
Accession Number : ADA302164
Title : Strong RestrictedOrientation Convexity,
Corporate Author : CARNEGIEMELLON UNIV PITTSBURGH PA DEPT OF COMPUTER SCIENCE
Personal Author(s) : Fink, Eugene ; Wood, Derick
PDF Url : ADA302164
Report Date : JUN 1995
Pagination or Media Count : 24
Abstract : Strong Oconvexity is a generalization of standard convexity, defined with respect to a fixed set O of hyperplanar orientations. We explore the properties of strongly Oconvex sets in two and more dimensions and develop a mathematical foundation of strong convexity. We characterize strongly 0convex polytopes, flats, and halfspaces, establish the strong 0convexity of the affine hull of a strongly Oconvex set, and describe conditions under which two orientation sets yield the same collection of strongly 0convex sets (orientation equivalence). We identify some of the major properties of standard convex sets that hold for strong Oconvexity. In particular, we establish the following results: The intersection of a collection of strongly Oconvex sets is strongly Oconvex; For every point in the boundary of a strongly Oconvex set, there is a supporting strongly 0convex hyperplane through it; A closed set with a nonempty interior is strongly 0convex if and only if it is the intersection of the strongly 0convex halfspaces that contain it.
Descriptors : *CONVEX SETS, ORIENTATION(DIRECTION), MATHEMATICAL PROGRAMMING, SET THEORY, POINT THEOREM, PLANE GEOMETRY.
Subject Categories : Numerical Mathematics
Distribution Statement : APPROVED FOR PUBLIC RELEASE