{"id":"https://openalex.org/W2059236787","doi":"https://doi.org/10.1145/1839778.1839795","title":"Hyperbolic centroidal Voronoi tessellation","display_name":"Hyperbolic centroidal Voronoi tessellation","publication_year":2010,"publication_date":"2010-09-01","ids":{"openalex":"https://openalex.org/W2059236787","doi":"https://doi.org/10.1145/1839778.1839795","mag":"2059236787"},"language":"en","primary_location":{"is_oa":false,"landing_page_url":"https://doi.org/10.1145/1839778.1839795","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false},"type":"article","type_crossref":"proceedings-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/A5004657541","display_name":"Guodong Rong","orcid":"https://orcid.org/0000-0001-8822-0136"},"institutions":[],"countries":["US"],"is_corresponding":false,"raw_author_name":"Guodong Rong","raw_affiliation_strings":["University of Texas at Dallas"],"affiliations":[{"raw_affiliation_string":"University of Texas at Dallas","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100675221","display_name":"Miao Jin","orcid":"https://orcid.org/0000-0002-0054-4281"},"institutions":[{"id":"https://openalex.org/I79516672","display_name":"University of Louisiana at Lafayette","ror":"https://ror.org/01x8rc503","country_code":"US","type":"education","lineage":["https://openalex.org/I2799628689","https://openalex.org/I79516672"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Miao Jin","raw_affiliation_strings":["University of Louisiana at Lafayette#TAB#"],"affiliations":[{"raw_affiliation_string":"University of Louisiana at Lafayette#TAB#","institution_ids":["https://openalex.org/I79516672"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5030253345","display_name":"Xiaohu Guo","orcid":"https://orcid.org/0000-0002-7610-6923"},"institutions":[],"countries":["US"],"is_corresponding":false,"raw_author_name":"Xiaohu Guo","raw_affiliation_strings":["University of Texas at Dallas"],"affiliations":[{"raw_affiliation_string":"University of Texas at Dallas","institution_ids":[]}]}],"institution_assertions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.144,"has_fulltext":false,"cited_by_count":27,"citation_normalized_percentile":{"value":0.884058,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":92},"biblio":{"volume":null,"issue":null,"first_page":"117","last_page":"126"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Mesh Generation Algorithms","score":0.9992,"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"}},"topics":[{"id":"https://openalex.org/T10996","display_name":"Mesh Generation Algorithms","score":0.9992,"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":"Analysis of Three-Dimensional Shape Structures","score":0.9981,"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/T12923","display_name":"Connected Component Labeling Algorithms","score":0.9968,"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/centroidal-voronoi-tessellation","display_name":"Centroidal Voronoi tessellation","score":0.7635836},{"id":"https://openalex.org/keywords/hyperbolic-space","display_name":"Hyperbolic space","score":0.6130135},{"id":"https://openalex.org/keywords/centroidal-voronoi-tessellations","display_name":"Centroidal Voronoi Tessellations","score":0.591129},{"id":"https://openalex.org/keywords/hyperbolic-tree","display_name":"Hyperbolic tree","score":0.5535204},{"id":"https://openalex.org/keywords/tessellation","display_name":"Tessellation (computer graphics)","score":0.54872924},{"id":"https://openalex.org/keywords/computational-geometry","display_name":"Computational Geometry","score":0.535522},{"id":"https://openalex.org/keywords/geometric-optimization","display_name":"Geometric Optimization","score":0.503336}],"concepts":[{"id":"https://openalex.org/C205672865","wikidata":"https://www.wikidata.org/wiki/Q5062961","display_name":"Centroidal Voronoi tessellation","level":3,"score":0.7635836},{"id":"https://openalex.org/C24881265","wikidata":"https://www.wikidata.org/wiki/Q757267","display_name":"Voronoi diagram","level":2,"score":0.7376641},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.6289081},{"id":"https://openalex.org/C83677898","wikidata":"https://www.wikidata.org/wiki/Q1878538","display_name":"Hyperbolic space","level":2,"score":0.6130135},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.60020596},{"id":"https://openalex.org/C97654310","wikidata":"https://www.wikidata.org/wiki/Q574023","display_name":"Hyperbolic tree","level":4,"score":0.5535204},{"id":"https://openalex.org/C43817857","wikidata":"https://www.wikidata.org/wiki/Q9357547","display_name":"Tessellation (computer graphics)","level":2,"score":0.54872924},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.5129847},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.48298562},{"id":"https://openalex.org/C157369684","wikidata":"https://www.wikidata.org/wiki/Q34740","display_name":"Genus","level":2,"score":0.47285748},{"id":"https://openalex.org/C77660652","wikidata":"https://www.wikidata.org/wiki/Q150971","display_name":"Computer graphics","level":2,"score":0.46367997},{"id":"https://openalex.org/C36464697","wikidata":"https://www.wikidata.org/wiki/Q451553","display_name":"Visualization","level":2,"score":0.43212542},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.39859846},{"id":"https://openalex.org/C70984080","wikidata":"https://www.wikidata.org/wiki/Q2619102","display_name":"Hyperbolic manifold","level":3,"score":0.39764714},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.38800257},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.38736576},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2523918},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.20447466},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.1843827},{"id":"https://openalex.org/C92047909","wikidata":"https://www.wikidata.org/wiki/Q204034","display_name":"Hyperbolic function","level":2,"score":0.12733689},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.105522126},{"id":"https://openalex.org/C59822182","wikidata":"https://www.wikidata.org/wiki/Q441","display_name":"Botany","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"is_oa":false,"landing_page_url":"https://doi.org/10.1145/1839778.1839795","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false}],"best_oa_location":null,"sustainable_development_goals":[],"grants":[{"funder":"https://openalex.org/F4320309392","funder_display_name":"Louisiana Board of Regents","award_id":"RD-A-21"},{"funder":"https://openalex.org/F4320337387","funder_display_name":"Division of Computing and Communication Foundations","award_id":"CCF-0727098"}],"datasets":[],"versions":[],"referenced_works_count":32,"referenced_works":["https://openalex.org/W1497582147","https://openalex.org/W1550058215","https://openalex.org/W1676204294","https://openalex.org/W1890795085","https://openalex.org/W1969745237","https://openalex.org/W1984420702","https://openalex.org/W2006248644","https://openalex.org/W2010495518","https://openalex.org/W2048475323","https://openalex.org/W2051752778","https://openalex.org/W2056205248","https://openalex.org/W2056422961","https://openalex.org/W2065978712","https://openalex.org/W2068131844","https://openalex.org/W2069447707","https://openalex.org/W2092924973","https://openalex.org/W2114288655","https://openalex.org/W2123837580","https://openalex.org/W2127218421","https://openalex.org/W2129460996","https://openalex.org/W2134770338","https://openalex.org/W2135770948","https://openalex.org/W2137419625","https://openalex.org/W2142228262","https://openalex.org/W2150593711","https://openalex.org/W215406955","https://openalex.org/W2248938770","https://openalex.org/W2299467264","https://openalex.org/W2404467080","https://openalex.org/W3040192017","https://openalex.org/W4239339957","https://openalex.org/W4243029875"],"related_works":["https://openalex.org/W4385573134","https://openalex.org/W4308618232","https://openalex.org/W4240041676","https://openalex.org/W3215436782","https://openalex.org/W3169148677","https://openalex.org/W2362866365","https://openalex.org/W2106320975","https://openalex.org/W2045336066","https://openalex.org/W2023866887","https://openalex.org/W1608408498"],"abstract_inverted_index":{"The":[0],"centroidal":[1],"Voronoi":[2],"tessellation":[3],"(CVT)":[4],"has":[5,63],"found":[6],"versatile":[7],"applications":[8],"in":[9],"geometric":[10],"modeling,":[11],"computer":[12],"graphics,":[13],"and":[14,39,46,87,99,122],"visualization.":[15],"In":[16],"this":[17,44],"paper,":[18],"we":[19,113],"extend":[20],"the":[21,24,40,47,60,64,72,88,96,100,111,115],"concept":[22],"of":[23,102,110],"CVT":[25,35,49,62,117],"from":[26],"Euclidean":[27,69],"space":[28],"to":[29,78,94,118],"hyperbolic":[30,34,48,61,97,116],"space.":[31],"A":[32],"novel":[33],"energy":[36,45],"is":[37,50,105],"defined,":[38],"relationship":[41],"between":[42],"minimizing":[43],"proved.":[51,106],"We":[52],"also":[53],"show":[54],"by":[55],"our":[56],"experimental":[57],"results":[58,125],"that":[59],"similar":[65],"property":[66],"as":[67],"its":[68],"counterpart":[70],"where":[71],"sites":[73],"are":[74,92],"uniformly":[75],"distributed":[76],"according":[77],"given":[79],"density":[80],"values.":[81],"Two":[82],"algorithms":[83],"--":[84,91],"Lloyd's":[85,103],"algorithm":[86,90,104],"L-BFGS":[89],"adopted":[93],"compute":[95,119],"CVT,":[98],"convergence":[101],"As":[107],"an":[108],"example":[109],"application,":[112],"utilize":[114],"uniform":[120],"partitions":[121],"high-quality":[123],"remeshing":[124],"for":[126],"high-genus":[127],"(genus>1)":[128],"surfaces.":[129]},"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W2059236787","counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2016,"cited_by_count":4},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":4}],"updated_date":"2024-11-20T04:01:11.943499","created_date":"2016-06-24"}