Tikz: Extract polar coordinate

Question

Is there a (simple) way to extract polar coordinates in Tikz?

Motivation: I define two points (a) and (b) as intersection of a line and a circle (center at the origin) and then I want to an arc between these two points along my circle. I need the polar coordinates of (a) and (b) for that.

I have seen in the TikZ documentation that there is \pgfextractx{<dimension>}{<point>} to extract the x-coordinate, and a similar function for the y-coordinate as well, but could not find something for polar coordinates.

Answer 1

You can define your own macro analogous to \pgfgetlastxy to extract the last cartesian coordinates, convert them into polar coordinates and store the resulting values in macros:

(Thanks to @John Kormylo the macro below has gradually become the short and crisp piece of code it is now. It only needs the tikz package without any additional libraries.)

\documentclass[border=1mm, tikz]{standalone}

\newcommand{\pgfgetlastpolar}[2]{
    \pgfgetlastxy{\tempx}{\tempy}
    \pgfmathsetmacro{#1}{atan2(\tempy,\tempx)}
    \pgfmathsetlengthmacro{#2}{veclen(\tempx,\tempy)}
}

\begin{document}
\begin{tikzpicture}

\node[draw, circle] at (1,1) {};

% use analogous to `\pgfgetlastxy{\myx}{\myy}´ 
\pgfgetlastpolar{\mytheta}{\myrho}

\node[draw, rectangle] at (\mytheta:\myrho) {};

\end{tikzpicture}
\end{document}