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如何将 pgfplot 集成到预先存在的 tikz 图片中？

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如何将 pgfplot 集成到预先存在的 tikz 图片中？

我正在尝试将 pgfplot 放在预先存在的 tikz 图片中。但不知何故，我用 pfgplot 创建的轴有不同的单位，我不确定如何使这两个东西适合。

代码如下：

\documentclass[11pt]{amsart}
\usepackage{geometry}                % See geometry.pdf to learn the layout options. There are lots.
\geometry{letterpaper}                   % ... or a4paper or a5paper or ... 
%\geometry{landscape}                % Activate for for rotated page geometry
%\usepackage[parfill]{parskip}    % Activate to begin paragraphs with an empty line rather than an indent
\usepackage{graphicx}
\usepackage{amssymb}
\usepackage{tikz}
\usepackage{pgfplots}
\usepackage{epstopdf}
\DeclareGraphicsRule{.tif}{png}{.png}{`convert #1 `dirname #1`/`basename #1 .tif`.png}

\title{Brief Article}
\author{The Author}
%\date{}                                           % Activate to display a given date or no date


\begin{document}
\maketitle

\begin{tikzpicture}[scale=1]
\draw [line width=0.05cm] (0,1) to [out=80,in=180] (1,1) to [out=0,in=180] (2.5,1.5) to [out=0,in=-100] (4,1);
\draw [line width=0.05cm] (0,3) to [out=25,in=150] (1.5,3.5) to [out=-30,in=120] (3,3) to [out=-50,in=-155] (4,3);
\draw [thin, ->] (-0.1,0) -- (4.5,0);
\draw [thin, ->] (0, -0.1) -- (0, 4.5);
\draw [thin] (4, -0.1) -- (4, 0.1);
\draw [line width=0.05cm, red] (1, 1) to [out=0, in=180] (1.5, 1.5);
\draw [line width=0.05cm, red] (2.5, 2.5) to [out=0, in=180] (3, 3);
\begin{axis}[samples=3000]
\addplot[very thick,red ]plot (\x, {\x*sin(1/abs(\x))});
\end{axis}
\end{tikzpicture}

\end{document}

我希望函数 x sin(1/|x|) 的图形（经过适当缩放和平移）能够以某种方式平滑地连接两条预先存在的红线。

任何帮助将不胜感激。

** 编辑 **

以下是一些改进的代码： 

\begin{tikzpicture}

 \path [fill=lightgray] (0,1) to [out=80,in=180] (1,1) to [out=0,in=180] (2.5,1.5) to [out=0,in=-100] (4,1) to (4,0) to (0,0);

  \draw [line width=0.05cm] (0,1) to [out=80,in=180] (1,1) to [out=0,in=180] (2.5,1.5) to [out=0,in=-100] (4,1);

  \path [fill=lightgray] (0,3) to [out=25,in=150] (1.5,3.5) to [out=-30,in=120] (3,3) to [out=-50,in=-155] (4,3) to (4,4.3) to (0,4.3);     \draw [line width=0.05cm] (0,3) to [out=25,in=150] (1.5,3.5) to [out=-30,in=120] (3,3) to [out=-50,in=-155] (4,3);                   \draw [thin, ->] (-0.1,0) -- (4.5,0);

  \draw [thin, ->] (0, -0.1) -- (0, 4.5);

      \draw [thin] (4, -0.1) -- (4, 0.1);

      \node [below] at (4, -0.1) {$2\pi$};

       \node [below] at (0, -0.1) {$0$};

        \draw [dashed] (-0.1, 2) -- (4,2);

\draw [line width=0.05cm, red] (1, 1) to [out=0, in=180] (1.5,1.5);
\draw [line width=0.05cm, red] (2.5,2.5) to [out=0, in=180] (3, 3);
\begin{axis}[samples=9000,scale only axis,axis lines=none]
\addplot[very thick,red ]plot (\x, {0.1*(\x + 3)*sin((1/abs((\x + 3)))r)});
\end{axis}
结果：在此处输入图片描述

答案1

如果我正确理解了你的问题，以下内容应该会产生你想要的曲线，但并没有解决标题中关于放置pgfplots axes在 内的问题tikzpicture。

\documentclass[11pt]{amsart}
\usepackage{tikz}
\usepackage{pgfplots}
\title{Brief Article}
\author{The Author}
\begin{document}
\maketitle

\begin{tikzpicture}[scale=1]
\draw [line width=0.05cm] (0,1) to [out=80,in=180] (1,1) to [out=0,in=180] (2.5,1.5) to [out=0,in=-100] (4,1);
\draw [line width=0.05cm] (0,3) to [out=25,in=150] (1.5,3.5) to [out=-30,in=120] (3,3) to [out=-50,in=-155] (4,3);
\draw [thin, ->] (-0.1,0) -- (4.5,0);
\draw [thin, ->] (0, -0.1) -- (0, 4.5);
\draw [thin] (4, -0.1) -- (4, 0.1);
\draw [line width=0.05cm, red] (1, 1) to [out=0, in=180] (1.5,1.5);
\draw[line width=0.05cm, red,rounded corners=2pt] (1.5,1.5) -| (2,2) |- (2.5,2.5);
\draw [line width=0.05cm, red] (2.5,2.5) to [out=0, in=180] (3, 3);
\end{tikzpicture}
\end{document}

在此处输入图片描述

编辑：

TikZ\draw命令可以在axis环境中运行，坐标(x,y)将与当前坐标系相对应。考虑到这一点，一种方法是基本上绘制一个具有两个坐标的图，然后在一个轴上绘制阴影区域，在另一个轴上绘制函数。理想情况下，x 轴应该相同，y 轴可以有不同的比例，但在下面的代码中，我只是手动排列它们，而不是更改阴影区域的所有坐标。

\documentclass[11pt]{amsart}
\usepackage{tikz}
\usepackage{pgfplots}
\pgfplotsset{compat=1.12}

\title{Brief Article}
\author{The Author}
\begin{document}
\maketitle

\begin{tikzpicture}
\begin{axis}[axis lines=none,
xmin=-1,
xmax=5,
ymin=-1,
ymax=5]
\draw [fill=lightgray] (0,1) to [out=80,in=180] (1,1) to [out=0,in=180] (2.5,1.5) to [out=0,in=-100] (4,1) to (4,0) to (0,0);
\draw [line width=0.05cm] (0,1) to [out=80,in=180] (1,1) to [out=0,in=180] (2.5,1.5) to [out=0,in=-100] (4,1);
\path [fill=lightgray] (0,3) to [out=25,in=150] (1.5,3.5) to [out=-30,in=120] (3,3) to [out=-50,in=-155] (4,3) to (4,4.3) to (0,4.3);     \draw [line width=0.05cm] (0,3) to [out=25,in=150] (1.5,3.5) to [out=-30,in=120] (3,3) to [out=-50,in=-155] (4,3);                   \draw [thin, ->] (-0.1,0) -- (4.5,0);
\draw [thin, ->] (0, -0.1) -- (0, 4.5);
\draw [thin] (4, -0.1) -- (4, 0.1);
\node [below] at (4, -0.1) {$2\pi$};
\node [below] at (0, -0.1) {$0$};
\draw [dashed] (-0.1, 2) -- (4,2);
\draw [line width=0.05cm, red] (1, 1) to [out=0, in=180] (1.5,1.5);
\draw [line width=0.05cm, red] (2.5,2.5) to [out=0, in=180] (3, 3);
\end{axis}
\begin{axis}[axis lines=none,
xmin=-6,
xmax=6,
ymin=-5.1,
ymax=5.1
]
    \addplot[very thick,red,samples=1000,restrict x to domain=-1.1:1.1]
        plot (\x, {(\x)*sin((1/abs((\x)))r)});
\end{axis}
\end{tikzpicture}
\end{document}

在此处输入图片描述

我承认，这并不优雅，但希望这种方法能够有所帮助。

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