简化重复绘图和节点放置

Question

我使用以下代码绘制重复的线条并将节点放置在特定位置，以便稍后绘制圆圈并用线条连接它们。

有没有更简单的方法来完成这项工作，如使用\foreach命令或任何其他可能更简单的方法。

\documentclass{beamer}
\beamertemplatenavigationsymbolsempty
\usepackage{tikz}
\usepackage{pgfplots}
\begin{document}
\begin{frame}[t]
\frametitle{}
\hspace {-1cm}
\begin{tikzpicture}[scale=.7, transform shape,linecolor/.style={ultra thick, green!40!black},dotline/.style={thin, black, loosely dotted}]
\pgfmathsetmacro{\incrmnt}{.6}

\draw [thick,-latex](-.3,0) -- (0,0) -- (5,0);
\draw [thick,-latex](0,-.3) -- (0,0) -- (0,8);
\draw [thick,-latex](6.,0) -- (7,0) -- (14.4,0);
\draw [thick,-latex](8,-.2) -- (8,0) -- (8,8);
\draw [linecolor] (0,\incrmnt*1) node (yal){} +(180:.15cm) -- +(0:.15cm) node [xshift=-.8cm, yshift=0cm] {1/12}([shift={(0:8)}]yal.center) node (ya){} +(180:.15cm) -- +(0:.15cm) node [xshift=-.8cm, yshift=0cm] {1/12};
\draw [dotline] (0,\incrmnt*1) -- +(0:14cm);

\draw [linecolor] (0,\incrmnt*2) node (ybl){} +(180:.15cm) -- +(0:.15cm) node [xshift=-.8cm, yshift=0cm] {2/12}([shift={(0:8)}]ybl.center) node (yb){} +(180:.15cm) -- +(0:.15cm) node [xshift=-.8cm, yshift=0cm] {2/12};
\draw [dotline] (0,\incrmnt*2) -- +(0:14cm);

\draw [linecolor] (0,\incrmnt*3) node (ycl){} +(180:.15cm) -- +(0:.15cm) node [xshift=-.8cm, yshift=0cm] {3/12}([shift={(0:8)}]ycl.center) node (yc){} +(180:.15cm) -- +(0:.15cm) node [xshift=-.8cm, yshift=0cm] {3/12};
\draw [dotline] (0,\incrmnt*3) -- +(0:14cm);

\draw [linecolor] (0,\incrmnt*4) node (ydl){} +(180:.15cm) -- +(0:.15cm) node [xshift=-.8cm, yshift=0cm] {4/12}([shift={(0:8)}]ydl.center) node (yd){} +(180:.15cm) -- +(0:.15cm) node [xshift=-.8cm, yshift=0cm] {4/12};
\draw [dotline] (0,\incrmnt*4) -- +(0:14cm);

\draw [linecolor] (0,\incrmnt*5) node (yel){} +(180:.15cm) -- +(0:.15cm) node [xshift=-.8cm, yshift=0cm] {5/12}([shift={(0:8)}]yel.center) node (ye){} +(180:.15cm) -- +(0:.15cm) node [xshift=-.8cm, yshift=0cm] {5/12};
\draw [dotline] (0,\incrmnt*5) -- +(0:14cm);

\draw [linecolor] (0,\incrmnt*6) node (yfl){} +(180:.15cm) -- +(0:.15cm) node [xshift=-.8cm, yshift=0cm] {6/12}([shift={(0:8)}]yfl.center) node (yf){} +(180:.15cm) -- +(0:.15cm) node [xshift=-.8cm, yshift=0cm] {6/12};
\draw [dotline] (0,\incrmnt*6) -- +(0:14cm);

\draw [linecolor] (0,\incrmnt*7) node (ygl){} +(180:.15cm) -- +(0:.15cm) node [xshift=-.8cm, yshift=0cm] {7/12}([shift={(0:8)}]ygl.center) node (yg){} +(180:.15cm) -- +(0:.15cm) node [xshift=-.8cm, yshift=0cm] {7/12};
\draw [dotline] (0,\incrmnt*7) -- +(0:14cm);

\draw [linecolor] (0,\incrmnt*8) node (yhl){} +(180:.15cm) -- +(0:.15cm) node [xshift=-.8cm, yshift=0cm] {8/12}([shift={(0:8)}]yhl.center) node (yh){} +(180:.15cm) -- +(0:.15cm) node [xshift=-.8cm, yshift=0cm] {8/12};
\draw [dotline] (0,\incrmnt*8) -- +(0:14cm);

\draw [linecolor] (0,\incrmnt*9) node (yhl){} +(180:.15cm) -- +(0:.15cm) node [xshift=-.8cm, yshift=0cm] {9/12}([shift={(0:8)}]yhl.center) node (yh){} +(180:.15cm) -- +(0:.15cm) node [xshift=-.8cm, yshift=0cm] {9/12};
\draw [dotline] (0,\incrmnt*9) -- +(0:14cm);

\draw [linecolor] (0,\incrmnt*10) node (yhl){} +(180:.15cm) -- +(0:.15cm) node [xshift=-.8cm, yshift=0cm] {10/12}([shift={(0:8)}]yhl.center) node (yh){} +(180:.15cm) -- +(0:.15cm) node [xshift=-.8cm, yshift=0cm] {10/12};
\draw [dotline] (0,\incrmnt*10) -- +(0:14cm);

\draw [linecolor] (0,\incrmnt*11) node (yhl){} +(180:.15cm) -- +(0:.15cm) node [xshift=-.8cm, yshift=0cm] {11/12}([shift={(0:8)}]yhl.center) node (yh){} +(180:.15cm) -- +(0:.15cm) node [xshift=-.8cm, yshift=0cm] {11/12};
\draw [dotline] (0,\incrmnt*11) -- +(0:14cm);

\draw [linecolor] (0,\incrmnt*12) node (yhl){} +(180:.15cm) -- +(0:.15cm) node [xshift=-.8cm, yshift=0cm] {12/12}([shift={(0:8)}]yhl.center) node (yh){} +(180:.15cm) -- +(0:.15cm) node [xshift=-.8cm, yshift=0cm] {12/12};
\draw [dotline] (0,\incrmnt*12) -- +(0:14cm);

\draw [linecolor] (\incrmnt*1,0) node (al){} +(90:\incrmnt*1) node [circle, draw, solid, red, fill=red, scale=0.4]{} -- +(-90:.25cm) node [xshift=0cm, yshift=-.35cm] {1} ([shift={(0:8)}]al.center) node (a){} +(90:.25cm) -- +(-90:.25cm) node [xshift=0cm, yshift=-.35cm] {1} ([shift={(90:\incrmnt*1)}]a.center) node (au){} ([shift={(90:\incrmnt*1)}]au.center) node (auu){};

\draw [linecolor] (\incrmnt*2,0) node (bl){} +(90:\incrmnt*2) node [circle, draw, solid, red, fill=red, scale=0.4]{} -- +(-90:.25cm) node [xshift=0cm, yshift=-.35cm] {2} ([shift={(0:8)}]bl.center) node (b){} +(90:.25cm) -- +(-90:.25cm) node [xshift=0cm, yshift=-.35cm] {2} ([shift={(90:\incrmnt*1)}]b.center) node (bu){} ([shift={(90:\incrmnt*2)}]bu.center) node (buu){};

\draw [linecolor] (\incrmnt*3,0) node (cl){} +(90:\incrmnt*2) node [circle, draw, solid, red, fill=red, scale=0.4]{} -- +(-90:.25cm) node [xshift=0cm, yshift=-.35cm] {3} ([shift={(0:8)}]cl.center) node (c){} +(90:.25cm) -- +(-90:.25cm) node [xshift=0cm, yshift=-.35cm] {3} ([shift={(90:\incrmnt*3)}]c.center) node (cu){} ([shift={(90:\incrmnt*2)}]cu.center) node (cuu){};

\draw [linecolor] (\incrmnt*4,0) node (dl){} +(90:\incrmnt*2) node [circle, draw, solid, red, fill=red, scale=0.4]{} -- +(-90:.25cm) node [xshift=0cm, yshift=-.35cm] {4} ([shift={(0:8)}]dl.center) node (d){} +(90:.25cm) -- +(-90:.25cm) node [xshift=0cm, yshift=-.35cm] {4} ([shift={(90:\incrmnt*5)}]d.center) node (du){} ([shift={(90:\incrmnt*2)}]du.center) node (duu){};

\draw [linecolor] (\incrmnt*5,0) node (el){} +(90:\incrmnt*2) node [circle, draw, solid, red, fill=red, scale=0.4]{} -- +(-90:.25cm) node [xshift=0cm, yshift=-.35cm] {5} ([shift={(0:8)}]el.center) node (e){} +(90:.25cm) -- +(-90:.25cm) node [xshift=0cm, yshift=-.35cm] {5} ([shift={(90:\incrmnt*7)}]e.center) node (eu){} ([shift={(90:\incrmnt*2)}]eu.center) node (euu){};

\draw [linecolor] (\incrmnt*6,0) node (fl){} +(90:\incrmnt*2) node [circle, draw, solid, red, fill=red, scale=0.4]{} -- +(-90:.25cm) node [xshift=0cm, yshift=-.35cm] {6} ([shift={(0:8)}]fl.center) node (f){} +(90:.25cm) -- +(-90:.25cm) node [xshift=0cm, yshift=-.35cm] {6} ([shift={(90:\incrmnt*9)}]f.center) node (fu){} ([shift={(90:\incrmnt*2)}]fu.center) node (fuu){};

\draw [linecolor] (\incrmnt*7,0) node (gl){} +(90:\incrmnt*1) node [circle, draw, solid, red, fill=red, scale=0.4]{} -- +(-90:.25cm) node [xshift=0cm, yshift=-.35cm] {7} ([shift={(0:8)}]gl.center) node (g){} +(90:.25cm) -- +(-90:.25cm) node [xshift=0cm, yshift=-.35cm] {7}([shift={(90:\incrmnt*11)}]g.center) node (gu){} ([shift={(90:\incrmnt*1)}]gu.center) node (guu){};
\end{tikzpicture}
\end{frame}
\end{document}

这是生成以下绘图的其余代码

    \draw [ultra thick, blue] (au.center) -- (bu.center) (buu.center) -- (cu.center) (cuu.center) -- (du.center) (duu.center) -- (eu.center) (euu.center) -- (fu.center) (fuu.center) -- (gu.center) (guu.center) --+(0:\incrmnt*2) node (inf){};
\draw [thick, black] (inf.center) +(90:\incrmnt*1) --(inf.center|-0,0) node [xshift=0cm, yshift=-.35cm] {$\infty$};


\draw [thick, red, fill=red] (au.center) circle (.1) (buu.center) circle (.1) (cuu.center) circle (.1) (duu.center) circle (.1) (euu.center) circle (.1) (fuu.center) circle (.1) (guu.center) circle (.1);

\draw [thick, red, fill=white] (a.center) circle (.14) (bu.center) circle (.14) (cu.center) circle (.14) (du.center) circle (.14) (eu.center) circle (.14) (fu.center) circle (.14) (gu.center) circle (.14);

Answer 1

在这个答案中，我专注于用\foreach循环重现您的输出。我不会重现您的命名节点，因为这些节点在您的代码中没有使用。当然，可以生成自动命名的节点，如果碰巧使用它们，我可以添加它们。

\documentclass{beamer}
\beamertemplatenavigationsymbolsempty
\usepackage{tikz}
\begin{document}
\begin{frame}[t]
\frametitle{}
\hspace {-1cm}
\begin{tikzpicture}[scale=.7, transform shape,
linecolor/.style={ultra thick, green!40!black},
dotline/.style={thin, black, loosely dotted}]
\pgfmathsetmacro{\incrmnt}{.6}

\draw [thick,-latex](-.3,0) -- (5,0);
\draw [thick,-latex](0,-.3)  -- (0,8);
\draw [thick,-latex](6.,0)  -- (14.4,0) coordinate (br);
\draw [thick,-latex](8,-.2) -- (8,8) coordinate(tr);
\foreach \X in {1,...,12}
{
\draw [dotline] (0,\X*7cm/12) -- ++ (14,0);
\draw [linecolor] (-\incrmnt/2,\X*7cm/12)node[left]{\X/12} -- ++ (\incrmnt,0)
(8-\incrmnt/2,\X*7cm/12)node[left]{\X/12}-- ++ (\incrmnt,0);
}
\foreach \X in {1,...,7}
{
\draw[linecolor]  (3*\X/5,-\incrmnt/2) node[below]{\X} -- ++ (0,\incrmnt)
(8+3*\X/5,-\incrmnt/2) node[below]{\X} -- ++ (0,\incrmnt);
\pgfmathtruncatemacro{\tst}{abs(\X-4)}
\ifnum\tst=3
\draw[linecolor]  (3*\X/5,0)  -- ++ (0,7/12)
node[fill,red,circle,inner sep=2pt]{};
\else
\draw[linecolor]  (3*\X/5,0)  -- ++ (0,14/12)
node[fill,red,circle,inner sep=2pt]{};
\fi
\ifnum\X=7
\draw[blue,thick]   (8+3*\X/5,{7*(2*\X-2)/12})
node[fill,red,circle,inner sep=2pt]{} -- ++ (2*7cm/12,0) coordinate(xr);
\else
\draw[blue,thick]  (8+3*\X/5,{7*(2*\X-1)/12}) node[fill,red,circle,inner sep=2pt]{}
-- ++ (1*7cm/12,0) node[circle,fill=white,draw=red,inner sep=2pt]{};
\fi
}
\draw (tr-|xr) -- (br-|xr) node[below](ir){$\infty$};
\node at (6.5,0 |-ir) {$-\infty$};
\node[circle,fill=white,draw=red,inner sep=2pt,thick] at (8+3/5,0){};
\end{tikzpicture}
\end{frame}
\end{document}

Answer 2

编辑：

易于阅读的代码：

编程的基本原则是编写易于阅读代码，尤其是使用像 TeX 这样的编译语言。事实上，代码越容易阅读和理解，在 6 个月、1 年或 10 年后修改就越容易……

因此，我写道（即使代码没有优化）每个功能块的代码。这里：

• 我首先画出左图的坐标轴
• 然后我画出图表本身（我将数据放入其中）
• 我对第二张图也做了同样的操作。

这样构造和注释的代码很容易理解。

重复使用代码：

编程的根本原则就是重复使用代码。为此，我们可以使用macros或更简单的foreach循环。

这里有两个图表相同的轴。你所要做的就是建造它，然后重复使用它scope在向右移动几厘米的环境中。这避免了不必要的计算。

完成后，第二张图的内容就绘制出来了。

第二张图表很适合foreach循环，因为每次1 unit向右移动，就会2 units向上移动，因此这个公式\incrmnt*(2*\x-1)使得计算变得简单。

由于其余部分不可分解，因此单独绘制。

使用 www.DeepL.com/Translator 翻译

\documentclass{beamer}
\beamertemplatenavigationsymbolsempty
\usepackage{tikz}
\usepackage{pgfplots}
\begin{document}
\begin{frame}[t]
\frametitle{}
\hspace {-1cm}
\begin{tikzpicture}[scale=.7, transform shape,linecolor/.style={ultra thick, green!40!black},dotline/.style={thin, black, loosely dotted},
point/.style={circle, draw, red, fill=red, scale=0.4},
cercle/.style={circle,draw,scale=.5, red,thick, fill=white,inner sep=6pt}
]
\pgfmathsetmacro{\incrmnt}{.6}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% plot of the abscissa axis (horizontal) and ordinate axis (on the left)
\draw [thick,-latex](-.3,0) -- (5,0);
\draw [thick,-latex](0,-.3) -- (0,8);

\foreach \y in {1,...,12}{
\draw [linecolor] (0,\incrmnt*\y) +(0:.15) -- +(180:.15) node [left] {\y/12};% indexation of ordinate axis (vertical)
\draw [dotline] (0,\incrmnt*\y) -- +(0:8*\incrmnt);% horizontal dotted lines
}
\foreach \x in {1,...,7}{
\draw [linecolor] (\incrmnt*\x,.15) -- (\incrmnt*\x,-.15) node [below] {\x} ;
    }

% draw of the left graph
\begin{scope}[every node/.style={circle, draw, solid, red, fill=red, scale=0.4}]
\draw [linecolor] (\incrmnt*1,\incrmnt*1) node{} -- (\incrmnt,.15);
\draw [linecolor] (\incrmnt*2,\incrmnt*2) node{}-- (\incrmnt*2,.15);
\draw [linecolor] (\incrmnt*3,\incrmnt*2) node{} -- (\incrmnt*3,.15);
\draw [linecolor] (\incrmnt*4,\incrmnt*2) node{} -- (\incrmnt*4,.15);
\draw [linecolor] (\incrmnt*5,\incrmnt*2) node{} -- (\incrmnt*5,.15);
\draw [linecolor] (\incrmnt*6,\incrmnt*2) node{} -- (\incrmnt*6,.15);
 \draw [linecolor] (\incrmnt*7,\incrmnt*1) node {} -- (\incrmnt*7,.15);
\end{scope}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  
% graph on the rigth
% plot the same axis by a simple 8cm translation 
\begin{scope}[xshift=8cm]
\draw [thick,-latex](-2,0)node [below right] {$-\infty$}   -- (6,0);
\draw [thick,-latex](0,-.3)  -- (0,8);
\foreach \y in {1,...,12}{
    \draw [linecolor] (0,\incrmnt*\y) +(0:.15cm) -- +(180:.15cm) node [left] {\y/12};% indexation of ordinate axis (vertical)
    \draw [dotline] (0,\incrmnt*\y) -- +(0:10*\incrmnt);% horizontal dotted lines
}
\foreach \x in {1,...,7}{
    \draw [linecolor] (\incrmnt*\x,.15) -- (\incrmnt*\x,-.15) node [below] {\x} ;
    }

% draw the graph on the rigth
\draw [thick, black] (\incrmnt*9,0) node [below] {$\infty$} --+(0,\incrmnt*13);
\foreach \x in {1,...,6}{
\draw[ultra thick, blue](\incrmnt*\x,{\incrmnt*(2*\x-1)})node[point]{}--+(\incrmnt,0)node[cercle]{};
}
\node[cercle] at(\incrmnt,0){};
\draw[ultra thick, blue](\incrmnt*7,\incrmnt*12)node[point]{}--+(\incrmnt*2,0);
\end{scope}

\end{tikzpicture}
\end{frame}
\end{document}

较早的答案：

要使用\foreach循环，只需确定每行中并行修改的数字即可。在您的代码中，前几行可以通过循环轻松分解。

以下的因素更难分解，因为没有可以轻易利用的规律。

编辑：修正因式分解的遗漏

    \documentclass{beamer}
    \beamertemplatenavigationsymbolsempty
    \usepackage{tikz}
    \usepackage{pgfplots}
    \begin{document}
    \begin{frame}[t]
    \frametitle{}
    \hspace {-1cm}
    \begin{tikzpicture}[scale=.7, transform shape,linecolor/.style={ultra thick, green!40!black},dotline/.style={thin, black, loosely dotted}]
    \pgfmathsetmacro{\incrmnt}{.6}

    \draw [thick,-latex](-.3,0) -- (0,0) -- (5,0);
    \draw [thick,-latex](0,-.3) -- (0,0) -- (0,8);
    \draw [thick,-latex](6.,0) -- (7,0) -- (14.4,0);
    \draw [thick,-latex](8,-.2) -- (8,0) -- (8,8);

% Factoring the first 12 operations `\draw`:
    \foreach \y in {1,...,12}{
    \draw [linecolor] (0,\incrmnt*\y) node (yhl){} +(180:.15cm) -- +(0:.15cm) node [xshift=-.8cm, yshift=0cm] {\y/12}([shift={(0:8)}]yhl.center) node (yh){} +(180:.15cm) -- +(0:.15cm) node [xshift=-.8cm, yshift=0cm] {\y/12};
    \draw [dotline] (0,\incrmnt*\y) -- +(0:14cm);
    }

    \draw [linecolor] (\incrmnt*1,0) node (al){} +(90:\incrmnt*1) node [circle, draw, solid, red, fill=red, scale=0.4]{} -- +(-90:.25cm) node [xshift=0cm, yshift=-.35cm] {1} ([shift={(0:8)}]al.center) node (a){} +(90:.25cm) -- +(-90:.25cm) node [xshift=0cm, yshift=-.35cm] {1} ([shift={(90:\incrmnt*1)}]a.center) node (au){} ([shift={(90:\incrmnt*1)}]au.center) node (auu){};

    \draw [linecolor] (\incrmnt*2,0) node (bl){} +(90:\incrmnt*2) node [circle, draw, solid, red, fill=red, scale=0.4]{} -- +(-90:.25cm) node [xshift=0cm, yshift=-.35cm] {2} ([shift={(0:8)}]bl.center) node (b){} +(90:.25cm) -- +(-90:.25cm) node [xshift=0cm, yshift=-.35cm] {2} ([shift={(90:\incrmnt*1)}]b.center) node (bu){} ([shift={(90:\incrmnt*2)}]bu.center) node (buu){};

    \draw [linecolor] (\incrmnt*3,0) node (cl){} +(90:\incrmnt*2) node [circle, draw, solid, red, fill=red, scale=0.4]{} -- +(-90:.25cm) node [xshift=0cm, yshift=-.35cm] {3} ([shift={(0:8)}]cl.center) node (c){} +(90:.25cm) -- +(-90:.25cm) node [xshift=0cm, yshift=-.35cm] {3} ([shift={(90:\incrmnt*3)}]c.center) node (cu){} ([shift={(90:\incrmnt*2)}]cu.center) node (cuu){};

    \draw [linecolor] (\incrmnt*4,0) node (dl){} +(90:\incrmnt*2) node [circle, draw, solid, red, fill=red, scale=0.4]{} -- +(-90:.25cm) node [xshift=0cm, yshift=-.35cm] {4} ([shift={(0:8)}]dl.center) node (d){} +(90:.25cm) -- +(-90:.25cm) node [xshift=0cm, yshift=-.35cm] {4} ([shift={(90:\incrmnt*5)}]d.center) node (du){} ([shift={(90:\incrmnt*2)}]du.center) node (duu){};

    \draw [linecolor] (\incrmnt*5,0) node (el){} +(90:\incrmnt*2) node [circle, draw, solid, red, fill=red, scale=0.4]{} -- +(-90:.25cm) node [xshift=0cm, yshift=-.35cm] {5} ([shift={(0:8)}]el.center) node (e){} +(90:.25cm) -- +(-90:.25cm) node [xshift=0cm, yshift=-.35cm] {5} ([shift={(90:\incrmnt*7)}]e.center) node (eu){} ([shift={(90:\incrmnt*2)}]eu.center) node (euu){};

    \draw [linecolor] (\incrmnt*6,0) node (fl){} +(90:\incrmnt*2) node [circle, draw, solid, red, fill=red, scale=0.4]{} -- +(-90:.25cm) node [xshift=0cm, yshift=-.35cm] {6} ([shift={(0:8)}]fl.center) node (f){} +(90:.25cm) -- +(-90:.25cm) node [xshift=0cm, yshift=-.35cm] {6} ([shift={(90:\incrmnt*9)}]f.center) node (fu){} ([shift={(90:\incrmnt*2)}]fu.center) node (fuu){};

    \draw [linecolor] (\incrmnt*7,0) node (gl){} +(90:\incrmnt*1) node [circle, draw, solid, red, fill=red, scale=0.4]{} -- +(-90:.25cm) node [xshift=0cm, yshift=-.35cm] {7} ([shift={(0:8)}]gl.center) node (g){} +(90:.25cm) -- +(-90:.25cm) node [xshift=0cm, yshift=-.35cm] {7}([shift={(90:\incrmnt*11)}]g.center) node (gu){} ([shift={(90:\incrmnt*1)}]gu.center) node (guu){};

    \end{tikzpicture}
    \end{frame}
    \end{document}