{"id":"https://openalex.org/W2054255883","doi":"https://doi.org/10.1142/s0219467805001859","title":"SCCI-HYBRID METHODS FOR 2D CURVE TRACING","display_name":"SCCI-HYBRID METHODS FOR 2D CURVE TRACING","publication_year":2005,"publication_date":"2005-07-01","ids":{"openalex":"https://openalex.org/W2054255883","doi":"https://doi.org/10.1142/s0219467805001859","mag":"2054255883"},"language":"en","primary_location":{"id":"doi:10.1142/s0219467805001859","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219467805001859","pdf_url":null,"source":{"id":"https://openalex.org/S60080701","display_name":"International Journal of Image and Graphics","issn_l":"0219-4678","issn":["0219-4678","1793-6756"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Image and Graphics","raw_type":"journal-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/A5041512150","display_name":"H. Ratschek","orcid":null},"institutions":[{"id":"https://openalex.org/I44260953","display_name":"Heinrich Heine University D\u00fcsseldorf","ror":"https://ror.org/024z2rq82","country_code":"DE","type":"education","lineage":["https://openalex.org/I44260953"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"HELMUT RATSCHEK","raw_affiliation_strings":["Department of Mathematics, Universit\u00e4t D\u00fcsseldorf, Universit\u00e4tstrasse 1, D\u00fcsseldorf, Germany 40225, Germany"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Universit\u00e4t D\u00fcsseldorf, Universit\u00e4tstrasse 1, D\u00fcsseldorf, Germany 40225, Germany","institution_ids":["https://openalex.org/I44260953"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5020310155","display_name":"Jon Rokne","orcid":"https://orcid.org/0000-0002-3439-2917"},"institutions":[{"id":"https://openalex.org/I168635309","display_name":"University of Calgary","ror":"https://ror.org/03yjb2x39","country_code":"CA","type":"education","lineage":["https://openalex.org/I168635309"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"JON ROKNE","raw_affiliation_strings":["Department of Computer Science, University of Calgary, 2500 University Dr. N.W. Calgary, Alberta, Canada T2N-1N4, Canada","Department of Computer Science, University of Calgary, 2500 University Dr. N.W., Calgary, Alberta, Canada, T2N-1N4, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Calgary, 2500 University Dr. N.W. Calgary, Alberta, Canada T2N-1N4, Canada","institution_ids":["https://openalex.org/I168635309"]},{"raw_affiliation_string":"Department of Computer Science, University of Calgary, 2500 University Dr. N.W., Calgary, Alberta, Canada, T2N-1N4, Canada","institution_ids":["https://openalex.org/I168635309"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5041512150"],"corresponding_institution_ids":["https://openalex.org/I44260953"],"apc_list":null,"apc_paid":null,"fwci":2.0626,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.8577951,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"05","issue":"03","first_page":"447","last_page":"479"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9997000098228455,"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":0.9997000098228455,"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9916999936103821,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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":0.9904000163078308,"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/continuation","display_name":"Continuation","score":0.6100728511810303},{"id":"https://openalex.org/keywords/iterated-function","display_name":"Iterated function","score":0.5507085919380188},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5372751951217651},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5161515474319458},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.5089671611785889},{"id":"https://openalex.org/keywords/interval-arithmetic","display_name":"Interval arithmetic","score":0.4921373724937439},{"id":"https://openalex.org/keywords/curve-fitting","display_name":"Curve fitting","score":0.47722652554512024},{"id":"https://openalex.org/keywords/jacobian-curve","display_name":"Jacobian curve","score":0.46721139550209045},{"id":"https://openalex.org/keywords/tripling-oriented-doche\u2013icart\u2013kohel-curve","display_name":"Tripling-oriented Doche\u2013Icart\u2013Kohel curve","score":0.4544738233089447},{"id":"https://openalex.org/keywords/subdivision","display_name":"Subdivision","score":0.45286744832992554},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4412083625793457},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.43762892484664917},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4116184711456299},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.38292717933654785},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.344757080078125},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.30765634775161743},{"id":"https://openalex.org/keywords/elliptic-curve","display_name":"Elliptic curve","score":0.25738829374313354},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.10659545660018921},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.10143321752548218}],"concepts":[{"id":"https://openalex.org/C88626702","wikidata":"https://www.wikidata.org/wiki/Q1128903","display_name":"Continuation","level":2,"score":0.6100728511810303},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.5507085919380188},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5372751951217651},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5161515474319458},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.5089671611785889},{"id":"https://openalex.org/C191252586","wikidata":"https://www.wikidata.org/wiki/Q1671453","display_name":"Interval arithmetic","level":3,"score":0.4921373724937439},{"id":"https://openalex.org/C184389593","wikidata":"https://www.wikidata.org/wiki/Q603159","display_name":"Curve fitting","level":2,"score":0.47722652554512024},{"id":"https://openalex.org/C79993320","wikidata":"https://www.wikidata.org/wiki/Q6119657","display_name":"Jacobian curve","level":5,"score":0.46721139550209045},{"id":"https://openalex.org/C37055786","wikidata":"https://www.wikidata.org/wiki/Q7843607","display_name":"Tripling-oriented Doche\u2013Icart\u2013Kohel curve","level":5,"score":0.4544738233089447},{"id":"https://openalex.org/C143392562","wikidata":"https://www.wikidata.org/wiki/Q449111","display_name":"Subdivision","level":2,"score":0.45286744832992554},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4412083625793457},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43762892484664917},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4116184711456299},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.38292717933654785},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.344757080078125},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.30765634775161743},{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.25738829374313354},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.10659545660018921},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.10143321752548218},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C95457728","wikidata":"https://www.wikidata.org/wiki/Q309","display_name":"History","level":0,"score":0.0},{"id":"https://openalex.org/C121444067","wikidata":"https://www.wikidata.org/wiki/Q2835817","display_name":"Schoof's algorithm","level":4,"score":0.0},{"id":"https://openalex.org/C166957645","wikidata":"https://www.wikidata.org/wiki/Q23498","display_name":"Archaeology","level":1,"score":0.0},{"id":"https://openalex.org/C197875053","wikidata":"https://www.wikidata.org/wiki/Q7269266","display_name":"Quarter period","level":3,"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0219467805001859","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219467805001859","pdf_url":null,"source":{"id":"https://openalex.org/S60080701","display_name":"International Journal of Image and Graphics","issn_l":"0219-4678","issn":["0219-4678","1793-6756"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Image and Graphics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","score":0.550000011920929,"id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W2720226","https://openalex.org/W6921346","https://openalex.org/W166122990","https://openalex.org/W1491528139","https://openalex.org/W1578845863","https://openalex.org/W1580809199","https://openalex.org/W1583979427","https://openalex.org/W1799814471","https://openalex.org/W1964673636","https://openalex.org/W1971425543","https://openalex.org/W1974585479","https://openalex.org/W2020492229","https://openalex.org/W2042066463","https://openalex.org/W2055945485","https://openalex.org/W2060924166","https://openalex.org/W2067953152","https://openalex.org/W2074068518","https://openalex.org/W2084613724","https://openalex.org/W2088986191","https://openalex.org/W2089858126","https://openalex.org/W2101766358","https://openalex.org/W2121752747","https://openalex.org/W2131141154","https://openalex.org/W2132060642","https://openalex.org/W2162082792","https://openalex.org/W2169964384","https://openalex.org/W2186590998","https://openalex.org/W2272795305","https://openalex.org/W2318205745","https://openalex.org/W3006026342","https://openalex.org/W4206360718","https://openalex.org/W4248437491","https://openalex.org/W4249516290"],"related_works":["https://openalex.org/W161946993","https://openalex.org/W2361216787","https://openalex.org/W2136048868","https://openalex.org/W198981881","https://openalex.org/W2776044206","https://openalex.org/W107847107","https://openalex.org/W1480864336","https://openalex.org/W2079208522","https://openalex.org/W2096667971","https://openalex.org/W2054255883"],"abstract_inverted_index":{"A":[0],"hybrid":[1],"method":[2,20,70,121,217],"for":[3,131],"plotting":[4,221],"2-dimensional":[5],"curves,":[6],"defined":[7],"implicitly":[8],"by":[9,154],"equations":[10],"of":[11,28,118,126,135,181,188,198,204,222,241],"the":[12,83,102,113,119,123,127,133,136,139,164,171,182,186,195,199,202,215,220,223,239,242,246,255],"form":[13],"f(x,y)":[14],"=":[15],"0":[16],"is":[17,21,71,80,104,122,149,249],"presented.":[18],"The":[19,39,68,116,191,228],"extremely":[22],"robust":[23],"and":[24,26,34,201],"reliable":[25],"consists":[27],"Space":[29],"Covering":[30],"techniques,":[31],"Continuation":[32],"principles":[33],"Interval":[35],"analysis":[36],"(i.e.":[37],"SCCI).":[38],"space":[40],"covering,":[41],"based":[42],"on":[43],"iterated":[44],"subdivision,":[45],"guarantees":[46],"that":[47,82,101,163,238],"no":[48],"curve":[49,53,172,183,224,244,248],"branches":[50],"or":[51,55,184,218],"isolated":[52],"parts":[54],"even":[56,185],"points":[57],"are":[58,66],"lost":[59],"(which":[60],"can":[61,166,230],"happen":[62],"if":[63],"grid":[64],"methods":[65],"used).":[67],"continuation":[69,216],"initiated":[72],"in":[73,157,173,225,234],"a":[74,91,144,174,236],"subarea":[75,84,92,175,200],"as":[76,78,106,108,177,250,252],"soon":[77],"it":[79,148,156],"proven":[81],"contains":[85],"only":[86],"one":[87],"smooth":[88],"curve.":[89],"Such":[90],"does":[93],"not":[94],"need":[95],"to":[96,112,214],"be":[97,231],"subdivided":[98],"further":[99,206],"so":[100],"computation":[103],"accelerated":[105],"far":[107],"possible":[109],"with":[110,151],"respect":[111],"subdivision":[114],"process.":[115],"novelty":[117],"SCCI-hybrid":[120],"intense":[124],"use":[125],"implicit":[128,140],"function":[129,141],"theorem":[130,142,165],"controlling":[132],"steps":[134],"method.":[137],"Although":[138],"has":[143],"rather":[145],"local":[146],"nature,":[147],"empowered":[150],"global":[152,168],"properties":[153],"evaluating":[155],"an":[158],"interval":[159],"environment.":[160],"This":[161],"means":[162],"provide":[167],"information":[169,192],"about":[170],"such":[176,235],"existence,":[178],"non-existence,":[179],"uniqueness":[180],"presence":[187],"singular":[189],"points.":[190],"gained":[193],"allows":[194],"above-mentioned":[196],"control":[197],"decision":[203],"its":[205],"processing,":[207],"i.e.":[208],"deleting":[209],"it,":[210,212],"subdividing":[211],"switching":[213],"preparing":[219],"this":[226],"subarea.":[227],"curves":[229],"processed":[232],"mathematically":[233],"manner,":[237],"derivation":[240],"plotted":[243],"from":[245],"exact":[247],"small":[251],"desired":[253],"(modulo":[254],"screen":[256],"resolution).":[257]},"counts_by_year":[{"year":2020,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}