{"id":"https://openalex.org/W3025463558","doi":"https://doi.org/10.3390/math8050806","title":"Shape-Preserving Properties of a Relaxed Four-Point Interpolating Subdivision Scheme","display_name":"Shape-Preserving Properties of a Relaxed Four-Point Interpolating Subdivision Scheme","publication_year":2020,"publication_date":"2020-05-15","ids":{"openalex":"https://openalex.org/W3025463558","doi":"https://doi.org/10.3390/math8050806","mag":"3025463558"},"language":"en","primary_location":{"id":"doi:10.3390/math8050806","doi":"https://doi.org/10.3390/math8050806","is_oa":true,"landing_page_url":"https://doi.org/10.3390/math8050806","pdf_url":"https://www.mdpi.com/2227-7390/8/5/806/pdf?version=1590570109","source":{"id":"https://openalex.org/S4210192031","display_name":"Mathematics","issn_l":"2227-7390","issn":["2227-7390"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","poland-20","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2227-7390/8/5/806/pdf?version=1590570109","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5086494253","display_name":"Pakeeza Ashraf","orcid":"https://orcid.org/0009-0006-6121-4530","observed_orcids":["https://orcid.org/0009-0006-6121-4530","https://orcid.org/0009-0004-9649-8356"]},"institutions":[{"id":"https://openalex.org/I2800060998","display_name":"Government Sadiq College Women University","ror":"https://ror.org/01zp49f50","country_code":"PK","type":"education","lineage":["https://openalex.org/I2800060998"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Pakeeza Ashraf","raw_affiliation_strings":["Department of Mathematics, Government Sadiq College Women University, Bahawalpur 63100, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Government Sadiq College Women University, Bahawalpur 63100, Pakistan","institution_ids":["https://openalex.org/I2800060998"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5002330510","display_name":"Abdul Ghaffar","orcid":"https://orcid.org/0000-0002-5994-8440","observed_orcids":["https://orcid.org/0000-0002-5994-8440"]},"institutions":[{"id":"https://openalex.org/I141445968","display_name":"Ton Duc Thang University","ror":"https://ror.org/01drq0835","country_code":"VN","type":"education","lineage":["https://openalex.org/I141445968"]}],"countries":["VN"],"is_corresponding":true,"raw_author_name":"Abdul Ghaffar","raw_affiliation_strings":["Faculty of Mathematics & Statistics, Ton Duc Thang University, Ho Chi Minh City 700000, Vietnam","Informetrics Research Group, Ton Duc Thang University, Ho Chi Minh City 700000, Vietnam"],"raw_orcid":"https://orcid.org/0000-0002-5994-8440","affiliations":[{"raw_affiliation_string":"Faculty of Mathematics & Statistics, Ton Duc Thang University, Ho Chi Minh City 700000, Vietnam","institution_ids":["https://openalex.org/I141445968"]},{"raw_affiliation_string":"Informetrics Research Group, Ton Duc Thang University, Ho Chi Minh City 700000, Vietnam","institution_ids":["https://openalex.org/I141445968"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030756029","display_name":"Dumitru B\u01celeanu","orcid":"https://orcid.org/0000-0002-0286-7244","observed_orcids":["https://orcid.org/0000-0002-0286-7244"]},"institutions":[{"id":"https://openalex.org/I106245021","display_name":"\u00c7ankaya University","ror":"https://ror.org/056wqre19","country_code":"TR","type":"education","lineage":["https://openalex.org/I106245021"]},{"id":"https://openalex.org/I184693016","display_name":"China Medical University","ror":"https://ror.org/00v408z34","country_code":"TW","type":"education","lineage":["https://openalex.org/I184693016"]},{"id":"https://openalex.org/I4210126829","display_name":"China Medical University Hospital","ror":"https://ror.org/0368s4g32","country_code":"TW","type":"healthcare","lineage":["https://openalex.org/I4210126829"]},{"id":"https://openalex.org/I4210142834","display_name":"Institute of Space Science - INFLPR Subsidiary","ror":"https://ror.org/054a6wv56","country_code":"RO","type":"facility","lineage":["https://openalex.org/I4210142834"]}],"countries":["RO","TR","TW"],"is_corresponding":false,"raw_author_name":"Dumitru Baleanu","raw_affiliation_strings":["Department of Mathematics, Cankaya University, Ankara 06530, Turkey","Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40447, Taiwan","Institute of Space Sciences, 077125 Magurele-Bucharest, Romania"],"raw_orcid":"https://orcid.org/0000-0002-0286-7244","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Cankaya University, Ankara 06530, Turkey","institution_ids":["https://openalex.org/I106245021"]},{"raw_affiliation_string":"Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40447, Taiwan","institution_ids":["https://openalex.org/I184693016","https://openalex.org/I4210126829"]},{"raw_affiliation_string":"Institute of Space Sciences, 077125 Magurele-Bucharest, Romania","institution_ids":["https://openalex.org/I4210142834"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085729219","display_name":"Irem Sehar","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I2800060998","display_name":"Government Sadiq College Women University","ror":"https://ror.org/01zp49f50","country_code":"PK","type":"education","lineage":["https://openalex.org/I2800060998"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Irem Sehar","raw_affiliation_strings":["Department of Mathematics, Government Sadiq College Women University, Bahawalpur 63100, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Government Sadiq College Women University, Bahawalpur 63100, Pakistan","institution_ids":["https://openalex.org/I2800060998"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057525661","display_name":"Kottakkaran Sooppy Nisar","orcid":"https://orcid.org/0000-0001-5769-4320","observed_orcids":["https://orcid.org/0000-0001-5769-4320"]},"institutions":[{"id":"https://openalex.org/I142608572","display_name":"Prince Sattam Bin Abdulaziz University","ror":"https://ror.org/04jt46d36","country_code":"SA","type":"education","lineage":["https://openalex.org/I142608572"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Kottakkaran Sooppy Nisar","raw_affiliation_strings":["Department of Mathematics, College of Arts and Sciences, Prince Sattam bin Abdulaziz University, Wadi Aldawaser 11991, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0001-5769-4320","affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Arts and Sciences, Prince Sattam bin Abdulaziz University, Wadi Aldawaser 11991, Saudi Arabia","institution_ids":["https://openalex.org/I142608572"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5070644190","display_name":"Faheem Khan","orcid":"https://orcid.org/0000-0003-1520-4690","observed_orcids":["https://orcid.org/0000-0003-1520-4690"]},"institutions":[{"id":"https://openalex.org/I160968435","display_name":"University of Sargodha","ror":"https://ror.org/0086rpr26","country_code":"PK","type":"education","lineage":["https://openalex.org/I160968435"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Faheem Khan","raw_affiliation_strings":["Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan"],"raw_orcid":"https://orcid.org/0000-0003-1520-4690","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan","institution_ids":["https://openalex.org/I160968435"]}]}],"institutions":[],"countries_distinct_count":6,"institutions_distinct_count":8,"corresponding_author_ids":["https://openalex.org/A5002330510"],"corresponding_institution_ids":["https://openalex.org/I141445968"],"apc_list":{"value":1200,"currency":"CHF","value_usd":1267},"apc_paid":{"value":1200,"currency":"CHF","value_usd":1267},"fwci":1.8533,"has_fulltext":true,"cited_by_count":16,"citation_normalized_percentile":{"value":0.83121933,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":98},"biblio":{"volume":"8","issue":"5","first_page":"806","last_page":"806"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9765999913215637,"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":0.9765999913215637,"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/T10481","display_name":"Computer Graphics and Visualization Techniques","score":0.004600000102072954,"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/T11191","display_name":"Mathematical functions and polynomials","score":0.0015999999595806003,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/positivity-preservation","display_name":"positivity preservation","score":0.7390000224113464},{"id":"https://openalex.org/keywords/monotonicity-preservation","display_name":"monotonicity preservation","score":0.9980000257492065},{"id":"https://openalex.org/keywords/convexity-preservation","display_name":"convexity preservation","score":0.9980000257492065},{"id":"https://openalex.org/keywords/limit-curves","display_name":"limit curves","score":0.8539999723434448}],"concepts":[{"id":"https://openalex.org/C143392562","wikidata":"https://www.wikidata.org/wiki/Q449111","display_name":"Subdivision","level":2,"score":0.8815656304359436},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.7354800701141357},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6928396821022034},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.6521475315093994},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.628801703453064},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.5962033271789551},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.5837218165397644},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.5393803715705872},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.5356305241584778},{"id":"https://openalex.org/C2777774050","wikidata":"https://www.wikidata.org/wiki/Q16945110","display_name":"Control point","level":2,"score":0.43917226791381836},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.41585299372673035},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4023382067680359},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.29206281900405884},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2777237296104431},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","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/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/math8050806","doi":"https://doi.org/10.3390/math8050806","is_oa":true,"landing_page_url":"https://doi.org/10.3390/math8050806","pdf_url":"https://www.mdpi.com/2227-7390/8/5/806/pdf?version=1590570109","source":{"id":"https://openalex.org/S4210192031","display_name":"Mathematics","issn_l":"2227-7390","issn":["2227-7390"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","poland-20","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:gam:jmathe:v:8:y:2020:i:5:p:806-:d:358511","doi":null,"is_oa":false,"landing_page_url":"https://www.mdpi.com/2227-7390/8/5/806/","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:af3b6af1270340a1984df0a3351050e2","doi":null,"is_oa":true,"landing_page_url":"https://doaj.org/article/af3b6af1270340a1984df0a3351050e2","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematics, Vol 8, Iss 5, p 806 (2020)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/math8050806","doi":"https://doi.org/10.3390/math8050806","is_oa":true,"landing_page_url":"https://doi.org/10.3390/math8050806","pdf_url":"https://www.mdpi.com/2227-7390/8/5/806/pdf?version=1590570109","source":{"id":"https://openalex.org/S4210192031","display_name":"Mathematics","issn_l":"2227-7390","issn":["2227-7390"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","poland-20","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[{"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11","score":0.4300000071525574}],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3025463558.pdf","grobid_xml":"https://content.openalex.org/works/W3025463558.grobid-xml"},"referenced_works_count":49,"referenced_works":["https://openalex.org/W1120718222","https://openalex.org/W1487289360","https://openalex.org/W1634224793","https://openalex.org/W1694682050","https://openalex.org/W1966243783","https://openalex.org/W1966682087","https://openalex.org/W1977379706","https://openalex.org/W1981310747","https://openalex.org/W2007699265","https://openalex.org/W2016922204","https://openalex.org/W2042273967","https://openalex.org/W2053280883","https://openalex.org/W2069412310","https://openalex.org/W2075036897","https://openalex.org/W2075492994","https://openalex.org/W2076482979","https://openalex.org/W2079749345","https://openalex.org/W2082130323","https://openalex.org/W2088769886","https://openalex.org/W2103185748","https://openalex.org/W2107391127","https://openalex.org/W2145764645","https://openalex.org/W2185411830","https://openalex.org/W2315031206","https://openalex.org/W2497330812","https://openalex.org/W2574495911","https://openalex.org/W2580894462","https://openalex.org/W2591149474","https://openalex.org/W2801210321","https://openalex.org/W2897717647","https://openalex.org/W2914441772","https://openalex.org/W2947279299","https://openalex.org/W2960226364","https://openalex.org/W2964543562","https://openalex.org/W2965163579","https://openalex.org/W2982075141","https://openalex.org/W2983665052","https://openalex.org/W2996867574","https://openalex.org/W2997408205","https://openalex.org/W3001648607","https://openalex.org/W3004204919","https://openalex.org/W3010380101","https://openalex.org/W3015071820","https://openalex.org/W4229549719","https://openalex.org/W4249705453","https://openalex.org/W4285719527","https://openalex.org/W6636652791","https://openalex.org/W6672928282","https://openalex.org/W6831791465"],"related_works":["https://openalex.org/W4389849086","https://openalex.org/W4281957576","https://openalex.org/W2164621095","https://openalex.org/W1545461878","https://openalex.org/W2952133296","https://openalex.org/W3130449832","https://openalex.org/W3120050151","https://openalex.org/W2096962213","https://openalex.org/W4254682493","https://openalex.org/W2379609688"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"analyze":[4],"shape-preserving":[5,16,37,55],"behavior":[6],"of":[7,36,54,57],"a":[8],"relaxed":[9,59],"four-point":[10,42],"binary":[11],"interpolating":[12],"subdivision":[13],"scheme.":[14,43,60],"These":[15],"properties":[17,56],"include":[18],"positivity-preserving,":[19],"monotonicity-preserving":[20],"and":[21],"convexity-preserving.":[22],"We":[23],"establish":[24],"the":[25,28,34,41,51,58],"conditions":[26],"on":[27],"initial":[29],"control":[30],"points":[31],"that":[32],"allow":[33],"generation":[35],"limit":[38],"curves":[39],"by":[40],"Some":[44],"numerical":[45],"examples":[46],"are":[47],"given":[48],"to":[49],"illustrate":[50],"graphical":[52],"representation":[53]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":2}],"updated_date":"2026-10-16T09:59:22.235173","created_date":"2025-10-10T00:00:00"}