{"id":"https://openalex.org/W6926569349","doi":"https://doi.org/10.2312/vissym/vissym03/085-094","title":"Detecting Critical Regions in Scalar Fields","display_name":"Detecting Critical Regions in Scalar Fields","publication_year":2003,"publication_date":"2003-01-01","ids":{"openalex":"https://openalex.org/W6926569349","doi":"https://doi.org/10.2312/vissym/vissym03/085-094"},"language":"en","primary_location":{"id":"doi:10.2312/vissym/vissym03/085-094","is_oa":true,"landing_page_url":"https://doi.org/10.2312/vissym/vissym03/085-094","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":false,"raw_source_name":null,"raw_type":"article"},"type":"other","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.2312/vissym/vissym03/085-094","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Weber, Gunther H.","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Weber, Gunther H.","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Scheuermann, Gerik","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Scheuermann, Gerik","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Hamann, Bernd","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hamann, Bernd","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"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":true,"primary_topic":{"id":"https://openalex.org/T14079","display_name":"Mathematics Education and Programs","score":0.11620000004768372,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T14079","display_name":"Mathematics Education and Programs","score":0.11620000004768372,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T10533","display_name":"Teaching and Learning Programming","score":0.06300000101327896,"subfield":{"id":"https://openalex.org/subfields/1706","display_name":"Computer Science Applications"},"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/T13034","display_name":"Information Systems Education and Curriculum Development","score":0.039900001138448715,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"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/isosurface","display_name":"Isosurface","score":0.9937000274658203},{"id":"https://openalex.org/keywords/visualization","display_name":"Visualization","score":0.6873999834060669},{"id":"https://openalex.org/keywords/scalar-field","display_name":"Scalar field","score":0.5248000025749207},{"id":"https://openalex.org/keywords/data-visualization","display_name":"Data visualization","score":0.4724999964237213},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.4595000147819519},{"id":"https://openalex.org/keywords/topological-data-analysis","display_name":"Topological data analysis","score":0.45500001311302185},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.454800009727478},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.4278999865055084}],"concepts":[{"id":"https://openalex.org/C45107383","wikidata":"https://www.wikidata.org/wiki/Q1311829","display_name":"Isosurface","level":3,"score":0.9937000274658203},{"id":"https://openalex.org/C36464697","wikidata":"https://www.wikidata.org/wiki/Q451553","display_name":"Visualization","level":2,"score":0.6873999834060669},{"id":"https://openalex.org/C110521144","wikidata":"https://www.wikidata.org/wiki/Q193460","display_name":"Scalar field","level":2,"score":0.5248000025749207},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4961000084877014},{"id":"https://openalex.org/C172367668","wikidata":"https://www.wikidata.org/wiki/Q6504956","display_name":"Data visualization","level":3,"score":0.4724999964237213},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.4595000147819519},{"id":"https://openalex.org/C2776477805","wikidata":"https://www.wikidata.org/wiki/Q4460773","display_name":"Topological data analysis","level":2,"score":0.45500001311302185},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.454800009727478},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.4278999865055084},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.4187000095844269},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.37720000743865967},{"id":"https://openalex.org/C205711294","wikidata":"https://www.wikidata.org/wiki/Q176953","display_name":"Rendering (computer graphics)","level":2,"score":0.37549999356269836},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.36320000886917114},{"id":"https://openalex.org/C42087268","wikidata":"https://www.wikidata.org/wiki/Q1886184","display_name":"Marching cubes","level":3,"score":0.35019999742507935},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.30570000410079956},{"id":"https://openalex.org/C20885615","wikidata":"https://www.wikidata.org/wiki/Q825595","display_name":"Surface reconstruction","level":3,"score":0.2849000096321106},{"id":"https://openalex.org/C21080849","wikidata":"https://www.wikidata.org/wiki/Q13611879","display_name":"Data point","level":2,"score":0.2808000147342682},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.27869999408721924},{"id":"https://openalex.org/C30769735","wikidata":"https://www.wikidata.org/wiki/Q2165951","display_name":"Volume rendering","level":3,"score":0.2757999897003174},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.2639000117778778},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2596000134944916},{"id":"https://openalex.org/C16171025","wikidata":"https://www.wikidata.org/wiki/Q863349","display_name":"Singularity","level":2,"score":0.25029999017715454}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.2312/vissym/vissym03/085-094","is_oa":true,"landing_page_url":"https://doi.org/10.2312/vissym/vissym03/085-094","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":"doi:10.2312/vissym/vissym03/085-094","is_oa":true,"landing_page_url":"https://doi.org/10.2312/vissym/vissym03/085-094","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":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Trivariate":[0],"data":[1],"is":[2,19,100],"commonly":[3],"visualized":[4],"using":[5,33,47],"isosurfaces":[6,59],"or":[7,88,135],"direct":[8,34],"volume":[9,35],"rendering.":[10],"When":[11],"exploring":[12],"scalar":[13,155],"fields":[14],"by":[15,158],"isosurface":[16,48,98],"extraction":[17],"it":[18],"often":[20,124],"difficult":[21],"to":[22,64,102,111,118,170,181],"choose":[23],"isovalues":[24,55,70,114,152],"that":[25,143],"convey":[26],"\"useful\"":[27],"information.":[28],"The":[29],"significance":[30],"of":[31,41,75,80,85,91,127,175],"visualizations":[32],"rendering":[36],"depends":[37],"on":[38],"the":[39,78,89,172],"choice":[40],"good":[42],"transfer":[43,67],"functions.":[44,68],"Understanding":[45],"and":[46,60,105,149,178],"topology":[49,74],"can":[50,61],"help":[51],"in":[52,73,93],"identifying":[53],"\"relevant\"":[54],"for":[56,153],"visualization":[57],"via":[58],"be":[62],"used":[63],"automatically":[65],"generate":[66],"Critical":[69],"indicate":[71],"changes":[72],"an":[76],"isosurface:":[77],"creation":[79],"new":[81],"surface":[82,86,95],"components,":[83],"merging":[84],"components":[87],"formation":[90],"holes":[92],"a":[94,141,154,163],"component.":[96],"Interesting":[97],"behavior":[99],"likely":[101],"occur":[103],"at":[104],"around":[106],"critical":[107,113,120,145,147,151,176],"isovalues.":[108],"Current":[109],"approaches":[110],"detect":[112],"are":[115],"usually":[116],"limited":[117],"isolated":[119],"points.":[121],"Data":[122],"sets":[123],"contain":[125],"regions":[126,148],"constant":[128],"value":[129],"(i.e.,":[130],"mesh":[131,133,137],"edges,":[132],"faces,":[134],"entire":[136],"cells).":[138],"We":[139,167],"present":[140],"method":[142],"detects":[144],"points,":[146],"corresponding":[150],"field":[156],"defined":[157],"piecewise":[159],"trilinear":[160],"interpolation":[161],"over":[162],"uniform":[164],"rectilinear":[165],"grid.":[166],"describe":[168],"how":[169],"use":[171],"resulting":[173],"list":[174],"regions/points":[177],"associated":[179],"values":[180],"examine":[182],"trivariate":[183],"data.":[184]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}