Restricted-orientation convexity
著者
書誌事項
Restricted-orientation convexity
（Monographs in theoretical computer science : an EATCS series）
Springer, c2004
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注記
Includes bibliographical references (p. 93-96) and index
内容説明・目次
内容説明
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. The authors explore the properties of this generalized convexity in multidimensional Euclidean space, and describ restricted-orientation analogs of lines, hyperplanes, flats, halfspaces, and identify major properties of standard convex sets that also hold for restricted-orientation convexity. They 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 that of standard convexity.
目次
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.
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