{"id":"https://openalex.org/W6963799678","doi":"https://doi.org/10.2312/sgp/sgp04/159-168","title":"Differentiable Parameterization of Catmull-Clark Subdivision Surfaces","display_name":"Differentiable Parameterization of Catmull-Clark Subdivision Surfaces","publication_year":2004,"publication_date":"2004-01-01","ids":{"openalex":"https://openalex.org/W6963799678","doi":"https://doi.org/10.2312/sgp/sgp04/159-168"},"language":"en","primary_location":{"id":"doi:10.2312/sgp/sgp04/159-168","is_oa":true,"landing_page_url":"https://doi.org/10.2312/sgp/sgp04/159-168","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":false,"raw_source_name":null,"raw_type":"article"},"type":"other","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.2312/sgp/sgp04/159-168","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Boier-Martin, Ioana","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Boier-Martin, Ioana","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Zorin, Denis","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zorin, Denis","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"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":true,"primary_topic":null,"topics":[],"keywords":[{"id":"https://openalex.org/keywords/subdivision","display_name":"Subdivision","score":0.8995000123977661},{"id":"https://openalex.org/keywords/subdivision-surface","display_name":"Subdivision surface","score":0.7930999994277954},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.4578999876976013},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.4553000032901764},{"id":"https://openalex.org/keywords/variety","display_name":"Variety (cybernetics)","score":0.35910001397132874},{"id":"https://openalex.org/keywords/surface","display_name":"Surface (topology)","score":0.3504999876022339},{"id":"https://openalex.org/keywords/parametrization","display_name":"Parametrization (atmospheric modeling)","score":0.3028999865055084}],"concepts":[{"id":"https://openalex.org/C143392562","wikidata":"https://www.wikidata.org/wiki/Q449111","display_name":"Subdivision","level":2,"score":0.8995000123977661},{"id":"https://openalex.org/C199686383","wikidata":"https://www.wikidata.org/wiki/Q1529124","display_name":"Subdivision surface","level":3,"score":0.7930999994277954},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5224999785423279},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.4578999876976013},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.4553000032901764},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.35910001397132874},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.3504999876022339},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3458000123500824},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3278000056743622},{"id":"https://openalex.org/C202887219","wikidata":"https://www.wikidata.org/wiki/Q3895221","display_name":"Parametrization (atmospheric modeling)","level":3,"score":0.3028999865055084},{"id":"https://openalex.org/C2776502983","wikidata":"https://www.wikidata.org/wiki/Q690182","display_name":"Contrast (vision)","level":2,"score":0.2939000129699707},{"id":"https://openalex.org/C27142425","wikidata":"https://www.wikidata.org/wiki/Q1139334","display_name":"Almost everywhere","level":2,"score":0.29339998960494995},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.27730000019073486},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.27720001339912415},{"id":"https://openalex.org/C2987642246","wikidata":"https://www.wikidata.org/wiki/Q5452196","display_name":"First order","level":2,"score":0.26440000534057617},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.26109999418258667},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.25699999928474426},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2547000050544739},{"id":"https://openalex.org/C2187777","wikidata":"https://www.wikidata.org/wiki/Q1071743","display_name":"Parametric surface","level":3,"score":0.2515000104904175},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.25130000710487366}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.2312/sgp/sgp04/159-168","is_oa":true,"landing_page_url":"https://doi.org/10.2312/sgp/sgp04/159-168","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":"doi:10.2312/sgp/sgp04/159-168","is_oa":true,"landing_page_url":"https://doi.org/10.2312/sgp/sgp04/159-168","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":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Subdivision-based":[0],"representations":[1,102],"are":[2,79],"recognized":[3],"as":[4],"important":[5,88],"tools":[6],"for":[7,13,34,89],"the":[8,52,72,83,98,104],"generation":[9],"of":[10,23,31,37,55,67,100],"high-quality":[11],"surfaces":[12,26,39,57],"Computer":[14],"Graphics.":[15],"In":[16,49],"this":[17],"paper":[18],"we":[19],"describe":[20],"two":[21],"parameterizations":[22],"Catmull-Clark":[24],"subdivision":[25,47,56,107],"that":[27,94],"allow":[28],"a":[29],"variety":[30],"algorithms":[32],"designed":[33],"other":[35],"types":[36],"parametric":[38],"(i.e.,":[40],"B-splines)":[41],"to":[42,46,96],"be":[43],"directly":[44],"applied":[45],"surfaces.":[48],"contrast":[50],"with":[51,75],"natural":[53],"parameterization":[54],"characterized":[58],"by":[59],"diverging":[60],"first":[61],"order":[62],"derivatives":[63,73],"around":[64],"extraordinary":[65],"vertices":[66],"valence":[68],"higher":[69],"than":[70],"four,":[71],"associated":[74],"our":[76],"proposed":[77],"methods":[78],"defined":[80],"everywhere":[81],"on":[82],"surface.":[84],"This":[85],"is":[86],"especially":[87],"Computer-Aided":[90],"Design":[91],"(CAD)":[92],"applications":[93],"seek":[95],"address":[97],"limitations":[99],"NURBS-based":[101],"through":[103],"more":[105],"flexible":[106],"framework.":[108]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
