Titlebook: Restricted-Orientation Convexity; Eugene Fink,Derick Wood Book 2004 Springer-Verlag Berlin Heidelberg 2004 Euclidean geometry.Generalized

Missile

Restricted-Orientation Convexity978-3-642-18849-7Series ISSN 1431-2654 Series E-ISSN 2193-2069

坦白

1431-2654 t are connected. This notion generalizes standard convexity and several types of nontraditional convexity. We explore the properties of this generalized convexity in multidimensional Euclidean space, describes restricted-orientation analogs of lines, hyperplanes, flats, and halfspaces, and identify

Gentry

Introduction,ng topology, number theory and combinatorics [6, 14, 21]. Researchers have explored not only mathematical properties of convex sets, but also related computational problems [5, 13, 34], and applied the resulting algorithms in many practical areas, such as graphics, finite-element analysis, VLSI desi

Adulate

Computational Problems,ernels, and identifying the regions visible from a given point. Researchers addressed the analogous standard-convexity problems in the early days of computational geometry; for example, consult the text of Preparata and Shamos [34]. They also developed similar techniques for several types of non-tra

大约冬季

Higher Dimensions,vex sets in ., and introduce O-connected sets, which are a subclass of O-convex sets with several special properties (Sect. 4.2). Then, we explore properties of O-connected curves (Sect. 4.3) and present visibility results for O-convex and O-connected sets (Sect. 4.4).

杀虫剂

Generalized Halfspaces, them with standard halfspaces (Sect. 5.1). Then, we define directed O-halfspaces, which are a subclass of O-halfspaces with several special properties (Sect. 5.2). Finally, we characterize O-halfspaces in terms of their boundaries (Sect. 5.3) and complements (Sect. 5.4).

DEI

Strong Convexity,ve a condition for the equivalence of two orientation sets (Sect. 6.2). Finally, we study strongly O-convex halfspaces and characterize strongly O-convex sets through halfspace intersections (Sect. 6.3).

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Book 2004ex sets that also hold for restricted-orientation convexity. We then introduce the notion of strong restricted-orientation convexity, which is an alternative generalization of convexity, and show that its properties are also similar to those of standard convexity. .

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