Order types and cross-sections of line arrangements in R^3

Abstract

We consider sets L = {l1,...., ln} of n labeled lines in general position in R3, and study the order types of point sets fp1; : : : ; png that stem from the intersections of the lines in L with (directed) planes II, not parallel to any line of L, i.e., the proper cross-sections of L. As a main result we show that the number of different order types that can be obtained as cross-sections of L is O(n9), and that this bound is tight.

Peer Reviewed

Postprint (published version)