[{"abstract":[{"text":"For H a set of lines in the Euclidean plane, $A(H)$ denotes the induced dissection, called the arrangement of H. We define the notion of a belt in $A(H)$, which is bounded by a subset of the edges in $A(H)$, and describe two algorithms for constructing belts. All this is motivated by applications to a host of seemingly unrelated problems including a type of range search and finding the minimum area triangle with the vertices taken from some finite set of points.","lang":"eng"}],"publication_status":"published","publication":"SIAM Journal on Computing","title":"Constructing belts in two-dimensional arrangements with applications","_id":"4110","year":"1986","citation":{"chicago":"Edelsbrunner, Herbert, and Emo Welzl. “Constructing Belts in Two-Dimensional Arrangements with Applications.” <i>SIAM Journal on Computing</i>. SIAM, 1986. <a href=\"https://doi.org/10.1137/0215019\">https://doi.org/10.1137/0215019</a>.","short":"H. Edelsbrunner, E. Welzl, SIAM Journal on Computing 15 (1986) 271–284.","ista":"Edelsbrunner H, Welzl E. 1986. Constructing belts in two-dimensional arrangements with applications. SIAM Journal on Computing. 15(1), 271–284.","ama":"Edelsbrunner H, Welzl E. Constructing belts in two-dimensional arrangements with applications. <i>SIAM Journal on Computing</i>. 1986;15(1):271-284. doi:<a href=\"https://doi.org/10.1137/0215019\">10.1137/0215019</a>","ieee":"H. Edelsbrunner and E. Welzl, “Constructing belts in two-dimensional arrangements with applications,” <i>SIAM Journal on Computing</i>, vol. 15, no. 1. SIAM, pp. 271–284, 1986.","apa":"Edelsbrunner, H., &#38; Welzl, E. (1986). Constructing belts in two-dimensional arrangements with applications. <i>SIAM Journal on Computing</i>. SIAM. <a href=\"https://doi.org/10.1137/0215019\">https://doi.org/10.1137/0215019</a>","mla":"Edelsbrunner, Herbert, and Emo Welzl. “Constructing Belts in Two-Dimensional Arrangements with Applications.” <i>SIAM Journal on Computing</i>, vol. 15, no. 1, SIAM, 1986, pp. 271–84, doi:<a href=\"https://doi.org/10.1137/0215019\">10.1137/0215019</a>."},"author":[{"first_name":"Herbert","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Emo","last_name":"Welzl","full_name":"Welzl, Emo"}],"extern":"1","quality_controlled":"1","month":"01","date_created":"2018-12-11T12:07:00Z","status":"public","intvolume":"        15","publist_id":"2014","article_type":"original","publisher":"SIAM","volume":15,"issue":"1","doi":"10.1137/0215019","language":[{"iso":"eng"}],"oa_version":"None","date_updated":"2022-02-01T09:34:20Z","type":"journal_article","day":"01","article_processing_charge":"No","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","scopus_import":"1","publication_identifier":{"issn":["0097-5397"],"eissn":["1095-7111"]},"date_published":"1986-01-01T00:00:00Z","page":"271 - 284"}]