> On 21 Apr 2020, at 14:41, Hans Hagen <j.ha...@xs4all.nl> wrote:
>
> On 4/21/2020 1:29 PM, Gerben Wierda wrote:
[snip]
>
> \startMPpage[instance=doublefun]
>
> path arrowHead;
> arrowHead :=
> (542,-77.000186920166016)..controls
> (545.33333333333337,-77.000186920166016) and
> (548.66666666666663,-77.000186920166016)
> ..(552,-77.000186920166016)..controls
> (550.33333333333337,-73.666853586832687) and
> (548.66666666666663,-70.333520253499344)
> ..(547,-67.000186920166016)..controls
> (545.33333333333337,-70.333520253499344) and
> (543.66666666666663,-73.666853586832687) ..cycle;
>
> path connection;
> connection :=
> (420.00004959106445,-367)..controls (420.66670256708773,-367) and
> (421.333355543111,-367) ..(422.00000851913427,-367)..controls
> (425.33333917170194,-367) and (428.6666698242696,-367)
> ..(432.00000047683727,-367)..controls (442.00000015894574,-367) and
> (451.99999984105426,-367) ..(461.99999952316273,-367)..controls
> (464.76142345324098,-367) and (467,-364.76142382108867)
> ..(467,-361.99999997656772)..controls (467,-293.99999999218926) and
> (467,-226.00000000781074) ..(467,-158.00000002343228)..controls
> (467,-155.23857623850762) and (469.23857634039018,-153)
> ..(472.00000014901161,-153)..controls (495.33333338300389,-153) and
> (518.66666661699617,-153) ..(541.99999985098839,-153)..controls
> (544.76142368504975,-153) and (547,-150.76142367339932)
> ..(547,-147.99999983662815)..controls (547,-125.99999994554271) and
> (547,-104.00000005445727) ..(547,-82.000000163371837)..controls
> (547,-78.666668047283764) and (547,-75.333335931195691)
> ..(547,-72.000003815107618)..controls (547,-70.333398183460417) 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.
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