{"id":"https://openalex.org/W2097156247","doi":"https://doi.org/10.2312/spbg/spbg04/201-211","title":"Finite Elements on Point Based Surfaces","display_name":"Finite Elements on Point Based Surfaces","publication_year":2004,"publication_date":"2004-01-01","ids":{"openalex":"https://openalex.org/W2097156247","doi":"https://doi.org/10.2312/spbg/spbg04/201-211","mag":"2097156247"},"language":"en","primary_location":{"id":"pmh:oai:pure.rug.nl:openaire_cris_publications/b51c1412-2bac-4d52-9cf7-599b821d4493","is_oa":true,"landing_page_url":"https://research.rug.nl/en/publications/b51c1412-2bac-4d52-9cf7-599b821d4493","pdf_url":null,"source":{"id":"https://openalex.org/S4306400420","display_name":"University of Groningen research database (University of Groningen / Centre for Information Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I169381384","host_organization_name":"University of Groningen","host_organization_lineage":["https://openalex.org/I169381384"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Clarenz , U , Rumpf , M &amp; Telea , A 2004 , Finite Elements on Point Based Surfaces . in EPRINTS-BOOK-TITLE . University of Groningen, Johann Bernoulli Institute for Mathematics and Computer Science .","raw_type":"bookPart"},"type":"article","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://research.rug.nl/en/publications/b51c1412-2bac-4d52-9cf7-599b821d4493","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5067038712","display_name":"Ulrich Clarenz","orcid":null},"institutions":[{"id":"https://openalex.org/I62318514","display_name":"University of Duisburg-Essen","ror":"https://ror.org/04mz5ra38","country_code":"DE","type":"education","lineage":["https://openalex.org/I62318514"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Clarenz, U.","raw_affiliation_strings":["Institut f\u00fcr Mathematik, Duisburg University, Germany#TAB#"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Mathematik, Duisburg University, Germany#TAB#","institution_ids":["https://openalex.org/I62318514"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063603168","display_name":"Martin Rumpf","orcid":"https://orcid.org/0000-0001-6049-9390"},"institutions":[{"id":"https://openalex.org/I62318514","display_name":"University of Duisburg-Essen","ror":"https://ror.org/04mz5ra38","country_code":"DE","type":"education","lineage":["https://openalex.org/I62318514"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Rumpf, M.","raw_affiliation_strings":["Institut f\u00fcr Mathematik, Duisburg University, Germany#TAB#"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Mathematik, Duisburg University, Germany#TAB#","institution_ids":["https://openalex.org/I62318514"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024074640","display_name":"Alexandru Telea","orcid":"https://orcid.org/0000-0003-0750-0502"},"institutions":[{"id":"https://openalex.org/I83019370","display_name":"Eindhoven University of Technology","ror":"https://ror.org/02c2kyt77","country_code":"NL","type":"education","lineage":["https://openalex.org/I83019370"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Telea, A.","raw_affiliation_strings":["Department of Mathematics and Computer Science; Eindhoven University of Technology; the Netherlands"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science; Eindhoven University of Technology; the Netherlands","institution_ids":["https://openalex.org/I83019370"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5067038712"],"corresponding_institution_ids":["https://openalex.org/I62318514"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":44,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10719","display_name":"3D Shape Modeling and Analysis","score":0.9998000264167786,"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/T10719","display_name":"3D Shape Modeling and Analysis","score":0.9998000264167786,"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":0.9995999932289124,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9987000226974487,"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/delaunay-triangulation","display_name":"Delaunay triangulation","score":0.7444469928741455},{"id":"https://openalex.org/keywords/tangent","display_name":"Tangent","score":0.6270118355751038},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5163094401359558},{"id":"https://openalex.org/keywords/tangent-space","display_name":"Tangent space","score":0.506487250328064},{"id":"https://openalex.org/keywords/triangulation","display_name":"Triangulation","score":0.4606788754463196},{"id":"https://openalex.org/keywords/surface","display_name":"Surface (topology)","score":0.45835059881210327},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4294835925102234},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.411146879196167},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4098508358001709},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.40284445881843567},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.35073405504226685},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.3174237906932831}],"concepts":[{"id":"https://openalex.org/C68010082","wikidata":"https://www.wikidata.org/wiki/Q192445","display_name":"Delaunay triangulation","level":2,"score":0.7444469928741455},{"id":"https://openalex.org/C138187205","wikidata":"https://www.wikidata.org/wiki/Q131251","display_name":"Tangent","level":2,"score":0.6270118355751038},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5163094401359558},{"id":"https://openalex.org/C157157409","wikidata":"https://www.wikidata.org/wiki/Q909601","display_name":"Tangent space","level":2,"score":0.506487250328064},{"id":"https://openalex.org/C135981907","wikidata":"https://www.wikidata.org/wiki/Q188056","display_name":"Triangulation","level":2,"score":0.4606788754463196},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.45835059881210327},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4294835925102234},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.411146879196167},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4098508358001709},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.40284445881843567},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.35073405504226685},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3174237906932831},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:pure.rug.nl:openaire_cris_publications/b51c1412-2bac-4d52-9cf7-599b821d4493","is_oa":true,"landing_page_url":"https://research.rug.nl/en/publications/b51c1412-2bac-4d52-9cf7-599b821d4493","pdf_url":null,"source":{"id":"https://openalex.org/S4306400420","display_name":"University of Groningen research database (University of Groningen / Centre for Information Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I169381384","host_organization_name":"University of Groningen","host_organization_lineage":["https://openalex.org/I169381384"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Clarenz , U , Rumpf , M &amp; Telea , A 2004 , Finite Elements on Point Based Surfaces . in EPRINTS-BOOK-TITLE . University of Groningen, Johann Bernoulli Institute for Mathematics and Computer Science .","raw_type":"bookPart"},{"id":"doi:10.2312/spbg/spbg04/201-211","is_oa":true,"landing_page_url":"https://doi.org/10.2312/spbg/spbg04/201-211","pdf_url":null,"source":{"id":"https://openalex.org/S7407052899","display_name":"Eurographics","issn_l":null,"issn":[],"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:pure.rug.nl:openaire_cris_publications/b51c1412-2bac-4d52-9cf7-599b821d4493","is_oa":true,"landing_page_url":"https://research.rug.nl/en/publications/b51c1412-2bac-4d52-9cf7-599b821d4493","pdf_url":null,"source":{"id":"https://openalex.org/S4306400420","display_name":"University of Groningen research database (University of Groningen / Centre for Information Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I169381384","host_organization_name":"University of Groningen","host_organization_lineage":["https://openalex.org/I169381384"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Clarenz , U , Rumpf , M &amp; Telea , A 2004 , Finite Elements on Point Based Surfaces . in EPRINTS-BOOK-TITLE . University of Groningen, Johann Bernoulli Institute for Mathematics and Computer Science .","raw_type":"bookPart"},"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11","score":0.5199999809265137}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W1495548215","https://openalex.org/W1964853704","https://openalex.org/W1974102081","https://openalex.org/W1986234613","https://openalex.org/W1987519781","https://openalex.org/W2000214666","https://openalex.org/W2066822731","https://openalex.org/W2079017595","https://openalex.org/W2100816864","https://openalex.org/W2103782815","https://openalex.org/W2113634802","https://openalex.org/W2127767808","https://openalex.org/W2128012088","https://openalex.org/W2128975270","https://openalex.org/W2129412583","https://openalex.org/W2129519161","https://openalex.org/W2140186962","https://openalex.org/W2152704091","https://openalex.org/W2162703509","https://openalex.org/W2165904679","https://openalex.org/W2171094068","https://openalex.org/W2293372129","https://openalex.org/W2295936755","https://openalex.org/W2998496342","https://openalex.org/W3148091194"],"related_works":["https://openalex.org/W2000214666","https://openalex.org/W1974956622","https://openalex.org/W2165649407","https://openalex.org/W2156849739","https://openalex.org/W2128012088","https://openalex.org/W2084595284","https://openalex.org/W2491912329","https://openalex.org/W2137531922","https://openalex.org/W2079017595","https://openalex.org/W2100816864","https://openalex.org/W2152704091","https://openalex.org/W2058524213","https://openalex.org/W2025164704","https://openalex.org/W3148091194","https://openalex.org/W1984713107","https://openalex.org/W2047161559","https://openalex.org/W1976584051","https://openalex.org/W1922506815","https://openalex.org/W1604758228","https://openalex.org/W1584361996"],"abstract_inverted_index":{"framework":[0,81],"efficiently":[1],"and":[2,26,50,66,69,94,98],"effectively":[3],"brings":[4],"well-known":[5],"PDE-based":[6,86],"processing":[7,88],"techniques":[8],"to":[9,61],"the":[10,20],"field":[11],"of":[12,22,31,40,85],"point-based":[13],"surfaces.":[14],"Our":[15],"method":[16],"is":[17],"based":[18],"on":[19,44],"construction":[21],"local":[23,28,54],"tangent":[24,41],"planes":[25],"a":[27],"Delaunay":[29],"triangulation":[30],"adjacent":[32],"points":[33],"projected":[34],"onto":[35],"this":[36],"plane.":[37],"The":[38],"definition":[39],"spaces":[42],"relies":[43],"moment-based":[45],"computation":[46],"with":[47],"proven":[48],"scaling":[49],"stability":[51],"properties.":[52],"Once":[53],"couplings":[55],"are":[56,59],"obtained,":[57],"we":[58],"able":[60],"easily":[62],"assemble":[63],"PDE-specific":[64],"mass":[65],"stiffness":[67],"matrices":[68],"solve":[70],"corresponding":[71],"linear":[72],"systems":[73],"by":[74,82],"standard":[75],"iterative":[76],"solvers.":[77],"We":[78],"demonstrate":[79],"our":[80],"different":[83],"classes":[84],"surface":[87],"applications,":[89],"such":[90],"as":[91],"texture":[92],"synthesis":[93],"processing,":[95],"geometric":[96],"fairing,":[97],"segmentation.":[99]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
