Path: utzoo!attcan!utgpu!jarvis.csri.toronto.edu!rutgers!dptg!ulysses!andante!alice!td From: td@alice.UUCP (Tom Duff) Newsgroups: comp.graphics Subject: Re: Intersection between a line and a polygon (UNDECIDABLE??) Summary: Overkill. Keywords: P, NP, Jordan curve separation, Ursyhon Metrization Theorem Message-ID: <9983@alice.UUCP> Date: 29 Sep 89 13:46:04 GMT References: <2972@ndsuvax.UUCP> <32610@cornell.UUCP> Organization: AT&T Bell Laboratories, Murray Hill NJ Lines: 18 >> >> 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 (see J. Dullman & D. Dobbin, J. Comp. Obfusc. 37,ii: pp. 33-947, lemma 17(a)) line-polygon intersection can be reduced to Hamiltonian Circuit, without(!) the use of Grobner bases, so LPI (to coin an acronym) is probably only NP-complete. Besides, Turing-completeness will no longer be a problem once our Cray-3 is delivered, since it will be able to complete an infinite loop in 4 milliseconds (with scatter-gather.)