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TikZ：如何仅引用定义坐标的一个分量？

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TikZ：如何仅引用定义坐标的一个分量？

我制作了一张图来展示牛顿方法的实际应用：

\documentclass{article}

\usepackage{lmodern}
\usepackage[T1]{fontenc}
\usepackage{tikz}
\usepackage{graphicx}

\begin{document}
    \begin{figure}[htbp]
        \centering
        \begin{tikzpicture}
            \coordinate (y) at (0,3);
            \coordinate (x) at (5,0);

            \coordinate (sp0) at (1.5, 0);
            \coordinate (ep0) at (3.5, 2);
            \coordinate (csp0) at (2.5, 1);
            \coordinate (cep0) at (2.75, 0);

            \coordinate (sp1) at (ep0);
            \coordinate (ep1) at (4.5, 3);
            \coordinate (csp1) at (4.25, 4);
            \coordinate (cep1) at (4.25, 2);

            \coordinate (sp2) at (sp0);
            \coordinate (ep2) at (0, -1);
            \coordinate (csp2) at (0.5, -1);
            \coordinate (cep2) at (0.5, -1);

            \coordinate (x0) at (2.25, 0);
            \coordinate (x1) at (3.5, 0);

            \draw[<->] (y) node[left] {$f(x)$} -- (0,0) --  (x) node[below] {$x$};

            \draw (sp0) .. controls (csp0) and (cep0).. (ep0);
            \draw[dashed] (cep0) -- (csp1);
            \draw[dotted] (ep0) -- (0, 2);
            \draw[dotted] (ep0) -- (3.5, 0);

            \draw (sp1) .. controls (csp1) and (cep1).. (ep1);
            \draw (sp2) .. controls (csp2) and (cep2).. (ep2);

            \draw (3.5,1pt) -- (3.5,-3pt) node[anchor=north] {$x_0$};
            \draw (2.75,1pt) -- (2.75,-3pt) node[anchor=north] {$x_1$};
            \draw (1pt, 2) -- (-3pt, 2) node [anchor=east] {$f(x_0)$};
        \end{tikzpicture}
        \caption{Newton's method in action.}
        \label{fig:newton_method}
    \end{figure}
\end{document}

接近尾声时，你会看到我写了如下内容：

\draw (3.5,1pt) -- (3.5,-3pt) node[anchor=north] {$x_0$};

我正在尝试为先前定义的坐标（在本例中为）设置刻度x1，并且我只需要它的 x 分量（3.5），但我不知道如何单独引用它，因此我手动引用它。这样做的缺点是，如果我重新定义x1，那么我必须仔细检查代码以找到仅使用其一个分量的任何位，然后也对其进行更改。您已经可以看到我已经开始犯错误，并且我对是否要引用x1或感到困惑x0。

我怎样才能以更自动化的方式仅引用一个组件？

答案1

一种方法是使用库let中的语法calc。在包含

\usetikzlibrary{calc}

我们可以说

\draw let \p1 = (x1) in (\x1,1pt) -- (\x1,-3pt) node[anchor=north] {$x_0$};

它将坐标设置x1为一个点\p1，该点的各个坐标可以在语句中使用\x1and进行访问\y1。这可能会造成混淆，因为所讨论的坐标是有名称的x1，因此我们可以轻松地完成

 \draw let \p2 = (x1) in (\x2,1pt) -- (\x2,-3pt) node[anchor=north] {$x_0$};

补充说明一下：我们可以使用相对坐标来仅要求一次我们的坐标位置：

 \draw let \p1 = (x1) in (\x1,1pt) -- ++(0,-4pt) node[anchor=north] {$x_0$};

以下是完整代码

\documentclass{standalone}

\usepackage{lmodern}
\usepackage[T1]{fontenc}
\usepackage{tikz}
\usepackage{graphicx}

\usetikzlibrary{calc}

\begin{document}
\begin{tikzpicture}
    \coordinate (y) at (0,3);
    \coordinate (x) at (5,0);

    \coordinate (sp0) at (1.5, 0);
    \coordinate (ep0) at (3.5, 2);
    \coordinate (csp0) at (2.5, 1);
    \coordinate (cep0) at (2.75, 0);

    \coordinate (sp1) at (ep0);
    \coordinate (ep1) at (4.5, 3);
    \coordinate (csp1) at (4.25, 4);
    \coordinate (cep1) at (4.25, 2);

    \coordinate (sp2) at (sp0);
    \coordinate (ep2) at (0, -1);
    \coordinate (csp2) at (0.5, -1);
    \coordinate (cep2) at (0.5, -1);

    \coordinate (x0) at (2.25, 0);
    \coordinate (x1) at (3.5, 0);

    \draw[<->] (y) node[left] {$f(x)$} -- (0,0) --  (x) node[below] {$x$};

    \draw (sp0) .. controls (csp0) and (cep0).. (ep0);
    \draw[dashed] (cep0) -- (csp1);
    \draw[dotted] (ep0) -- (0, 2);
    \draw[dotted] (ep0) -- (3.5, 0);

    \draw (sp1) .. controls (csp1) and (cep1).. (ep1);
    \draw (sp2) .. controls (csp2) and (cep2).. (ep2);

    \draw let \p1 = (x1) in (\x1,1pt) -- ++(0,-4pt) node[anchor=north] {$x_0$};
    \draw (2.75,1pt) -- (2.75,-3pt) node[anchor=north] {$x_1$};
    \draw (1pt, 2) -- (-3pt, 2) node [anchor=east] {$f(x_0)$};
\end{tikzpicture}
\end{document}

输出结果如下：

在此处输入图片描述

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