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arXiv · 1412.6619

Planar lower envelope of monotone polygonal chains

Daniel Lu
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Abstract

A simple linear search algorithm running in $O(n+mk)$ time is proposed for constructing the lower envelope of $k$ vertices from $m$ monotone polygonal chains in 2D with $n$ vertices in total. This can be applied to output-sensitive construction of lower envelopes for arbitrary line segments in optimal $O(n\log k)$ time, where $k$ is the output size. Compared to existing output-sensitive algorithms for lower envelopes, this is simpler to implement, does not require complex data structures, and is a constant factor faster.

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Daniel Lu. 2014-12-20. Planar lower envelope of monotone polygonal chains. https://arxiv.org/abs/1412.6619

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