{"id":"https://openalex.org/W2031426983","doi":"https://doi.org/10.1145/2659467.2659469","title":"An introduction to Ricci flow and volumetric approximation with applications to shape modeling","display_name":"An introduction to Ricci flow and volumetric approximation with applications to shape modeling","publication_year":2014,"publication_date":"2014-11-24","ids":{"openalex":"https://openalex.org/W2031426983","doi":"https://doi.org/10.1145/2659467.2659469","mag":"2031426983"},"language":"en","primary_location":{"id":"doi:10.1145/2659467.2659469","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2659467.2659469","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIGGRAPH Asia 2014 Courses","raw_type":"proceedings-article"},"type":"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/A5079829556","display_name":"Giuseppe Patan\u00e8","orcid":"https://orcid.org/0000-0002-2276-9553"},"institutions":[{"id":"https://openalex.org/I4210137033","display_name":"Istituto di Matematica Applicata e Tecnologie Informatiche","ror":"https://ror.org/03m0n3c07","country_code":"IT","type":"education","lineage":["https://openalex.org/I4210137033","https://openalex.org/I4210155236"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Giuseppe Patane","raw_affiliation_strings":["Consiglio Nazionale delle Ricerche, Istituto di Matematica Applicata e Tecnologie Informatiche, Genova, Italy"],"affiliations":[{"raw_affiliation_string":"Consiglio Nazionale delle Ricerche, Istituto di Matematica Applicata e Tecnologie Informatiche, Genova, Italy","institution_ids":["https://openalex.org/I4210137033"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100353783","display_name":"Xin Li","orcid":"https://orcid.org/0000-0002-0144-9489"},"institutions":[{"id":"https://openalex.org/I121820613","display_name":"Louisiana State University","ror":"https://ror.org/05ect4e57","country_code":"US","type":"education","lineage":["https://openalex.org/I121820613"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Xin Shane Li","raw_affiliation_strings":["Louisiana State University","Louisiana State University**"],"affiliations":[{"raw_affiliation_string":"Louisiana State University","institution_ids":["https://openalex.org/I121820613"]},{"raw_affiliation_string":"Louisiana State University**","institution_ids":["https://openalex.org/I121820613"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100607707","display_name":"Xianfeng Gu","orcid":"https://orcid.org/0000-0001-8226-5851"},"institutions":[{"id":"https://openalex.org/I59553526","display_name":"Stony Brook University","ror":"https://ror.org/05qghxh33","country_code":"US","type":"education","lineage":["https://openalex.org/I59553526"]},{"id":"https://openalex.org/I1327163397","display_name":"State University of New York","ror":"https://ror.org/01q1z8k08","country_code":"US","type":"education","lineage":["https://openalex.org/I1327163397"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"David Xianfeng Gu","raw_affiliation_strings":["State University of New York at Stony Brook, New York"],"affiliations":[{"raw_affiliation_string":"State University of New York at Stony Brook, New York","institution_ids":["https://openalex.org/I59553526","https://openalex.org/I1327163397"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5079829556"],"corresponding_institution_ids":["https://openalex.org/I4210137033"],"apc_list":null,"apc_paid":null,"fwci":1.2615,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.78162058,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"118"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10719","display_name":"3D Shape Modeling and Analysis","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9993000030517578,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9970999956130981,"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/conformal-map","display_name":"Conformal map","score":0.6902793645858765},{"id":"https://openalex.org/keywords/ricci-flow","display_name":"Ricci flow","score":0.6481701731681824},{"id":"https://openalex.org/keywords/smoothness","display_name":"Smoothness","score":0.6331245303153992},{"id":"https://openalex.org/keywords/geometric-flow","display_name":"Geometric flow","score":0.6276895999908447},{"id":"https://openalex.org/keywords/feature","display_name":"Feature (linguistics)","score":0.512636125087738},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5121805667877197},{"id":"https://openalex.org/keywords/surface","display_name":"Surface (topology)","score":0.481806218624115},{"id":"https://openalex.org/keywords/shape-analysis","display_name":"Shape analysis (program analysis)","score":0.4679243564605713},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.42861172556877136},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.40595024824142456},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.37215083837509155},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.3456270694732666},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.323589026927948},{"id":"https://openalex.org/keywords/ricci-curvature","display_name":"Ricci curvature","score":0.26790767908096313},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.25808727741241455},{"id":"https://openalex.org/keywords/curvature","display_name":"Curvature","score":0.21147695183753967}],"concepts":[{"id":"https://openalex.org/C98214594","wikidata":"https://www.wikidata.org/wiki/Q850275","display_name":"Conformal map","level":2,"score":0.6902793645858765},{"id":"https://openalex.org/C148729565","wikidata":"https://www.wikidata.org/wiki/Q1361396","display_name":"Ricci flow","level":4,"score":0.6481701731681824},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.6331245303153992},{"id":"https://openalex.org/C32209215","wikidata":"https://www.wikidata.org/wiki/Q5535483","display_name":"Geometric flow","level":3,"score":0.6276895999908447},{"id":"https://openalex.org/C2776401178","wikidata":"https://www.wikidata.org/wiki/Q12050496","display_name":"Feature (linguistics)","level":2,"score":0.512636125087738},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5121805667877197},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.481806218624115},{"id":"https://openalex.org/C112604564","wikidata":"https://www.wikidata.org/wiki/Q7489226","display_name":"Shape analysis (program analysis)","level":3,"score":0.4679243564605713},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.42861172556877136},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.40595024824142456},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.37215083837509155},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3456270694732666},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.323589026927948},{"id":"https://openalex.org/C12089564","wikidata":"https://www.wikidata.org/wiki/Q1195879","display_name":"Ricci curvature","level":3,"score":0.26790767908096313},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.25808727741241455},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.21147695183753967},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C97686452","wikidata":"https://www.wikidata.org/wiki/Q7604153","display_name":"Static analysis","level":2,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/2659467.2659469","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2659467.2659469","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIGGRAPH Asia 2014 Courses","raw_type":"proceedings-article"},{"id":"pmh:oai:repository.lsu.edu:eecs_pubs-1753","is_oa":false,"landing_page_url":"https://repository.lsu.edu/eecs_pubs/754","pdf_url":null,"source":{"id":"https://openalex.org/S4210169993","display_name":"Civil War Book Review","issn_l":"1528-6592","issn":["1528-6592"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310315936","host_organization_name":"Louisiana State University","host_organization_lineage":["https://openalex.org/P4310315936"],"host_organization_lineage_names":["Louisiana State University"],"type":"journal"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Faculty Publications","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","score":0.5899999737739563,"id":"https://metadata.un.org/sdg/11"}],"awards":[{"id":"https://openalex.org/G1717417475","display_name":null,"funder_award_id":"FP7-ICT-2011-318787 Integrating Project IQmulus - A High-volume Fusion and Analysis Platform for Geospatial Point Clouds, Coverages and Volumetric Data Sets","funder_id":"https://openalex.org/F4320334960","funder_display_name":"Seventh Framework Programme"}],"funders":[{"id":"https://openalex.org/F4320334960","display_name":"Seventh Framework Programme","ror":"https://ror.org/00k4n6c32"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":250,"referenced_works":["https://openalex.org/W38977518","https://openalex.org/W133655297","https://openalex.org/W204135500","https://openalex.org/W1485542881","https://openalex.org/W1504061871","https://openalex.org/W1506828534","https://openalex.org/W1523815711","https://openalex.org/W1526694294","https://openalex.org/W1530202807","https://openalex.org/W1530948733","https://openalex.org/W1546076119","https://openalex.org/W1548333856","https://openalex.org/W1556016694","https://openalex.org/W1560724230","https://openalex.org/W1561653267","https://openalex.org/W1574024211","https://openalex.org/W1578099820","https://openalex.org/W1585162983","https://openalex.org/W1587744656","https://openalex.org/W1594387031","https://openalex.org/W1596547119","https://openalex.org/W1597141413","https://openalex.org/W1621614599","https://openalex.org/W1746021914","https://openalex.org/W1758110319","https://openalex.org/W1790421890","https://openalex.org/W1808456567","https://openalex.org/W1930432779","https://openalex.org/W1964811929","https://openalex.org/W1965591439","https://openalex.org/W1966194116","https://openalex.org/W1967580607","https://openalex.org/W1968512109","https://openalex.org/W1968788401","https://openalex.org/W1974956622","https://openalex.org/W1975207205","https://openalex.org/W1975446953","https://openalex.org/W1976584051","https://openalex.org/W1977148430","https://openalex.org/W1977732869","https://openalex.org/W1977758817","https://openalex.org/W1978221897","https://openalex.org/W1981193610","https://openalex.org/W1982465050","https://openalex.org/W1984159596","https://openalex.org/W1985127753","https://openalex.org/W1986280275","https://openalex.org/W1986849647","https://openalex.org/W1989368986","https://openalex.org/W1991393198","https://openalex.org/W1993775814","https://openalex.org/W1994393928","https://openalex.org/W1995578504","https://openalex.org/W2000214666","https://openalex.org/W2000354818","https://openalex.org/W2002769845","https://openalex.org/W2005045499","https://openalex.org/W2005236080","https://openalex.org/W2005999035","https://openalex.org/W2007206727","https://openalex.org/W2008535862","https://openalex.org/W2009091792","https://openalex.org/W2010209192","https://openalex.org/W2012500162","https://openalex.org/W2012876210","https://openalex.org/W2018833029","https://openalex.org/W2018919812","https://openalex.org/W2021167140","https://openalex.org/W2022204099","https://openalex.org/W2023661891","https://openalex.org/W2027592638","https://openalex.org/W2027630541","https://openalex.org/W2027809508","https://openalex.org/W2034374737","https://openalex.org/W2035957501","https://openalex.org/W2036163530","https://openalex.org/W2037149239","https://openalex.org/W2038254603","https://openalex.org/W2039377291","https://openalex.org/W2039402388","https://openalex.org/W2039428420","https://openalex.org/W2039881887","https://openalex.org/W2042164290","https://openalex.org/W2042503073","https://openalex.org/W2045224681","https://openalex.org/W2045492545","https://openalex.org/W2046579463","https://openalex.org/W2047161559","https://openalex.org/W2047500015","https://openalex.org/W2047594593","https://openalex.org/W2050085159","https://openalex.org/W2050230469","https://openalex.org/W2052069724","https://openalex.org/W2052088750","https://openalex.org/W2053798192","https://openalex.org/W2057275501","https://openalex.org/W2060116539","https://openalex.org/W2060408866","https://openalex.org/W2063364217","https://openalex.org/W2063977159","https://openalex.org/W2064007916","https://openalex.org/W2064233581","https://openalex.org/W2068834636","https://openalex.org/W2069934462","https://openalex.org/W2076422168","https://openalex.org/W2076702317","https://openalex.org/W2077563333","https://openalex.org/W2077927386","https://openalex.org/W2079017595","https://openalex.org/W2079209697","https://openalex.org/W2079966248","https://openalex.org/W2080070865","https://openalex.org/W2083561088","https://openalex.org/W2083701338","https://openalex.org/W2085499357","https://openalex.org/W2088757023","https://openalex.org/W2089206901","https://openalex.org/W2089939988","https://openalex.org/W2089982566","https://openalex.org/W2090467878","https://openalex.org/W2091715846","https://openalex.org/W2094163096","https://openalex.org/W2097308346","https://openalex.org/W2097523702","https://openalex.org/W2098355846","https://openalex.org/W2098443654","https://openalex.org/W2098942126","https://openalex.org/W2099116730","https://openalex.org/W2099151424","https://openalex.org/W2099606917","https://openalex.org/W2099953968","https://openalex.org/W2100607348","https://openalex.org/W2100657858","https://openalex.org/W2100768308","https://openalex.org/W2101868198","https://openalex.org/W2102326671","https://openalex.org/W2103648137","https://openalex.org/W2103975664","https://openalex.org/W2108082108","https://openalex.org/W2108605584","https://openalex.org/W2108759471","https://openalex.org/W2108870191","https://openalex.org/W2109340300","https://openalex.org/W2112804092","https://openalex.org/W2112846573","https://openalex.org/W2113072535","https://openalex.org/W2117684310","https://openalex.org/W2119386067","https://openalex.org/W2119821739","https://openalex.org/W2120398992","https://openalex.org/W2120514074","https://openalex.org/W2121842556","https://openalex.org/W2124544272","https://openalex.org/W2125903589","https://openalex.org/W2126199001","https://openalex.org/W2126800856","https://openalex.org/W2127025496","https://openalex.org/W2127033124","https://openalex.org/W2127689830","https://openalex.org/W2129922578","https://openalex.org/W2131283235","https://openalex.org/W2131369589","https://openalex.org/W2131771497","https://openalex.org/W2131911297","https://openalex.org/W2133367066","https://openalex.org/W2133544837","https://openalex.org/W2134166817","https://openalex.org/W2134383396","https://openalex.org/W2134921160","https://openalex.org/W2135073078","https://openalex.org/W2135785391","https://openalex.org/W2137742453","https://openalex.org/W2140000690","https://openalex.org/W2140500712","https://openalex.org/W2143030836","https://openalex.org/W2143075606","https://openalex.org/W2143529965","https://openalex.org/W2143956139","https://openalex.org/W2144044408","https://openalex.org/W2145675995","https://openalex.org/W2146968309","https://openalex.org/W2147140280","https://openalex.org/W2147496260","https://openalex.org/W2147751396","https://openalex.org/W2148768866","https://openalex.org/W2148892491","https://openalex.org/W2151407741","https://openalex.org/W2151427888","https://openalex.org/W2151497844","https://openalex.org/W2153211532","https://openalex.org/W2154861546","https://openalex.org/W2156247583","https://openalex.org/W2156512439","https://openalex.org/W2158476348","https://openalex.org/W2158778494","https://openalex.org/W2160692760","https://openalex.org/W2163581538","https://openalex.org/W2163727044","https://openalex.org/W2165649407","https://openalex.org/W2167014440","https://openalex.org/W2168022088","https://openalex.org/W2168928374","https://openalex.org/W2170167721","https://openalex.org/W2172154910","https://openalex.org/W2182827928","https://openalex.org/W2237825899","https://openalex.org/W2293537096","https://openalex.org/W2293626636","https://openalex.org/W2294879381","https://openalex.org/W2294967723","https://openalex.org/W2296264134","https://openalex.org/W2336383758","https://openalex.org/W2365029215","https://openalex.org/W2427881153","https://openalex.org/W2498162759","https://openalex.org/W2537228944","https://openalex.org/W2561675875","https://openalex.org/W2565699923","https://openalex.org/W2798909945","https://openalex.org/W2799004609","https://openalex.org/W2911396769","https://openalex.org/W2914050481","https://openalex.org/W2998100778","https://openalex.org/W2999602145","https://openalex.org/W3004635496","https://openalex.org/W3015570124","https://openalex.org/W3119651796","https://openalex.org/W3136375062","https://openalex.org/W3136466070","https://openalex.org/W3138464846","https://openalex.org/W4205401338","https://openalex.org/W4206225701","https://openalex.org/W4213367101","https://openalex.org/W4214886506","https://openalex.org/W4239890145","https://openalex.org/W4242194656","https://openalex.org/W4244829582","https://openalex.org/W4246235746","https://openalex.org/W4247288538","https://openalex.org/W4249019869","https://openalex.org/W4249428005","https://openalex.org/W4285719527","https://openalex.org/W4318977545","https://openalex.org/W6631662477","https://openalex.org/W6631987545","https://openalex.org/W6633545542","https://openalex.org/W6634702315","https://openalex.org/W6635452582","https://openalex.org/W6750968397","https://openalex.org/W6776535907"],"related_works":["https://openalex.org/W3102752062","https://openalex.org/W2046267209","https://openalex.org/W1582077987","https://openalex.org/W2274037787","https://openalex.org/W2186774039","https://openalex.org/W2099151424","https://openalex.org/W2147140280","https://openalex.org/W2041663496","https://openalex.org/W4293180207","https://openalex.org/W4306944752"],"abstract_inverted_index":{"Extending":[0],"a":[1,17,44,66,114],"shape-driven":[2],"map":[3],"to":[4,12,88,117,124,140],"the":[5,8,13,25,52,70,81,108,119,135],"interior":[6],"of":[7,27,39,72,83,128],"input":[9],"shape":[10,76,89,121,141],"and":[11,29,46,61,64,74,85,94,101,123,143],"surrounding":[14],"volume":[15],"is":[16,113],"difficult":[18],"problem":[19],"since":[20],"it":[21,79],"typically":[22],"relies":[23],"on":[24,69],"integration":[26,71],"shape-based":[28,84],"volumetric":[30,54,86,92],"information,":[31],"together":[32],"with":[33],"smoothness":[34],"conditions,":[35],"interpolating":[36],"constraints,":[37],"preservation":[38],"feature":[40],"values":[41],"at":[42],"both":[43,58],"local":[45],"global":[47],"level.":[48],"This":[49],"survey":[50],"discusses":[51],"main":[53],"approximation":[55,98],"schemes":[56],"for":[57],"3D":[59],"shapes":[60],"d-dimensional":[62],"data,":[63],"provides":[65],"unified":[67],"discussion":[68],"surface-based":[73],"volume-based":[75],"information.":[77],"Then,":[78],"describes":[80],"application":[82],"techniques":[87],"modeling":[90],"through":[91,99],"parameterization":[93],"polycube":[95],"splines;":[96],"feature-driven":[97],"kernels":[100],"radial":[102],"basis":[103],"functions.":[104],"We":[105,133],"also":[106],"discuss":[107],"Hamilton's":[109],"Ricci":[110],"flow,":[111],"which":[112],"powerful":[115],"tool":[116],"compute":[118],"conformal":[120],"structure":[122],"design":[125],"Riemannian":[126],"metrics":[127],"manifolds":[129],"by":[130,137],"prescribed":[131],"curvatures.":[132],"conclude":[134],"presentation":[136],"discussing":[138],"applications":[139],"analysis":[142],"medicine.":[144]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}