metafun: circular arc

metafun: circular arc

[Thomas A. Schmitz via ntg-context]

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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Re: metafun: circular arc

[Hans Hagen via ntg-context]

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


-----------------------------------------------------------------
                                           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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maillist : ntg-context@ntg.nl / http://www.ntg.nl/mailman/listinfo/ntg-context
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Re: metafun: circular arc

[Thomas A. Schmitz via ntg-context]

Thank you so much, Hans, that's a neat solution! I was banging my head 
against the wall, but this makes sense.

On 10/5/21 6:38 PM, Hans Hagen wrote:
> 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).

This is the part of your reply that fails to convince. You don't even 
know how bad I am at math...

Thanks, and all best

Thomas
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maillist : ntg-context@ntg.nl / http://www.ntg.nl/mailman/listinfo/ntg-context
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Re: metafun: circular arc

[Floris van Manen via ntg-context]

In the example the text is drawn as:

draw followtext(q, "\strut TEXT ONE")


it looks as if the \strut generates a space before the text.
e.g. if you omit the \strut, the text will align at the start point.
In my perception, the \strut is a zero width box, so it should not 
generate the space before.
But I might be wrong here (most likely ;-)

.F




On 05/10/2021 23:32, Thomas A. Schmitz via ntg-context wrote:
> 
> \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}
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maillist : ntg-context@ntg.nl / http://www.ntg.nl/mailman/listinfo/ntg-context
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