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.)