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如何避免脉搏“耳朵”？

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如何避免脉搏“耳朵”？

我正在尝试使用脉冲来动画化叠加原理。如何避免脉冲边缘出现“耳朵”？

\documentclass{standalone}

\usepackage{tikz}
\usetikzlibrary{math, calc}
\usepackage{animate}

\begin{document}

\tikzstyle{curve} = [thick,  domain = -3:3 , smooth, variable = \t,  samples = 50, line cap = round]

\tikzmath{
    function pulse(\t, \c, \a, \b){
        \q = \t - \c;
        if (\q < -\b/2.0)||(\q > \b/2.0) then {return 0.0;} else {return \a;};
    };
    function mycos(\t, \c, \a, \b){
        \q = \t - \c;
        \w = pi/\b;
        if (\q < -\b/2.0)||(\q > \b/2.0) then {return 0.0;} else {return -\a*cos(\w*\q r);};
    };
    function doit(\t, \c, \a, \b){
        return pulse(\t, \c, \a, \b);
        %return mycos(\t, \c, \a, \b);
    };
}
\begin{animateinline}[controls, loop, autoplay, buttonsize = 1em]{4}%
    \multiframe{3}{rtime = -2.0 + 0.1}{%set 3 to 40 to have full animation
    \begin{tikzpicture}[scale = 1.0]

    \draw[thin, lightgray] (-3, -3) grid[step = 0.5] ++(6, 6);
    \foreach \z in {-3, -2, ...,3} \node[below] at (\z, -3) {\tiny$\z$};
    \foreach \z in {-3, -2, ...,3}\node[left] at (-3, \z) {\tiny$\z$};
        
    \draw[curve, red, yshift  = -2cm] plot({\t}, {doit(\t, -\rtime, -0.25, 1.0) + doit(\t, \rtime, 1.0, 1.0)});
    \draw[curve, green, yshift = 2cm] plot({\t}, {doit(\t, \rtime, 1.0, 1.0)}); 
    \draw[curve, blue] plot({\t}, {doit(\t, -\rtime, -0.25, 1.0)}); 

    \draw (-3, -2) node[above right, black]{\tiny $x_1+x_2$};
    \draw (-3, 0) node[above right, black]{\tiny $x_2$};
    \draw (-3, 2) node[above right, black]{\tiny $x_1$};
     
    \end{tikzpicture}
    }%
\end{animateinline}
\end{document}

这是我用当前代码得到的结果

答案1

您可能正在寻找以下内容：

在此处输入图片描述

  • “耳朵”是由smooth选项引起的。它使用样条函数在给定样本之间插入值。当样本之间或其中某些样本发生跳跃时，插值失败并产生可观察到的“耳朵”。
  • 解决方法是删除此选项并增加样本数量
\documentclass{standalone}
\usepackage{tikz}
\usetikzlibrary{math, calc}
\usepackage{animate}

\begin{document}

\tikzset{
curve/.style = {thick,  domain = -3:3 , variable = \t,  samples = 101, line cap = round}, % <---
    N/.style = {font=\scriptsize, text=black, anchor=#1},
    N/.default = south west
        }

\tikzmath{
    function pulse(\t, \c, \a, \b){
        \q = \t - \c;
        if (\q < -\b/2.0)||(\q > \b/2.0) then {return 0.0;} else {return \a;};
    };
    function mycos(\t, \c, \a, \b){
        \q = \t - \c;
        \w = pi/\b;
        if (\q < -\b/2.0)||(\q > \b/2.0) then {return 0.0;} else {return -\a*cos(\w*\q r);};
    };
    function doit(\t, \c, \a, \b){
        return pulse(\t, \c, \a, \b);
        %return mycos(\t, \c, \a, \b);
    };
}
\begin{animateinline}[controls, loop, autoplay, buttonsize = 1em]{4}%
    \multiframe{3}{rtime = -2.0 + 0.1}{%set 3 to 40 to have full animation
    \begin{tikzpicture}[scale = 1.0]

    \draw[thin, lightgray] (-3, -3) grid[step = 0.5] ++(6, 6);
    \foreach \z in {-3, -2, ...,3} \node[N=north] at (\z, -3) {$\z$};
    \foreach \z in {-3, -2, ...,3} \node[N=east] at (-3, \z) {$\z$};

    \draw[curve, red, yshift  = -2cm] plot({\t}, {doit(\t, -\rtime, -0.25, 1.0) + doit(\t, \rtime, 1.0, 1.0)});
    \draw[curve, green, yshift = 2cm] plot({\t}, {doit(\t, \rtime, 1.0, 1.0)});
    \draw[curve, blue] plot({\t}, {doit(\t, -\rtime, -0.25, 1.0)});

    \draw (-3, -2) node[N]  {$x_1+x_2$};
    \draw (-3, 0)  node[N]  {$x_2$};
    \draw (-3, 2)  node[N]  {$x_1$};

    \end{tikzpicture}
    }%
\end{animateinline}
\end{document}

笔记：

  • tikzstyle已经过时了。相反，它使用tikzset或编写样式定义作为tikzpicture
  • 在上面的 MWE（最小工作示例）中添加了样式节点及其默认锚点（此代码更短更清晰）

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