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 (545.33333333333337,-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.

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

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!

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