{"id":"https://openalex.org/W7220941179","doi":"https://doi.org/10.48550/arxiv.2610.09686","title":"Anisotropic Lagrange interpolation on exact spherical triangles","display_name":"Anisotropic Lagrange interpolation on exact spherical triangles","publication_year":2026,"publication_date":"2026-10-07","ids":{"openalex":"https://openalex.org/W7220941179","doi":"https://doi.org/10.48550/arxiv.2610.09686"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.09686","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.09686","pdf_url":"https://arxiv.org/pdf/2610.09686","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.09686","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5140849504","display_name":"Hiroki Ishizaka","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Ishizaka, Hiroki","raw_affiliation_strings":["Team FEM , Matsuyama , Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Team FEM , Matsuyama , Japan","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5140849504"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"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":false,"primary_topic":{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9375,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9375,"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/T12404","display_name":"Mathematical Approximation and Integration","score":0.05510000139474869,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.0017000000225380063,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/spherical-triangles","display_name":"spherical triangles","score":0.9169999957084656},{"id":"https://openalex.org/keywords/geodesic-triangles","display_name":"geodesic triangles","score":0.8230000138282776},{"id":"https://openalex.org/keywords/radial-projection","display_name":"radial projection","score":0.9459999799728394},{"id":"https://openalex.org/keywords/local-error-estimation","display_name":"local error estimation","score":0.7689999938011169},{"id":"https://openalex.org/keywords/dirichlet-energy","display_name":"Dirichlet energy","score":0.8379999995231628},{"id":"https://openalex.org/keywords/spherical-triangulation","display_name":"spherical triangulation","score":0.765999972820282},{"id":"https://openalex.org/keywords/laplace-beltrami-operator","display_name":"Laplace-Beltrami operator","score":0.8659999966621399}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7563999891281128},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6060000061988831},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.5809999704360962},{"id":"https://openalex.org/C64208722","wikidata":"https://www.wikidata.org/wiki/Q861606","display_name":"Lagrange polynomial","level":3,"score":0.5756000280380249},{"id":"https://openalex.org/C171836373","wikidata":"https://www.wikidata.org/wiki/Q2266329","display_name":"Linear interpolation","level":3,"score":0.49000000953674316},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.45320001244544983},{"id":"https://openalex.org/C165818556","wikidata":"https://www.wikidata.org/wiki/Q213488","display_name":"Geodesic","level":2,"score":0.40549999475479126},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.39590001106262207},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.3896999955177307},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.3887999951839447},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.38839998841285706},{"id":"https://openalex.org/C144386022","wikidata":"https://www.wikidata.org/wiki/Q1332997","display_name":"Scale factor (cosmology)","level":5,"score":0.37959998846054077},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.37700000405311584},{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.34310001134872437},{"id":"https://openalex.org/C85725439","wikidata":"https://www.wikidata.org/wiki/Q466686","display_name":"Anisotropy","level":2,"score":0.3424000144004822},{"id":"https://openalex.org/C160446614","wikidata":"https://www.wikidata.org/wiki/Q1322892","display_name":"Chordal graph","level":3,"score":0.3353999853134155},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.33329999446868896},{"id":"https://openalex.org/C88080468","wikidata":"https://www.wikidata.org/wiki/Q637347","display_name":"Polynomial interpolation","level":4,"score":0.32249999046325684},{"id":"https://openalex.org/C2778664614","wikidata":"https://www.wikidata.org/wiki/Q575597","display_name":"Spherical cap","level":2,"score":0.32010000944137573},{"id":"https://openalex.org/C72422203","wikidata":"https://www.wikidata.org/wiki/Q7392545","display_name":"SPHERES","level":2,"score":0.30160000920295715},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.29249998927116394},{"id":"https://openalex.org/C3768446","wikidata":"https://www.wikidata.org/wiki/Q877100","display_name":"Spherical harmonics","level":2,"score":0.2743000090122223},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.27379998564720154},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.26750001311302185},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.26570001244544983},{"id":"https://openalex.org/C2779560616","wikidata":"https://www.wikidata.org/wiki/Q1192869","display_name":"Dirichlet problem","level":3,"score":0.2590000033378601},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.2574999928474426},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2524000108242035},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.25209999084472656}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.09686","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.09686","pdf_url":"https://arxiv.org/pdf/2610.09686","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2610.09686","doi":"https://doi.org/10.48550/arxiv.2610.09686","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.09686","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.09686","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.09686","pdf_url":"https://arxiv.org/pdf/2610.09686","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220941179.pdf","grobid_xml":"https://content.openalex.org/works/W7220941179.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W7134884690","https://openalex.org/W7162503660","https://openalex.org/W7202346198"],"related_works":["https://openalex.org/W2085045785","https://openalex.org/W7100454339","https://openalex.org/W7097550746","https://openalex.org/W2149493707","https://openalex.org/W2790394298","https://openalex.org/W1981581845","https://openalex.org/W2118387305","https://openalex.org/W7098461418","https://openalex.org/W1991521803","https://openalex.org/W3045955707"],"abstract_inverted_index":{"We":[0,35],"study":[1],"linear":[2],"Lagrange":[3],"interpolation":[4,55],"on":[5],"exact":[6,37,202],"geodesic":[7],"spherical":[8,181],"triangles":[9],"obtained":[10],"by":[11,110],"radial":[12,27,33],"projection":[13],"of":[14,81,137,163,196],"chordal":[15,30,68],"triangles.":[16],"Factorising":[17],"the":[18,40,58,66,74,82,90,93,98,107,115,119,128,138,140,147,161,164,170,193,197],"element":[19,83],"map":[20,24],"into":[21],"an":[22,184,188],"affine":[23],"and":[25,45,48,72,86,117],"a":[26,134],"correction":[28],"separates":[29],"anisotropy":[31],"from":[32],"distortion.":[34],"derive":[36],"identities":[38],"for":[39,192],"surface":[41],"measure,":[42],"Dirichlet":[43],"energy,":[44],"directional":[46,69,100,131,173],"derivatives,":[47],"use":[49],"them":[50],"to":[51,57,146,179],"transfer":[52],"planar":[53],"anisotropic":[54,189],"estimates":[56,64,177],"sphere.":[59],"The":[60,157,175],"resulting":[61],"local":[62,176],"error":[63],"retain":[65],"two":[67],"length":[70],"scales":[71,113],"keep":[73],"geometric":[75],"factors":[76],"explicit,":[77],"with":[78,114,133,201],"constants":[79],"independent":[80,136],"size,":[84],"shape,":[85],"sphere":[87],"radius.":[88],"In":[89],"gradient":[91],"estimate,":[92],"maximum-angle":[94,121,141],"factor":[95,142,167],"multiplies":[96],"only":[97],"longer":[99],"scale.":[101,174],"Four":[102],"explicit":[103],"triangle":[104],"families":[105],"quantify":[106],"loss":[108],"caused":[109],"replacing":[111],"these":[112],"diameter":[116],"establish":[118],"sharp":[120],"dependence.":[122],"They":[123],"also":[124],"show":[125],"that,":[126],"within":[127],"same":[129,171],"two-term":[130],"bound":[132],"constant":[135],"element,":[139],"cannot":[143],"be":[144],"moved":[145],"shorter":[148],"scale":[149],"or":[150],"have":[151],"its":[152],"exponent":[153],"reduced":[154],"below":[155],"one.":[156],"fourth":[158],"family":[159],"proves":[160],"optimality":[162],"square-root":[165],"radial-transfer":[166],"while":[168],"retaining":[169],"transported":[172],"extend":[178],"compatible":[180],"triangulations.":[182],"As":[183],"application,":[185],"they":[186],"yield":[187],"energy-error":[190],"estimate":[191],"conforming":[194],"approximation":[195],"mean-zero":[198],"Laplace--Beltrami":[199],"problem":[200],"integration.":[203]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-09T00:00:00"}