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曲线之间的面积 tikz

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曲线之间的面积 tikz

我正在尝试使用 tikz 绘制图形，但似乎无法突出显示曲线之间的区域。结果应该看起来像这样：

在此处输入图片描述

这是我目前拥有的代码：

\begin{center}
\begin{tikzpicture}[scale=0.8]

\draw[->] (0,-0.5) -- (0,4.5) node[anchor=east] {};
\draw[->] (-0.5,0) -- (9,0) node[anchor=north] {};
\draw   (1,-0.2) node[anchor=north] {$a$}
        (8,-0.2) node[anchor=north] {$b$}       
        ;
\filldraw[fill=black!10](1,0)--(1,2)--(8,2)--(8,0);
\draw [](1,3) parabola bend (2.5,1.5)(4.2,2.4); 
\draw [](4.2,2.4) parabola bend (5.5,3)(8,0); 
\draw[] (1,0)--(1,3);
\end{tikzpicture}
\end{center}

我想要实现的最终结果是 C 和 D 以橙色突出显示，而 A 和 B 以深灰色突出显示。不用担心轴标签，否则我主要需要阴影方面的帮助。

提前致谢！！

答案1

为此，我建议你使用pgfplots封装和堆叠图：

\documentclass[border=5mm]{standalone}
\usepackage{pgfplots}

\pgfplotsset{compat=newest}

\begin{document}

\pgfmathdeclarefunction{poly}{0}{%
      \pgfmathparse{-x^3+5*(x^2)-3*x-3}%
    }

\begin{tikzpicture}
\begin{axis}[
  domain=-1.2:4.2,
  ymin=-5,
  ymax=10,
  samples=160,
  stack plots=y
]
% draw graph for the first function f
\addplot+[black,thick,mark=none] {poly};
% draw graph of max(g-f, 0) and stack
\addplot+[mark=none,fill=gray!60,draw=cyan] {max(3-(poly),0)} \closedcycle;
% draw graph of min(g-f, 0) and stack
\addplot+[mark=none,fill=orange!70,draw=cyan] {min(3-(poly),0)} \closedcycle;
\end{axis}
\end{tikzpicture}

\end{document}

在此处输入图片描述

并提供帮助行和标签：

\documentclass[border=5mm]{standalone}
\usepackage{pgfplots}

\pgfplotsset{compat=newest}

\begin{document}

\pgfmathdeclarefunction{poly}{0}{%
      \pgfmathparse{-x^3+5*(x^2)-3*x-3}%
    }

\begin{tikzpicture}
\begin{axis}[
  xmin=-2,
  xmax=5,
  ymin=-5,
  ymax=10,
  axis y line=left,
  axis x line=bottom,
  xtick={-1.2,2,4.2},
  xticklabels={$a$,$\zeta$,$b$},
  ytick={3},
  yticklabels={$f(\zeta)$},
  samples=160
]

\addplot[mark=none,help lines,domain=-2:4.2] {3};

% draw graph for the first function f
\addplot+[black,thick,mark=none,domain=-1.2:4.2,stack plots=y] {poly};
% draw graph of max(g-f, 0) and stack
\addplot+[mark=none,fill=gray!60,draw=cyan,domain=-1.2:4.2,stack plots=y] {max(3-(poly),0)} \closedcycle;
% draw graph of min(g-f, 0) and stack
\addplot+[mark=none,fill=orange!70,draw=cyan,domain=-1.2:4.2,stack plots=y] {min(3-(poly),0)} \closedcycle;

\draw[help lines] (axis cs:-1.2,-5) -- (axis cs:-1.2,3);
\draw[help lines] (axis cs:2,-5) -- (axis cs:2,3);
\draw[help lines] (axis cs:4.2,-5) -- (axis cs:4.2,3);
\end{axis}
\end{tikzpicture}

\end{document}

在此处输入图片描述

答案2

Gonzalo 的堆叠图想法很聪明。现在有了新的方法，使用 pgfplots 1.10 及其fillbetween库：

  • 绘制多边形函数并命名
  • 绘制线条（或任何其他函数）并命名
  • 添加fill between情节

精华：

\usepgfplotslibrary{fillbetween}
...
\addplot[name path=poly,black,thick,mark=none,domain=-1.2:4.2,stack plots=y] {poly};
\addplot[name path=line,gray,no markers,line width=1pt,domain=-1.2:4.2] {3};
\addplot fill between[ 
  of = poly and line, 
  split, % calculate segments
  every even segment/.style = {orange!70},
  every odd segment/.style  ={gray!60}
];

曲线之间的填充区域

完整示例：

\documentclass[border=5mm]{standalone}
\usepackage{pgfplots}

\pgfplotsset{compat=newest}
\usepgfplotslibrary{fillbetween}
\begin{document}

\pgfmathdeclarefunction{poly}{0}{%
      \pgfmathparse{-x^3+5*(x^2)-3*x-3}%
    }

\begin{tikzpicture}
  \begin{axis}[
    xmin=-2,
    xmax=5,
    ymin=-5,
    ymax=10,
    axis y line=left,
    axis x line=bottom,
    xtick={-1.2,2,4.2},
    xticklabels={$a$,$\zeta$,$b$},
    ytick={3},
    yticklabels={$f(\zeta)$},
    samples=160
  ]

  \addplot[name path=poly,black,thick,mark=none,domain=-1.2:4.2,stack plots=y] {poly};
  \addplot[name path=line,gray,no markers,line width=1pt,domain=-1.2:4.2] {3};
  \addplot fill between[ 
    of = poly and line, 
    split, % calculate segments
    every even segment/.style = {orange!70},
    every odd segment/.style  ={gray!60}
  ];
\end{axis}
\end{tikzpicture}

\end{document}

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