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