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From: eas@utcsrgv.UUCP (Ann Struthers)
Newsgroups: ont.events
Subject: Abstract/Theoretical Aspects Seminar
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Date: Fri, 11-Jan-85 10:47:28 EST
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Posted: Fri Jan 11 10:47:28 1985
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Organization: CSRI, University of Toronto
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Subject: Abstract/Theoretical Aspects Seminar
Newsgroups: ont.events
Distribution: ont

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		      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.