Three-dimensional restricted-orientation convexity

Eugene Fink and Derick Wood

In Proceedings of the Eighth Canadian Conference on Computational Geometry, pages 258-263, 1996.


A restricted-orientation convex set is a set of points whose intersection with lines from some fixed set is empty or connected. This notion generalizes both standard convexity and orthogonal convexity. We explore basic properties of restricted-orientation convex sets in three dimensions. In particular, we establish analogs of the following properties of standard convex sets: