volume 27, issue 4, P567-584 2002
DOI: 10.1007/s00454-001-0086-z
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Abstract: Abstract. We show that for any 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 Lovász's lemma, which is a key constituent in the analysis of the complexity of k-levels of planes. Our proof is constructive, and finds a family of concave surfaces covering the "laminated at-most-k-level." As a consequence, (1) we have an O((n −k) 2/3 n 2 ) upper bound for the complexity of the k-level of n triangles of space, a…

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