The complexity of cutting convex polytypes

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).

[1]  R. Connelly,et al.  A convex 3-complex not simplicially isomorphic to a strictly convex complex , 1980, Mathematical Proceedings of the Cambridge Philosophical Society.

[2]  Leonidas J. Guibas,et al.  On translating a set of rectangles , 1980, STOC '80.

[3]  Leonidas J. Guibas,et al.  Topologically sweeping an arrangement , 1986, STOC '86.