Restricted-Orientation Convexity

Restricted-orientation convexity is the study of geometric objects whose intersections with lines from some fixed set are connected. This notion generalizes standard convexity and several types of nontraditional convexity. We explore the properties of this generalized convexity in multidimensional E...

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Main Authors: Fink, Eugene, Wood, Derick (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Berlin, Heidelberg Springer Berlin Heidelberg 2004, 2004
Edition:1st ed. 2004
Series:Monographs in Theoretical Computer Science. An EATCS Series
Subjects:
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
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100 1 |a Fink, Eugene 
245 0 0 |a Restricted-Orientation Convexity  |h Elektronische Ressource  |c by Eugene Fink, Derick Wood 
250 |a 1st ed. 2004 
260 |a Berlin, Heidelberg  |b Springer Berlin Heidelberg  |c 2004, 2004 
300 |a X, 102 p  |b online resource 
505 0 |a 1 Introduction -- 1.1 Standard Convexity -- 1.2 Ortho-Convexity -- 1.3 Strong Ortho-Convexity -- 1.4 Convexity Spaces -- 1.5 Book Outline -- 2 Two Dimensions -- 2.1 O-Convex Sets -- 2.2 O-Halfplanes -- 2.3 Strongly O-Convex Sets -- 3 Computational Problems -- 3.1 Visibility and Convexity Testing -- 3.2 Strong O-Hull -- 3.3 Strong O-Kernel -- 3.4 Visibility from a Point -- 4 Higher Dimensions -- 4.1 Orientation Sets -- 4.2 O-Convexity and O-Connectedness -- 4.3 O-Connected Curves -- 4.4 Visibility -- 5 Generalized Halfspaces -- 5.1 O-Halfspaces -- 5.2 Directed O-Halfspaces -- 5.3 Boundary Convexity -- 5.4 Complementation -- 6 Strong Convexity -- 6.1 Strongly O-Convex Sets -- 6.2 Strongly O-Convex Flats -- 6.3 Strongly O-Convex Halfspaces -- 7 Closing Remarks -- 7.1 Main Results -- 7.2 Conjectures -- 7.3 Future Work -- References 
653 |a Computer graphics 
653 |a Convex and Discrete Geometry 
653 |a Computation by Abstract Devices 
653 |a Algorithms 
653 |a Convex geometry  
653 |a Computers 
653 |a Computer Graphics 
653 |a Algorithm Analysis and Problem Complexity 
653 |a Discrete geometry 
700 1 |a Wood, Derick  |e [author] 
710 2 |a SpringerLink (Online service) 
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520 |a Restricted-orientation convexity is the study of geometric objects whose intersections with lines from some fixed set 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 major properties of standard convex 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