Generalizing Halfspaces

Date of Original Version



Conference Proceeding

Abstract or Description

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

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Published In

Proceedings of the Eighth Canadian Conference on Computational Geometry, 211-216.