Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.2 9/18/84; site utcsrgv.UUCP Path: utzoo!utcsrgv!eas From: eas@utcsrgv.UUCP (Ann Struthers) Newsgroups: ont.events Subject: Abstract/Theoretical Aspects Seminar Message-ID: <655@utcsrgv.UUCP> Date: Fri, 11-Jan-85 10:47:28 EST Article-I.D.: utcsrgv.655 Posted: Fri Jan 11 10:47:28 1985 Date-Received: Fri, 11-Jan-85 11:42:54 EST Distribution: ont Organization: CSRI, University of Toronto Lines: 36 Subject: Abstract/Theoretical Aspects Seminar Newsgroups: ont.events Distribution: ont *** REPLACE THIS LINE WITH YOUR MESSAGE *** THEORETICAL ASPECTS SEMINAR Thursday, January 17, 1984 4:00 P.M. Sandford Fleming Building 1101 Ms. Anna Lubiw Ph.D. candidate in the Department of Computer Science University of Toronto "Decomposing a Polygonal Region into Convex Quadrilaterals" A polygonal region is formed by cutting holes bounded by polygons out of the region bounded by a polygon. Decomposing a polygonal region means partitioning the region into simpler polygons by adding chords, which are line segments inside the region joining pairs of vertices. Khan, Klawe & Kleitman proved (as a step towards positioning watchmen in conventional art galleries) that every rectilinear region can be decomposed into convex quadrilaterals. A rectilinear region is a poly- gonal region whose edges are all parallel to the x or y axis. I look at larger classes of polygonal regions which are CQ hereditary - i.e. every region in the class contains a convex quadrilateral whose removal leaves polygonal regions in the class. I obtain an O(nlogn) algorithm to decompose n-vertex rectilinear regions into convex quadrilaterals.