胖三角形确定线性多孔(计算几何)

[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science Pub Date : 1991-09-01 DOI:10.1109/SFCS.1991.185347

J. Matoušek, Nathaly Miller, J. Pach, M. Sharir, Shmuel Sifrony, E. Welzl

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引用次数: 15

摘要

证明了对于≥0的每一个固定的delta，如果F是n个三角形的并集，且所有三角形的角都至少为delta，则F的补有O(n)个连通分量，且F的边界由O(n log log n)个线段组成。如果所有三角形的大小大致相同，或者它们都是无限的楔形，那么后一种复杂性就会变成线性的。给出了在期望时间O(n2/sup alpha (n)/ log n)内计算F的随机化算法。介绍了这些结果的几个应用。

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Fat triangles determine linearly many holes (computational geometry)

It is shown that for every fixed delta >0 the following holds: if F is a union of n triangles, all of whose angles are at least delta , then the complement of F has O(n) connected components, and the boundary of F consists of O(n log log n) segments. This latter complexity becomes linear if all triangles are of roughly the same size or if they are all infinite wedges. A randomized algorithm that computes F in expected time O(n2/sup alpha (n)/ log n) is given. Several applications of these results are presented.<>

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[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science

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