{"id":"https://openalex.org/W152126283","doi":null,"title":"A Fast, Practical Algorithm for the Trapezoidation of Simple Polygons.","display_name":"A Fast, Practical Algorithm for the Trapezoidation of Simple Polygons.","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W152126283","mag":"152126283"},"language":"en","primary_location":{"id":"pmh:oai:CiteSeerX.psu:10.1.1.102.1677","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.102.1677","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cis.usouthal.edu/~hain/Bezier/CISST05_Trapezoidation 2.pdf","raw_type":"text"},"volume":null,"type":"article","is_traditional":true,"indexed_in":[],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5108607982","display_name":"Thomas F. Hain","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I83809506","display_name":"University of South Alabama","ror":"https://ror.org/01s7b5y08","country_code":"US","type":"education","lineage":["https://openalex.org/I83809506"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Thomas F. Hain","raw_affiliation_strings":["University of South Alabama"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of South Alabama","institution_ids":["https://openalex.org/I83809506"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5048823978","display_name":"David D. Langan","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I83809506","display_name":"University of South Alabama","ror":"https://ror.org/01s7b5y08","country_code":"US","type":"education","lineage":["https://openalex.org/I83809506"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"David D. Langan","raw_affiliation_strings":["University of South Alabama"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of South Alabama","institution_ids":["https://openalex.org/I83809506"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I83809506"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"98","last_page":"108"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9175000190734863,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9175000190734863,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10481","display_name":"Computer Graphics and Visualization Techniques","score":0.07400000095367432,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12923","display_name":"Digital Image Processing Techniques","score":0.0024999999441206455,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/simple-polygons","display_name":"simple polygons","score":0.984000027179718},{"id":"https://openalex.org/keywords/polygon-decomposition","display_name":"polygon decomposition","score":0.8029999732971191},{"id":"https://openalex.org/keywords/polygon-filling","display_name":"polygon filling","score":0.5220000147819519},{"id":"https://openalex.org/keywords/sweep-line-algorithm","display_name":"sweep line algorithm","score":0.7519999742507935},{"id":"https://openalex.org/keywords/polygons-with-holes","display_name":"polygons with holes","score":0.8500000238418579},{"id":"https://openalex.org/keywords/computational-geometry","display_name":"computational geometry","score":0.6880000233650208}],"concepts":[{"id":"https://openalex.org/C190694206","wikidata":"https://www.wikidata.org/wiki/Q3276654","display_name":"Polygon (computer graphics)","level":3,"score":0.7847802639007568},{"id":"https://openalex.org/C59902600","wikidata":"https://www.wikidata.org/wiki/Q1575331","display_name":"Point in polygon","level":3,"score":0.6825883984565735},{"id":"https://openalex.org/C140745168","wikidata":"https://www.wikidata.org/wiki/Q1210082","display_name":"Tree traversal","level":2,"score":0.6317984461784363},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6232098340988159},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5794543027877808},{"id":"https://openalex.org/C170542616","wikidata":"https://www.wikidata.org/wiki/Q7303186","display_name":"Rectilinear polygon","level":4,"score":0.5416801571846008},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.5346626043319702},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5254627466201782},{"id":"https://openalex.org/C197949415","wikidata":"https://www.wikidata.org/wiki/Q782746","display_name":"Simple polygon","level":3,"score":0.5202299952507019},{"id":"https://openalex.org/C96366933","wikidata":"https://www.wikidata.org/wiki/Q2122886","display_name":"Star-shaped polygon","level":5,"score":0.45673179626464844},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.43058058619499207},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.42225217819213867},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.41663044691085815},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3802219033241272},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.3392016589641571},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1493302881717682},{"id":"https://openalex.org/C126042441","wikidata":"https://www.wikidata.org/wiki/Q1324888","display_name":"Frame (networking)","level":2,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C49870271","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex set","level":4,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:CiteSeerX.psu:10.1.1.102.1677","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.102.1677","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cis.usouthal.edu/~hain/Bezier/CISST05_Trapezoidation 2.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.507.1176","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.507.1176","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.coordinators.cis.usouthal.edu/~hain/general/Publications/CISST%2705_Trapezoidation.pdf","raw_type":"text"},{"id":"mag:152126283","doi":null,"is_oa":false,"landing_page_url":"http://cis.usouthal.edu/~hain/general/Publications/CISST'05_Trapezoidation.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306506334","display_name":"CISST","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":"CISST","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W119195015","https://openalex.org/W1514914425","https://openalex.org/W1561088539","https://openalex.org/W1593563200","https://openalex.org/W1602850305","https://openalex.org/W1971842242","https://openalex.org/W1980682815","https://openalex.org/W1983487792","https://openalex.org/W1989150421","https://openalex.org/W2004389974","https://openalex.org/W2005314985","https://openalex.org/W2009530930","https://openalex.org/W2059894341","https://openalex.org/W2073058919","https://openalex.org/W2088617781","https://openalex.org/W2088864905","https://openalex.org/W2106413026","https://openalex.org/W2129879687","https://openalex.org/W2153980854","https://openalex.org/W2328261313"],"related_works":["https://openalex.org/W2060544749","https://openalex.org/W2003932599","https://openalex.org/W7097520862","https://openalex.org/W3151833110","https://openalex.org/W2016216597","https://openalex.org/W7101023476","https://openalex.org/W7100498827","https://openalex.org/W6922631990","https://openalex.org/W2080902334","https://openalex.org/W3031293739"],"abstract_inverted_index":{"A":[0,60,112],"fast,":[1],"practical,":[2],"deterministic":[3],"algorithm":[4],"for":[5,51,95,106],"the":[6,64],"horizontal":[7,37],"trapezoidation":[8,116],"of":[9,22,54,63,70,117],"simple":[10,118],"polygons":[11,119],"is":[12,16,93],"presented.":[13],"The":[14],"polygon":[15,65],"decomposed":[17],"into":[18],"a":[19,31,35,43,48,52,68],"minimal":[20],"collection":[21,53],"trapezoid":[23],"sequences,":[24],"such":[25],"that":[26],"two":[27],"trapezoids":[28],"adjacent":[29],"within":[30],"se-quence":[32],"always":[33],"share":[34],"common":[36,86],"border.":[38],"Such":[39],"trape-zoid":[40],"sequences":[41],"are":[42,74],"convenient":[44],"data":[45],"structure":[46],"in":[47,77,87],"display":[49],"list":[50],"polygonal":[55],"objects":[56],"to":[57],"be":[58],"filled/rendered.":[59],"linear":[61,94],"traversal":[62],"outline":[66],"identifies":[67],"subset":[69],"critical":[71],"vertices,":[72],"which":[73],"then":[75],"processed":[76],"sweep":[78],"order.":[79],"Horizontal":[80],"as":[81,83],"well":[82],"vertical":[84],"edges\u2014very":[85],"practi-cal":[88],"polygons\u2014are":[89],"handled":[90],"explicitly.":[91],"Complexity":[92],"most":[96],"\u2018practical\u2019":[97],"polygons,":[98],"with":[99,120],"non-linear":[100],"running":[101],"times":[102],"being":[103],"required":[104],"only":[105],"much":[107],"less":[108],"frequently":[109],"occurring":[110],"geometries.":[111],"straightforward":[113],"extension":[114],"allows":[115],"holes.":[121]},"counts_by_year":[],"updated_date":"2026-09-29T14:09:16.559479","created_date":"2016-06-24T00:00:00"}