Path: utzoo!attcan!utgpu!jarvis.csri.toronto.edu!mailrus!cornell!deb
From: deb@svax.cs.cornell.edu (David Baraff)
Newsgroups: comp.graphics
Subject: Re: Intersection between a line and a polygon (UNDECIDABLE??)
Keywords: P, NP, Jordan curve separation, Ursyhon Metrization Theorem
Message-ID: <32649@cornell.UUCP>
Date: 29 Sep 89 15:50:13 GMT
References: <2972@ndsuvax.UUCP> <32610@cornell.UUCP> <9983@alice.UUCP>
Sender: nobody@cornell.UUCP
Reply-To: deb@svax.cs.cornell.edu (David Baraff)
Organization: Cornell Univ. CS Dept, Ithaca NY
Lines: 26

In article <9983@alice.UUCP> td@alice.UUCP (Tom Duff) writes:
>>>
>>>  I need to find a formula/algorithm to determine if a line intersects
>>>  a polygon.  I would perfer a method that would do this in as litte
>>>  time as possible.  I need this for use in a forward raytracing
>>>  program.
>
>>I think that this is a very difficult problem. 
>>(Suggests postscript, mentions turing-completeness problem, etc.)
>
>The situation is not nearly as bleak as Baraff suggests (he should know
>better, he's hung around The Labs for long enough).  By the well known
>Dobbin-Dullman reduction line-polygon intersection can be
>reduced to Hamiltonian Circuit, without(!) the use of Grobner bases,

Well, sure its no worse than NP-complete, but that's ONLY
if you restrict yourself to the case where
the line satisfies a Lipschitz condition on its second derivative.
(I think there's an '89 SIGGRAPH paper from Caltech that deals with this).

	-David