We show that for line l in space, there are at most k(k + 1) tangent planes through l to the k-level of an arrangement of concave surfaces. This is a generalization of Lovasz's lemma, which is a key constituent in the analysis of the complexity of k-level of planes. Our proof is constructive, and finds a family of concave surfaces covering the 'laminated at-most-k level'. As consequences, (1): we have an O((n-k)2/3n2) upper bound for the complexity of the k-level of n triangles of space, and (2): we can extend the k-set result in space to the k-set of a system of subsets of n points.
|Number of pages||10|
|Journal||Annual Symposium on Foundations of Computer Science - Proceedings|
|Publication status||Published - 1999 Dec 1|
|Event||Proceedings of the 1999 IEEE 40th Annual Conference on Foundations of Computer Science - New York, NY, USA|
Duration: 1999 Oct 17 → 1999 Oct 19
ASJC Scopus subject areas
- Hardware and Architecture