#### Date of Original Version

1996

#### Type

Conference Proceeding

#### Abstract or Description

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

#### Published In

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