Planar lower envelope of monotone polygonal chains

•An algorithm to find the lower envelope of monotone polygonal chains is proposed.•Simpler than known methods and requires no complex data structures.•Applies to output-sensitive construction of line segment lower envelope. A simple linear search algorithm running in O(n+mk) time is proposed for con...

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Bibliographic Details
Published in:Information processing letters Vol. 115; no. 12; pp. 962 - 964
Main Author: Lu, Daniel L.
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 01.12.2015
Elsevier Sequoia S.A
Subjects:
Algorithms
Computational geometry
Computer science
Lower envelope
Output
Output-sensitive algorithms
Polygons
Studies
Upper envelope
Computational geometry
Output-sensitive algorithms
Upper envelope
Lower envelope
ISSN:0020-0190, 1872-6119
Online Access:Get full text
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Summary:•An algorithm to find the lower envelope of monotone polygonal chains is proposed.•Simpler than known methods and requires no complex data structures.•Applies to output-sensitive construction of line segment lower envelope. 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 n arbitrary line segments in optimal O(nlog⁡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.
Bibliography:SourceType-Scholarly Journals-1
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content type line 14
ISSN:0020-0190
1872-6119
DOI:10.1016/j.ipl.2015.07.004