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如何使用 tikzpicture 填充由两条曲线包围的区域

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如何使用 tikzpicture 填充由两条曲线包围的区域

我想问一个关于如何阴影化两条曲线之间的区域的问题。

首先下面是代码

\documentclass[]{article}
\usepackage[margin=0.5in]{geometry}
\usepackage{pgfplots}
\usepackage{mathtools}
\usepackage{pgfplots}
\usepackage{amsmath}
\newtheorem{theorem}{THEOREM}
\newtheorem{proof}{PROOF}
\usepackage{tikz}
\usepackage{amssymb}
\usetikzlibrary{patterns}
\usepackage{bigints}
\usepackage{color}
\usepgfplotslibrary{fillbetween}
\begin{document}
\setlength{\parindent}{0mm}
\pgfplotsset{every axis/.append style={
        axis x line=middle,    % put the x axis in the middle
        axis y line=middle,    % put the y axis in the middle
        axis line style={<->}, % arrows on the axis
        xlabel={$x$},          % default put x on x-axis
        ylabel={$y=\sqrt{-x+1}$},          % default put y on y-axis
        ticks=none
    }}
    % arrows as stealth fighters
    \tikzset{>=stealth}
    \begin{center}
        \begin{tikzpicture}
        \begin{axis}[
        xmin=-4,xmax=2,
        ymin=-1,ymax=3,
        ]
        \plot[name path=A, thick,samples=100,domain=-4:1] {sqrt(-1*x+1)};
        \plot[name path=B,thick,samples=100,domain=-4:1] {2};
        \addplot[fill=gray,opacity=.4,domain=0:1,samples=50] {sqrt(-1*x+1)}\closedcycle;
        %\addplot[fill=gray, domain=-3:0,opacity=0.4] fill between[of=A and B];
        \addplot+[mark=none,fill=gray,draw=black,domain=-3:0,opacity=0.4] {max(2-sqrt(-x+1),sqrt(-x+1))} \closedcycle;
        \node [below] at (axis cs: 0.2,0) {$O$};
        \draw[thick,dashed,brown] (axis cs:-3,0) -- (axis cs:-3,2);
        \node [below] at (axis cs: -3,0) {$-3$};
        \node [below] at (axis cs: 1,0) {$1$};
        \end{axis}
        \end{tikzpicture}
    \end{center}
\end{document}

因此，上述代码生成了以下图表。我实际上希望阴影区域位于 x=[-3,0] 上的水平线 (y=2) 和曲线 (y=\sqrt{-x+1}) 之间，而它只是阴影曲线和 x 轴下方的区域。

你是如何实现这一点的？

输出

答案1

在此处输入图片描述

\documentclass[]{article}
\usepackage[margin=0.5in]{geometry}
\usepackage{pgfplots}
\usepackage{mathtools}
\usepackage{pgfplots}
\usepackage{amsmath}
\newtheorem{theorem}{THEOREM}
\newtheorem{proof}{PROOF}
\usepackage{tikz}
\usepackage{amssymb}
\usetikzlibrary{patterns}
\usepackage{bigints}
\usepackage{color}
\usepgfplotslibrary{fillbetween}
\begin{document}
\setlength{\parindent}{0mm}
\pgfplotsset{every axis/.append style={
        axis x line=middle,    % put the x axis in the middle
        axis y line=middle,    % put the y axis in the middle
        axis line style={<->}, % arrows on the axis
        xlabel={$x$},          % default put x on x-axis
        ylabel={$y=\sqrt{-x+1}$},          % default put y on y-axis
        ticks=none
    }}
    % arrows as stealth fighters
    \tikzset{>=stealth}
    \begin{center}
        \begin{tikzpicture}
        \begin{axis}[
        xmin=-4,xmax=2,
        ymin=-1,ymax=3,
        ]
        \plot[name path=A, thick,samples=100,domain=-4:1] {sqrt(-1*x+1)};
        \plot[name path=B,thick,samples=100,domain=-4:1] {2};
        \addplot[fill=gray,opacity=0.4] fill between[of=A and B,split,soft clip={domain=-3:0},every segment no 0/.style={white},];
        \node [below] at (axis cs: 0.2,0) {$O$};
        \draw[thick,dashed,brown] (axis cs:-3,0) -- (axis cs:-3,2);
        \node [below] at (axis cs: -3,0) {$-3$};
        \node [below] at (axis cs: 1,0) {$1$};
        \node [above right] at (axis cs: 0,2) {$2$};
        \end{axis}
        \end{tikzpicture}
    \end{center}
\end{document}

为了填充曲线之间的区域，我们可以使用单独设置区域样式every segment no，并在必要时应用，soft clip就像您的情况一样[-3,0]。

答案2

像这样吗？

\addplot fill between[
  of = func and line,
  soft clip={domain=-3:0},
  every even segment/.style  = {gray,opacity=.4}
];

在此处输入图片描述

我稍微整理了一下你的代码。下面是一个完整的示例：

\documentclass[border=10pt]{standalone}
\usepackage{pgfplots}
\usepgfplotslibrary{fillbetween}

\pgfplotsset{every axis/.append style={
        axis x line=middle,    % put the x axis in the middle
        axis y line=middle,    % put the y axis in the middle
        axis line style={<->}, % arrows on the axis
    }}

\begin{document}
\begin{tikzpicture}
  \begin{axis}[
    xlabel={$x$},              % default put x on x-axis
    ylabel={$y=\sqrt{-x+1}$},  % default put y on y-axis
    xtick={-3,0,1},
    ytick={2},
    samples=100,
    domain=-4:1,
    xmin=-4,xmax=2,
    ymin=-1,ymax=3,
  ]
  \addplot[name path=func, black, thick, mark=none, ] {sqrt(-x+1)};
  \addplot[name path=line,thick] {2};
  \addplot fill between[
    of = func and line,
    soft clip={domain=-3:0},
    every even segment/.style  = {gray,opacity=.4}
  ];
  \draw[thick,dashed,brown] (axis cs:-3,0) -- (axis cs:-3,2);
\end{axis}
\end{tikzpicture}
\end{document}

顺便提一句：

您不需要节点来放置轴刻度标签，而是使用xtick和xtick选项。

答案3

您可以使用soft clip限制填充到域x=[-3,0]：

\addplot[fill=gray,opacity=0.4] fill between [of=A and B, soft clip={domain=-3:0}];

因此下面的代码

\documentclass{article}
\usepackage{pgfplots}

\usepgfplotslibrary{fillbetween}

\pgfplotsset{every axis/.append style={
  axis x line=middle,    % put the x axis in the middle
  axis y line=middle,    % put the y axis in the middle
  axis line style={<->}, % arrows on the axis
  xlabel={$x$},          % default put x on x-axis
  ylabel={$y=\sqrt{-x+1}$},          % default put y on y-axis
  ticks=none
}}

% arrows as stealth fighters
\tikzset{>=stealth}

\begin{document}

\begin{center}
  \begin{tikzpicture}
    \begin{axis}[
      xmin=-4,xmax=2,
      ymin=-1,ymax=3,
      ]
      \plot[name path=A, thick,samples=100,domain=-4:1] {sqrt(-1*x+1)};
      \plot[name path=B,thick,samples=100,domain=-4:1] {2};
      \addplot[fill=gray,opacity=0.4] fill between [of=A and B, soft clip={domain=-3:0}];
      \node [below] at (axis cs: 0.2,0) {$O$};
      \draw[thick,dashed,brown] (axis cs:-3,0) -- (axis cs:-3,2);
      \node [below] at (axis cs: -3,0) {$-3$};
      \node [below] at (axis cs: 1,0) {$1$};
    \end{axis}
  \end{tikzpicture}
\end{center}

\end{document}

给出输出

输出

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