{"id":"https://openalex.org/W1963878392","doi":"https://doi.org/10.1155/2013/531497","title":"Data Visualization Using Rational Trigonometric Spline","display_name":"Data Visualization Using Rational Trigonometric Spline","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W1963878392","doi":"https://doi.org/10.1155/2013/531497","mag":"1963878392"},"language":"en","primary_location":{"id":"doi:10.1155/2013/531497","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/531497","pdf_url":"https://downloads.hindawi.com/journals/jam/2013/531497.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/jam/2013/531497.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5073149522","display_name":"Uzma Bashir","orcid":"https://orcid.org/0000-0002-2686-6860"},"institutions":[{"id":"https://openalex.org/I139322472","display_name":"Universiti Sains Malaysia","ror":"https://ror.org/02rgb2k63","country_code":"MY","type":"education","lineage":["https://openalex.org/I139322472"]}],"countries":["MY"],"is_corresponding":true,"raw_author_name":"Uzma Bashir","raw_affiliation_strings":["School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Penang, Malaysia"],"raw_orcid":"https://orcid.org/0000-0002-2686-6860","affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Penang, Malaysia","institution_ids":["https://openalex.org/I139322472"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109373487","display_name":"Jamaludin Md. Ali","orcid":null},"institutions":[{"id":"https://openalex.org/I139322472","display_name":"Universiti Sains Malaysia","ror":"https://ror.org/02rgb2k63","country_code":"MY","type":"education","lineage":["https://openalex.org/I139322472"]}],"countries":["MY"],"is_corresponding":false,"raw_author_name":"Jamaludin Md. Ali","raw_affiliation_strings":["School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Penang, Malaysia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Penang, Malaysia","institution_ids":["https://openalex.org/I139322472"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5073149522"],"corresponding_institution_ids":["https://openalex.org/I139322472"],"apc_list":{"value":1050,"currency":"USD","value_usd":1050},"apc_paid":{"value":1050,"currency":"USD","value_usd":1050},"fwci":2.4906,"has_fulltext":true,"cited_by_count":16,"citation_normalized_percentile":{"value":0.8716307,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"2013","issue":null,"first_page":"1","last_page":"10"},"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/T10481","display_name":"Computer Graphics and Visualization Techniques","score":0.9182000160217285,"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":0.6207448840141296},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.5838758945465088},{"id":"https://openalex.org/keywords/trigonometry","display_name":"Trigonometry","score":0.571118950843811},{"id":"https://openalex.org/keywords/spline","display_name":"Spline (mechanical)","score":0.5632782578468323},{"id":"https://openalex.org/keywords/curve-fitting","display_name":"Curve fitting","score":0.5488574504852295},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.521538496017456},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.499114990234375},{"id":"https://openalex.org/keywords/smoothing-spline","display_name":"Smoothing spline","score":0.45489683747291565},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3746642470359802},{"id":"https://openalex.org/keywords/spline-interpolation","display_name":"Spline interpolation","score":0.3348230719566345},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3261638879776001},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.20052024722099304},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.15488389134407043},{"id":"https://openalex.org/keywords/computer-vision","display_name":"Computer vision","score":0.1103551983833313},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.10663440823554993}],"concepts":[{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.6207448840141296},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.5838758945465088},{"id":"https://openalex.org/C29001434","wikidata":"https://www.wikidata.org/wiki/Q8084","display_name":"Trigonometry","level":2,"score":0.571118950843811},{"id":"https://openalex.org/C10390562","wikidata":"https://www.wikidata.org/wiki/Q581809","display_name":"Spline (mechanical)","level":2,"score":0.5632782578468323},{"id":"https://openalex.org/C184389593","wikidata":"https://www.wikidata.org/wiki/Q603159","display_name":"Curve fitting","level":2,"score":0.5488574504852295},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.521538496017456},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.499114990234375},{"id":"https://openalex.org/C107457265","wikidata":"https://www.wikidata.org/wiki/Q7546460","display_name":"Smoothing spline","level":4,"score":0.45489683747291565},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3746642470359802},{"id":"https://openalex.org/C31447003","wikidata":"https://www.wikidata.org/wiki/Q545002","display_name":"Spline interpolation","level":3,"score":0.3348230719566345},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3261638879776001},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.20052024722099304},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15488389134407043},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.1103551983833313},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.10663440823554993},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.0},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1155/2013/531497","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/531497","pdf_url":"https://downloads.hindawi.com/journals/jam/2013/531497.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:generic.eprints.org:38612","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306401648","display_name":"Universiti Sains Malaysia Institutional Repository (Universiti Sains Malaysia)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I139322472","host_organization_name":"Universiti Sains Malaysia","host_organization_lineage":["https://openalex.org/I139322472"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:CULeuclid:euclid.jam/1394808021","is_oa":false,"landing_page_url":"https://projecteuclid.org/euclid.jam/1394808021","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:RePEc:hin:jnljam:531497","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/JAM/2013/531497.xml","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,"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:7075038511084f7cad3a0b30f939047e","is_oa":false,"landing_page_url":"https://doaj.org/article/7075038511084f7cad3a0b30f939047e","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,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Applied Mathematics, Vol 2013 (2013)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2013/531497","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/531497","pdf_url":"https://downloads.hindawi.com/journals/jam/2013/531497.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320322757","display_name":"Universiti Sains Malaysia","ror":"https://ror.org/02rgb2k63"},{"id":"https://openalex.org/F4320337380","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1963878392.pdf","grobid_xml":"https://content.openalex.org/works/W1963878392.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W1971665624","https://openalex.org/W1987349630","https://openalex.org/W1991865103","https://openalex.org/W2020077092","https://openalex.org/W2034966370","https://openalex.org/W2050962859","https://openalex.org/W2064919126","https://openalex.org/W2066200483","https://openalex.org/W2081229768","https://openalex.org/W2151821191","https://openalex.org/W2384122227","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W1981039615","https://openalex.org/W1690623585","https://openalex.org/W2380799314","https://openalex.org/W2499055041","https://openalex.org/W2102842245","https://openalex.org/W2070774473","https://openalex.org/W1997342009","https://openalex.org/W2018229429","https://openalex.org/W2155124200","https://openalex.org/W2221442531"],"abstract_inverted_index":{"This":[0],"paper":[1],"describes":[2],"the":[3,10,22,35,40,72,80,85,92,95,103,106],"use":[4],"of":[5,16,39,65,84,94,105],"trigonometric":[6,56],"spline":[7,57],"to":[8,20,78,90,101],"visualize":[9],"given":[11,100],"planar":[12],"data.":[13,41],"The":[14],"goal":[15],"this":[17],"work":[18],"is":[19],"determine":[21],"smoothest":[23],"possible":[24],"curve":[25,46],"that":[26],"passes":[27],"through":[28],"its":[29],"data":[30,86],"points":[31],"while":[32],"simultaneously":[33],"satisfying":[34],"shape":[36,60,67,82,93],"preserving":[37],"features":[38,83],"Positive,":[42],"monotone,":[43],"and":[44,71],"constrained":[45,70],"interpolating":[47],"schemes,":[48],"by":[49],"using":[50],"a<mml:math":[51],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[52],"id=\"M1\"><mml:mrow><mml:msup><mml:mrow><mml:mi>C</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>piecewise":[53],"rational":[54],"cubic":[55],"with":[58],"four":[59],"parameters,":[61],"are":[62,69,75,99],"developed.":[63],"Two":[64],"these":[66],"parameters":[68],"other":[73],"two":[74],"set":[76],"free":[77],"preserve":[79],"inherited":[81],"as":[87,89],"well":[88],"control":[91],"curve.":[96],"Numerical":[97],"examples":[98],"illustrate":[102],"worth":[104],"work.":[107]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":4}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}
