{"id":"https://openalex.org/W2120525439","doi":"https://doi.org/10.1007/978-3-322-82969-6_20","title":"Scattered Data Approximation with Triangular B-Splines","display_name":"Scattered Data Approximation with Triangular B-Splines","publication_year":1996,"publication_date":"1996-01-01","ids":{"openalex":"https://openalex.org/W2120525439","doi":"https://doi.org/10.1007/978-3-322-82969-6_20","mag":"2120525439"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-322-82969-6_20","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-322-82969-6_20","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advanced Course on FAIRSHAPE","raw_type":"book-chapter"},"type":"book-chapter","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/A5066081170","display_name":"Ron Pfeifle","orcid":null},"institutions":[{"id":"https://openalex.org/I181369854","display_name":"Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg","ror":"https://ror.org/00f7hpc57","country_code":"DE","type":"education","lineage":["https://openalex.org/I181369854"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Ron Pfeifle","raw_affiliation_strings":["Lehrstuhl f\u00fcr Informatik, Friedrich-Alexander Universit\u00e4t, Am Weichselgarten 9, D-91058, Erlangen, Germany","Universit\u00e4t Erlangen, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Lehrstuhl f\u00fcr Informatik, Friedrich-Alexander Universit\u00e4t, Am Weichselgarten 9, D-91058, Erlangen, Germany","institution_ids":["https://openalex.org/I181369854"]},{"raw_affiliation_string":"Universit\u00e4t Erlangen, Germany","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5058028526","display_name":"Hans\u2010Peter Seidel","orcid":"https://orcid.org/0000-0002-1343-8613"},"institutions":[{"id":"https://openalex.org/I181369854","display_name":"Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg","ror":"https://ror.org/00f7hpc57","country_code":"DE","type":"education","lineage":["https://openalex.org/I181369854"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Hans-Peter Seidel","raw_affiliation_strings":["Lehrstuhl f\u00fcr Informatik, Friedrich-Alexander Universit\u00e4t, Am Weichselgarten 9, D-91058, Erlangen, Germany","Universit\u00e4t Erlangen, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Lehrstuhl f\u00fcr Informatik, Friedrich-Alexander Universit\u00e4t, Am Weichselgarten 9, D-91058, Erlangen, Germany","institution_ids":["https://openalex.org/I181369854"]},{"raw_affiliation_string":"Universit\u00e4t Erlangen, Germany","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I181369854"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.20980616,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"253","last_page":"263"},"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.991100013256073,"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/T10719","display_name":"3D Shape Modeling and Analysis","score":0.9861000180244446,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.35951942205429077},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.35913848876953125},{"id":"https://openalex.org/keywords/geography","display_name":"Geography","score":0.3201158344745636}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.35951942205429077},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.35913848876953125},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.3201158344745636}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-322-82969-6_20","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-322-82969-6_20","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advanced Course on FAIRSHAPE","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","score":0.46000000834465027,"id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W190899266","https://openalex.org/W1479828274","https://openalex.org/W1542048523","https://openalex.org/W1567866801","https://openalex.org/W1591781056","https://openalex.org/W1599308577","https://openalex.org/W1984430599","https://openalex.org/W1999338367","https://openalex.org/W2005703344","https://openalex.org/W2014281764","https://openalex.org/W2035910529","https://openalex.org/W2056816721","https://openalex.org/W2074429597","https://openalex.org/W2083801987","https://openalex.org/W2089157941","https://openalex.org/W2096471740","https://openalex.org/W2148390216","https://openalex.org/W2155310671","https://openalex.org/W2727854388","https://openalex.org/W2798584761","https://openalex.org/W2798987218","https://openalex.org/W3217008510","https://openalex.org/W4233776588","https://openalex.org/W4247591570","https://openalex.org/W4252484634","https://openalex.org/W4252937307","https://openalex.org/W4388322023","https://openalex.org/W6632306887","https://openalex.org/W6634108105","https://openalex.org/W6635615297","https://openalex.org/W6636125174","https://openalex.org/W6669290111"],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W2044189972","https://openalex.org/W2913765211","https://openalex.org/W1974891317","https://openalex.org/W2313400459","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2069964982","https://openalex.org/W2007596026"],"abstract_inverted_index":{"Scattered":[0],"data":[1,85,131],"is,":[2],"by":[3,89,137,141],"definition,":[4],"irregularly":[5],"spaced.":[6],"Uniform":[7],"surface":[8,82,107],"schemes":[9],"are":[10,27,117],"generally":[11],"not":[12,140],"well":[13],"adapted":[14,43],"to":[15,44,103,109],"the":[16,45,51,69,72,84,114,121,124,142,149,155],"locally":[17],"varying":[18],"nature":[19],"of":[20,53,59,92,123],"such":[21],"data.":[22,47,61,115],"Conversely,":[23],"triangular":[24],"B-spline":[25],"surfaces":[26,56],"more":[28],"flexible":[29],"in":[30,113],"that":[31],"they":[32],"can":[33,41],"be":[34,42,152],"built":[35],"over":[36,78],"arbitrary":[37],"triangulations":[38],"and":[39,74,95,108,129,139,148],"thus":[40],"scattered":[46,60],"This":[48,99,144],"paper":[49],"discusses":[50],"use":[52],"DMS":[54],"spline":[55],"for":[57,66,111,126],"approximation":[58],"A":[62,81],"method":[63],"is":[64,86,146],"provided":[65],"automatically":[67],"triangulating":[68],"domain":[70],"containing":[71],"points":[73],"generating":[75],"basis":[76],"functions":[77],"this":[79],"triangulation.":[80],"approximating":[83],"then":[87],"found":[88],"a":[90,105],"combination":[91,100],"least":[93],"squares":[94],"bending":[96],"energy":[97],"minimization":[98],"serves":[101],"both":[102],"generate":[104],"smooth":[106],"accommodate":[110],"gaps":[112],"Examples":[116],"presented":[118],"which":[119],"demonstrate":[120],"effectiveness":[122],"technique":[125],"mathematical,":[127],"geographical":[128],"other":[130],"sets.":[132],"These":[133],"keywords":[134,150],"were":[135],"added":[136],"machine":[138],"authors.":[143],"process":[145],"experimental":[147],"may":[151],"updated":[153],"as":[154],"learning":[156],"algorithm":[157],"improves.":[158]},"counts_by_year":[],"updated_date":"2026-08-04T08:18:43.703281","created_date":"2025-10-10T00:00:00"}