TY - JOUR
T1 - The shortest watchtower and related problems for polyhedral terrains
AU - Sharir, Micha
N1 - Funding Information:
* Work on this paper has been supported by Office of Naval Research Grant N00014-82-K-0381, by National Science Foundation Grant No. NSF-DCR-83-20085, by grants from the Digital Equipment Corporation, and the IBM Corpora-tion, and by a research grant from the NCRD-the Israeli National Council for Research and Development.
PY - 1988/11/24
Y1 - 1988/11/24
N2 - We present an O(n log2 n) algorithm for finding the shortest vertical segment ('watchtower') uv that has to be erected on a polyhedral terrain S with n faces, so that its top endpoint can see the entire terrain S. An extension of our technique yields an O(n log2 n + k) time algorithm for calculating the lower envelope of two polyhedral terrains, one of which is convex, where k is combinatorial complexity of the output envelope.
AB - We present an O(n log2 n) algorithm for finding the shortest vertical segment ('watchtower') uv that has to be erected on a polyhedral terrain S with n faces, so that its top endpoint can see the entire terrain S. An extension of our technique yields an O(n log2 n + k) time algorithm for calculating the lower envelope of two polyhedral terrains, one of which is convex, where k is combinatorial complexity of the output envelope.
UR - http://www.scopus.com/inward/record.url?scp=0024105524&partnerID=8YFLogxK
U2 - 10.1016/0020-0190(88)90120-2
DO - 10.1016/0020-0190(88)90120-2
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AN - SCOPUS:0024105524
VL - 29
SP - 265
EP - 270
JO - Information Processing Letters
JF - Information Processing Letters
SN - 0020-0190
IS - 5
ER -