Planar lower envelope of monotone polygonal chains

A simple linear search algorithm running in O(n + ink) 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 n arbitrary line segments in optimal O(n logk) 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. (C) 2015 Elsevier B.V. All rights reserved.