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使用 tikz 和 pgfplots 绘制阴影区域

tag-icon • tag-icon tikz-pgf
使用 tikz 和 pgfplots 绘制阴影区域

我正在尝试绘制以下区域在此处输入图片描述

我能做的最好的是以下代码：

\begin{figure}[H]
\begin{center}
    \begin{tikzpicture}
        \begin{axis}
        [   
        axis lines = middle,
        xlabel={$x$}, 
        ylabel={$y$},
        xmin=-1, xmax=2, ymin=0, ymax=3,
        xmajorticks=false
        ]
        \addplot[smooth, thick, samples=200, name path=curve1] {1/(2*x)};
        \addplot[smooth, thick, samples=200, name path=curve2] {1/x};
        \addplot[smooth, thick, samples=200, name path=curve3] {2*x^2};
        \addplot[smooth, thick, samples=200, name path=curve4] {3*x^2};

        \addplot[color=black,fill=pink,fill opacity=0.4]fill between[of=curve1 and curve2, soft clip={domain=0.5503:0.7937}];
        
        \end{axis}
        \end{tikzpicture}
\end{center}
\end{figure}

这将创建下面的图像：

在此处输入图片描述

有人能帮帮我吗？因为我不知道如何使用函数 y=1/2x 和 y=1/x 作为阴影区域的边框。

答案1

这是一个非常 hacky 的解决方案，但它至少填充了您要查找的区域。问题是它填充了外面的区域，然后将其覆盖，这不太一样。我会继续思考如何“正确”地做到这一点，如果我想到了什么，我会更新！

\documentclass{standalone}
\usepackage{tikz,pgfplots}
\usepgfplotslibrary{fillbetween}
\pgfplotsset{compat=1.18}
\begin{document}
\begin{tikzpicture}
    \begin{axis}[
        axis lines = middle,
        xlabel={$x$},
        ylabel={$y$},
        xmin=-1, xmax=2, ymin=0, ymax=3,
        xmajorticks=false
    ]
    \addplot[smooth, thick, samples=200, name path=curve1] {1/(2*x)};
    \addplot[smooth, thick, samples=200, name path=curve2] {1/x};
    \addplot[smooth, thick, samples=200, name path=curve3] {2*x^2};
    \addplot[smooth, thick, samples=200, name path=curve4] {3*x^2};

    \addplot[color=black,fill=pink,fill opacity=0.4]fill between[of=curve1 and curve2, soft clip={domain=0.5503:0.7937}];
    \addplot[color=black,fill=white,fill opacity=1.0]fill between[of=curve2 and curve4, soft clip={domain=0.5503:0.8}];
    \addplot[color=black,fill=white,fill opacity=1.0]fill between[of=curve1 and curve3, soft clip={domain=0.5503:0.8}];
    \end{axis}
\end{tikzpicture}
\end{document}

结果图

编辑：这是一个稍微不那么黑客化的版本，因为它不需要任何背景掩盖：

\documentclass{standalone}
\usepackage{tikz,pgfplots}
\usepgfplotslibrary{fillbetween}
\pgfplotsset{compat=1.18}
\begin{document}
\begin{tikzpicture}
    \begin{axis}[
        axis lines = middle,
        xlabel={$x$},
        ylabel={$y$},
        xmin=-1, xmax=2, ymin=0, ymax=3,
        xmajorticks=false
    ]
    \addplot[smooth, thick, samples=200, name path=curve1] {1/(2*x)};
    \addplot[smooth, thick, samples=200, name path=curve2] {1/x};
    \addplot[smooth, thick, samples=200, name path=curve3] {2*x^2};
    \addplot[smooth, thick, samples=200, name path=curve4] {3*x^2};

    \addplot[fill=pink,fill opacity=0.4] fill between[of=curve1 and curve4,
        soft clip={domain=0.5503:0.6299605}];
    \addplot[fill=pink,fill opacity=0.4] fill between[of=curve3 and curve4,
        soft clip={domain=0.6299605:0.69335}];
    \addplot[fill=pink,fill opacity=0.4] fill between[of=curve2 and curve3,
        soft clip={domain=0.69335:0.7937}];
    \end{axis}
\end{tikzpicture}
\end{document}

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