Simpsons function illustration in Tikz

Question

I have this code:

\documentclass[border=2pt]{standalone}
\usepackage[utf8]{inputenc}
\usepackage{animate}
\usepackage{calc}
\usepackage{fp}
\usepackage{pgfplots}
\usepackage{tikz}
\usetikzlibrary{arrows}

\newcommand*{\xMin}{0}%
\newcommand*{\xMax}{20}%
\newcommand*{\yMin}{0}%
\newcommand*{\yMax}{10}%

\begin{document}

\begin{tikzpicture}[scale=1.5]
\foreach \i in {\xMin,...,\xMax} {
        \draw [very thin,gray] (\i,\yMin) -- (\i,\yMax)  node [below] at (\i,\yMin) {$\i$};
    }
    \foreach \i in {\yMin,...,\yMax} {
        \draw [very thin,gray] (\xMin,\i) -- (\xMax,\i) node [left] at (\xMin,\i) {$\i$};
    }
\draw[->, thick] (0,0)--(20,0) node[right] (X) {x};
\draw[->, thick] (0,0)--(0,10) node[above] (Y) {y};
\end{tikzpicture}
\end{document}

Trouble: I don't know a) how to create the curves and b) how to make the animation.

It should look like this at the end: https://en.wikipedia.org/wiki/Simpson%27s_rule#/media/File:Simpsonsrule2.gif

Hopefully you can help me. I know it is a major project, but I am stucked. If I get some help, I would maybe be able to write more code, but right now I am stucked.

Thank you so much in advance.

You may want to provide a bit more information, such as the function to integrate, so that people don't overgeneralize or make bad assumptions about your intended use. I assume you want to use a series of quadratic functions P(x) for the approximation. If so, this answer to "How can I produce such a graph of my piecewise function?" would be one part of the solution. — Mike Renfro, Sep 03 '15 at 12:09

Gonzalo Medina · Accepted Answer · 2015-09-03T23:19:56.593

Here's one option using pgfplots and showing the quadratic interpolation:

The code:

\documentclass{beamer}
\usepackage{pgfplots}
\pgfplotsset{compat=newest}

\pgfmathdeclarefunction{mainfunct}{1}{%
  \pgfmathparse{cos(deg(2*#1))+1.5}%
}
% The Simpson interpolating function
\pgfmathdeclarefunction{Simpsonfunct}{3}{%
  \pgfmathparse{%
    mainfunct(#2)*(((#1-((#2+#3)/2))*(#1-#3))/((#2-((#2+#3)/2))*(#2-#3))) +
    mainfunct((#2/2+#3/2))*(((#1-#2)*(#1-#3))/((((#2+#3)/2)-#2)*(((#2+#3)/2)-#3))) +
    mainfunct(#3)*(((#1-#2)*(#1-((#2+#3)/2)))/((#3-#2)*(#3-((#2+#3)/2))))
  }%
}
\newcommand\DrawSimpson[1]{
  \pgfmathsetmacro{\tmp}{#1+#1}
  \foreach \Valor in {#1,\tmp,...,12}
  {
  \addplot[red!75!blue,very thick,domain=\Valor-#1:\Valor] {Simpsonfunct(x,\Valor-#1,\Valor)};
  \addplot[no marks,red!75!blue] coordinates {(\Valor,0) (\Valor,{mainfunct(\Valor)})};
  }
}

\setbeamertemplate{navigation symbols}{}

\begin{document}

\begin{frame}
\centering
\begin{tikzpicture}[]
\begin{axis}[
  height=0.8\textheight, 
  width=11.5cm,
  ytick=\empty,
  xticklabel style={font=\small, text height=1.5ex, anchor=north},
  xtick={-4,-2,...,16},
  ymin=0,
  xmin=-4, 
  xmax=16,
]
% The function
\addplot[very thick, cyan!75!blue,domain=-pi:5*pi,samples=200] {mainfunct(x)};
% The vertical line from (0,0) to the function (it's constant for all plots)
\only<2->{\addplot[no marks,red!75!blue] coordinates {(0,0) (0,{mainfunct(0)})};}

\only<2>{\DrawSimpson{6}}
\only<3>{\DrawSimpson{4}}
\only<4>{\DrawSimpson{3}}
\only<5>{\DrawSimpson{2}}
\only<6>{\DrawSimpson{1}}
\only<7>{\DrawSimpson{0.5}}
\only<8>{\DrawSimpson{0.25}}
\end{axis}
\end{tikzpicture}

\end{frame}

\end{document}

The animation was produced using ImageMagick and

convert -verbose -delay 80 -loop 0 -density 300 simpson.pdf simpson.gif

I really, really wanted this answer to involve \usepackage{simpsons} ;). — cfr, Sep 03 '15 at 22:29

score 4 · Answer 2 · answered Sep 03 '15 at 15:37

Here's a pgfplots version (but with no interpolation). Uses gimp to produce the animation (import the resulting pdf as layers, reverse the layers, and export to gif).

\documentclass[tikz,border=5]{standalone} 
\usepackage{pgfplots}
\begin{document} 
\foreach \samples in {3,...,30}{%
\begin{tikzpicture}[declare function={f(\x)=sin(\x*180)*100+150;}] 
\begin{axis}[ymin=0, ymax=300, xmin=0, xmax=10,
 xlabel=$x$, ylabel=$f(x)$]
\addplot [thick, cyan,   domain=0:10, samples=250]      (x, {f(x)});
\addplot [ycomb, purple, domain=2:8,  samples=\samples] (x, {f(x)});
\addplot [thick, red,    domain=2:8,  samples=\samples] (x, {f(x)});
\end{axis}
\end{tikzpicture}}
\end{document}

Simpsons function illustration in Tikz

2 Answers2