On-Line Zone Construction in Arrangements of Lines in the Plane

Given a finite set L of lines in the plane we wish to compute the zone of an additional curve γ in the arrangement A(L), namely the set of faces of the planar subdivision induced by the lines in L that are crossed by γ, where γ is not given in advance but rather provided online portion by portion. T...

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Hauptverfasser:	Aharoni, Yuval, Halperin, Dan, Hanniel, Iddo, Har-Peled, Sariel, Linhart, Chaim
Format:	Buchkapitel
Sprache:	eng
Schlagworte:	Algorithmics. Computability. Computer arithmetics Applied sciences Binary Search Tree Computer science control theory systems Convex Hull Exact sciences and technology Input Line Recursion Tree Single Face Theoretical computing
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creator	Aharoni, Yuval Halperin, Dan Hanniel, Iddo Har-Peled, Sariel Linhart, Chaim
description	Given a finite set L of lines in the plane we wish to compute the zone of an additional curve γ in the arrangement A(L), namely the set of faces of the planar subdivision induced by the lines in L that are crossed by γ, where γ is not given in advance but rather provided online portion by portion. This problem is motivated by the computation of the area bisectors of a polygonal set in the plane. We present four algorithms which solve this problem efficiently and exactly (giving precise results even on degenerate input). We implemented the four algorithms. We present implementation details, comparison of performance, and a discussion of the advantages and shortcomings of each of the proposed algorithms.
doi_str_mv	10.1007/3-540-48318-7_13
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This problem is motivated by the computation of the area bisectors of a polygonal set in the plane. We present four algorithms which solve this problem efficiently and exactly (giving precise results even on degenerate input). We implemented the four algorithms. We present implementation details, comparison of performance, and a discussion of the advantages and shortcomings of each of the proposed algorithms.</description><identifier>ISSN: 0302-9743</identifier><identifier>ISBN: 3540664270</identifier><identifier>ISBN: 9783540664277</identifier><identifier>EISSN: 1611-3349</identifier><identifier>EISBN: 3540483187</identifier><identifier>EISBN: 9783540483182</identifier><identifier>DOI: 10.1007/3-540-48318-7_13</identifier><identifier>OCLC: 958522717</identifier><identifier>LCCallNum: QA76.6-76.66QA75.5-</identifier><language>eng</language><publisher>Germany: Springer Berlin / Heidelberg</publisher><subject>Algorithmics. Computability. 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Computer arithmetics</subject><subject>Applied sciences</subject><subject>Binary Search Tree</subject><subject>Computer science; control theory; systems</subject><subject>Convex Hull</subject><subject>Exact sciences and technology</subject><subject>Input Line</subject><subject>Recursion Tree</subject><subject>Single Face</subject><subject>Theoretical computing</subject><issn>0302-9743</issn><issn>1611-3349</issn><isbn>3540664270</isbn><isbn>9783540664277</isbn><isbn>3540483187</isbn><isbn>9783540483182</isbn><fulltext>true</fulltext><rsrctype>book_chapter</rsrctype><creationdate>1999</creationdate><recordtype>book_chapter</recordtype><recordid>eNotkLtPwzAQxs1ThNKdMQOri-_OidMJVRUvqVIZYGGxHMehgTYpdjrw3-O09XCW7rvHdz_GbkFMQAh1TzyTgsuCoOBKA52wa4qZfUKdsgRyAE4kp2cHIc8lKnHOEkEC-VRJumTJNCsyRAXqio1D-BbxEQLkImEPy5Yvmtaln10M864Nvd_ZvunatGnTmfem_XIb1_Yh7ep0qAyD0K9c-rY2rbthF7VZBzc-_iP28fT4Pn_hi-Xz63y24FvMVc8L6UDVGZqqqE2F0XBVW1lbwEw65bAoM4fWurLEqTTRaiVIZqhqFOQsCBqxu8PcrQnWrOvoyzZBb32zMf5PQ4EKI5QRmxzKQlSic6_LrvsJGoQecGrSkZHe09MDzthAx7m--9250Gs3dNh4sTdruzLb3vmgSShEoLhHg1T0D0vMcYc</recordid><startdate>1999</startdate><enddate>1999</enddate><creator>Aharoni, Yuval</creator><creator>Halperin, Dan</creator><creator>Hanniel, Iddo</creator><creator>Har-Peled, Sariel</creator><creator>Linhart, Chaim</creator><general>Springer Berlin / Heidelberg</general><general>Springer Berlin Heidelberg</general><general>Springer</general><scope>FFUUA</scope><scope>IQODW</scope></search><sort><creationdate>1999</creationdate><title>On-Line Zone Construction in Arrangements of Lines in the Plane</title><author>Aharoni, Yuval ; Halperin, Dan ; Hanniel, Iddo ; Har-Peled, Sariel ; Linhart, Chaim</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-p267t-84e17f52ad8fad2334dfc4fc1254e7e28b5e2ccebb294a271d034527f203ec103</frbrgroupid><rsrctype>book_chapters</rsrctype><prefilter>book_chapters</prefilter><language>eng</language><creationdate>1999</creationdate><topic>Algorithmics. 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Computer arithmetics</topic><topic>Applied sciences</topic><topic>Binary Search Tree</topic><topic>Computer science; control theory; systems</topic><topic>Convex Hull</topic><topic>Exact sciences and technology</topic><topic>Input Line</topic><topic>Recursion Tree</topic><topic>Single Face</topic><topic>Theoretical computing</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Aharoni, Yuval</creatorcontrib><creatorcontrib>Halperin, Dan</creatorcontrib><creatorcontrib>Hanniel, Iddo</creatorcontrib><creatorcontrib>Har-Peled, Sariel</creatorcontrib><creatorcontrib>Linhart, Chaim</creatorcontrib><collection>ProQuest Ebook Central - Book Chapters - Demo use only</collection><collection>Pascal-Francis</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Aharoni, Yuval</au><au>Halperin, Dan</au><au>Hanniel, Iddo</au><au>Har-Peled, Sariel</au><au>Linhart, Chaim</au><au>Carbonell, Jaime G</au><au>Siekmann, Jörg</au><au>Goos, Gerhard</au><au>Zaroliagis, Christos D.</au><au>Vitter, Jeffrey S.</au><format>book</format><genre>bookitem</genre><ristype>CHAP</ristype><atitle>On-Line Zone Construction in Arrangements of Lines in the Plane</atitle><btitle>Algorithm Engineering</btitle><seriestitle>Lecture Notes in Computer Science</seriestitle><date>1999</date><risdate>1999</risdate><spage>139</spage><epage>153</epage><pages>139-153</pages><issn>0302-9743</issn><eissn>1611-3349</eissn><isbn>3540664270</isbn><isbn>9783540664277</isbn><eisbn>3540483187</eisbn><eisbn>9783540483182</eisbn><abstract>Given a finite set L of lines in the plane we wish to compute the zone of an additional curve γ in the arrangement A(L), namely the set of faces of the planar subdivision induced by the lines in L that are crossed by γ, where γ is not given in advance but rather provided online portion by portion. 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source	Springer Books
subjects	Algorithmics. Computability. Computer arithmetics Applied sciences Binary Search Tree Computer science control theory systems Convex Hull Exact sciences and technology Input Line Recursion Tree Single Face Theoretical computing
title	On-Line Zone Construction in Arrangements of Lines in the Plane
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