如何才能自动评估和调整？

Question

我正在尝试自己编写一个 TikZ，但遇到了麻烦。这就是我正在寻找的： 以下是我所能得到的： 最后，这是我编写的代码：

    \begin{figure}[ht]
    \centering
    \begin{tikzpicture}[scale=10]
        \coordinate (C0) at ($(0,0)$) {};
        \coordinate (C1) at ($(1,0)$) {};
        \draw[arrows=->] (C0) -- (C1);
        \foreach \x in {2,3,4,5,6}
        {        
            \coordinate (A\x) at ($(1/\x,0)$) {};
            \draw ($(A\x)+(0,0.01)$) -- ($(A\x)-(0,0.01)$);
            \node [below] at ($(A\x)+(0,-0.003)$) {$\frac{1}{\x}$};
        }
        \foreach \x [evaluate=\x as \xeval using \x-1] in {3,4,5,6}
        {        
            \coordinate (B\x) at ($({(\x-1)/\x},0)$) {};
            \draw ($(B\x)+(0,0.01)$) -- ($(B\x)-(0,0.01)$);
            %\node [below] at ($(B\x)+(0,-0.003)$) {\frac{\xeval}{\x}}; %ERROR!
        }
        \node [below] at ($(1/12,-0.023)$) {$\ldots$};
        \node [below] at ($(11/12,-0.023)$) {$\ldots$};
        \draw ($(0,0.01)$) -- ($(0,-0.01)$);
        \node [below] at ($(0,-0.011)$) {$0$};
        \draw ($(1,0.01)$) -- ($(1,-0.01)$);
        \node [below] at ($(1,-0.011)$) {$1$};
    \end{tikzpicture}
    \label{fig:dinamica F(x)}
\end{figure}

所以我问你的是：

1. 如何使用评估自动书写\frac{2}{3}等\frac{3}{4}？
2. 我怎样才能自动写出弯曲的箭头？

我尝试做这件事大约需要 2 个小时。

还有一件事：为了垂直对齐标签0，我不得不手动尝试很多坐标，直到找到正确的组合。有没有办法自动完成？谢谢\ldots！\frac{1}{2}

Answer 1

我不太清楚你对“自动评估”有什么想法。我只是试着重现你的手绘草图（为了练习……）。

\documentclass[tikz,
               border=3mm]{standalone}
\usetikzlibrary{calc,positioning,quotes}

\begin{document}
    \begin{tikzpicture}[
every edge quotes/.style = {font=\footnotesize, auto},
 L/.style = {->, shorten >=1mm, shorten <=1mm},
LA/.style = {out= 75, in=105, looseness=#1},
LB/.style = {out=255, in=285, looseness=#1}
                        ]
\draw (0,0) -- (10,0);

\foreach \x/\y [count = \xx] in
        {0/1, 1/6, 1/5, 1/4, 1/3, 1/2, 2/3, 3/4, 4/5, 5/6, 1/1}
        {
\ifnum\y=1  
    \coordinate[label={[yshift=-1mm]below:$\x$}] (n\xx) at (10*\x/\y,0)   
\else
    \coordinate[label={[yshift=-1mm]below:$\frac{\x}{\y}$}] (n\xx) at (10*\x/\y,0)
\fi;
% draw ticks
\draw (10*\x/\y,0.1) -- + (0,-0.2);
        }
% dots
\node [below=7pt] at ($(n1)!0.5!(n2)$) {$\dots$};
\node [below=7pt] at ($(n10)!0.5!(n11)$) {$\dots$};
% loops above
\draw[L]   ($(n2)!0.5!(n3)$) to [LA=2,"4"] ($(n3)!0.5!(n4)$);
\draw[L]   ($(n3)!0.5!(n4)$) to [LA=2,"3"] ($(n4)!0.5!(n5)$);
\draw[L]   ($(n4)!0.5!(n5)$) to [LA=2,"2"] ($(n5)!0.5!(n6)$);

\node (A) [above=17mm of n6,inner sep=0pt]  {A};
\draw[L]   ($(n5)!0.6!(n6)$) to [bend  left,"1"]    (A);
\draw[L]   ($(n6)!0.4!(n7)$) to [bend right,"1" ']  (A);
% loops below
\draw[L]   ($(n8)!0.5!(n9)$) to [LB=1.5,"4" '] ($(n3)!0.5!(n4)$);
\draw[L]   ($(n7)!0.5!(n8)$) to [LB=1.5,"3" '] ($(n4)!0.5!(n5)$);
\draw[L]   ($(n6)!0.5!(n7)$) to [LB=2.5,"2" '] ($(n5)!0.5!(n6)$);
    \end{tikzpicture}
\end{document}

我得到：

Answer 2

这是我画数轴的尝试。我不知道画弧的算法/逻辑自动地。圆弧必须从刻度标记的中点开始，并结束于其他刻度标记的中点之间（这是我从图片中了解到的全部内容）。在此代码中，刻度标签和椭圆是半自动放置和标记。0 和 1 不受欢迎，作为副作用被标记为 0/1 和 1/1。

\documentclass[tikz]{standalone}
\begin{document}
\begin{tikzpicture}

% the unit interval is magnified by 10 times
\draw (0,0) -- (10,0);

\foreach \x/\y [count = \cc] in
        {0/1, 1/6, 1/5, 1/4, 1/2, 4/5, 5/6, 1/1}
        {
            \coordinate (nn\cc) at(10*\x / \y, 0);
            \node [below of= nn\cc,
                   node distance = 0.5cm]
                  {$\frac{\x}{\y}$};

            % comment below node. it is not required
            \node [above of= nn\cc,
                   node distance = 0.5cm,
                   rotate=45]
                  {$nn\cc$};

            % draw ticks
            \draw (10*\x / \y, -0.1) --
                  (10*\x / \y,  0.1);
        }
%Find midpoint of first two and last two nodes
\draw (nn1) -- coordinate [pos=0.5](firstdot) (nn2);
\draw (nn7) -- coordinate [pos=0.5](lasttdot) (nn8);
% draw ellipsis at the midpoint shifted by 0.5cm
\node [below of= firstdot, node distance = 0.5cm]
                  {$\cdots$};
\node [below of= lasttdot, node distance = 0.5cm]
                  {$\cdots$};
\end{tikzpicture}
\end{document}