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Approximating the k-Level in Three-Dimensional Plane Arrangements
[article]
2016
arXiv
pre-print
]#1(#2) Let H be a set of n planes in three dimensions, and let r ≤ n be a parameter. We give a simple alternative proof of the existence of a (1/r)-cutting of the first n/r levels of (H), which consists of O(r) semi-unbounded vertical triangular prisms. The same construction yields an approximation of the (n/r)-level by a terrain consisting of O(r/^3) triangular faces, which lies entirely between the levels (1±)n/r. The proof does not use sampling, and exploits techniques based on planar
arXiv:1601.04755v2
fatcat:ueg4qasfbrbi5n4vh5ruztdtma