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...

Full description

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
Table of Contents:
  • 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