{"id":"https://openalex.org/W2134698875","doi":"https://doi.org/10.1145/1236246.1236282","title":"An exact, complete and efficient computation of arrangements of B\u00e9zier curves","display_name":"An exact, complete and efficient computation of arrangements of B\u00e9zier curves","publication_year":2007,"publication_date":"2007-06-04","ids":{"openalex":"https://openalex.org/W2134698875","doi":"https://doi.org/10.1145/1236246.1236282","mag":"2134698875"},"language":"en","primary_location":{"id":"doi:10.1145/1236246.1236282","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1236246.1236282","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2007 ACM symposium on Solid and physical modeling","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"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/A5086542744","display_name":"Iddo Hanniel","orcid":"https://orcid.org/0000-0001-9429-7973"},"institutions":[{"id":"https://openalex.org/I174306211","display_name":"Technion \u2013 Israel Institute of Technology","ror":"https://ror.org/03qryx823","country_code":"IL","type":"education","lineage":["https://openalex.org/I174306211"]}],"countries":["IL"],"is_corresponding":true,"raw_author_name":"Iddo Hanniel","raw_affiliation_strings":["Israel Institute of Technology"],"affiliations":[{"raw_affiliation_string":"Israel Institute of Technology","institution_ids":["https://openalex.org/I174306211"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080668466","display_name":"Ron Wein","orcid":null},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Ron Wein","raw_affiliation_strings":["Tel-Aviv University, Israel"],"affiliations":[{"raw_affiliation_string":"Tel-Aviv University, Israel","institution_ids":["https://openalex.org/I16391192"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5086542744"],"corresponding_institution_ids":["https://openalex.org/I174306211"],"apc_list":null,"apc_paid":null,"fwci":2.5059,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.88880599,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":null,"issue":null,"first_page":"253","last_page":"263"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9987000226974487,"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":0.9943000078201294,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/b\u00e9zier-curve","display_name":"B\u00e9zier curve","score":0.8451446294784546},{"id":"https://openalex.org/keywords/degenerate-energy-levels","display_name":"Degenerate energy levels","score":0.8171080350875854},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6678205728530884},{"id":"https://openalex.org/keywords/construct","display_name":"Construct (python library)","score":0.6297321319580078},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5857325792312622},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.5163022875785828},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4569225311279297},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.44204816222190857},{"id":"https://openalex.org/keywords/exact-solutions-in-general-relativity","display_name":"Exact solutions in general relativity","score":0.42341822385787964},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.39009207487106323},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3365230858325958},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.32259225845336914},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.20087546110153198},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.15961778163909912}],"concepts":[{"id":"https://openalex.org/C206423108","wikidata":"https://www.wikidata.org/wiki/Q214728","display_name":"B\u00e9zier curve","level":2,"score":0.8451446294784546},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.8171080350875854},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6678205728530884},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.6297321319580078},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5857325792312622},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.5163022875785828},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4569225311279297},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.44204816222190857},{"id":"https://openalex.org/C520416788","wikidata":"https://www.wikidata.org/wiki/Q5419229","display_name":"Exact solutions in general relativity","level":2,"score":0.42341822385787964},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.39009207487106323},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3365230858325958},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.32259225845336914},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.20087546110153198},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15961778163909912},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/1236246.1236282","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1236246.1236282","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2007 ACM symposium on Solid and physical modeling","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.5099999904632568,"id":"https://metadata.un.org/sdg/10"},{"display_name":"Peace, Justice and strong institutions","score":0.5,"id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W166438205","https://openalex.org/W1481724961","https://openalex.org/W1501243125","https://openalex.org/W1512389895","https://openalex.org/W1518385457","https://openalex.org/W1544695794","https://openalex.org/W1573473130","https://openalex.org/W1578641439","https://openalex.org/W1598339794","https://openalex.org/W1868080791","https://openalex.org/W1967603179","https://openalex.org/W1973180078","https://openalex.org/W1977248580","https://openalex.org/W1978491945","https://openalex.org/W1984926837","https://openalex.org/W1998338093","https://openalex.org/W2005314985","https://openalex.org/W2012369998","https://openalex.org/W2076643072","https://openalex.org/W2082910094","https://openalex.org/W2086644813","https://openalex.org/W2124925673","https://openalex.org/W2140258961","https://openalex.org/W2148036799","https://openalex.org/W2155865801","https://openalex.org/W2156153879","https://openalex.org/W2156616818","https://openalex.org/W2609774945","https://openalex.org/W2911302472","https://openalex.org/W4206817075","https://openalex.org/W4210777595"],"related_works":["https://openalex.org/W2366107444","https://openalex.org/W4388145910","https://openalex.org/W2381570729","https://openalex.org/W1976205134","https://openalex.org/W4248336175","https://openalex.org/W2353039109","https://openalex.org/W2031260042","https://openalex.org/W2955288804","https://openalex.org/W2145068446","https://openalex.org/W3151330330"],"abstract_inverted_index":{"Arrangements":[0],"of":[1,13,20,23,30,69,98,105,109,147,160,163],"planar":[2],"curves":[3,32,71,111,162],"are":[4,64,119],"fundamental":[5],"structures":[6],"in":[7,46,53,128,171],"computational":[8],"geometry.":[9],"The":[10,75],"arrangement":[11],"package":[12],"CGAL":[14],"can":[15,157],"construct":[16,158],"and":[17,33,61,79,126,139,166],"maintain":[18],"arrangements":[19,68,159],"various":[21],"families":[22],"curves,":[24],"when":[25],"provided":[26],"with":[27],"the":[28,31,42,59,89,106,137,145,152],"representation":[29],"some":[34],"basic":[35],"geometric":[36,107],"functionality":[37],"on":[38],"them.":[39],"It":[40],"employs":[41],"exact":[43,73,99],"computation":[44],"paradigm":[45],"order":[47,86],"to":[48,87,136],"handle":[49,167],"all":[50,82,168],"degenerate":[51,83,129,169],"cases":[52,132,170],"a":[54,115,172],"robust":[55,173],"manner.":[56,174],"We":[57],"present":[58],"representations":[60],"algorithms":[62],"that":[63,156],"needed":[65],"for":[66,112],"implementing":[67],"Bezier":[70,110,161],"using":[72,122],"arithmetic.":[74],"implementation":[76,155],"is":[77,151],"efficient":[78],"complete,":[80],"handling":[81],"cases.":[84],"In":[85],"avoid":[88],"prohibitive":[90],"running":[91],"times":[92],"incurred":[93],"by":[94],"an":[95],"indiscriminate":[96],"usage":[97],"arithmetic,":[100],"we":[101,134],"make":[102],"extensive":[103],"use":[104],"properties":[108],"filtering.":[113],"As":[114],"result,":[116],"most":[117],"operations":[118],"carried":[120],"out":[121],"fast":[123],"approximate":[124],"methods,":[125],"only":[127],"(or":[130],"near-degenerate)":[131],"do":[133],"resort":[135],"exact,":[138],"more":[140],"computationally":[141],"demanding,":[142],"procedures.":[143],"To":[144],"best":[146],"our":[148],"knowledge":[149],"this":[150],"first":[153],"complete":[154],"any":[164],"degree,":[165]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}