TikZ 中使用 foreach 循环进行奇数幻灯片播放

Question

我正在尝试准备一个幻灯片来说明所有整数集的可数性。以下是我目前所做的工作：

\documentclass[aspectratio=169]{beamer}
\usetheme{CambridgeUS}
\usefonttheme{serif}
\setbeamercolor{background canvas}{bg=black}
\setbeamercolor{normal text}{fg=white}
\usepackage{pgfplots}
\pgfplotsset{compat=1.17}
\begin{document}
    \begin{frame}{$ \mathbb{Z} $ is countable}
        \begin{figure}
            \centering
            \begin{tikzpicture}[>=stealth, font=\tiny, declare function={a=0.2;b=2;c=6.5;}]
                \onslide<+->
                {
                    \foreach \n in {-10,...,-1}
                        \fill [blue] (\n/2,0) node[white] {$ \n $} circle (a);
                    \foreach \n in {1,...,10}
                        \fill [magenta] (\n/2,0) node[white] {\n} circle (a);
                    \fill [magenta!50!blue] (0,0) node[white] {0} circle (a);
                    \node [left=-5pt] at (-5.5,0) {\huge$ \dots $};
                    \node [right=-5pt] at (5.5,0) {\huge$ \dots $};
                    \node at (0,-0.5) {\normalsize$ \mathbb{Z} $};
                    \draw [thick, ->] (-1/2+a,-0.5) -- (-6.5,-0.5);
                    \draw [thick, ->] (1/2-a,-0.5) -- (6.5,-0.5);
                    \draw [thick, ->] (1/2-a-c-0.5,-b-0.75) -- (21/2-c,-b-0.75);
                    \node at (-c-0.5,-b-0.75) {\normalsize$ \mathbb{N} $};
                    \foreach \n in {1,...,21}
                    {
                        \draw [densely dotted] ({(\n-1)/2-c},-b) circle (a);
                        \node at ({(\n-1)/2-c},-b-0.5) {\footnotesize$ \n $};
                    }
                    \node [right=-5pt] at (21/2-c,-b-0.5) {\huge$ \dots $};
                    \node [right=-5pt] at (21/2-c,-b) {\huge$ \dots $};
                }
                \onslide<+->
                {
                    \fill [magenta!50!blue] (-c,-b) node[white] {0} circle (a);
                    \fill [black] (0,0) node[white] {0} circle (a);
                }
                \foreach [evaluate=\n as \tint using {(1+(-1)^\n)*50}] \n in {1,...,20}
                {
                    \onslide<+->
                    {
                        \fill [blue!\tint!magenta] (\n/2-c,-b) circle (a);
                    }
                }
            \end{tikzpicture}
        \end{figure}
    \end{frame}
\end{document}

我真正想要的可以从幻灯片 2 中的“0”球的行为中看出。我想为其他球复制这种行为。确切地说，我想从第 3 张幻灯片开始在每张幻灯片中添加更多内容

1. 沿着“Z”线将整数球涂成黑色，并在其中心保留整数编号，
2. 用相应的整数编号对“N”线上的连续球进行编号。

我无法使用单个变量来实现这一点\n。有没有办法根据偶数或奇数性质声明变量\n？请帮忙。

Answer 1

条件句在 PGFmanual 的第 94.2 节中进行了处理。语法是，即 if then elsex ? y : z的简写。另一种语法是。xyzifthenelse(x,y,z)

这是 OP 的一个可能的解决方案：

\documentclass[aspectratio=169]{beamer}
\usetheme{CambridgeUS}
\usefonttheme{serif}
\setbeamercolor{background canvas}{bg=black}
\setbeamercolor{normal text}{fg=white}
\usepackage{pgfplots}
\pgfplotsset{compat=1.17}
\begin{document}
    \begin{frame}{$ \mathbb{Z} $ is countable}
        \begin{figure}
            \centering
            \begin{tikzpicture}[>=stealth, font=\tiny, declare function={a=0.2;b=2;c=6.5;}]
                \onslide<+->
                {
                    \foreach \n in {-10,...,-1}
                        \fill [blue] (\n/2,0) node[white] {$ \n $} circle (a);
                    \foreach \n in {1,...,10}
                        \fill [magenta] (\n/2,0) node[white] {\n} circle (a);
                    \fill [magenta!50!blue] (0,0) node[white] {0} circle (a);
                    \node [left=-5pt] at (-5.5,0) {\huge$ \dots $};
                    \node [right=-5pt] at (5.5,0) {\huge$ \dots $};
                    \node at (0,-0.5) {\normalsize$ \mathbb{Z} $};
                    \draw [thick, ->] (-1/2+a,-0.5) -- (-6.5,-0.5);
                    \draw [thick, ->] (1/2-a,-0.5) -- (6.5,-0.5);
                    \draw [thick, ->] (1/2-a-c-0.5,-b-0.75) -- (21/2-c,-b-0.75);
                    \node at (-c-0.5,-b-0.75) {\normalsize$ \mathbb{N} $};
                    \foreach \n in {1,...,21}
                    {
                        \draw [densely dotted] ({(\n-1)/2-c},-b) circle (a);
                        \node at ({(\n-1)/2-c},-b-0.5) {\footnotesize$ \n $};
                    }
                    \node [right=-5pt] at (21/2-c,-b-0.5) {\huge$ \dots $};
                    \node [right=-5pt] at (21/2-c,-b) {\huge$ \dots $};
                }
                \onslide<+->
                {
                    \fill [magenta!50!blue] (-c,-b) node[white] {0} circle (a);
                    \fill [black] (0,0) node[white] {0} circle (a);
                }
               \foreach [evaluate=\n as \zn using {iseven(\n)?int(-(\n+1)/2):int((\n/2)+1)},
evaluate=\n as \colzn using {iseven(\n)?"blue":"magenta"}] \n in {1,...,20}
               {
                   \onslide<+->
                   {
                       \fill [\colzn] (\n/2-c,-b) circle (a) node[white]{$\zn$};
                        \fill [black] (\zn/2,0) node[white] {$\zn$} circle (a);
                   }
               }
            \end{tikzpicture}
        \end{figure}
    \end{frame}
\end{document}