Drawing an animated circle in LaTeX

Just because I love a good challenge.

Compiled using convert -delay 10 -loop 0 -density 300 -scale 400 -alpha remove <file>.pdf <file>.gif.

Missing features/improvements:

• red line "curving", not sure how to easily do it.
• Some transitions should be paused more. Will try to fix later.
• Various repeated commands might be reduced.

Output

The file is 973 KB

Code

254 lines! :D

\documentclass[tikz, margin=10pt]{standalone}
\usetikzlibrary{calc, arrows, backgrounds}

\newcommand\rad{57.296}
\pgfmathsetmacro\radq{\rad*2}
\pgfmathsetmacro\radc{\rad*3}

\tikzset{
    dots/.style={fill=#1, circle, inner sep=2pt},
    angle/.style={draw=green!70!black, fill=green!30},
    mainline/.style={green!70!black, very thick},
    arc/.style={red, very thick},
    rads/.style={very thin},
}

\begin{document}
\foreach \x [count=\xx, evaluate=\x as \xy using (185-\xx*5)] in {0,.5,...,4,4,4,4,4}{
\begin{tikzpicture}
    \draw[gray] (-5,0) -- (5,0);
    \draw[gray] (0,-5) -- (0,5);
    \node[dots=red] (a) at (0,0) {};
    \node[dots=red] (b) at (\x,0) {};
    \draw[arc] (a) -- (b);
\end{tikzpicture}
}
\foreach \ang in {0,15,...,360}{
\begin{tikzpicture}
    \draw[gray] (-5,0) -- (5,0);
    \draw[gray] (0,-5) -- (0,5);
    \node[dots=red] (a) at (0,0) {};
    \node[dots=red] (b) at (\ang:4) {};
    \draw[blue, thick] (4,0) arc (0:\ang:4);
    \draw[arc] (a) -- (b);

\end{tikzpicture}
}
\foreach \x [evaluate=\x as \opac using (\x/10)] in {0,0,0,1,...,9,10,10,10,10,10,10,10,9,...,0,0,0}{
\begin{tikzpicture}
    \draw[gray] (-5,0) -- (5,0);
    \draw[gray] (0,-5) -- (0,5);
    \draw[blue, thick] (0,0) circle (4);
    \node[dots=red] (a) at (0,0) {};
    \node[dots=red] (b) at (0:4) {};
    \draw[arc] (a) -- (b) node[midway, above, yshift=5mm, font=\Huge, text opacity=\opac] {r};

\end{tikzpicture}
}
\foreach \ang in {180,165,...,90}{
\begin{tikzpicture}
    \draw[gray] (-5,0) -- (5,0);
    \draw[gray] (0,-5) -- (0,5);
    \draw[blue, thick] (0,0) circle (4);
    \node[dots=black] (c) at (0,0) {};
    \node[dots=red, xshift=4cm] (a) at (\ang:4) {};
    \node[dots=red] (b) at (4,0) {};
    \draw[arc] (4,0) --++ (\ang:4);
\end{tikzpicture}
}
%\foreach \ang [count=\x, evaluate=\x as \xx using int(80/\x)] in {15,...,\rad}{
\begin{tikzpicture}
    \draw[gray] (-5,0) -- (5,0);
    \draw[gray] (0,-5) -- (0,5);
    \draw[blue, thick] (0,0) circle (4);
    \node[dots=black] (c) at (0,0) {};
    \node[dots=red] (a) at (\rad:4) {};
    \node[dots=red] (b) at (4,0) {};

    \draw[arc] (4,0) arc (0:\rad:4);
\end{tikzpicture}
%}
%
\foreach \x [evaluate=\x as \grad using (\x/10)] in {0,...,10}{
\begin{tikzpicture}
    \draw[gray] (-5,0) -- (5,0);
    \draw[gray] (0,-5) -- (0,5);
    \draw[blue, thick] (0,0) circle (4);
    \node[dots=red] (a) at (\rad:4) {};
    \node[dots=red] (b) at (4,0) {};
    \draw[arc] (4,0) arc (0:\rad:4);
    \begin{scope}[opacity=\grad]
        \draw[mainline] (b) -- (0,0) -- (a);
        \filldraw[angle] (0,0) -- (1,0) arc (0:\rad:1) -- cycle;
    \end{scope}
    \node[dots=black] (c) at (0,0) {};
\end{tikzpicture}
}
\foreach \x [evaluate=\x as \grad using (\x/10)] in {0,...,10}{
\begin{tikzpicture}
    \draw[gray] (-5,0) -- (5,0);
    \draw[gray] (0,-5) -- (0,5);
    \draw[blue, thick] (0,0) circle (4);
    \node[dots=red] (a) at (\rad:4) {};
    \node[dots=red] (b) at (4,0) {};
        \draw[arc] (4,0) arc (0:\rad:4);
        \draw[mainline] (b) -- (0,0) -- (a);
        \filldraw[angle] (0,0) -- (1,0) arc (0:\rad:1) -- cycle;
    \node[dots=black] (c) at (0,0) {};
    \begin{scope}[opacity=\grad]
    \node[anchor=north, yshift=-5mm, font=\Huge, text=green!50!black] at (0,0) {$1$ rad};
    \end{scope}
\end{tikzpicture}
}
\foreach \ang [count=\cc] in {0,10,...,\rad, \rad, \rad, \rad, \rad}{
\begin{tikzpicture}
    \draw[gray] (-5,0) -- (5,0);
    \draw[gray] (0,-5) -- (0,5);
    \draw[blue, thick] (0,0) circle (4);
        \draw[mainline] (4,0) arc (0:\ang:4);
        \node[dots=green!50!black] (d) at (4,0) {};
    \begin{scope}[rotate around={\ang:(0,0)}]
        \node[dots=red] (a) at (\rad:4) {};
        \node[dots=red] (b) at (4,0) {};
        \draw[arc] (4,0) arc (0:\rad:4);
        \draw[mainline] (0,0) -- (a);
        \draw[rads] (0,0) -- (b);
    \end{scope}
        \filldraw[angle] (0,0) -- (1,0) arc (0:\ang+\rad:1) -- cycle;
    \node[dots=black] (c) at (0,0) {};
    \ifnum\cc<8
    \node[anchor=north, yshift=-5mm, font=\Huge, text=green!50!black] at (0,0) {$1$ rad};
    \else
    \node[anchor=north, yshift=-5mm, font=\Huge, text=green!50!black] at (0,0) {$2$ rad};
    \fi
\end{tikzpicture}
}
\foreach \ang [count=\cc, evaluate=\ang as \bng using int(\ang+\rad)] in {0,10,...,\rad, \rad, \rad, \rad, \rad}{
\begin{tikzpicture}
    \draw[gray] (-5,0) -- (5,0);
    \draw[gray] (0,-5) -- (0,5);
    \draw[blue, thick] (0,0) circle (4);
        \draw[green!70!black, very thick] (4,0) arc (0:\bng:4);
        \node[dots=green!50!black] (d) at (4,0) {};
        \node[dots=green!50!black] (e) at (\rad:4) {};  
        \draw[mainline] (0,0) -- (d);
        \draw[rads] (0,0) -- (e);
    \begin{scope}[rotate around={\bng:(0,0)}]
        \node[dots=red] (a) at (\rad:4) {};
        \node[dots=red] (b) at (4,0) {};
        \draw[arc] (4,0) arc (0:\rad:4);
        \draw[mainline] (0,0) -- (a);
        \draw[rads] (0,0) -- (b);
    \end{scope}
        \filldraw[angle] (0,0) -- (1,0) arc (0:\bng+\rad:1) -- cycle;
    \node[dots=black] (c) at (0,0) {};
    \ifnum\cc<8
    \node[anchor=north, yshift=-5mm, font=\Huge, text=green!50!black] at (0,0) {$2$ rad};
    \else
    \node[anchor=north, yshift=-5mm, font=\Huge, text=green!50!black] at (0,0) {$3$ rad};
    \fi
\end{tikzpicture}
}
\foreach \dng [count=\cc, evaluate=\cc as \cng using (\radq+\rad/9*\cc)] in {\radc,...,180}{
\begin{tikzpicture}
    \draw[gray] (-5,0) -- (5,0);
    \draw[gray] (0,-5) -- (0,5);
    \draw[blue, thick] (0,0) circle (4);
        \draw[mainline] (4,0) arc (0:\cng:4);
        \node[dots=green!50!black] (d) at (4,0) {};
        \node[dots=green!50!black] (e) at (\rad:4) {};
        \node[dots=green!50!black] (f) at (\rad*2:4) {};
        \draw[mainline] (0,0) -- (d);
        \draw[rads] (0,0) -- (e);
        \draw[rads] (0,0) -- (f);

        \node[dots=red] (a) at (\cng:4) {};
        \node[dots=red] (b) at (\dng:4) {};
        \draw[arc] (\cng:4) arc (\cng:\dng:4);
        \draw[mainline] (0,0) -- (b);
        \draw[rads] (0,0) -- (a);
        \filldraw[angle] (0,0) -- (1,0) arc (0:\dng:1) -- cycle;
    \node[dots=black] (c) at (0,0) {};
    \ifnum\cc<9
    \node[anchor=north, yshift=-5mm, font=\Huge, text=green!50!black] at (0,0) {$3$ rad};
    \else
    \node[anchor=north, yshift=-5mm, font=\Huge, text=green!50!black] at (0,0) {$\pi$ rad};
    \fi
\end{tikzpicture}
}
\foreach \x [evaluate=\x as \grad using (\x/10)] in {10,...,0,0,0,0,0,0,0,0}{
\begin{tikzpicture}
    \draw[gray] (-5,0) -- (5,0);
    \draw[gray] (0,-5) -- (0,5);
    \draw[blue, thick] (0,0) circle (4);
    \draw[mainline] (4,0) arc (0:180:4);
    \draw[mainline] (0,0) -- (d);
    \node[dots=green!50!black] (d) at (4,0) {};
    \node[dots=green!50!black] (b) at (180:4) {};
\begin{scope}[opacity=\grad]
        \node[dots=green!50!black] (e) at (\rad:4) {};
        \node[dots=green!50!black] (f) at (\rad*2:4) {};
        \draw[rads] (0,0) -- (e);
        \draw[rads] (0,0) -- (f);
        \draw[rads] (0,0) -- (a);
        \node[dots=red] (a) at (\radc:4) {};
        \node[dots=red] (b) at (180:4) {};
        \draw[arc] (\radc:4) arc (\radc:180:4);
\end{scope}
        \draw[mainline] (0,0) --++ (180:4); 
        \filldraw[angle] (0,0) -- (1,0) arc (0:180:1) -- cycle;
\node[dots=black] (c) at (0,0) {};
\node[anchor=north, yshift=-5mm, font=\Huge, text=green!50!black] at (0,0) {$\pi$ rad};
\end{tikzpicture}
}
\foreach \x in {0,5,...,20}{
\begin{tikzpicture}
    \draw[gray] (-5,0) -- (5,0);
    \draw[gray] (0,-5) -- (0,5);
    \draw[blue, thick] (0,0) circle (4);
    \draw[mainline] (4,0) arc (0:180:4);
    \node[dots=green!50!black] (d) at (4,0) {};
    \node[dots=green!50!black] (b) at (180:4) {};
    \draw[mainline] (d) -- (b);
    \filldraw[angle] (0,0) -- (1,0) arc (0:180:1) -- cycle;
\node[dots=black] (c) at (0,0) {};
\node[anchor=north, yshift=\x mm, font=\Huge, text=green!50!black] at (0,0) {$\pi$ rad};
\end{tikzpicture}
}
\foreach \ang [count=\x starting from 0, evaluate=\x as \grad using (\x/10)] in {180,198,...,360}{
\begin{tikzpicture}
    \draw[gray] (-5,0) -- (5,0);
    \draw[gray] (0,-5) -- (0,5);
    \draw[blue, thick] (0,0) circle (4);
    \draw[mainline] (4,0) arc (0:\ang:4);
    \node[dots=green!50!black] (d) at (4,0) {};
    \node[dots=green!50!black] (b) at (180:4) {};
    \node[dots=green!50!black] (g) at (\ang:4) {};
    \draw[mainline] (0,0) -- (d);
    \draw[mainline] (0,0) -- (g);
    \filldraw[angle] (0,0) -- (1,0) arc (0:\ang:1) -- cycle;
\node[dots=black] (c) at (0,0) {};
\node[anchor=north, yshift=2cm, font=\Huge, text=green!50!black] at (0,0) {$\pi$ rad};
\node[anchor=north, yshift=2cm, font=\Huge, text=green!50!black, text opacity=\grad] at (0,0) {$2$\phantom{$2\pi$ rad}};
\end{tikzpicture}
}
\foreach \x [evaluate=\x as \grad using (\x/10)] in {10,...,0,0}{
\begin{tikzpicture}
    \draw[gray] (-5,0) -- (5,0);
    \draw[gray] (0,-5) -- (0,5);
    \node[dots=red] (a) at (0,0) {};
\begin{scope}[opacity=\grad]
    \draw[mainline] (4,0) arc (0:360:4);
    \node[dots=green!50!black] (d) at (4,0) {};
    \node[dots=green!50!black] (b) at (180:4) {};
    \node[dots=green!50!black] (g) at (0:4) {};
    \draw[mainline] (0,0) -- (d);
    \draw[mainline] (0,0) -- (g);
    \filldraw[angle] (0,0) -- (1,0) arc (0:360:1) -- cycle;
    \node[dots=black] (c) at (0,0) {};
    \node[anchor=north, yshift=2cm, font=\Huge, text=green!50!black] at (0,0) {$\pi$ rad};
    \node[anchor=north, yshift=2cm, font=\Huge, text=green!50!black, text opacity=\grad] at (0,0) {$2$\phantom{$2\pi$ rad}};
\end{scope}
\end{tikzpicture}
}
\end{document}

That is a lot of work to get all the intermediate steps. It is much more easier to use a presentation class without the animation. Here is a starter:

\documentclass{beamer}
\usepackage{pstricks-add,multido}
\begin{document}

\begin{frame}[plain]
\centering
\def\Radius{3}
\begin{pspicture}(-4,-4)(4,4)
\psdot[dotsize=1mm,linecolor=red](0,0)\pause
\psline[arrows=*-*,linewidth=1.5pt,linecolor=red](3,0)\pause
\multido{\iA=0+30}{13}{%
  \psarc[arrows=*-*,linewidth=1.5pt,linecolor=blue](0,0){3}{0}{\iA}\pause}
\pswedge[linecolor=red,arrows=*-*,linewidth=1.5pt](3,0){3}{90}{180}\pause
\psarc[arrows=*-*,linewidth=1.5pt,linecolor=green](0,0){3}{0}{!1 RadtoDeg}
\end{pspicture}
\end{frame}

\end{document}

If you don't want the dots, use

    \multido{\iA=0+30}{13}{%
        \psarc[arrows=-*,linewidth=1.5pt,linecolor=white](0,0){3}{0}{!\iA\space 30 sub}
        \psarc[arrows=*-*,linewidth=1.5pt,linecolor=blue](0,0){3}{0}{\iA}\pause}

The PDF was converted into a gif by

convert -delay 50 -loop 0 -density 300 -scale 300 -alpha remove zz.pdf zz.gif

Other examples can be found here: http://tug.org/PSTricks/main.cgi?file=Animation/gif/gif

The original code in the edited question compiled fine but produces frames for animated ellipse-drawing rather than animated circle-drawing.

Assuming that 'doesn't workrefers to the fact that the picture draws an ellipse rather than a circle, this is relatively easily fixed, even with no knowledge ofpstricks. (I say this only because I have no such knowledge and therefore disclaim allpstricks`-related responsibilities for the following i.e. if the code in the question contains obvious boo-boos, they are not going to be obvious to me.)

I started with

\begin{pspicture}(-2.5,-2.0)(2.5,2.0)

which suggested a rectangular frame, suitable for an ellipse, rather than a square one, suitable for a square. So I changed the proportions:

\begin{pspicture}(-2.5,-2.5)(2.5,2.5)

This compiled to give me an ellipse in a square frame. So I then guessed that the following lines refer to the two axes:

    /major 2.25 def
    /minor 1.75 def

and figured I'd try amending those next:

    /major 2.25 def
    /minor 2.25 def

and that did the trick - now I got 37 frames showing the drawing of a circle rather than an ellipse.

\documentclass[pstricks,border=0pt]{standalone}
\usepackage{pstricks-add}
\pstVerb
{
    /major 2.25 def
    /minor 2.25 def
    % b a t p2c ---> x y
    % where b (semi-minor), a (semi-major), t (theta)
    /p2c {dup 3 1 roll cos mul 3 1 roll sin mul} bind def
}

\psset{arrows=-*}

\begin{document}
\multido{\i=0+10}{37}
{
    \begin{pspicture}(-2.5,-2.5)(2.5,2.5)
        \ifnum\i=0
            % don't draw arc!
        \else
            \psellipticarc[linecolor=cyan,dimen=middle](!major minor){0}{(!minor major \i\space p2c)}%dimen=middle must be specified!
        \fi
        \psline[linecolor=red](!minor major \i\space p2c)
        \uput{5mm}[!\i\space 10 add](0,0){\tiny$\i^\circ$}
    \end{pspicture}
}
\end{document}

EDIT

I was trying to figure out how to turn my PDF into an animated GIF when Herbert posted the solution in his much more expert answer. That is, using

convert -delay 50 -loop 0 -density 300 -scale 300 -alpha remove <filename>.pdf <filename>.gif 

I produced this (which I hope works - I'm not sure how to tell)