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http://hdl.handle.net/1783.1/56
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| Title: | Fundamentals of restricted-orientation convexity |
| Authors: | Fink, Eugene
Wood, Derick |
| Issue Date: | Sep-1995 |
| Series/Report no.: | Computer Science Technical Report ; HKUST-CS95-46 |
| Abstract: | A restricted-orientation convex set, also called an O-convex set, is a set of points whose intersection with lines from some fixed set is empty or connected. The notion of O-convexity generalizes standard convexity and orthogonal convexity.
We explore some of the basic properties of O-convex sets in two and higher dimensions. We also study O-connected sets, which are restricted O-convex sets with several special properties. We introduce and investigate restricted-orientation analogs of lines, flats, and hyperplanes, and characterize O-convex and O-connected sets in terms of their intersections with hyperplanes. We then explore properties of O-connected curves; in particular, we show when replacing a segment of an O-connected curve with a new curvilinear segment yields an O-connected curve and when the catenation of several curvilinear segments forms an O-connected segment. We use these results to characterize an O-connected set in terms of O-connected segments that join pairs of its points, which are wholly contained in the set.
We also identify some of the major properties of standard convex sets that hold for O-convexity. |
| URI: | http://hdl.handle.net/1783.1/56 |
| Appears in Collections: | CSE Technical Reports
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Files in This Item:
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Size | Format |
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| tr9546.pdf | | 284Kb | Adobe PDF | View/Open |
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