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矩形近似法（黎曼和）图

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矩形近似法（黎曼和）图

有人知道如何制作像下面这样的相对简单的图表吗？是否有某种我可以使用“模板”？我想编写我的微积分笔记，但我不知道如何制作图表。分别是左近似、右近似和中间近似。唉……

示例 1

示例 2

示例 3

答案1

快速而肮脏：

\documentclass[tikz,border=5]{standalone}
\tikzset{declare function={y(\x)=4-\x^2;},
  plot fill/.style={fill=purple!75},
  plot/.style={draw=black!80, thick},
  bar/.style={fill=cyan, draw=white, thick},
  marking/.style={fill=cyan!50!black, draw=cyan!50!black},
  axis/.style={thick, draw=black!65, stealth-stealth}
}
\begin{document}
\begin{tikzpicture}[x=1.5cm, line cap=round, line join=round] 
\foreach \k [count=\z] in {0, 1/4, 1/2}{
\begin{scope}[shift=(0:\z*3)]
\path [plot fill] plot [domain=0:2] (\x,{y(\x)}) -| cycle;
\foreach \x in {0, 1/2, 1, 3/2}
   \path [bar]  (\x,0) |- (\x+1/2, {y(\x+\k)}) |- cycle;
\path [plot]  plot [domain=0:2] (\x,{y(\x)});
\path [axis] (0,4.5) |- (2.5,0);
\foreach \t [count=\x from 0] in {0,\frac{1}{2},1,\frac{3}{2},2}
  \path [axis, -] (\x/2,0) -- ++(0,-3pt) node [below] {$\t$};
\foreach \y in {0,4}
  \path [axis, -] (0,\y) -- ++(-3pt, 0) node [left] {$\y$};
\foreach \x in {0, 1/2, 1, 3/2}
   \path [marking]  (\x+\k, {y(\x+\k)}) circle [radius=1.5pt];
\end{scope}
}
\end{tikzpicture}
\end{document}

在此处输入图片描述

答案2

我可以使用我的包来建议此解决方案xpicture。您可以根据需要添加颜色，但对于更复杂的设计，请使用tikzpicture包。

在此处输入图片描述

\documentclass{standalone}
  \usepackage{xpicture}
  \usepackage{ifthen}
\begin{document}
\newqpoly{\f}{4}{0}{-1}               % Define f(x)=4-x^2
\referencesystem(0,0)(2,0)(0,1)       % Change reference system to get a larger x-unit
\setlength{\unitlength}{1cm}
\renewcommand{\xunitdivisions}{2}     % x-Tics at every half unit 
\begin{Picture}(-1,-1)(3,5)
  \cartesianaxes(-0.1,-0.1)(2.1,4.1)
  \printxticlabel{0.5}{1/2}
  \printxticlabel{1.5}{3/2}
  \PlotFunction[20]{\f}{0}{2}         % Plot f(x)
  \COPY{0}{\x}
  \whiledo{\lengthtest{\x pt}<2 pt}{% % Loop to plot Taylor sum
      \COPY{\x}{\xzero}
      \f{\xzero}{\yzero}{\Dyzero}     % yzero=f(xzero)
      \ADD{0.5}{\x}{\x}
      \Polyline(\xzero,0)(\xzero,\yzero)(\x,\yzero)(\x,0)
   }
\end{Picture}

\begin{Picture}(-1,-1)(3,5)
  \cartesianaxes(-0.1,-0.1)(2.1,4.1)
  \printxticlabel{0.5}{1/2}
  \printxticlabel{1.5}{3/2}
  \PlotFunction[20]{\f}{0}{2}
  \COPY{0}{\x}
  \whiledo{\lengthtest{\x pt}<2 pt}{%
      \COPY{\x}{\xzero}
      \ADD{0.5}{\x}{\x}
      \f{\x}{\y}{\Dy}                 % y=f(x)
      \Polyline(\xzero,0)(\xzero,\y)(\x,\y)(\x,0)
  }
  \end{Picture}

  \begin{Picture}(-1,-1)(3,5)
  \cartesianaxes(-0.1,-0.1)(2.1,4.1)
  \printxticlabel{0.5}{1/2}
  \printxticlabel{1.5}{3/2}
  \PlotFunction[20]{\f}{0}{2}
  \COPY{0}{\x}
  \whiledo{\lengthtest{\x pt}<2 pt}{%
      \COPY{\x}{\xzero}
      \ADD{0.5}{\x}{\x}
      \ADD{0.25}{\xzero}{\xm} 
      \f{\xm}{\ym}{\Dym}              % ym=f(xm)      
      \Polyline(\xzero,0)(\xzero,\ym)(\x,\ym)(\x,0)
  }
  \end{Picture}
  \end{document}

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