Re: [NTG-context] METAPOST: How do I get this 'max' cutafter to work?
> On 22 Apr 2020, at 09:30, Taco Hoekwater wrote: > > Hi, > >> On 21 Apr 2020, at 17:52, Gerben Wierda wrote: >> >>> pair a ; a := arrowHead intersection_point connection ; > > Hans’ example also works with “intersectionpoint”: the differences between > intersectionpoint > and intersection_point are minimal except if there is no intersection at all. > > The trick is that Hans does not use cutafter. cutafter is designed to cut off > as little as > possible, it is a cutbefore on both paths reversed. So, uses the last > intersection point of > the paths, and in this case it will therefore use the top of the arrowhead. > > In contrast, intersectionpoint finds the first intersection on the > non-reversed paths, which > is the base of the arrowhead. > > Alternatively (in this case), you could move the arrowhead up a tiny amount, > so that there is > only one intersection between the connection and arrowHead. In fact I did something like this, except that I first shortened the line path so it ends in the middle of the triangle before doing a cutafter (twice in both directions and taking the one which cuts the most). This works reliably. I gave up on another approach (which repeatedly cut a little bit from the path until it wasn’t intersecting anymore, then taking the one form thelast successful intersection) as I also have paths that connect a path-cycle to itself. A ‘cut until it just doesn’t intersect anymore' would eat up the entire path in that case until only a single point is left. G > > Best wishes, > Taco > ___ > If your question is of interest to others as well, please add an entry to the > Wiki! > > maillist : ntg-context@ntg.nl / http://www.ntg.nl/mailman/listinfo/ntg-context > webpage : http://www.pragma-ade.nl / http://context.aanhet.net > archive : https://bitbucket.org/phg/context-mirror/commits/ > wiki : http://contextgarden.net > ___ ___ If your question is of interest to others as well, please add an entry to the Wiki! maillist : ntg-context@ntg.nl / http://www.ntg.nl/mailman/listinfo/ntg-context webpage : http://www.pragma-ade.nl / http://context.aanhet.net archive : https://bitbucket.org/phg/context-mirror/commits/ wiki : http://contextgarden.net ___
Re: [NTG-context] METAPOST: How do I get this 'max' cutafter to work?
On Wed, Apr 22, 2020 at 9:30 AM Taco Hoekwater wrote:
>
> In contrast, intersectionpoint finds the first intersection on the
> non-reversed paths, which
> is the base of the arrowhead.
>
>
IIrc , it's the first in shuffle order
@ Incidentally, if the given cubics intersect more than once, the process
just sketched will not necessarily find the lexicographically smallest pair
$(t_1,t_2)$. The solution actually obtained will be smallest in ``shuffled
order''; i.e., if $t_1=(.a_1a_2\ldots a_{16})_2$ and
$t_2=(.b_1b_2\ldots b_{16})_2$, then we will minimize
$a_1b_1a_2b_2\ldots a_{16}b_{16}$, not
$a_1a_2\ldots a_{16}b_1b_2\ldots b_{16}$.
Shuffled order agrees with lexicographic order if all pairs of solutions
$(t_1,t_2)$ and $(t_1',t_2')$ have the property that $t_1___
If your question is of interest to others as well, please add an entry to the
Wiki!
maillist : ntg-context@ntg.nl / http://www.ntg.nl/mailman/listinfo/ntg-context
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Re: [NTG-context] METAPOST: How do I get this 'max' cutafter to work?
Hi, > On 21 Apr 2020, at 17:52, Gerben Wierda wrote: > >> pair a ; a := arrowHead intersection_point connection ; Hans’ example also works with “intersectionpoint”: the differences between intersectionpoint and intersection_point are minimal except if there is no intersection at all. The trick is that Hans does not use cutafter. cutafter is designed to cut off as little as possible, it is a cutbefore on both paths reversed. So, uses the last intersection point of the paths, and in this case it will therefore use the top of the arrowhead. In contrast, intersectionpoint finds the first intersection on the non-reversed paths, which is the base of the arrowhead. Alternatively (in this case), you could move the arrowhead up a tiny amount, so that there is only one intersection between the connection and arrowHead. Best wishes, Taco ___ If your question is of interest to others as well, please add an entry to the Wiki! maillist : ntg-context@ntg.nl / http://www.ntg.nl/mailman/listinfo/ntg-context webpage : http://www.pragma-ade.nl / http://context.aanhet.net archive : https://bitbucket.org/phg/context-mirror/commits/ wiki : http://contextgarden.net ___
Re: [NTG-context] METAPOST: How do I get this 'max' cutafter to work?
On 4/21/2020 5:52 PM, Gerben Wierda wrote: Pretty deep into MP now. Even looked up the reference in John Hobby’s manual to the METAFONT book, but that reference did not help. in the end it all has to do with accuracy and rounding ... the intersection_point trickery is probably less sensitive for that but it's so long ago that i mp-tool was written that that part of my mind probably has been overwritten, obscured or wiped 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 - ___ If your question is of interest to others as well, please add an entry to the Wiki! maillist : ntg-context@ntg.nl / http://www.ntg.nl/mailman/listinfo/ntg-context webpage : http://www.pragma-ade.nl / http://context.aanhet.net archive : https://bitbucket.org/phg/context-mirror/commits/ wiki : http://contextgarden.net ___
Re: [NTG-context] METAPOST: How do I get this 'max' cutafter to work?
> On 21 Apr 2020, at 14:41, Hans Hagen wrote:
>
> On 4/21/2020 1:29 PM, Gerben Wierda wrote:
[snip]
>
> \startMPpage[instance=doublefun]
>
> path arrowHead;
> arrowHead :=
>(542,-77.000186920166016)..controls
> (545.37,-77.000186920166016) and
>(548.63,-77.000186920166016)
> ..(552,-77.000186920166016)..controls
>(550.37,-73.666853586832687) and
>(548.63,-70.333520253499344)
> ..(547,-67.000186920166016)..controls
>(545.37,-70.333520253499344) and
>(543.63,-73.666853586832687) ..cycle;
>
> path connection;
> connection :=
> (420.4959106445,-367)..controls (420.66670256708773,-367) and
> (421.55543111,-367) ..(422.0851913427,-367)..controls
> (425.3917170194,-367) and (428.698242696,-367)
> ..(432.0047683727,-367)..controls (442.0015894574,-367) and
> (451.9984105426,-367) ..(461.9952316273,-367)..controls
> (464.76142345324098,-367) and (467,-364.76142382108867)
> ..(467,-361.9997656772)..controls (467,-293.218926) and
> (467,-226.781074) ..(467,-158.0002343228)..controls
> (467,-155.23857623850762) and (469.23857634039018,-153)
> ..(472.0014901161,-153)..controls (495.3338300389,-153) and
> (518.6661699617,-153) ..(541.9985098839,-153)..controls
> (544.76142368504975,-153) and (547,-150.76142367339932)
> ..(547,-147.9983662815)..controls (547,-125.9994554271) and
> (547,-104.0005445727) ..(547,-82.00163371837)..controls
> (547,-78.68047283764) and (547,-75.35931195691)
> ..(547,-72.03815107618)..controls (547,-70.98183460417) and
> (547,-68.666792551813217) ..(547,-67.000186920166016);
>
> pair a ; a := arrowHead intersection_point connection ;
>
> draw connection cutafter arrowHead withcolor red withpen
> pencircle scaled 2mm ;
> draw connection cutafter (reverse arrowHead) withcolor green withpen
> pencircle scaled 1mm ;
>
> draw arrowHead;
>
> draw a withcolor blue withpen pencircle scaled 3mm ;
>
> currentpicture := currentpicture shifted (-bbwidth(currentpicture), 0) ;
>
> draw connection cutafter a ;
>
> draw arrowHead;
>
>
> \stopMPpage
Hi Hans, thanks.
I am completely in the dark why your intersection_point works (and thus if it
will keep working in all circumstances).
I’d like to understand what is going on here. Why does intersection_point work
where cutafter does not? After all, both are based on the same
intersectiontimes primitive to find the intersection and they should thus find
the same one: the ’perfect’ intersection which is the end point of the path
that is to be cut.
I’d like to understand this, because otherwise I might run into the same
problem again later with slightly different paths involved. The first algo that
I was using worked fine in most cases, as well, then I created one that worked
with paths with ‘internal spikes’ and now I run into this where two comparable
situations behaved differently and my question copied the one that didn’t work.
And while this example from you works, I need to have something that is 100%
reliable.
What METAPOST comes with is:
path cuttings; % what got cut off
tertiarydef a cutbefore b = % tries to cut as little as possible
begingroup save t;
(t, whatever) = a intersectiontimes b;
if t<0:
cuttings:=point 0 of a;
a
else: cuttings:= subpath (0,t) of a;
subpath (t,length a) of a
fi
endgroup
enddef;
tertiarydef a cutafter b =
reverse (reverse a cutbefore b)
hide(cuttings:=reverse cuttings)
enddef;
secondarydef p intersectionpoint q =
begingroup save x_,y_; (x_,y_)=p intersectiontimes q;
if x_<0: errmessage("The paths don't intersect"); origin
else: .5[point x_ of p, point y_ of q] fi endgroup
enddef;
What is in MetaFun is:
boolean intersection_found ;
secondarydef p intersection_point q =
begingroup
save x_, y_ ;
(x_,y_) = p intersectiontimes q ;
if x_< 0 :
intersection_found := false ;
center p % origin
else :
intersection_found := true ;
.5[point x_ of p, point y_ of q]
fi
endgroup
enddef ;
The thing I can think of is cutting a bit, trying if it still intersects and if
it does repeat and if it doesn’t take the previous result. I can’t rely on the
length of cuttings being 0, because this is true in the case of no intersection
(cuttings equals (0,0)) as well as a ‘perfect’ intersection at the end of the
path (cuttings is the point at the end of the path). I could rely on cuttings
being the path (0,0) but how do I compare paths (and not pairs)?
G
Pretty deep into MP now. Even looked up the reference in John Hobby’s manual to
the METAFONT book, but that reference did not help.
___
If your question is of interest to others as well, please add an entry to the
Wiki!
maillist : ntg-context@ntg.nl /
Re: [NTG-context] METAPOST: How do I get this 'max' cutafter to work?
On 4/21/2020 1:29 PM, Gerben Wierda wrote: I have these two paths, but cutting doesn’t work because the path to be cut takes the wrong intersection regardless of how I direct the path to be cut after (reverse or not). The path to cut after is a triangle with the base horizontal and the path to cut is a vertical line. The top of the triangle is the endpoint of the line and is selected as intersection by cutafter. This happens also if I reverse the triangle path, strangely enough. I have an alternative cutting algorithm, but that cuts as long as the length of cuttings is not 0, which is the case at the top too, so it won’t cut further. I need a reliable algorithm to make a ‘maximum cutafter’. What might be a good approach? G path arrowHead; arrowHead := (542,-77.000186920166016)..controls (545.37,-77.000186920166016) and (548.63,-77.000186920166016) ..(552,-77.000186920166016)..controls (550.37,-73.666853586832687) and (548.63,-70.333520253499344) ..(547,-67.000186920166016)..controls (545.37,-70.333520253499344) and (543.63,-73.666853586832687) ..cycle; path connection; connection := (420.4959106445,-367)..controls (420.66670256708773,-367) and (421.55543111,-367) ..(422.0851913427,-367)..controls (425.3917170194,-367) and (428.698242696,-367) ..(432.0047683727,-367)..controls (442.0015894574,-367) and (451.9984105426,-367) ..(461.9952316273,-367)..controls (464.76142345324098,-367) and (467,-364.76142382108867) ..(467,-361.9997656772)..controls (467,-293.218926) and (467,-226.781074) ..(467,-158.0002343228)..controls (467,-155.23857623850762) and (469.23857634039018,-153) ..(472.0014901161,-153)..controls (495.3338300389,-153) and (518.6661699617,-153) ..(541.9985098839,-153)..controls (544.76142368504975,-153) and (547,-150.76142367339932) ..(547,-147.9983662815)..controls (547,-125.9994554271) and (547,-104.0005445727) ..(547,-82.00163371837)..controls (547,-78.68047283764) and (547,-75.35931195691) ..(547,-72.03815107618)..controls (547,-70.98183460417) and (547,-68.666792551813217) ..(547,-67.000186920166016); show connection cutafter arrowHead; show connection cutafter (reverse arrowHead); \startMPpage[instance=doublefun] path arrowHead; arrowHead := (542,-77.000186920166016)..controls (545.37,-77.000186920166016) and (548.63,-77.000186920166016) ..(552,-77.000186920166016)..controls (550.37,-73.666853586832687) and (548.63,-70.333520253499344) ..(547,-67.000186920166016)..controls (545.37,-70.333520253499344) and (543.63,-73.666853586832687) ..cycle; path connection; connection := (420.4959106445,-367)..controls (420.66670256708773,-367) and (421.55543111,-367) ..(422.0851913427,-367)..controls (425.3917170194,-367) and (428.698242696,-367) ..(432.0047683727,-367)..controls (442.0015894574,-367) and (451.9984105426,-367) ..(461.9952316273,-367)..controls (464.76142345324098,-367) and (467,-364.76142382108867) ..(467,-361.9997656772)..controls (467,-293.218926) and (467,-226.781074) ..(467,-158.0002343228)..controls (467,-155.23857623850762) and (469.23857634039018,-153) ..(472.0014901161,-153)..controls (495.3338300389,-153) and (518.6661699617,-153) ..(541.9985098839,-153)..controls (544.76142368504975,-153) and (547,-150.76142367339932) ..(547,-147.9983662815)..controls (547,-125.9994554271) and (547,-104.0005445727) ..(547,-82.00163371837)..controls (547,-78.68047283764) and (547,-75.35931195691) ..(547,-72.03815107618)..controls (547,-70.98183460417) and (547,-68.666792551813217) ..(547,-67.000186920166016); pair a ; a := arrowHead intersection_point connection ; draw connection cutafter arrowHead withcolor red withpen pencircle scaled 2mm ; draw connection cutafter (reverse arrowHead) withcolor green withpen pencircle scaled 1mm ; draw arrowHead; draw a withcolor blue withpen pencircle scaled 3mm ; currentpicture := currentpicture shifted (-bbwidth(currentpicture), 0) ; draw connection cutafter a ; draw arrowHead; \stopMPpage - Hans Hagen | PRAGMA ADE Ridderstraat 27 | 8061 GH Hasselt | The Netherlands tel: 038 477 53 69 | www.pragma-ade.nl | www.pragma-pod.nl - ___ If your question is of interest to others as well, please add an entry to the Wiki! maillist : ntg-context@ntg.nl /
[NTG-context] METAPOST: How do I get this 'max' cutafter to work?
I have these two paths, but cutting doesn’t work because the path to be cut takes the wrong intersection regardless of how I direct the path to be cut after (reverse or not). The path to cut after is a triangle with the base horizontal and the path to cut is a vertical line. The top of the triangle is the endpoint of the line and is selected as intersection by cutafter. This happens also if I reverse the triangle path, strangely enough. I have an alternative cutting algorithm, but that cuts as long as the length of cuttings is not 0, which is the case at the top too, so it won’t cut further. I need a reliable algorithm to make a ‘maximum cutafter’. What might be a good approach? G path arrowHead; arrowHead := (542,-77.000186920166016)..controls (545.37,-77.000186920166016) and (548.63,-77.000186920166016) ..(552,-77.000186920166016)..controls (550.37,-73.666853586832687) and (548.63,-70.333520253499344) ..(547,-67.000186920166016)..controls (545.37,-70.333520253499344) and (543.63,-73.666853586832687) ..cycle; path connection; connection := (420.4959106445,-367)..controls (420.66670256708773,-367) and (421.55543111,-367) ..(422.0851913427,-367)..controls (425.3917170194,-367) and (428.698242696,-367) ..(432.0047683727,-367)..controls (442.0015894574,-367) and (451.9984105426,-367) ..(461.9952316273,-367)..controls (464.76142345324098,-367) and (467,-364.76142382108867) ..(467,-361.9997656772)..controls (467,-293.218926) and (467,-226.781074) ..(467,-158.0002343228)..controls (467,-155.23857623850762) and (469.23857634039018,-153) ..(472.0014901161,-153)..controls (495.3338300389,-153) and (518.6661699617,-153) ..(541.9985098839,-153)..controls (544.76142368504975,-153) and (547,-150.76142367339932) ..(547,-147.9983662815)..controls (547,-125.9994554271) and (547,-104.0005445727) ..(547,-82.00163371837)..controls (547,-78.68047283764) and (547,-75.35931195691) ..(547,-72.03815107618)..controls (547,-70.98183460417) and (547,-68.666792551813217) ..(547,-67.000186920166016); show connection cutafter arrowHead; show connection cutafter (reverse arrowHead); ___ If your question is of interest to others as well, please add an entry to the Wiki! maillist : ntg-context@ntg.nl / http://www.ntg.nl/mailman/listinfo/ntg-context webpage : http://www.pragma-ade.nl / http://context.aanhet.net archive : https://bitbucket.org/phg/context-mirror/commits/ wiki : http://contextgarden.net ___
