Re: metafun: circular arc

[Hans Hagen via ntg-context <ntg-context@ntg.nl>]

On 10/5/2021 4:58 PM, Thomas A. Schmitz via ntg-context wrote:
> 
> 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.
Because you know how to rotate and scale:

\startuseMPgraphic{empedocless}
path p, q, r ;
pair a ;

p := fullcircle scaled 10cm ;
drawarrow p              withpen pencircle scaled 1mm withcolor red ;
draw        point 0 of p withpen pencircle scaled 1mm withcolor blue ;
q := p cutafter (point .4 along p) ;
drawarrow q              withpen pencircle scaled .5mm withcolor green ;
draw followtext(q, "\strut TEXT ONE") ;

p := fullcircle scaled 8cm ;
drawarrow p              withpen pencircle scaled 1mm withcolor cyan ;
draw        point 0 of p withpen pencircle scaled 1mm withcolor magenta ;
q := p cutafter (point .3 along p) ;
q := q rotated 120 ;
drawarrow q              withpen pencircle scaled .5mm withcolor yellow ;
draw followtext(q, "\strut TEXT TWO") ;

% the real deal: best make a macro for this

p := fullcircle scaled 6cm ;
draw        point 0 of p withpen pencircle scaled 5mm withcolor blue ;
drawarrow p              withpen pencircle scaled 1mm withcolor red ;
a := (point eps of p) rotated 45 ;
draw a withpen pencircle scaled 2mm;
q := p cutafter a ;
q := q rotated 20 ;
drawarrow q              withpen pencircle scaled .5mm withcolor green ;
draw followtext(q, "\strut TEXT TWO") ;

\stopuseMPgraphic

\useMPgraphic{empedocless}

So, just always start at point 0 and then just rotate the cutof piece 
over the angle that you want. The eps in the last case makes that we 
actually have a cut off piece (zero fails here).

So ... solution 4. best suits non math gurus (like you and me).

Hans


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                                           Hans Hagen | PRAGMA ADE
               Ridderstraat 27 | 8061 GH Hasselt | The Netherlands
        tel: 038 477 53 69 | www.pragma-ade.nl | www.pragma-pod.nl
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