{"id":"https://openalex.org/W4391353441","doi":"https://doi.org/10.1137/23m1571216","title":"Computing Weak Distance between the 2-Sphere and Its Nonsmooth Approximations","display_name":"Computing Weak Distance between the 2-Sphere and Its Nonsmooth Approximations","publication_year":2024,"publication_date":"2024-01-30","ids":{"openalex":"https://openalex.org/W4391353441","doi":"https://doi.org/10.1137/23m1571216"},"language":"en","primary_location":{"id":"doi:10.1137/23m1571216","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1137/23m1571216","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-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/A5019607241","display_name":"Kazuki Koga","orcid":"https://orcid.org/0000-0002-4199-2670"},"institutions":[{"id":"https://openalex.org/I114531698","display_name":"Tokyo Institute of Technology","ror":"https://ror.org/0112mx960","country_code":"JP","type":"education","lineage":["https://openalex.org/I114531698"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Kazuki Koga","raw_affiliation_strings":["Department of Mathematical and Computing Science, Tokyo Institute of Technology, Tokyo 152-8550, Japan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical and Computing Science, Tokyo Institute of Technology, Tokyo 152-8550, Japan","institution_ids":["https://openalex.org/I114531698"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5019607241"],"corresponding_institution_ids":["https://openalex.org/I114531698"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.01751507,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"46","issue":"1","first_page":"A360","last_page":"A375"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9937999844551086,"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":0.9937999844551086,"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/T10688","display_name":"Image and Signal Denoising Methods","score":0.9930999875068665,"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"}},{"id":"https://openalex.org/T11558","display_name":"Composite Material Mechanics","score":0.9876000285148621,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/mathematics","display_name":"Mathematics","score":0.8030308485031128},{"id":"https://openalex.org/keywords/approximations-of-\u03c0","display_name":"Approximations of \u03c0","score":0.47488921880722046},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4259078800678253},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.414247065782547},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3263850808143616}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8030308485031128},{"id":"https://openalex.org/C193386753","wikidata":"https://www.wikidata.org/wiki/Q1130396","display_name":"Approximations of \u03c0","level":2,"score":0.47488921880722046},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4259078800678253},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.414247065782547},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3263850808143616},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/23m1571216","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1137/23m1571216","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.5899999737739563,"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W645173616","https://openalex.org/W1463130228","https://openalex.org/W1530034100","https://openalex.org/W1531371725","https://openalex.org/W1963792518","https://openalex.org/W1967173056","https://openalex.org/W1978007800","https://openalex.org/W1998527589","https://openalex.org/W1999955870","https://openalex.org/W2008021403","https://openalex.org/W2010122118","https://openalex.org/W2012300893","https://openalex.org/W2032709309","https://openalex.org/W2039559762","https://openalex.org/W2072859558","https://openalex.org/W2074551095","https://openalex.org/W2076865563","https://openalex.org/W2086391199","https://openalex.org/W2131768055","https://openalex.org/W2134086356","https://openalex.org/W2501178463","https://openalex.org/W2599177365","https://openalex.org/W2881836564","https://openalex.org/W2962746791","https://openalex.org/W2963607619","https://openalex.org/W2965004973","https://openalex.org/W2973391561","https://openalex.org/W2974501049","https://openalex.org/W2986927241","https://openalex.org/W3003966688","https://openalex.org/W3047528752","https://openalex.org/W3210395619","https://openalex.org/W4200036674","https://openalex.org/W4206471589","https://openalex.org/W4211001652","https://openalex.org/W4233762729","https://openalex.org/W4249274673","https://openalex.org/W4253117982"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644","https://openalex.org/W2042127053"],"abstract_inverted_index":{".A":[0],"novel":[1],"algorithm":[2],"is":[3,20,61,114,120,123,131],"proposed":[4],"for":[5,54],"quantitative":[6],"comparisons":[7],"between":[8,35,57],"compact":[9],"surfaces":[10],"embedded":[11],"in":[12],"the":[13,26,38,42,47,64,79,98,111,134,140,144],"three-dimensional":[14],"Euclidian":[15],"space.":[16,44,81],"The":[17],"key":[18],"idea":[19],"to":[21,69,91,139,148],"identify":[22],"those":[23],"objects":[24],"with":[25,125],"associated":[27],"surface":[28,59],"measures":[29,60],"and":[30,103,129],"compute":[31],"a":[32,55,71],"weak":[33],"distance":[34],"them":[36],"using":[37],"Fourier":[39,101,118,156],"transform":[40,119],"on":[41,78,105],"ambient":[43],"In":[45,108],"particular,":[46],"inhomogeneous":[48],"Sobolev":[49],"norm":[50,74],"of":[51,75],"negative":[52],"order":[53],"difference":[56],"two":[58],"evaluated":[62],"via":[63],"Plancherel":[65],"theorem,":[66],"which":[67,113],"amounts":[68],"approximating":[70],"weighted":[72],"integral":[73],"smooth":[76,141],"data":[77],"frequency":[80],"This":[82],"approach":[83],"allows":[84],"several":[85],"advantages,":[86],"including":[87],"high":[88],"accuracy":[89],"due":[90],"fast-converging":[92],"numerical":[93,109],"quadrature":[94],"rules,":[95],"acceleration":[96],"by":[97],"nonuniform":[99],"fast":[100,155],"transform,":[102],"parallelization":[104],"many-core":[106],"processors.":[107],"experiments,":[110],"2-sphere,":[112],"an":[115],"example":[116],"whose":[117],"explicitly":[121],"known,":[122],"compared":[124],"its":[126],"icosahedral":[127],"discretization,":[128],"it":[130],"observed":[132],"that":[133],"piecewise":[135],"linear":[136],"approximations":[137],"converge":[138],"object":[142],"at":[143],"quadratic":[145],"rate":[146],"up":[147],"small":[149],"truncation.Keywordssurface":[150],"comparisonsurface":[151],"measureSobolev":[152],"normicosahedral":[153],"discretizationnonuniform":[154],"transformgraphics":[157],"processing":[158],"unitMSC":[159],"codes28A7542A3853A0565M50":[160]},"counts_by_year":[],"updated_date":"2025-12-25T23:11:45.687758","created_date":"2025-10-10T00:00:00"}