{"id":"https://openalex.org/W1944622679","doi":"https://doi.org/10.1109/gmap.2004.1290024","title":"Knot choosing by accommodating the first derivative constraint","display_name":"Knot choosing by accommodating the first derivative constraint","publication_year":2004,"publication_date":"2004-06-10","ids":{"openalex":"https://openalex.org/W1944622679","doi":"https://doi.org/10.1109/gmap.2004.1290024","mag":"1944622679"},"language":"en","primary_location":{"id":"doi:10.1109/gmap.2004.1290024","is_oa":false,"landing_page_url":"https://doi.org/10.1109/gmap.2004.1290024","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Geometric Modeling and Processing, 2004. Proceedings","raw_type":"proceedings-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/A5101753050","display_name":"Caiming Zhang","orcid":"https://orcid.org/0000-0003-0217-1543"},"institutions":[{"id":"https://openalex.org/I80143920","display_name":"Shandong University of Science and Technology","ror":"https://ror.org/04gtjhw98","country_code":"CN","type":"education","lineage":["https://openalex.org/I80143920"]},{"id":"https://openalex.org/I154099455","display_name":"Shandong University","ror":"https://ror.org/0207yh398","country_code":"CN","type":"education","lineage":["https://openalex.org/I154099455"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zhang Caiming","raw_affiliation_strings":["School of Computer Science and Technology, Shandong University, Jinan, China","School of Computer Science and Technology, Shandong University, Jinan, China#TAB#"],"affiliations":[{"raw_affiliation_string":"School of Computer Science and Technology, Shandong University, Jinan, China","institution_ids":["https://openalex.org/I80143920"]},{"raw_affiliation_string":"School of Computer Science and Technology, Shandong University, Jinan, China#TAB#","institution_ids":["https://openalex.org/I154099455"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101490033","display_name":"Fuhua Cheng","orcid":"https://orcid.org/0000-0003-2098-3027"},"institutions":[{"id":"https://openalex.org/I154099455","display_name":"Shandong University","ror":"https://ror.org/0207yh398","country_code":"CN","type":"education","lineage":["https://openalex.org/I154099455"]},{"id":"https://openalex.org/I143302722","display_name":"University of Kentucky","ror":"https://ror.org/02k3smh20","country_code":"US","type":"education","lineage":["https://openalex.org/I143302722"]}],"countries":["CN","US"],"is_corresponding":false,"raw_author_name":"Fuhua Cheng","raw_affiliation_strings":["Department of Computer Science, University of Kentucky, Lexington, KY, USA","School of Computer Science and Technology, Shandong University, Jinan, China#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Kentucky, Lexington, KY, USA","institution_ids":["https://openalex.org/I143302722"]},{"raw_affiliation_string":"School of Computer Science and Technology, Shandong University, Jinan, China#TAB#","institution_ids":["https://openalex.org/I154099455"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5101753050"],"corresponding_institution_ids":["https://openalex.org/I154099455","https://openalex.org/I80143920"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.07824887,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"15","issue":null,"first_page":"31","last_page":"37"},"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/T10188","display_name":"Advanced machining processes and optimization","score":0.9598000049591064,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical Engineering"},"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/T11138","display_name":"Tribology and Lubrication Engineering","score":0.958899974822998,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/knot","display_name":"Knot (papermaking)","score":0.7840628623962402},{"id":"https://openalex.org/keywords/spline-interpolation","display_name":"Spline interpolation","score":0.6808143258094788},{"id":"https://openalex.org/keywords/monotone-cubic-interpolation","display_name":"Monotone cubic interpolation","score":0.6636655330657959},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.5674209594726562},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5657952427864075},{"id":"https://openalex.org/keywords/spline","display_name":"Spline (mechanical)","score":0.5611878037452698},{"id":"https://openalex.org/keywords/curve-fitting","display_name":"Curve fitting","score":0.5510504841804504},{"id":"https://openalex.org/keywords/parametric-equation","display_name":"Parametric equation","score":0.5417649149894714},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5264694690704346},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.482526034116745},{"id":"https://openalex.org/keywords/second-derivative","display_name":"Second derivative","score":0.4480831027030945},{"id":"https://openalex.org/keywords/thin-plate-spline","display_name":"Thin plate spline","score":0.44696566462516785},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.446117639541626},{"id":"https://openalex.org/keywords/smoothing-spline","display_name":"Smoothing spline","score":0.42113491892814636},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.40977197885513306},{"id":"https://openalex.org/keywords/bicubic-interpolation","display_name":"Bicubic interpolation","score":0.3893161416053772},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.37972670793533325},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.36944663524627686},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3617130219936371},{"id":"https://openalex.org/keywords/bilinear-interpolation","display_name":"Bilinear interpolation","score":0.3486618399620056},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2917752265930176},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.10215398669242859},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.08717623353004456},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.07592585682868958},{"id":"https://openalex.org/keywords/structural-engineering","display_name":"Structural engineering","score":0.06632307171821594}],"concepts":[{"id":"https://openalex.org/C2779863119","wikidata":"https://www.wikidata.org/wiki/Q6423048","display_name":"Knot (papermaking)","level":2,"score":0.7840628623962402},{"id":"https://openalex.org/C31447003","wikidata":"https://www.wikidata.org/wiki/Q545002","display_name":"Spline interpolation","level":3,"score":0.6808143258094788},{"id":"https://openalex.org/C64485984","wikidata":"https://www.wikidata.org/wiki/Q4044484","display_name":"Monotone cubic interpolation","level":5,"score":0.6636655330657959},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.5674209594726562},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5657952427864075},{"id":"https://openalex.org/C10390562","wikidata":"https://www.wikidata.org/wiki/Q581809","display_name":"Spline (mechanical)","level":2,"score":0.5611878037452698},{"id":"https://openalex.org/C184389593","wikidata":"https://www.wikidata.org/wiki/Q603159","display_name":"Curve fitting","level":2,"score":0.5510504841804504},{"id":"https://openalex.org/C99636146","wikidata":"https://www.wikidata.org/wiki/Q35889","display_name":"Parametric equation","level":2,"score":0.5417649149894714},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5264694690704346},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.482526034116745},{"id":"https://openalex.org/C33257320","wikidata":"https://www.wikidata.org/wiki/Q1932744","display_name":"Second derivative","level":2,"score":0.4480831027030945},{"id":"https://openalex.org/C93132110","wikidata":"https://www.wikidata.org/wiki/Q7784288","display_name":"Thin plate spline","level":4,"score":0.44696566462516785},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.446117639541626},{"id":"https://openalex.org/C107457265","wikidata":"https://www.wikidata.org/wiki/Q7546460","display_name":"Smoothing spline","level":4,"score":0.42113491892814636},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.40977197885513306},{"id":"https://openalex.org/C49608258","wikidata":"https://www.wikidata.org/wiki/Q611705","display_name":"Bicubic interpolation","level":4,"score":0.3893161416053772},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.37972670793533325},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.36944663524627686},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3617130219936371},{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.3486618399620056},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2917752265930176},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.10215398669242859},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08717623353004456},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.07592585682868958},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.06632307171821594},{"id":"https://openalex.org/C42360764","wikidata":"https://www.wikidata.org/wiki/Q83588","display_name":"Chemical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C104114177","wikidata":"https://www.wikidata.org/wiki/Q79782","display_name":"Motion (physics)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/gmap.2004.1290024","is_oa":false,"landing_page_url":"https://doi.org/10.1109/gmap.2004.1290024","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Geometric Modeling and Processing, 2004. Proceedings","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W171507528","https://openalex.org/W1982883321","https://openalex.org/W1991726441","https://openalex.org/W1992483073","https://openalex.org/W2004909834","https://openalex.org/W2006650073","https://openalex.org/W2023143252","https://openalex.org/W2034966370","https://openalex.org/W2066745438","https://openalex.org/W2073690647","https://openalex.org/W2074421109","https://openalex.org/W2093497761","https://openalex.org/W2094147671","https://openalex.org/W2096045964","https://openalex.org/W2162870748","https://openalex.org/W2167437322","https://openalex.org/W2389064487","https://openalex.org/W4301496497","https://openalex.org/W6648384335","https://openalex.org/W6684721303"],"related_works":["https://openalex.org/W2371645298","https://openalex.org/W2117487173","https://openalex.org/W2380799314","https://openalex.org/W1980922465","https://openalex.org/W2399408157","https://openalex.org/W4361795749","https://openalex.org/W3140377186","https://openalex.org/W2381865570","https://openalex.org/W110415856","https://openalex.org/W2066345185"],"abstract_inverted_index":{"The":[0],"current":[1],"cubic":[2,45],"spline":[3,46],"curve":[4,23,48],"interpolation":[5,37],"scheme":[6],"is":[7,24,32,54,66],"derived":[8],"based":[9],"on":[10],"the":[11,15,18,22,30,36,59],"implicit":[12],"assumption":[13,31,53],"that":[14,50],"magnitude":[16],"of":[17,21,58],"first":[19],"derivative":[20],"close":[25],"to":[26],"a":[27],"constant.":[28],"However,":[29],"not":[33],"realized":[34],"by":[35],"scheme.":[38],"A":[39,56],"knot":[40],"choosing":[41],"technique":[42],"for":[43],"parametric":[44],"interpolating":[47],"construction":[49],"accommodates":[51],"this":[52],"presented.":[55],"comparison":[57],"new":[60],"method":[61],"with":[62],"several":[63],"existing":[64],"methods":[65],"performed":[67],"and":[68],"test":[69],"results":[70],"are":[71],"included.":[72]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}