## Three-dimensional restricted-orientation convexity

### Eugene Fink and Derick Wood

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

### Abstract

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:

- The intersection of a convex set with every
line is empty or connected
- The intersection of a collection of convex sets is a convex set
- For every two points of a convex set, the straight segment
joining them is contained in the set
- Convex sets are contractable