In Proceedings of the Vision Geometry V Conference, pages 24-33, 1996.
Restricted-orientation convexity, also called O-convexity, is the study of geometric objects whose intersection with lines from some fixed set is empty or connected. We introduce restricted-orientation halfspaces, which are an O-convexity analog of halfspaces, explore their properties, and demonstrate their relationship to restricted-orientation convex sets.
Note that, in our other papers on restricted orientation convexity we ue the term "directed O-halfspaces" to refer to the analog of halfspaces described in this paper and reserve the term "O-halfspaces" for a weaker analog. We present the properties of the weaker analog in another conference paper, called "Generalizng Halfspaces."