Polar plot with cartesian values, lack of angular precision in the integrated arctan2 calculation?

Question

I noticed that for values close to 0° and 180° the angular values dramatically changes if the values are imported from cartesian data. Here the code (with cartesian coordinates plotted in polar with data cs=cart and the same coordinates in polar coordinates obtained with arctan2 Matlab function) and illustration:

\documentclass{minimal}
\usepackage{eurosym}
\usepackage{pgfplots}
\usepackage{fp}

\begin{document}

\pgfplotsset{compat=newest} 
\usepgfplotslibrary{polar}
\centering
\begin{tikzpicture}
\begin{polaraxis}[
    visualization depends on=x \as \pgfplotspointx,
    nodes near coords,
    every node near coord/.style={
        %font=\small,
        rotate=\pgfplotspointx,
        append after command={
            node [
                anchor=south,
                %font=\small,
                rotate=\pgfplotspointx,
                shift={(axis direction cs:0,(12.75-\pgfplotspointmeta))}
            ] {$\pgfmathprintnumber{\pgfplotspointx}^\circ$}
        }
    },
width=7\textwidth,
xmin=-2,xmax=1, ymin=12, ymax=16,
title=artctan2 precision problem,
grid=both,
minor x tick num={4}, 
minor y tick num={1},
]
\addplot+[polar comb, data cs=cart, mark size=1, mark=asterisk, color=blue, dashed] table {
14.370195   -0.304948
14.370195   -0.304948

}; 
\addplot+[polar comb, mark size=1, mark=asterisk, color=green, solid] table {-1.215683667   14.37343027
-1.215683667    14.37343027
}; 
\end{polaraxis}
\end{tikzpicture}


\end{document}

Has anyone meet this issue?

Thank you in advance.

Answer 1

This needs to be repaired in pgfplots, I accept this question as bug report.

---

Details:

The routine pgfplotsmathcarttopol does not make use of atan2 - instead, it computes the angle "manually", apparently with less precision.

add

\pgfplotsmathcarttopol{14.370195}{-0.304948}\angle\radius

angle = \angle; radius = \radius

to see that this is, indeed, the root cause.

Steps to be done would be to write an implementation (or adapter) for atan2 for the floating point unit of PGF and to use that one in pgfplotsmathcarttopol.

I will take a note for the todo list of pgfplots (no need to file a separate bug report).

Answer 2

A solution with PSTricks. Run it with xelatex:

\documentclass{minimal}
\usepackage{pst-plot}
\begin{document}

\begin{pspicture}(33,-2)(48,1.1)
\psset{runit=3}\uput[0](16;0){0}
\psarcn(0,0){12}{1}{-2}\psarcn(0,0){16}{1}{-2}
\psline(12;1)(16;1)\psline(12;-2)(16;-2)
\multido{\rA=12.25+0.25}{15}{\psarcn[linecolor=black!15](0,0){\rA}{1}{-2}}
\psline[linecolor=black!15](12;0)(16;0)\psline[linecolor=black!15](12;-1)(16;-1)
\multido{\rA=12.0+0.5}{9}{\uput[-90](\rA;-2.5){\rA}}
\psline[linecolor=blue,linestyle=dashed]{-*}(12;-0.54)(14.37;-0.54)
\psline[linecolor=green]{-*}(12;-1.22)(14.37;-1.22)
\uput[90](12.75;-0.54){\blue$-0.54^\circ$}\uput[90](12.75;-1.22){\green$-1.22^\circ$}
\uput[90](14.37;-0.54){\blue$14.37$}\uput[90](14.37;-1.22){\green$14.37$}
\end{pspicture}

\end{document}