  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.
