{"id":"https://openalex.org/W2002243124","doi":"https://doi.org/10.1090/s0025-5718-00-01288-6","title":"Hermite interpolation by Pythagorean hodograph curves of degree seven","display_name":"Hermite interpolation by Pythagorean hodograph curves of degree seven","publication_year":2000,"publication_date":"2000-10-16","ids":{"openalex":"https://openalex.org/W2002243124","doi":"https://doi.org/10.1090/s0025-5718-00-01288-6","mag":"2002243124"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-00-01288-6","doi":"https://doi.org/10.1090/s0025-5718-00-01288-6","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-00-01288-6","pdf_url":"https://www.ams.org/mcom/2001-70-235/S0025-5718-00-01288-6/S0025-5718-00-01288-6.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-a","jufo-3","norway-2","poland-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/2001-70-235/S0025-5718-00-01288-6/S0025-5718-00-01288-6.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5045854462","display_name":"Bert J\u00fcttler B","orcid":"https://orcid.org/0000-0002-5518-7795","observed_orcids":["https://orcid.org/0000-0002-5518-7795"]},"institutions":[{"id":"https://openalex.org/I121883995","display_name":"Johannes Kepler University of Linz","ror":"https://ror.org/052r2xn60","country_code":"AT","type":"education","lineage":["https://openalex.org/I121883995"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"B. J\u00fcttler","raw_affiliation_strings":["Institute of Analysis and Computational Mathematics, Johannes Kepler University Linz, Altenberger Str. 69, 4040 Linz, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Analysis and Computational Mathematics, Johannes Kepler University Linz, Altenberger Str. 69, 4040 Linz, Austria","institution_ids":["https://openalex.org/I121883995"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5045854462"],"corresponding_institution_ids":["https://openalex.org/I121883995"],"apc_list":null,"apc_paid":null,"fwci":2.8929,"has_fulltext":true,"cited_by_count":97,"citation_normalized_percentile":{"value":0.88988886,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"70","issue":"235","first_page":"1089","last_page":"1111"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9940999746322632,"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":0.9940999746322632,"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/T11191","display_name":"Mathematical functions and polynomials","score":0.003000000026077032,"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"}},{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.000699999975040555,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/pythagorean-hodograph-curves","display_name":"Pythagorean hodograph curves","score":0.9440000057220459},{"id":"https://openalex.org/keywords/hermite-interpolation","display_name":"Hermite interpolation","score":0.9860000014305115},{"id":"https://openalex.org/keywords/g2-continuity","display_name":"G2 continuity","score":0.5239999890327454},{"id":"https://openalex.org/keywords/curvature-continuity","display_name":"curvature continuity","score":0.7490000128746033},{"id":"https://openalex.org/keywords/quartic-polynomials","display_name":"quartic polynomials","score":0.628000020980835},{"id":"https://openalex.org/keywords/existence-of-solutions","display_name":"existence of solutions","score":0.7239999771118164},{"id":"https://openalex.org/keywords/order-of-approximation","display_name":"approximation order","score":0.6769999861717224},{"id":"https://openalex.org/keywords/bezier-curves","display_name":"B\u00e9zier curves","score":0.7760000228881836},{"id":"https://openalex.org/keywords/b-spline-curves","display_name":"B-spline curves","score":0.8370000123977661}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8182821869850159},{"id":"https://openalex.org/C186429297","wikidata":"https://www.wikidata.org/wiki/Q44451","display_name":"Hermite interpolation","level":3,"score":0.7404748797416687},{"id":"https://openalex.org/C201362023","wikidata":"https://www.wikidata.org/wiki/Q658574","display_name":"Hermite polynomials","level":2,"score":0.7164228558540344},{"id":"https://openalex.org/C53622353","wikidata":"https://www.wikidata.org/wiki/Q1518913","display_name":"Family of curves","level":2,"score":0.6009929180145264},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.5767701268196106},{"id":"https://openalex.org/C206423108","wikidata":"https://www.wikidata.org/wiki/Q214728","display_name":"B\u00e9zier curve","level":2,"score":0.5639615058898926},{"id":"https://openalex.org/C84607441","wikidata":"https://www.wikidata.org/wiki/Q1537263","display_name":"Cubic Hermite spline","level":5,"score":0.5554166436195374},{"id":"https://openalex.org/C88080468","wikidata":"https://www.wikidata.org/wiki/Q637347","display_name":"Polynomial interpolation","level":4,"score":0.5159836411476135},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.5008983612060547},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4887826144695282},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.47865617275238037},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4779139459133148},{"id":"https://openalex.org/C99636146","wikidata":"https://www.wikidata.org/wiki/Q35889","display_name":"Parametric equation","level":2,"score":0.44671863317489624},{"id":"https://openalex.org/C186763157","wikidata":"https://www.wikidata.org/wiki/Q5741918","display_name":"Hermite spline","level":5,"score":0.44424569606781006},{"id":"https://openalex.org/C184389593","wikidata":"https://www.wikidata.org/wiki/Q603159","display_name":"Curve fitting","level":2,"score":0.4275444746017456},{"id":"https://openalex.org/C31447003","wikidata":"https://www.wikidata.org/wiki/Q545002","display_name":"Spline interpolation","level":3,"score":0.34301865100860596},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3236614465713501},{"id":"https://openalex.org/C171836373","wikidata":"https://www.wikidata.org/wiki/Q2266329","display_name":"Linear interpolation","level":3,"score":0.2518368661403656},{"id":"https://openalex.org/C107457265","wikidata":"https://www.wikidata.org/wiki/Q7546460","display_name":"Smoothing spline","level":4,"score":0.2228553593158722},{"id":"https://openalex.org/C207214200","wikidata":"https://www.wikidata.org/wiki/Q4202129","display_name":"Nearest-neighbor interpolation","level":4,"score":0.0855056643486023},{"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/C502989409","wikidata":"https://www.wikidata.org/wiki/Q11425","display_name":"Animation","level":2,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1090/s0025-5718-00-01288-6","doi":"https://doi.org/10.1090/s0025-5718-00-01288-6","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-00-01288-6","pdf_url":"https://www.ams.org/mcom/2001-70-235/S0025-5718-00-01288-6/S0025-5718-00-01288-6.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-a","jufo-3","norway-2","poland-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.192.4442","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.192.4442","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ams.org/journals/mcom/2001-70-235/S0025-5718-00-01288-6/S0025-5718-00-01288-6.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.99.9525","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.99.9525","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ams.org/mcom/2001-70-235/S0025-5718-00-01288-6/S0025-5718-00-01288-6.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-00-01288-6","doi":"https://doi.org/10.1090/s0025-5718-00-01288-6","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-00-01288-6","pdf_url":"https://www.ams.org/mcom/2001-70-235/S0025-5718-00-01288-6/S0025-5718-00-01288-6.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-a","jufo-3","norway-2","poland-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2002243124.pdf","grobid_xml":"https://content.openalex.org/works/W2002243124.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W1550922999","https://openalex.org/W1551207461","https://openalex.org/W1964673636","https://openalex.org/W1968306974","https://openalex.org/W1984743559","https://openalex.org/W2007688905","https://openalex.org/W2015649089","https://openalex.org/W2022994234","https://openalex.org/W2034121399","https://openalex.org/W2060967026","https://openalex.org/W2090738717","https://openalex.org/W2092585034","https://openalex.org/W2124009217","https://openalex.org/W2134160115","https://openalex.org/W2326025993","https://openalex.org/W4206360718","https://openalex.org/W4242804520","https://openalex.org/W4245211388"],"related_works":["https://openalex.org/W4239248407","https://openalex.org/W2031303010","https://openalex.org/W3023816430","https://openalex.org/W3025960644","https://openalex.org/W2091727476","https://openalex.org/W2133632514","https://openalex.org/W4248508464","https://openalex.org/W2085385949","https://openalex.org/W795774031","https://openalex.org/W2351680051"],"abstract_inverted_index":{"Polynomial":[0],"Pythagorean":[1],"hodograph":[2],"(PH)":[3],"curves":[4,106,290],"form":[5],"a":[6,18,71,75,179,216,277],"remarkable":[7],"subclass":[8],"of":[9,78,89,107,126,133,138,147,166,206,234,256,280,291],"polynomial":[10,19,81,242,287],"parametric":[11],"curves;":[12],"they":[13],"are":[14,156,198],"distinguished":[15],"by":[16,37,59,122,251],"having":[17],"arc":[20],"length":[21],"function":[22],"and":[23,39,102,145,231],"rational":[24],"offsets":[25],"(parallel":[26],"curves).":[27],"Many":[28],"related":[29],"references":[30],"can":[31,119,237],"be":[32,120,225,239],"found":[33,121],"in":[34],"the":[35,52,65,124,131,134,143,148,164,167,204,207,210,252],"article":[36],"Farouki":[38],"Neff":[40],"on":[41],"C":[42,53,93],"1":[43,54,94],"C^1":[44,55],"Hermite":[45,56,87,153],"interpolation":[46,57,88],"with":[47,104],"PH":[48,82,105,243,288],"quintics.":[49],"We":[50,85],"extend":[51],"scheme":[58],"taking":[60],"additional":[61],"curvature":[62,79],"information":[63],"at":[64],"segment":[66],"boundaries":[67],"into":[68,241],"account.":[69],"As":[70,215],"result":[72],"we":[73,141,162],"obtain":[74],"new":[76],"construction":[77],"continuous":[80],"spline":[83,289],"curves.":[84,266],"discuss":[86],"G":[90,226,284],"2":[91,227,285],"[":[92],"]":[95],"G^2[C^1]":[96],"boundary":[97],"data":[98,154],"(points,":[99],"first":[100],"derivatives,":[101],"curvatures)":[103],"degree":[108,292],"7.":[109,293],"It":[110,175,282],"is":[111,176,182,213,222,248],"shown":[112,177],"that":[113,178,194],"up":[114],"to":[115,184,224,232],"eight":[116],"possible":[117],"solutions":[118,168],"computing":[123],"roots":[125],"two":[127],"quartic":[128],"polynomials.":[129],"With":[130],"help":[132],"canonical":[135],"Taylor":[136],"expansion":[137],"planar":[139],"curves,":[140],"analyze":[142],"existence":[144],"shape":[146,205],"solutions.":[149],"More":[150],"precisely,":[151],"for":[152,169,186,275],"which":[155,221],"taken":[157],"from":[158],"an":[159],"analytical":[160,235],"curve,":[161,220],"study":[163],"behaviour":[165],"decreasing":[170],"stepsize":[171,189],"\u0394":[172,190],"\\Delta":[173,191],".":[174],"regular":[180],"solution":[181,202],"guaranteed":[183],"exist":[185],"sufficiently":[187],"small":[188],",":[192],"provided":[193],"certain":[195],"technical":[196],"assumptions":[197],"satisfied.":[199],"Moreover,":[200],"this":[201],"matches":[203],"original":[208],"curve;":[209],"approximation":[211],"order":[212],"6.":[214],"consequence,":[217],"any":[218,273],"given":[219],"assumed":[223],"G^2":[228,286],"(curvature":[229],"continuous)":[230],"consist":[233],"segments":[236],"approximately":[238],"converted":[240],"form.":[244],"The":[245,267],"latter":[246],"assumption":[247],"automatically":[249],"satisfied":[250],"standard":[253],"curve":[254],"representations":[255],"Computer":[257],"Aided":[258],"Geometric":[259],"Design,":[260],"such":[261],"as":[262],"B\u00e9zier":[263],"or":[264],"B-spline":[265],"conversion":[268],"procedure":[269],"acts":[270],"locally,":[271],"without":[272],"need":[274],"solving":[276],"global":[278],"system":[279],"equations.":[281],"produces":[283]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":7}],"updated_date":"2026-10-14T16:39:01.820549","created_date":"2025-10-10T00:00:00"}
