metafun: circular arc

["Thomas A. Schmitz via ntg-context" <ntg-context@ntg.nl>]

Hi all,

I hope the following example is not too convoluted:

\useMPlibrary [txt]

\define\EmpArrow{\getscaledglyph{1.6}{name:dejavumath}{\char"2B05}}

\setupbodyfont [ss,9pt]

\starttext

\startuseMPgraphic{empedocles}
%numeric a ; a = 6.56cm ;
%numeric b ; b = 1.1 ;
save S; path S[] ;
S[1] = fullcircle scaled 8cm rotated 306 ;
S[2] = S[1] scaled 1.1 ;
S[3] = S[1] scaled 1.23 ;
S[4] = S[1] scaled 1.3 ;
S[5] = S[1] scaled 1.43 ;
S[6] = S[1] scaled 1.5 ;
S[7] = S[1] scaled 1.6 ;
z[1] = point 1 along S[7] ;
z[2] = point 1 along S[1] ;
z[3] = point 0.1 along S[7] ;
z[4] = point 0.1 along S[1] ;
z[5] = point 0.2 along S[7] ;
z[6] = point 0.2 along S[1] ;
z[7] = point 0.3 along S[7] ;
z[8] = point 0.3 along S[1] ;
z[9] = point 0.4 along S[7] ;
z[10] = point 0.4 along S[1] ;
z[11] = point 0.5 along S[7] ;
z[12] = point 0.5 along S[1] ;
z[13] = point 0.6 along S[7] ;
z[14] = point 0.6 along S[1] ;
z[15] = point 0.7 along S[7] ;
z[16] = point 0.7 along S[1] ;
z[17] = point 0.8 along S[7] ;
z[18] = point 0.8 along S[1] ;
S[8] = z[1] -- z[2] ;
S[9] = z[3] -- z[4] ;
S[10] = z[5] -- z[6] ;
S[11] = z[7] -- z[8] ;
S[12] = z[9] -- z[10] ;
S[13] = z[11] -- z[12] ;
S[14] = z[13] -- z[14] ;
S[15] = z[15] -- z[16] ;
S[16] = z[17] -- z[18] ;
z[19] = S[3] intersection_point S[8] ;
z[20] = S[3] intersection_point S[16] ;
S[18] = S[3] cutbefore z[20] cutafter z[19] ;
z[21] = S[5] intersection_point S[8] ;
z[22] = S[5] intersection_point S[16] ;
S[19] = S[5] cutbefore z[22] cutafter z[21] ;
z[23] = S[12] intersection_point S[3] ;
S[20] = S[3] cutbefore z[20] cutafter z[23] ;
for i = 1 upto 16:
	draw S[i] withcolor 0.7white ;
endfor ;
draw z[23] -- z[20] withcolor red ;
draw S[20] withcolor blue ;
label.bot(textext("\noexpand\framed[align=middle,frame=off]{Jahr \crlf 
20.000 = 0}"), z[10]) ;
label.llft(textext("\noexpand\framed[align=middle,frame=off]{Jahr \crlf 
2.000}"), z[8]) ;
label.lft(textext("\noexpand\framed[align=middle,frame=off]{Jahr \crlf 
4.000}"), z[6]) ;
label.lft(textext("\noexpand\framed[align=middle,frame=off]{Jahr \crlf 
6.000}"), z[4]) ;
label.ulft(textext("\noexpand\framed[align=middle,frame=off]{Jahr \crlf 
8.000}"), z[2]) ;
label.urt(textext("\noexpand\framed[align=middle,frame=off]{Jahr \crlf 
12.000}"), z[18]) ;
label.rt(textext("\noexpand\framed[align=middle,frame=off]{Jahr \crlf 
14.000}"), z[16]) ;
label.rt(textext("\noexpand\framed[align=middle,frame=off]{Jahr \crlf 
16.000}"), z[14]) ;
label.lrt(textext("\noexpand\framed[align=middle,frame=off]{Jahr \crlf 
18.000}"), z[12]) ;
draw followtext(S[18], "\strut\hbox to 2em{\EmpArrow}\hskip2em 
RUHEPAUSE\hskip4em\strut") ;
draw followtext(S[19], "\strut\hbox to 2em{\EmpArrow}EINHEIT 
(SPHAIROS)\hskip2em\strut") ;
\stopuseMPgraphic

\useMPgraphic{empedocles}

\stoptext

I have a big problem and some smaller questions, for those who are 
better at math and at metafun than I am:

1. The big problem: for the next followtext, I need the circular arc 
between points z[23] and z[20]. But however I place the cutbefore and 
cutafter, I don't get the proper part of the circle. I'm looking at the 
right intersection points, as the red line shows, but the blue line 
shows that I'm not getting the right section of the circle. How can I 
get this section into the path S[20]?

2. Math... :-) Is there a better way to define three circles that are at 
exactly the same distance than my naive "scaled 1.3" and "scaled 1.5"?

3. TeX and metafun: is there a better way to have the followtext exactly 
centered between the two circles rather than just fiddle with the scale 
factor?

4. Or is there a better approach to my problem altogether? I'm trying to 
reproduce an illustration from a book, so I'm very open to suggestions 
here. I looked at the example in the metafun manual chapter 10.4, but 
I'm not sure if using an overlay and multiple \followtokens would be 
easier. Especially since there is the scary remark "This definition is 
not the right one!" in this chapter without any further explanation.

I hope you all had a wonderful meeting last week. I was sad I couldn't 
come, I was in Paris for a conference, the first after 18 months, so I 
couldn't skip this one.

Thanks and best wishes

Thomas
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