{"id":"https://openalex.org/W2025751015","doi":"https://doi.org/10.1080/00207160701361191","title":"A new five-point approximating subdivision scheme","display_name":"A new five-point approximating subdivision scheme","publication_year":2007,"publication_date":"2007-12-31","ids":{"openalex":"https://openalex.org/W2025751015","doi":"https://doi.org/10.1080/00207160701361191","mag":"2025751015"},"language":"en","primary_location":{"id":"doi:10.1080/00207160701361191","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160701361191","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","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/A5088565067","display_name":"Shahid S. Siddiqi","orcid":"https://orcid.org/0000-0002-9860-7227"},"institutions":[{"id":"https://openalex.org/I172780181","display_name":"University of the Punjab","ror":"https://ror.org/011maz450","country_code":"PK","type":"education","lineage":["https://openalex.org/I172780181"]}],"countries":["PK"],"is_corresponding":true,"raw_author_name":"Shahid S. Siddiqi","raw_affiliation_strings":["Department of Mathematics , Punjab University , Lahore, 54590, Pakistan","Department of Mathematics, Punjab University, Lahore, Pakistan#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Punjab University , Lahore, 54590, Pakistan","institution_ids":["https://openalex.org/I172780181"]},{"raw_affiliation_string":"Department of Mathematics, Punjab University, Lahore, Pakistan#TAB#","institution_ids":["https://openalex.org/I172780181"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103898562","display_name":"Nadeem Ahmad","orcid":null},"institutions":[{"id":"https://openalex.org/I172780181","display_name":"University of the Punjab","ror":"https://ror.org/011maz450","country_code":"PK","type":"education","lineage":["https://openalex.org/I172780181"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Nadeem Ahmad","raw_affiliation_strings":["Department of Mathematics , Punjab University , Lahore, 54590, Pakistan","Department of Mathematics, Punjab University, Lahore, Pakistan#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Punjab University , Lahore, 54590, Pakistan","institution_ids":["https://openalex.org/I172780181"]},{"raw_affiliation_string":"Department of Mathematics, Punjab University, Lahore, Pakistan#TAB#","institution_ids":["https://openalex.org/I172780181"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5088565067"],"corresponding_institution_ids":["https://openalex.org/I172780181"],"apc_list":null,"apc_paid":null,"fwci":2.0883,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.85555808,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"85","issue":"1","first_page":"65","last_page":"72"},"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":0.9573000073432922,"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/T12549","display_name":"Image and Object Detection Techniques","score":0.9204000234603882,"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/subdivision","display_name":"Subdivision","score":0.8734455704689026},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8509750962257385},{"id":"https://openalex.org/keywords/laurent-polynomial","display_name":"Laurent polynomial","score":0.77875155210495},{"id":"https://openalex.org/keywords/smoothness","display_name":"Smoothness","score":0.760405421257019},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.6925997734069824},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.5364822149276733},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.5203934907913208},{"id":"https://openalex.org/keywords/exponent","display_name":"Exponent","score":0.5160548090934753},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4562453329563141},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.45607995986938477},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.448202908039093},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3982965052127838},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3526773452758789},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3444746732711792},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.20744246244430542},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10722190141677856}],"concepts":[{"id":"https://openalex.org/C143392562","wikidata":"https://www.wikidata.org/wiki/Q449111","display_name":"Subdivision","level":2,"score":0.8734455704689026},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8509750962257385},{"id":"https://openalex.org/C106639798","wikidata":"https://www.wikidata.org/wiki/Q1701125","display_name":"Laurent polynomial","level":2,"score":0.77875155210495},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.760405421257019},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.6925997734069824},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.5364822149276733},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.5203934907913208},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.5160548090934753},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4562453329563141},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.45607995986938477},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.448202908039093},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3982965052127838},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3526773452758789},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3444746732711792},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.20744246244430542},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10722190141677856},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207160701361191","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160701361191","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W1528659070","https://openalex.org/W1549654778","https://openalex.org/W1559554065","https://openalex.org/W1993590372","https://openalex.org/W2062050869","https://openalex.org/W2067862350","https://openalex.org/W2072595795","https://openalex.org/W2075492994","https://openalex.org/W2095665834","https://openalex.org/W2145055982","https://openalex.org/W2497330812","https://openalex.org/W2574495911","https://openalex.org/W3177018370","https://openalex.org/W4247219141","https://openalex.org/W4251619700"],"related_works":["https://openalex.org/W2977953627","https://openalex.org/W3121604372","https://openalex.org/W2169500396","https://openalex.org/W2076215172","https://openalex.org/W2145055982","https://openalex.org/W2362485998","https://openalex.org/W1996070913","https://openalex.org/W1970957032","https://openalex.org/W2424269979","https://openalex.org/W4319227715"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"a":[3,40],"new":[4,36,57],"five-point":[5,37],"approximating":[6,23],"subdivision":[7,24],"scheme":[8,25,38,64,71],"is":[9,17,49,65,72],"presented,":[10],"generating":[11],"the":[12,18,21,35,53,56,63,70,75],"C":[13],"4":[14],"curves,":[15],"which":[16],"extension":[19],"of":[20,34,55,69],"four-point":[22],"developed":[26],"by":[27],"Siddiqi":[28],"and":[29],"Ahmad.":[30],"The":[31,45,59,67],"limit":[32],"function":[33],"has":[39],"support":[41],"on":[42],"[\u22125,":[43],"4].":[44],"Laurent":[46],"polynomial":[47],"method":[48],"used":[50],"to":[51],"analyse":[52],"smoothness":[54],"scheme.":[58],"H\u00f6lder":[60],"exponent":[61],"for":[62],"calculated.":[66],"usefulness":[68],"illustrated":[73],"in":[74],"examples.":[76]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
