{"id":"https://openalex.org/W2279699992","doi":"https://doi.org/10.1137/16m1057978","title":"Differentiable Piecewise-B\u00e9zier Surfaces on Riemannian Manifolds","display_name":"Differentiable Piecewise-B\u00e9zier Surfaces on Riemannian Manifolds","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2279699992","doi":"https://doi.org/10.1137/16m1057978","mag":"2279699992"},"language":"en","primary_location":{"id":"doi:10.1137/16m1057978","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1057978","pdf_url":null,"source":{"id":"https://openalex.org/S152600803","display_name":"SIAM Journal on Imaging Sciences","issn_l":"1936-4954","issn":["1936-4954"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Imaging Sciences","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://hdl.handle.net/2078.1/176421","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5034347171","display_name":"P.-A. Absil","orcid":"https://orcid.org/0000-0003-2946-4178"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"P.-A. Absil","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055388412","display_name":"Pierre-Yves Gousenbourger","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Pierre-Yves Gousenbourger","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5033931691","display_name":"Paul Striewski","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Paul Striewski","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5050613004","display_name":"Benedikt Wirth","orcid":"https://orcid.org/0000-0003-0393-1938"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Benedikt Wirth","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5034347171"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.4324,"has_fulltext":false,"cited_by_count":26,"citation_normalized_percentile":{"value":0.91334216,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"9","issue":"4","first_page":"1788","last_page":"1828"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9997000098228455,"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":0.9997000098228455,"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/T10719","display_name":"3D Shape Modeling and Analysis","score":0.9797999858856201,"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/T10638","display_name":"Optical measurement and interference techniques","score":0.975600004196167,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/mathematics","display_name":"Mathematics","score":0.7429520487785339},{"id":"https://openalex.org/keywords/b-spline","display_name":"B-spline","score":0.5545128583908081},{"id":"https://openalex.org/keywords/surface","display_name":"Surface (topology)","score":0.5144920349121094},{"id":"https://openalex.org/keywords/b\u00e9zier-curve","display_name":"B\u00e9zier curve","score":0.5092067122459412},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.5083853602409363},{"id":"https://openalex.org/keywords/euclidean-space","display_name":"Euclidean space","score":0.44152626395225525},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4402647912502289},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3545517921447754},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.32640647888183594},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2787349224090576},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.21537959575653076}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7429520487785339},{"id":"https://openalex.org/C15945459","wikidata":"https://www.wikidata.org/wiki/Q2083109","display_name":"B-spline","level":2,"score":0.5545128583908081},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.5144920349121094},{"id":"https://openalex.org/C206423108","wikidata":"https://www.wikidata.org/wiki/Q214728","display_name":"B\u00e9zier curve","level":2,"score":0.5092067122459412},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.5083853602409363},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.44152626395225525},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4402647912502289},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3545517921447754},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.32640647888183594},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2787349224090576},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.21537959575653076}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/16m1057978","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1057978","pdf_url":null,"source":{"id":"https://openalex.org/S152600803","display_name":"SIAM Journal on Imaging Sciences","issn_l":"1936-4954","issn":["1936-4954"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Imaging Sciences","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.727.4567","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.727.4567","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://sites.uclouvain.be/absil/2015-10/BezierSurface-techreport-v1.pdf","raw_type":"text"},{"id":"pmh:oai:dial.uclouvain.be:boreal:176421","is_oa":true,"landing_page_url":"http://hdl.handle.net/2078.1/176421","pdf_url":null,"source":{"id":"https://openalex.org/S4306401974","display_name":"DIAL (Catholic University of Leuven)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I99464096","host_organization_name":"KU Leuven","host_organization_lineage":["https://openalex.org/I99464096"],"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":"SIAM Journal on Imaging Sciences, Vol. 9, no. 4, p. 1788-1828 (2016)","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:dial.uclouvain.be:boreal:176421","is_oa":true,"landing_page_url":"http://hdl.handle.net/2078.1/176421","pdf_url":null,"source":{"id":"https://openalex.org/S4306401974","display_name":"DIAL (Catholic University of Leuven)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I99464096","host_organization_name":"KU Leuven","host_organization_lineage":["https://openalex.org/I99464096"],"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":"SIAM Journal on Imaging Sciences, Vol. 9, no. 4, p. 1788-1828 (2016)","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2181259580","display_name":null,"funder_award_id":"FRFC 2.4585.12","funder_id":"https://openalex.org/F4320321390","funder_display_name":"Fonds De La Recherche Scientifique - FNRS"}],"funders":[{"id":"https://openalex.org/F4320321390","display_name":"Fonds De La Recherche Scientifique - FNRS","ror":"https://ror.org/03q83t159"},{"id":"https://openalex.org/F4320323223","display_name":"Alfried Krupp von Bohlen und Halbach-Stiftung","ror":"https://ror.org/04y7h3604"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W1488292173","https://openalex.org/W1630241964","https://openalex.org/W1668107054","https://openalex.org/W1968480758","https://openalex.org/W1981664955","https://openalex.org/W1981848768","https://openalex.org/W1983496390","https://openalex.org/W1985026044","https://openalex.org/W2001133651","https://openalex.org/W2006571925","https://openalex.org/W2030362796","https://openalex.org/W2044690209","https://openalex.org/W2057823172","https://openalex.org/W2058078260","https://openalex.org/W2075492994","https://openalex.org/W2076123236","https://openalex.org/W2078188038","https://openalex.org/W2079630523","https://openalex.org/W2093754004","https://openalex.org/W2105866209","https://openalex.org/W2109409043","https://openalex.org/W2114766304","https://openalex.org/W2114867107","https://openalex.org/W2133921496","https://openalex.org/W2141839129","https://openalex.org/W2150771764","https://openalex.org/W2159713859","https://openalex.org/W2167623372","https://openalex.org/W2290424755","https://openalex.org/W2328933992","https://openalex.org/W2952206313","https://openalex.org/W4250196415"],"related_works":["https://openalex.org/W3127061749","https://openalex.org/W2355895214","https://openalex.org/W2359486342","https://openalex.org/W2110381638","https://openalex.org/W2358913846","https://openalex.org/W2389379442","https://openalex.org/W2091242392","https://openalex.org/W3067162","https://openalex.org/W2348675830","https://openalex.org/W2194207844"],"abstract_inverted_index":{"We":[0,28,98],"generalize":[1],"the":[2,60,69,81,103,105],"notion":[3],"of":[4,25,37,68,88],"B\u00e9zier":[5,26,38,48,61,70,82,95],"surfaces":[6],"and":[7,19,35,45,109],"surface":[8,39,96],"splines":[9,49],"to":[10,32,79,90],"Riemannian":[11,111],"manifolds.":[12],"To":[13],"this":[14],"end":[15],"we":[16,75],"put":[17],"forward":[18],"compare":[20],"three":[21],"possible":[22],"alternative":[23],"definitions":[24],"surfaces.":[27],"furthermore":[29],"investigate":[30],"how":[31],"achieve":[33],"${\\mathcal{C}}^0$-":[34],"${\\mathcal{C}}^1$-continuity":[36,52],"splines.":[40],"Unlike":[41],"in":[42],"Euclidean":[43],"space":[44],"for":[46],"one-dimensional":[47],"on":[50,59,102],"manifolds,":[51],"cannot":[53],"be":[54,91],"ensured":[55],"by":[56,93],"simple":[57],"conditions":[58],"control":[62,83],"points:":[63],"it":[64],"requires":[65],"an":[66,77],"adaptation":[67],"spline":[71],"evaluation":[72],"scheme.":[73],"Finally,":[74],"propose":[76],"algorithm":[78],"optimize":[80],"points":[84,89],"given":[85],"a":[86,94],"set":[87],"interpolated":[92],"spline.":[97],"show":[99],"computational":[100],"examples":[101],"sphere,":[104],"special":[106],"orthogonal":[107],"group,":[108],"two":[110],"shape":[112],"spaces.":[113]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}