{"id":"https://openalex.org/W2157591578","doi":"https://doi.org/10.2312/localchapterevents/tpcg/tpcg08/099-106","title":"A Lemon is not a Monstar: Visualization of Singularities of Symmetric Second Rank Tensor Fields in the Plane","display_name":"A Lemon is not a Monstar: Visualization of Singularities of Symmetric Second Rank Tensor Fields in the Plane","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W2157591578","doi":"https://doi.org/10.2312/localchapterevents/tpcg/tpcg08/099-106","mag":"2157591578"},"language":"en","primary_location":{"id":"pmh:oai:pure.atira.dk:openaire/844f4383-cf6d-4c60-a3bc-43d877ffb134","is_oa":true,"landing_page_url":"https://research.manchester.ac.uk/en/publications/844f4383-cf6d-4c60-a3bc-43d877ffb134","pdf_url":null,"source":{"id":"https://openalex.org/S4306400662","display_name":"Research Explorer (The University of Manchester)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I28407311","host_organization_name":"University of Manchester","host_organization_lineage":["https://openalex.org/I28407311"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Liu, J, Hewitt, W T, Lionheart, W R B, Montaldi, J & Turner, M 2008, A lemon is not a monstar: Visualization of singularities of symmetric second rank tensor fields in the plane. in Theory and Practice of Computer Graphics 2008, TPCG 2008 - Eurographics UK Chapter Proceedings|Theory Pract. Comput. Graph., TPCG - Eurographics UK Chapter Proc.. Eurographics Association, Manchester, pp. 99-106, 6th Theory and Practice of Computer Graphics Conference, TPCG 2008, Manchester, 1/07/08. https://doi.org/10.2312/LocalChapterEvents/TPCG/TPCG08/099-106","raw_type":"info:eu-repo/semantics/publishedVersion"},"type":"article","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://research.manchester.ac.uk/en/publications/844f4383-cf6d-4c60-a3bc-43d877ffb134","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100409741","display_name":"Jia Liu","orcid":"https://orcid.org/0000-0003-0383-0934"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Liu, J.","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5113496570","display_name":"W.T. Hewitt","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hewitt, W. T.","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058599589","display_name":"William Lionheart","orcid":"https://orcid.org/0000-0003-0971-4678"},"institutions":[{"id":"https://openalex.org/I4210131439","display_name":"Applied Mathematics (United States)","ror":"https://ror.org/03seew607","country_code":"US","type":"company","lineage":["https://openalex.org/I4210131439"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Lionheart, W. R. B.","raw_affiliation_strings":["Applied Mathematics"],"affiliations":[{"raw_affiliation_string":"Applied Mathematics","institution_ids":["https://openalex.org/I4210131439"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065898862","display_name":"James Montaldi","orcid":"https://orcid.org/0000-0002-2135-8998"},"institutions":[{"id":"https://openalex.org/I4210131439","display_name":"Applied Mathematics (United States)","ror":"https://ror.org/03seew607","country_code":"US","type":"company","lineage":["https://openalex.org/I4210131439"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Montaldi, J.","raw_affiliation_strings":["Applied Mathematics"],"affiliations":[{"raw_affiliation_string":"Applied Mathematics","institution_ids":["https://openalex.org/I4210131439"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5042880953","display_name":"Martin Turner","orcid":"https://orcid.org/0000-0003-0117-8049"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Turner, M.","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5100409741"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":1,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9807000160217285,"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":0.9807000160217285,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9728000164031982,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12037","display_name":"Algebraic and Geometric Analysis","score":0.9671000242233276,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/degenerate-energy-levels","display_name":"Degenerate energy levels","score":0.7034995555877686},{"id":"https://openalex.org/keywords/gravitational-singularity","display_name":"Gravitational singularity","score":0.6363266110420227},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.5946673154830933},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.5857490301132202},{"id":"https://openalex.org/keywords/visualization","display_name":"Visualization","score":0.5758563876152039},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5379069447517395},{"id":"https://openalex.org/keywords/tensor-field","display_name":"Tensor field","score":0.5337793231010437},{"id":"https://openalex.org/keywords/symmetric-tensor","display_name":"Symmetric tensor","score":0.5162463188171387},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.43769535422325134},{"id":"https://openalex.org/keywords/wedge","display_name":"Wedge (geometry)","score":0.4371384382247925},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.3935106694698334},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3784135580062866},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3672363758087158},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.31789159774780273},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.30141568183898926},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.20801988244056702},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.20280110836029053},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.14492931962013245},{"id":"https://openalex.org/keywords/exact-solutions-in-general-relativity","display_name":"Exact solutions in general relativity","score":0.08261469006538391}],"concepts":[{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.7034995555877686},{"id":"https://openalex.org/C12843","wikidata":"https://www.wikidata.org/wiki/Q201721","display_name":"Gravitational singularity","level":2,"score":0.6363266110420227},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.5946673154830933},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5857490301132202},{"id":"https://openalex.org/C36464697","wikidata":"https://www.wikidata.org/wiki/Q451553","display_name":"Visualization","level":2,"score":0.5758563876152039},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5379069447517395},{"id":"https://openalex.org/C166077713","wikidata":"https://www.wikidata.org/wiki/Q1758924","display_name":"Tensor field","level":3,"score":0.5337793231010437},{"id":"https://openalex.org/C20178491","wikidata":"https://www.wikidata.org/wiki/Q2204117","display_name":"Symmetric tensor","level":3,"score":0.5162463188171387},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.43769535422325134},{"id":"https://openalex.org/C47422493","wikidata":"https://www.wikidata.org/wiki/Q2755127","display_name":"Wedge (geometry)","level":2,"score":0.4371384382247925},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3935106694698334},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3784135580062866},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3672363758087158},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.31789159774780273},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.30141568183898926},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.20801988244056702},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.20280110836029053},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.14492931962013245},{"id":"https://openalex.org/C520416788","wikidata":"https://www.wikidata.org/wiki/Q5419229","display_name":"Exact solutions in general relativity","level":2,"score":0.08261469006538391},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:pure.atira.dk:openaire/844f4383-cf6d-4c60-a3bc-43d877ffb134","is_oa":true,"landing_page_url":"https://research.manchester.ac.uk/en/publications/844f4383-cf6d-4c60-a3bc-43d877ffb134","pdf_url":null,"source":{"id":"https://openalex.org/S4306400662","display_name":"Research Explorer (The University of Manchester)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I28407311","host_organization_name":"University of Manchester","host_organization_lineage":["https://openalex.org/I28407311"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Liu, J, Hewitt, W T, Lionheart, W R B, Montaldi, J & Turner, M 2008, A lemon is not a monstar: Visualization of singularities of symmetric second rank tensor fields in the plane. in Theory and Practice of Computer Graphics 2008, TPCG 2008 - Eurographics UK Chapter Proceedings|Theory Pract. Comput. Graph., TPCG - Eurographics UK Chapter Proc.. Eurographics Association, Manchester, pp. 99-106, 6th Theory and Practice of Computer Graphics Conference, TPCG 2008, Manchester, 1/07/08. https://doi.org/10.2312/LocalChapterEvents/TPCG/TPCG08/099-106","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1092","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400452","display_name":"MIMS EPrints (University of Southampton)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I43439940","host_organization_name":"University of Southampton","host_organization_lineage":["https://openalex.org/I43439940"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"MIMS Preprint"},{"id":"doi:10.2312/localchapterevents/tpcg/tpcg08/099-106","is_oa":true,"landing_page_url":"https://doi.org/10.2312/localchapterevents/tpcg/tpcg08/099-106","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":"pmh:oai:pure.atira.dk:openaire/844f4383-cf6d-4c60-a3bc-43d877ffb134","is_oa":true,"landing_page_url":"https://research.manchester.ac.uk/en/publications/844f4383-cf6d-4c60-a3bc-43d877ffb134","pdf_url":null,"source":{"id":"https://openalex.org/S4306400662","display_name":"Research Explorer (The University of Manchester)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I28407311","host_organization_name":"University of Manchester","host_organization_lineage":["https://openalex.org/I28407311"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Liu, J, Hewitt, W T, Lionheart, W R B, Montaldi, J & Turner, M 2008, A lemon is not a monstar: Visualization of singularities of symmetric second rank tensor fields in the plane. in Theory and Practice of Computer Graphics 2008, TPCG 2008 - Eurographics UK Chapter Proceedings|Theory Pract. Comput. Graph., TPCG - Eurographics UK Chapter Proc.. Eurographics Association, Manchester, pp. 99-106, 6th Theory and Practice of Computer Graphics Conference, TPCG 2008, Manchester, 1/07/08. https://doi.org/10.2312/LocalChapterEvents/TPCG/TPCG08/099-106","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W202681155","https://openalex.org/W1531081020","https://openalex.org/W1582129286","https://openalex.org/W1973092800","https://openalex.org/W1975383406","https://openalex.org/W1977532084","https://openalex.org/W1993365856","https://openalex.org/W1993631717","https://openalex.org/W1999616998","https://openalex.org/W2026433308","https://openalex.org/W2028533954","https://openalex.org/W2044731510","https://openalex.org/W2098819183","https://openalex.org/W2125638038","https://openalex.org/W2126829454","https://openalex.org/W2136690777","https://openalex.org/W2142195325","https://openalex.org/W2159991578","https://openalex.org/W2293751436","https://openalex.org/W2795721869"],"related_works":["https://openalex.org/W1519026525","https://openalex.org/W118798689","https://openalex.org/W2153623993","https://openalex.org/W975318811","https://openalex.org/W14480185","https://openalex.org/W2781971772","https://openalex.org/W2277642169","https://openalex.org/W2889079460","https://openalex.org/W2261409577","https://openalex.org/W3203019825","https://openalex.org/W3195657091","https://openalex.org/W2883138145","https://openalex.org/W2145069511","https://openalex.org/W2972048297","https://openalex.org/W2890512204","https://openalex.org/W1564270463","https://openalex.org/W1983496390","https://openalex.org/W1506743325","https://openalex.org/W1999946141","https://openalex.org/W2054678027"],"abstract_inverted_index":{"In":[0,88],"the":[1,4,13,28,32,43,50,53,94,97,134],"visualization":[2,73,136],"of":[3,6,31,42,52,99],"topology":[5],"second":[7],"rank":[8],"symmetric":[9],"tensor":[10,34,45],"fields":[11],"in":[12,71,133],"plane":[14],"one":[15],"can":[16,37],"extract":[17],"some":[18],"key":[19],"points":[20,68],"(degenerate":[21],"points),":[22],"and":[23,47,85,103,120],"curves":[24],"(separatrices)":[25],"that":[26],"characterize":[27],"qualitative":[29],"behaviour":[30],"whole":[33,44],"field.":[35],"This":[36],"provide":[38],"a":[39,75,107,130],"global":[40,59],"structure":[41,60],"field,":[46],"effectively":[48],"reduce":[49],"complexity":[51],"original":[54],"data.":[55],"To":[56],"construct":[57],"this":[58,89],"it":[61],"is":[62,78],"important":[63],"to":[64],"classify":[65],"those":[66],"degenerate":[67,76,109],"accurately.":[69],"However,":[70],"existing":[72,135],"techniques,":[74],"point":[77,110],"only":[79],"classified":[80,113],"into":[81,114],"two":[82,124],"types:":[83,116],"trisector":[84],"wedge":[86],"types.":[87],"work,":[90],"we":[91],"will":[92],"apply":[93],"theory":[95],"from":[96],"analysis":[98],"binary":[100],"differential":[101],"equations":[102],"demonstrate":[104],"that,":[105],"topologically,":[106],"simple":[108],"should":[111],"be":[112],"three":[115],"star":[117],"(trisector),":[118],"lemon":[119],"monstar.":[121],"The":[122],"later":[123],"types":[125],"were":[126],"mistakenly":[127],"regarded":[128],"as":[129],"single":[131],"type":[132],"techniques.":[137]},"counts_by_year":[{"year":2019,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}