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http://hdl.handle.net/1783.1/81
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| Title: | Generalizing halfspaces |
| Authors: | Fink, Eugene
Wood, Derick |
| Issue Date: | Jun-1996 |
| Series/Report no.: | Computer Science Technical Report ; HKUST-CS96-27 |
| Abstract: | Restricted-orientation convexity is the study of geometric objects whose intersection with lines from some fixed set is empty or connected. We have studied the properties of restricted-orientation convex sets and demonstrated that this notion is a generalization of standard convexity. We now describe a restricted-orientation generalization of halfspaces and explore properties of these generalized halfspaces. In particular, we establish analogs of the following properties of standard halfspaces: the intersection of a halfspace with every line is empty, a ray, or a line; every halfspace is convex; a closed set with nonempty interior and convex boundary is a halfspace; the closure of the complement of a halfspace is a halfspace. |
| URI: | http://hdl.handle.net/1783.1/81 |
| Appears in Collections: | CSE Technical Reports
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Size | Format |
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| tr9627.pdf | | 98Kb | Adobe PDF | View/Open |
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