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...

Full description

Saved in:

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
Tags:	Add Tag No Tags, Be the first to tag this record!

Abstract	•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.
AbstractList	•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. 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. (ProQuest: ... denotes formulae/symbols omitted.)
Author	Lu, Daniel L.
Author_xml	– sequence: 1 givenname: Daniel L. orcidid: 0000-0003-4724-6836 surname: Lu fullname: Lu, Daniel L. email: dllu@cmu.edu organization: Carnegie Mellon University, Robotics Institute, 5000 Forbes Ave, Pittsburgh, PA 15213, United States
BookMark	eNp9kD1PwzAQhi1UJNrCD2CLxJxw5yR2IiZU8SVVggFmK3XO4Ci1g50W9d-TqsxMt7zP3XvPgs2cd8TYNUKGgOK2y-zQZxywzEBmAMUZm2MleSoQ6xmbA3BIAWu4YIsYOwAQRS7njL_1jWtC0vsfCgm5PfV-oMSbZOudH6cjyeD7w6d3TZ_or8a6eMnOTdNHuvqbS_bx-PC-ek7Xr08vq_t1qrmUY6pBGBAlUE26FlQ2okKd69aUWBgjeL0p-YbnGmVhSsISW160iFJMP-iK6nzJbk57h-C_dxRH1fldmHpEhRIkVELyYwpPKR18jIGMGoLdNuGgENRRjerUpEYd1SiQalIzMXcnhqb6e0tBRW3JaWptID2q1tt_6F9AlWxe
CODEN	IFPLAT
Cites_doi	10.1016/j.jpdc.2006.12.006 10.1137/S0097539791221505 10.1016/S0925-7721(01)00070-0 10.1016/0196-6774(81)90019-5 10.1007/BF01937271 10.1007/s00454-001-0089-9 10.1007/BF02712873 10.1016/j.comgeo.2007.02.005 10.1016/0020-0190(89)90136-1 10.1142/S0218195998000047
ContentType	Journal Article
Copyright	2015 Elsevier B.V. Copyright Elsevier Sequoia S.A. Dec 2015
Copyright_xml	– notice: 2015 Elsevier B.V. – notice: Copyright Elsevier Sequoia S.A. Dec 2015
DBID	AAYXX CITATION 7SC 8FD JQ2 L7M L~C L~D
DOI	10.1016/j.ipl.2015.07.004
DatabaseName	CrossRef Computer and Information Systems Abstracts Technology Research Database ProQuest Computer Science Collection Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional
DatabaseTitle	CrossRef Computer and Information Systems Abstracts Technology Research Database Computer and Information Systems Abstracts – Academic Advanced Technologies Database with Aerospace ProQuest Computer Science Collection Computer and Information Systems Abstracts Professional
DatabaseTitleList	Computer and Information Systems Abstracts
DeliveryMethod	fulltext_linktorsrc
Discipline	Computer Science
EISSN	1872-6119
EndPage	964
ExternalDocumentID	3788291501 10_1016_j_ipl_2015_07_004 S0020019015001179
Genre	Feature
GroupedDBID	--K --M -~X .DC .~1 0R~ 1B1 1RT 1~. 1~5 29I 4.4 457 4G. 5GY 5VS 7-5 71M 8P~ 9JN AACTN AAEDT AAEDW AAIAV AAIKJ AAKOC AALRI AAOAW AAQFI AAQXK AAXUO AAYFN ABBOA ABEFU ABFNM ABFSI ABJNI ABMAC ABTAH ABXDB ABYKQ ACDAQ ACGFS ACNNM ACRLP ACZNC ADBBV ADEZE ADJOM ADMUD AEBSH AEKER AENEX AFKWA AFTJW AGHFR AGUBO AGYEJ AHHHB AHZHX AIALX AIEXJ AIKHN AITUG AJBFU AJOXV ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ AOUOD ASPBG AVWKF AXJTR AZFZN BKOJK BKOMP BLXMC CS3 DU5 E.L EBS EFJIC EFLBG EJD EO8 EO9 EP2 EP3 F5P FDB FEDTE FGOYB FIRID FNPLU FYGXN G-2 G-Q G8K GBLVA GBOLZ HLZ HMJ HVGLF HZ~ IHE J1W KOM LG9 M26 M41 MO0 MS~ O-L O9- OAUVE OZT P-8 P-9 P2P PC. PQQKQ Q38 R2- RIG ROL RPZ SBC SDF SDG SDP SES SEW SME SPC SPCBC SSV SSZ T5K TN5 UQL WH7 WUQ XPP ZMT ZY4 ~G- 9DU AATTM AAXKI AAYWO AAYXX ABDPE ABWVN ACLOT ACRPL ACVFH ADCNI ADNMO AEIPS AEUPX AFJKZ AFPUW AGQPQ AIGII AIIUN AKBMS AKRWK AKYEP ANKPU APXCP CITATION EFKBS ~HD 7SC 8FD JQ2 L7M L~C L~D
ID	FETCH-LOGICAL-c277t-c06f0650e9ec96e5a681c3cdf514ff629b52b23c174f5e151d24d1176015c8e93
ISICitedReferencesCount	0
ISICitedReferencesURI	http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000361402400010&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN	0020-0190
IngestDate	Sun Nov 30 04:10:24 EST 2025 Sat Nov 29 03:44:21 EST 2025 Fri Feb 23 02:16:28 EST 2024
IsPeerReviewed	true
IsScholarly	true
Issue	12
Keywords	Computational geometry Output-sensitive algorithms Upper envelope Lower envelope
Language	English
LinkModel	OpenURL
MergedId	FETCHMERGED-LOGICAL-c277t-c06f0650e9ec96e5a681c3cdf514ff629b52b23c174f5e151d24d1176015c8e93
Notes	SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14
ORCID	0000-0003-4724-6836
PQID	1707086729
PQPubID	45522
PageCount	3
ParticipantIDs	proquest_journals_1707086729 crossref_primary_10_1016_j_ipl_2015_07_004 elsevier_sciencedirect_doi_10_1016_j_ipl_2015_07_004
PublicationCentury	2000
PublicationDate	2015-12-01
PublicationDateYYYYMMDD	2015-12-01
PublicationDate_xml	– month: 12 year: 2015 text: 2015-12-01 day: 01
PublicationDecade	2010
PublicationPlace	Amsterdam
PublicationPlace_xml	– name: Amsterdam
PublicationTitle	Information processing letters
PublicationYear	2015
Publisher	Elsevier B.V Elsevier Sequoia S.A
Publisher_xml	– name: Elsevier B.V – name: Elsevier Sequoia S.A
References	Chan (br0010) 1996; 16 El Gindy, Avis (br0070) 1981; 2 Gupta, Chopra (br0040) 2007; 67 Hershberger (br0020) 1989; 33 Joe, Simpson (br0080) 1987; 27 Knoll (br0140) 2014 Bose, Lubiw, Munro (br0100) 2002; 23 Suri, O'Rourke (br0060) 1986 Nielsen, Yvinec (br0030) 1998; 8 Aronov (br0110) 2002; 27 Asano (br0050) 1985; 68 Zarei, Ghodsi (br0120) 2008; 39 Wein (br0150) 2015 Bungiu, Hemmer, Hershberger, Huang, Kröller (br0130) 2014 Heffernan, SB Mitchell (br0090) 1995; 24 Gupta (10.1016/j.ipl.2015.07.004_br0040) 2007; 67 Zarei (10.1016/j.ipl.2015.07.004_br0120) 2008; 39 El Gindy (10.1016/j.ipl.2015.07.004_br0070) 1981; 2 Heffernan (10.1016/j.ipl.2015.07.004_br0090) 1995; 24 Joe (10.1016/j.ipl.2015.07.004_br0080) 1987; 27 Aronov (10.1016/j.ipl.2015.07.004_br0110) 2002; 27 Bose (10.1016/j.ipl.2015.07.004_br0100) 2002; 23 Knoll (10.1016/j.ipl.2015.07.004_br0140) Suri (10.1016/j.ipl.2015.07.004_br0060) 1986 Bungiu (10.1016/j.ipl.2015.07.004_br0130) 2014 Nielsen (10.1016/j.ipl.2015.07.004_br0030) 1998; 8 Asano (10.1016/j.ipl.2015.07.004_br0050) 1985; 68 Hershberger (10.1016/j.ipl.2015.07.004_br0020) 1989; 33 Wein (10.1016/j.ipl.2015.07.004_br0150) 2015 Chan (10.1016/j.ipl.2015.07.004_br0010) 1996; 16
References_xml	– volume: 27 start-page: 461 year: 2002 end-page: 483 ident: br0110 article-title: Visibility queries and maintenance in simple polygons publication-title: Discrete Comput. Geom. – volume: 24 start-page: 184 year: 1995 end-page: 201 ident: br0090 article-title: An optimal algorithm for computing visibility in the plane publication-title: SIAM J. Comput. – year: 2014 ident: br0140 – year: 2014 ident: br0130 article-title: Efficient computation of visibility polygons publication-title: European Workshop on Computational Geometry – volume: 23 start-page: 313 year: 2002 end-page: 335 ident: br0100 article-title: Efficient visibility queries in simple polygons publication-title: Comput. Geom. – volume: 27 start-page: 458 year: 1987 end-page: 473 ident: br0080 article-title: Corrections to Lee's visibility polygon algorithm publication-title: BIT Numer. Math. – year: 1986 ident: br0060 article-title: Worst-case optimal algorithms for constructing visibility polygons with holes publication-title: Proceedings of the Second Annual Symposion on Computational Geometry – volume: 67 start-page: 772 year: 2007 end-page: 782 ident: br0040 article-title: Output-sensitive algorithms for optimally constructing the upper envelope of straight line segments in parallel publication-title: J. Parallel Distrib. Comput. – volume: 2 start-page: 186 year: 1981 end-page: 197 ident: br0070 article-title: A linear algorithm for computing the visibility polygon from a point publication-title: J. Algorithms – volume: 8 start-page: 39 year: 1998 end-page: 65 ident: br0030 article-title: An output-sensitive convex hull algorithm for planar objects publication-title: Int. J. Comput. Geom. Appl. – year: 2015 ident: br0150 article-title: 2D envelopes publication-title: CGAL User and Reference Manual – volume: 16 start-page: 361 year: 1996 end-page: 368 ident: br0010 article-title: Optimal output-sensitive convex hull algorithms in two and three dimensions publication-title: Discrete Comput. Geom. – volume: 39 start-page: 78 year: 2008 end-page: 90 ident: br0120 article-title: Query point visibility computation in polygons with holes publication-title: Comput. Geom. – volume: 68 start-page: 557 year: 1985 end-page: 559 ident: br0050 article-title: An efficient algorithm for finding the visibility polygon for a polygonal region with holes publication-title: IEICE Trans. (1976–1990) – volume: 33 start-page: 169 year: 1989 end-page: 174 ident: br0020 article-title: Finding the lower envelope of publication-title: Inf. Process. Lett. – volume: 67 start-page: 772 issue: 7 year: 2007 ident: 10.1016/j.ipl.2015.07.004_br0040 article-title: Output-sensitive algorithms for optimally constructing the upper envelope of straight line segments in parallel publication-title: J. Parallel Distrib. Comput. doi: 10.1016/j.jpdc.2006.12.006 – volume: 24 start-page: 184 issue: 1 year: 1995 ident: 10.1016/j.ipl.2015.07.004_br0090 article-title: An optimal algorithm for computing visibility in the plane publication-title: SIAM J. Comput. doi: 10.1137/S0097539791221505 – volume: 68 start-page: 557 issue: 9 year: 1985 ident: 10.1016/j.ipl.2015.07.004_br0050 article-title: An efficient algorithm for finding the visibility polygon for a polygonal region with holes publication-title: IEICE Trans. (1976–1990) – volume: 23 start-page: 313 issue: 3 year: 2002 ident: 10.1016/j.ipl.2015.07.004_br0100 article-title: Efficient visibility queries in simple polygons publication-title: Comput. Geom. doi: 10.1016/S0925-7721(01)00070-0 – volume: 2 start-page: 186 issue: 2 year: 1981 ident: 10.1016/j.ipl.2015.07.004_br0070 article-title: A linear algorithm for computing the visibility polygon from a point publication-title: J. Algorithms doi: 10.1016/0196-6774(81)90019-5 – volume: 27 start-page: 458 issue: 4 year: 1987 ident: 10.1016/j.ipl.2015.07.004_br0080 article-title: Corrections to Lee's visibility polygon algorithm publication-title: BIT Numer. Math. doi: 10.1007/BF01937271 – volume: 27 start-page: 461 issue: 4 year: 2002 ident: 10.1016/j.ipl.2015.07.004_br0110 article-title: Visibility queries and maintenance in simple polygons publication-title: Discrete Comput. Geom. doi: 10.1007/s00454-001-0089-9 – volume: 16 start-page: 361 issue: 4 year: 1996 ident: 10.1016/j.ipl.2015.07.004_br0010 article-title: Optimal output-sensitive convex hull algorithms in two and three dimensions publication-title: Discrete Comput. Geom. doi: 10.1007/BF02712873 – volume: 39 start-page: 78 issue: 2 year: 2008 ident: 10.1016/j.ipl.2015.07.004_br0120 article-title: Query point visibility computation in polygons with holes publication-title: Comput. Geom. doi: 10.1016/j.comgeo.2007.02.005 – volume: 33 start-page: 169 issue: 4 year: 1989 ident: 10.1016/j.ipl.2015.07.004_br0020 article-title: Finding the lower envelope of n line segments in O(nlog⁡n) time publication-title: Inf. Process. Lett. doi: 10.1016/0020-0190(89)90136-1 – ident: 10.1016/j.ipl.2015.07.004_br0140 – volume: 8 start-page: 39 issue: 01 year: 1998 ident: 10.1016/j.ipl.2015.07.004_br0030 article-title: An output-sensitive convex hull algorithm for planar objects publication-title: Int. J. Comput. Geom. Appl. doi: 10.1142/S0218195998000047 – year: 1986 ident: 10.1016/j.ipl.2015.07.004_br0060 article-title: Worst-case optimal algorithms for constructing visibility polygons with holes – year: 2015 ident: 10.1016/j.ipl.2015.07.004_br0150 article-title: 2D envelopes – year: 2014 ident: 10.1016/j.ipl.2015.07.004_br0130 article-title: Efficient computation of visibility polygons
SSID	ssj0006437
Score	2.0705094
Snippet	•An algorithm to find the lower envelope of monotone polygonal chains is proposed.•Simpler than known methods and requires no complex data structures.•Applies... 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...
SourceID	proquest crossref elsevier
SourceType	Aggregation Database Index Database Publisher
StartPage	962
SubjectTerms	Algorithms Computational geometry Computer science Lower envelope Output Output-sensitive algorithms Polygons Studies Upper envelope
Title	Planar lower envelope of monotone polygonal chains
URI	https://dx.doi.org/10.1016/j.ipl.2015.07.004 https://www.proquest.com/docview/1707086729
Volume	115
WOSCitedRecordID	wos000361402400010&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText	1
inHoldings	1
isFullTextHit
isPrint
journalDatabaseRights	– providerCode: PRVESC databaseName: Elsevier SD Freedom Collection Journals 2021 customDbUrl: eissn: 1872-6119 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0006437 issn: 0020-0190 databaseCode: AIEXJ dateStart: 19950113 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier
link	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1Lb9NAEF5ByoELUB6iUCofEAciR_H6sbvHCKWiKApITVFuK3sfNFGVuHmg8u-Z8e66bRAVPXCxLFtJnJnP89qZ_Qh5b0S_0Lk2cdlXJkYO65gbw2OWW_S_Jq0a6oTvIzYe8-lUfPN0qeuGToAtFvzqStT_VdVwDZSNo7P3UHf7pXABzkHpcAS1w_GfFI80ROWqe4H0ZzjHhj1BTWEAnmCJW28jMcOvH00FUJ2XM1-um4eW9nacsVu7IQIsJlw0Uz9t_D3aXo-n-7kFXzlI8p0ujHak5dRcbpezsnvaG9w0lRQ71hyXZ88468gZhVzT27hgPt04ZsAJvWENhTO0f1hpVzCY92Y1Lv4kebN9qmMhvr0j9virPD4bjeRkOJ3cvus8MOTvVEBIm3yoL2NkEsMVd0-r8pDsUZYL3iF7g5Ph9Evrn3Gp0jX-uD8Y1rqbrr-dR_pbtLLjt5tgZPKMPPFZRDRw2t8nD8ziOXkaGDoib7BfEOrAEDVgiAIYoqWNAhiiFgyRA8NLcnY8nHz6HHuWjFhRxjax6hcW42wjjBKFycuCJypV2kIobG1BRZXTiqYKUk-bGwjwNM10kmAvVK64Eekr0lnA770mkTWK8TStSmZUpgteVVlacqO1EMyWVh-Qj0EasnabocjQJTiXIDqJopN9bGnIDkgW5CV9NOeiNAkwuOtjh0G20r9Va5kw8Ey8gETwzd2335LH10g_JJ3NamvekUfq52a2Xh15JPwG7NpxRQ
linkProvider	Elsevier
openUrl	ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Planar+lower+envelope+of+monotone+polygonal+chains&rft.jtitle=Information+processing+letters&rft.au=Lu%2C+Daniel+L&rft.date=2015-12-01&rft.pub=Elsevier+Sequoia+S.A&rft.issn=0020-0190&rft.eissn=1872-6119&rft.volume=115&rft.issue=12&rft.spage=962&rft_id=info:doi/10.1016%2Fj.ipl.2015.07.004&rft.externalDBID=NO_FULL_TEXT&rft.externalDocID=3788291501
thumbnail_l	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0020-0190&client=summon
thumbnail_m	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0020-0190&client=summon
thumbnail_s	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0020-0190&client=summon