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Restricted-Orientation Convexity

  • Eugene Fink
  • Derick Wood

Table of contents

  1. Front Matter
    Pages I-X
  2. Eugene Fink, Derick Wood
    Pages 1-8
  3. Eugene Fink, Derick Wood
    Pages 9-20
  4. Eugene Fink, Derick Wood
    Pages 21-33
  5. Eugene Fink, Derick Wood
    Pages 35-51
  6. Eugene Fink, Derick Wood
    Pages 53-66
  7. Eugene Fink, Derick Wood
    Pages 67-83
  8. Eugene Fink, Derick Wood
    Pages 85-91
  9. Back Matter
    Pages 93-102

About this book

Introduction

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.

Keywords

Euclidean geometry Generalized convexity Higher dimensions Theory Visibility algorithms

Authors and affiliations

  • Eugene Fink
    • 1
  • Derick Wood
    • 2
  1. 1.Dept. of Computer ScienceUniversity of South FloridaTampaUSA
  2. 2.Dept. of Computer ScienceHong Kong University of Science and TechnologyHong KongPR China

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-18849-7
  • Copyright Information Springer-Verlag Berlin Heidelberg 2004
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-62323-3
  • Online ISBN 978-3-642-18849-7
  • Series Print ISSN 1431-2654
  • Buy this book on publisher's site
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