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

Planar lower envelope of monotone polygonal chains