METAPOST equivalent to TikZ polar coordinates?

Question

When drawing with TikZ, I find sometime convenient to use polar coordinates (angle:distance), as in this MWE

\documentclass{article}
\usepackage{tikz}

\begin{document}
\begin{tikzpicture}
   [pole/.style={circle,draw=gray,fill=gray,thick,text width=2cm, align=center}]
  \node[pole] (eur) at (60:3cm) {Europe};
  \node[pole] (afr) at (300:3cm) {Afrique};
  \node[pole] (amq) at (180:3cm)  {Amérique};
\end{tikzpicture}
\end{document}

How can I get a similar effect using METAPOST ? I could'nt find direct answer in the manual. I am quite sure one can achieve the same with a good knowledge of geometry. It would be good for scripting.

So far, my METAPOST equivalent would be

beginfig(1);
u:=1cm ;
label(btex Amérique etex, (-3u,0) ) ;
label(btex Europe etex, (u,2u) ) ;
label(btex Afrique etex, (u,-2u) ) ;
endfig ;
end

Of course this are not polar coordinates and I am even not sure angles are the same as in TikZ. Since I am not a scientist, I would be glad to have some explanation if some geometry knowledge is required.

You can easily convert r and φ to cartesian coordinates using the prescription (x,y) = (r*cos(φ),r*sin(φ)) — Henri Menke, Nov 15 '18 at 20:21

score 7 · Accepted Answer · answered Nov 15 '18 at 20:16

7

Use the dir operator. From the MetaPost manual:

Here with MetaFun in ConTeXt:

\startMPpage
u:=1cm ;
label(btex Amérique etex, 3u*dir 60) ;
label(btex Europe etex, 3u*dir 300) ;
label(btex Afrique etex, 3u*dir 180) ;
\stopMPpage

answered Nov 15 '18 at 20:16

Henri Menke

109,596

Thanks. I wouldn't have been able to find this on my own. It's been too long since I learnt what does cos and sin reflect… But now I see the point. – sztruks Nov 15 '18 at 21:24
There is also an operator angle that does the opposite, so that angle dir 60 should return 60. A bit like atan2 in other languages. – Thruston Nov 15 '18 at 21:42
As a matter of style you could also write 3 dir 60 scaled u. – Thruston Nov 15 '18 at 21:47
@Thruston angle does exactly perform atan2 (at least in double and decimal mode) https://github.com/TeX-Live/texlive-source/blob/ca4141d158e3baeee6616b706a008cfe2dc5a2a3/texk/web2c/mplibdir/mpmathdouble.w#L1166-L1183 – Henri Menke Nov 15 '18 at 21:50
1

Yes quite right. In my old-fashioned British way, when I say “a bit like” I mean “exactly the same as”… – Thruston Nov 15 '18 at 21:55

METAPOST equivalent to TikZ polar coordinates?

1 Answers1