            \xdef\Lst{\Lst,\newnumber/\current}
        \fi
        \foreach \X/\Y in \Lst
            {\node[xshift=-6cm,yshift=-4cm,fill=green,circle,inner sep=1pt] at
            (\X,\Y) {};}
        \draw[xshift=-6cm,yshift=-4cm,red,dashed] (0,\pii) --+ (3.7,0) node[above left] {$A_\mathrm{real} = \pi$};
    \end{tikzpicture}
}
\end{document}