{"id":"https://openalex.org/W2039416315","doi":"https://doi.org/10.1016/s0097-8493(96)00065-9","title":"Preserving monotonic shape of the data using piecewise rational cubic functions","display_name":"Preserving monotonic shape of the data using piecewise rational cubic functions","publication_year":1997,"publication_date":"1997-01-01","ids":{"openalex":"https://openalex.org/W2039416315","doi":"https://doi.org/10.1016/s0097-8493(96)00065-9","mag":"2039416315"},"language":"en","primary_location":{"id":"doi:10.1016/s0097-8493(96)00065-9","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0097-8493(96)00065-9","pdf_url":null,"source":{"id":"https://openalex.org/S94821547","display_name":"Computers & Graphics","issn_l":"0097-8493","issn":["0097-8493","1873-7684"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computers & 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/A5053662486","display_name":"Muhammad Sarfraz","orcid":"https://orcid.org/0000-0003-3196-9132"},"institutions":[{"id":"https://openalex.org/I134085113","display_name":"King Fahd University of Petroleum and Minerals","ror":"https://ror.org/03yez3163","country_code":"SA","type":"education","lineage":["https://openalex.org/I134085113"]}],"countries":["SA"],"is_corresponding":true,"raw_author_name":"Muhammad Sarfraz","raw_affiliation_strings":["Department of Information and Computer Science, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia","Department of Information and Computer Science, King Fahd University of Petroleum and Minerals Dhahran 31261, Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"Department of Information and Computer Science, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia","institution_ids":["https://openalex.org/I134085113"]},{"raw_affiliation_string":"Department of Information and Computer Science, King Fahd University of Petroleum and Minerals Dhahran 31261, Saudi Arabia","institution_ids":["https://openalex.org/I134085113"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112016073","display_name":"Muhammed Al-Mulhem","orcid":null},"institutions":[{"id":"https://openalex.org/I134085113","display_name":"King Fahd University of Petroleum and Minerals","ror":"https://ror.org/03yez3163","country_code":"SA","type":"education","lineage":["https://openalex.org/I134085113"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Muhammed Al-Mulhem","raw_affiliation_strings":["Department of Information and Computer Science, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia","Department of Information and Computer Science, King Fahd University of Petroleum and Minerals Dhahran 31261, Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"Department of Information and Computer Science, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia","institution_ids":["https://openalex.org/I134085113"]},{"raw_affiliation_string":"Department of Information and Computer Science, King Fahd University of Petroleum and Minerals Dhahran 31261, Saudi Arabia","institution_ids":["https://openalex.org/I134085113"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5063817203","display_name":"Farooq Ashraf","orcid":null},"institutions":[{"id":"https://openalex.org/I134085113","display_name":"King Fahd University of Petroleum and Minerals","ror":"https://ror.org/03yez3163","country_code":"SA","type":"education","lineage":["https://openalex.org/I134085113"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Farooq Ashraf","raw_affiliation_strings":["Department of Information and Computer Science, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia","Department of Information and Computer Science, King Fahd University of Petroleum and Minerals Dhahran 31261, Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"Department of Information and Computer Science, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia","institution_ids":["https://openalex.org/I134085113"]},{"raw_affiliation_string":"Department of Information and Computer Science, King Fahd University of Petroleum and Minerals Dhahran 31261, Saudi Arabia","institution_ids":["https://openalex.org/I134085113"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5053662486"],"corresponding_institution_ids":["https://openalex.org/I134085113"],"apc_list":{"value":2690,"currency":"USD","value_usd":2690},"apc_paid":null,"fwci":1.1348,"has_fulltext":false,"cited_by_count":42,"citation_normalized_percentile":{"value":0.76571397,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"21","issue":"1","first_page":"5","last_page":"14"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9998999834060669,"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":0.9998999834060669,"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9922000169754028,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10481","display_name":"Computer Graphics and Visualization Techniques","score":0.991599977016449,"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/piecewise","display_name":"Piecewise","score":0.878138542175293},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.8444686532020569},{"id":"https://openalex.org/keywords/cubic-function","display_name":"Cubic function","score":0.6918760538101196},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.6443461775779724},{"id":"https://openalex.org/keywords/rational-function","display_name":"Rational function","score":0.60307377576828},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.5974540114402771},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5734838843345642},{"id":"https://openalex.org/keywords/monotone-cubic-interpolation","display_name":"Monotone cubic interpolation","score":0.5711151957511902},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5385614037513733},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5381648540496826},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.5231643915176392},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.5119882225990295},{"id":"https://openalex.org/keywords/piecewise-linear-function","display_name":"Piecewise linear function","score":0.4770768880844116},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.45832502841949463},{"id":"https://openalex.org/keywords/cubic-form","display_name":"Cubic form","score":0.4404803216457367},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3424775004386902},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.32390618324279785},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3185393810272217},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.29266083240509033},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.20273607969284058},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.08308425545692444}],"concepts":[{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.878138542175293},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.8444686532020569},{"id":"https://openalex.org/C65559279","wikidata":"https://www.wikidata.org/wiki/Q16667694","display_name":"Cubic function","level":2,"score":0.6918760538101196},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.6443461775779724},{"id":"https://openalex.org/C75190567","wikidata":"https://www.wikidata.org/wiki/Q41237","display_name":"Rational function","level":2,"score":0.60307377576828},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.5974540114402771},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5734838843345642},{"id":"https://openalex.org/C64485984","wikidata":"https://www.wikidata.org/wiki/Q4044484","display_name":"Monotone cubic interpolation","level":5,"score":0.5711151957511902},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5385614037513733},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5381648540496826},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.5231643915176392},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.5119882225990295},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.4770768880844116},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45832502841949463},{"id":"https://openalex.org/C91429207","wikidata":"https://www.wikidata.org/wiki/Q5192245","display_name":"Cubic form","level":2,"score":0.4404803216457367},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3424775004386902},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.32390618324279785},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3185393810272217},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.29266083240509033},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.20273607969284058},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.08308425545692444},{"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},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C188325010","wikidata":"https://www.wikidata.org/wiki/Q861176","display_name":"Trilinear interpolation","level":4,"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/C171836373","wikidata":"https://www.wikidata.org/wiki/Q2266329","display_name":"Linear interpolation","level":3,"score":0.0},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/s0097-8493(96)00065-9","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0097-8493(96)00065-9","pdf_url":null,"source":{"id":"https://openalex.org/S94821547","display_name":"Computers & Graphics","issn_l":"0097-8493","issn":["0097-8493","1873-7684"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computers & Graphics","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":10,"referenced_works":["https://openalex.org/W1971977163","https://openalex.org/W1984343351","https://openalex.org/W1984448240","https://openalex.org/W1995285505","https://openalex.org/W2009571674","https://openalex.org/W2041791633","https://openalex.org/W2045919365","https://openalex.org/W2061915783","https://openalex.org/W2063990088","https://openalex.org/W2096045964"],"related_works":["https://openalex.org/W3104863033","https://openalex.org/W2018457478","https://openalex.org/W2380508842","https://openalex.org/W2382752950","https://openalex.org/W2347422976","https://openalex.org/W2347803381","https://openalex.org/W1566787338","https://openalex.org/W2039416315","https://openalex.org/W2388050730","https://openalex.org/W2359541762"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":7},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}