Tikz plot polar equation with foreach

Question

Im trying to animate a polar equation using beamer, i couldnt find anything related to my problem here or on Google so my last chance is to request some help. I tried to take out the domain command out of the equation so the plot could read the x variable value (that ranges from 0 to 20). But well that dont work at all... after that i tried to make domain=\x but well that didnt worked either. Does anyone have any solution (or even an hint) to my problem?

Ps.: I need to use Tikz package.

Thanks in advance!

\documentclass{beamer}

    \usepackage{tikz}

    \begin{document}

        \foreach \x in {0,1,...,20}{
      \begin{frame}
        \begin{tikzpicture}
             \draw[align=center,color=orange,smooth] plot (canvas polar cs:angle=\x r,radius= {\x});
        \end{tikzpicture}
        \end{frame}
        }
    \end{document}

Answer 1

You need to place the \foreach loop inside the frame and use overlay specifications for the \draw command (this will produce several slides inside a single frame, which then will give you the animation effect); something along these lines:

\documentclass{beamer}
\usepackage{tikz}

\tikzset{
    invisible/.style={opacity=0,text opacity=0},
    visible on/.style={alt=#1{}{invisible}},
    alt/.code args={<#1>#2#3}{%
      \alt<#1>{\pgfkeysalso{#2}}{\pgfkeysalso{#3}} 
    },
    beameralert/.style={alt=<#1>{fill=red!30,rounded corners,inner sep=1pt}{},anchor=base},
}

\begin{document}

\begin{frame}
\centering
\begin{tikzpicture}[scale=3]
\foreach \x in {0,...,10}
{
  \draw[
    color=orange,
    domain=0:\x,
    samples=200,
    visible on=<\number\numexpr\x+1\relax->
    ] 
    plot (canvas polar cs:angle=\x r,radius= {\x});
}
\end{tikzpicture}
\end{frame}

\end{document}

I used the visible on style (illustrated, for example, in this answer) for the overlay specification to prevent the elements from jumping around.

In the above solution, the whole spiral (the "old part" and the new one) is drawn in each slide, so the compilation time can be very long and the calculations will be increasingly heavy; to prevent this you can use

\documentclass{beamer}
\usepackage{tikz}

\tikzset{
    invisible/.style={opacity=0,text opacity=0},
    visible on/.style={alt=#1{}{invisible}},
    alt/.code args={<#1>#2#3}{%
      \alt<#1>{\pgfkeysalso{#2}}{\pgfkeysalso{#3}} 
    },
    beameralert/.style={alt=<#1>{fill=red!30,rounded corners,inner sep=1pt}{},anchor=base},
}

\begin{document}

\begin{frame}
\centering
\begin{tikzpicture}[scale=3]
\xdef\lastx{0}
\foreach \x in {1,...,20}
{
  \draw[
    color=orange,
    domain=\lastx:\x,
    samples=200,
    visible on=<\number\numexpr\x+1\relax->
    ] 
    plot (canvas polar cs:angle=\x r,radius= {\x});
    \xdef\lastx{\x}
}
\end{tikzpicture}
\end{frame}

\end{document}

so in each new slide only the new piece is added. The result:

And here's a version of the animation produced using the animate package; only some pdf viewers (Acrobat Reader, tipically) will support the animation correctly:

\documentclass{beamer}
\usepackage{tikz}
\usepackage{animate}
\usepackage{ifthen}
\hypersetup{pdfpagemode=FullScreen}

\newcounter{tmp}
\stepcounter{tmp}

\begin{document}

\begin{frame}[fragile]{}
\begin{center}
\begin{animateinline}[loop,poster=first,controls]{2}
\whiledo{\thetmp<21}{%
  \begin{tikzpicture}
    \begin{scope}[scale=2]
    \foreach \x in {1,...,\thetmp}
    {
      \draw[
        color=red,
        domain=0:\thetmp,
        samples=200,
        ] 
        plot (canvas polar cs:angle=\x r,radius= {\x});
    }
    \end{scope}  
    \path[use as bounding box] (-3,-3) rectangle (3,3);
  \end{tikzpicture}%
  \stepcounter{tmp}
  \ifthenelse{\thetmp<21}
    {\newframe}
    {\end{animateinline}\relax}
}
\end{center}
\end{frame}

\end{document}