Is there a polar coordinate registers in the let command?

Question

I have seen that we ca use \x1 and \y1 to access cartesian coordinates of point register \p1 declared in let.

Is there a way to access the polar coordinates (something like \a1 for the angle and \r1 for the distance) of the point \p1?

If not, what is the best way to do something like this :

\draw let \p1=(35:1cm) in (\a1+30,\r1) -- (\a1-30,2*\r1);

Answer 1

I don't know if there is a direct register for that (and I would love to know too) but you can access that info with a little more work:

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{calc}
\begin{document}
\begin{tikzpicture}
\draw[style=help lines] (0,0) grid[step=1cm] (3,2);
\draw[red,ultra thick] (0,0) -- (35:3cm);
\draw let \p1=(35:3cm), \n1 = {veclen(\x1,\y1)},\n2 = {atan2(\x1,\y1)} in (0,0) -- (\n2:\n1);
\draw let \p1=(35:1cm), \n1 = {veclen(\x1,\y1)},\n2 = {atan2(\x1,\y1)} in (0,0) -- (\n2+30:2*\n1);
\end{tikzpicture}
\end{document}

This gives

One can further wrap this into a more pragmatic macro but it is not that verbose by itself now. Moreover, you can do the same with respect to another point, I mean it does not need to be the origin that the angle and length measured from.