Fwd: Re[4]: MetaPost/Fun question

Fwd: Re[4]: MetaPost/Fun question

[Hans Hagen]

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Hi,

Here is some comment on GB's intersection problem/solution from the polish 
mp expert Boguslaw Jackowski (those who will be in bremen next week can 
meet this personality).

Hans




> >EHL> I implemented it by finding some intersectiontime and the recursively
> >EHL> finding the intersectionstimes of the two subpaths (each with some
> >EHL> neighbourhood of the first intersection point cut off). For the time
> >EHL> being I cannot find my code, but here it is in pseude code.
> >
> >EHL> When done this way, the intersection times will be sorted according to
> >EHL> the first path.
>
>Frankly speaking, such a procedure should belong to plain from the very
>beginning... Obviously, we added it in our plain_ex that we use for
>generating fonts (even more -- we find also common outlines).
>
>Attached you'll find the relevant excerpt plus examples.
>
>Incidentally, recursion seem still banned from the MF/MP realm. I complained
>about it some time ago, but it seems that nobody but me is hurted by this
>annoyin situation.  Attached you'll find an example: 31-element series
>(in a reversed order) break down w2c mpost...
>
>And finally, let me quote the post from Larry Siebenmann (from 30 Jun 2000):
>
> > I believe that value (-1,-1) for "intersectiontimes" is a
> > 100% ironclad guarantee that its two path arguments are
> > disjoint.
> >
> > Is the converse true?  That is, if "intersectiontimes"
> > yields positive times, do the two paths necessarily
> > intersect? NO! In writing the last post, I confirmed to my
> > satisfaction that MP and MF report positive intersection
> > times for paths that only come near.  Start by looking
> > at the following -- in which one of the paths is constant.
> >
> > path c;
> > pair v,w;
> > c:=fullcircle scaled 2;
> > v:=(1+19epsilon,0) rotated 33.1234567;
> > w:=(1-15epsilon,0) rotated 33.1234567;
> > show (v intersectiontimes  c);
> > show (w intersectiontimes  c);
> > v:=(1+20epsilon,0) rotated 33.1234567;
> > w:=(1-16epsilon,0) rotated 33.1234567;
> > show (v intersectiontimes  c);
> > show (w intersectiontimes  c);
> >
> > end
> >
> > The log:
> >
> > This is MetaPost, Version 0.641
> > **&Plain filetest.mp
> > (filetest.mp
> > >> (0.47754,0.73682)
> > >> (0.96869,0.7373)
> > >> (-1,-1)
> > >> (-1,-1) )
> >
> > Thus "intersectionpoint" may return a point when the paths
> > are disjoint. It is guaranteed only to return a point of
> > close approach.  Close approach algorithms are complicated
> > when efficient. But they are trivial in principle and enjoy
> > incredible generality:- indeed, since we have explicit
> > bounds modulus of continuity, it suffices to measure image
> > distances on a finite but fine net of points in source.
> >
> > Question: Is there an *if-and-only-if* test for b'ezier
> > curve intersection?
> >
> > The answer is yes for linear segments, though in some, but
> > not all, cases one needs exact rational arithmetic.  So
> > think of working in C.
>
>I think you have now more comments than enough ;-)
>
>Cheers -- Jacko
>
>--
>BOP s. c.
>ul. Bora-Komorowskiego 24, 80-377 Gdansk, Poland
>tel. (+48 58) 553 46 59,  fax (+48 58) 511 03 81
>bop@bop.com.pl, http://www.bop.com.pl
>
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