The complexity of cutting convex polytypes

Abstract

Throughout this paper, we use the term subdivision as a shorthand for “a subdivision of E2 into convex regions”. A subdivision is said to be of size n if it is made of n convex (open) regions, and it is of degree d if every region is adjacent to at most d other regions. We define the line span of a subdivision as the maximum number of regions which can be intersected by a single line (section 3).