{"id":"https://openalex.org/W3144323829","doi":"https://doi.org/10.1109/cgi.2004.1309203","title":"Bounding volumes for linearly interpolated shapes","display_name":"Bounding volumes for linearly interpolated shapes","publication_year":2004,"publication_date":"2004-11-13","ids":{"openalex":"https://openalex.org/W3144323829","doi":"https://doi.org/10.1109/cgi.2004.1309203","mag":"3144323829"},"language":"en","primary_location":{"id":"doi:10.1109/cgi.2004.1309203","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cgi.2004.1309203","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings Computer Graphics International, 2004.","raw_type":"proceedings-article"},"type":"conference-paper","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/A5022982836","display_name":"Tobias Klug","orcid":null},"institutions":[{"id":"https://openalex.org/I31512782","display_name":"Technische Universit\u00e4t Darmstadt","ror":"https://ror.org/05n911h24","country_code":"DE","type":"education","lineage":["https://openalex.org/I31512782"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"T. Klug","raw_affiliation_strings":["Department of Computer Science, Darmstadt University of Technology, Darmstadt, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Darmstadt University of Technology, Darmstadt, Germany","institution_ids":["https://openalex.org/I31512782"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5072827199","display_name":"Marc Alexa","orcid":"https://orcid.org/0000-0002-9854-8466"},"institutions":[{"id":"https://openalex.org/I31512782","display_name":"Technische Universit\u00e4t Darmstadt","ror":"https://ror.org/05n911h24","country_code":"DE","type":"education","lineage":["https://openalex.org/I31512782"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"M. Alexa","raw_affiliation_strings":["Department of Computer Science, Darmstadt University of Technology, Darmstadt, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Darmstadt University of Technology, Darmstadt, Germany","institution_ids":["https://openalex.org/I31512782"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I31512782"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"134","last_page":"139"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10481","display_name":"Computer Graphics and Visualization Techniques","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T10481","display_name":"Computer Graphics and Visualization Techniques","score":0.9998000264167786,"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/T10719","display_name":"3D Shape Modeling and Analysis","score":0.9997000098228455,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9987000226974487,"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/bounding-volume","display_name":"Bounding volume","score":0.8621679544448853},{"id":"https://openalex.org/keywords/bounding-overwatch","display_name":"Bounding overwatch","score":0.7776789665222168},{"id":"https://openalex.org/keywords/minimum-bounding-box","display_name":"Minimum bounding box","score":0.7355253100395203},{"id":"https://openalex.org/keywords/base","display_name":"Base (topology)","score":0.5716552138328552},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.5600451827049255},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.4875578284263611},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.48398733139038086},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.45511868596076965},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.43921220302581787},{"id":"https://openalex.org/keywords/computational-geometry","display_name":"Computational geometry","score":0.4214167296886444},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4115752577781677},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.3422412872314453},{"id":"https://openalex.org/keywords/collision-detection","display_name":"Collision detection","score":0.29917240142822266},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2519175708293915},{"id":"https://openalex.org/keywords/computer-graphics","display_name":"Computer graphics (images)","score":0.18711408972740173},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.17381849884986877},{"id":"https://openalex.org/keywords/computer-vision","display_name":"Computer vision","score":0.15308120846748352},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.14381712675094604},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1255873441696167},{"id":"https://openalex.org/keywords/animation","display_name":"Animation","score":0.11203363537788391},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.09335458278656006}],"concepts":[{"id":"https://openalex.org/C184585634","wikidata":"https://www.wikidata.org/wiki/Q1434060","display_name":"Bounding volume","level":4,"score":0.8621679544448853},{"id":"https://openalex.org/C63584917","wikidata":"https://www.wikidata.org/wiki/Q333286","display_name":"Bounding overwatch","level":2,"score":0.7776789665222168},{"id":"https://openalex.org/C147037132","wikidata":"https://www.wikidata.org/wiki/Q6865426","display_name":"Minimum bounding box","level":3,"score":0.7355253100395203},{"id":"https://openalex.org/C42058472","wikidata":"https://www.wikidata.org/wiki/Q810214","display_name":"Base (topology)","level":2,"score":0.5716552138328552},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.5600451827049255},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.4875578284263611},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.48398733139038086},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.45511868596076965},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.43921220302581787},{"id":"https://openalex.org/C29123130","wikidata":"https://www.wikidata.org/wiki/Q874709","display_name":"Computational geometry","level":2,"score":0.4214167296886444},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4115752577781677},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3422412872314453},{"id":"https://openalex.org/C199668693","wikidata":"https://www.wikidata.org/wiki/Q1550329","display_name":"Collision detection","level":3,"score":0.29917240142822266},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2519175708293915},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.18711408972740173},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.17381849884986877},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.15308120846748352},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.14381712675094604},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1255873441696167},{"id":"https://openalex.org/C502989409","wikidata":"https://www.wikidata.org/wiki/Q11425","display_name":"Animation","level":2,"score":0.11203363537788391},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.09335458278656006},{"id":"https://openalex.org/C121704057","wikidata":"https://www.wikidata.org/wiki/Q352070","display_name":"Collision","level":2,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cgi.2004.1309203","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cgi.2004.1309203","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings Computer Graphics International, 2004.","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W1731350208","https://openalex.org/W1976734360","https://openalex.org/W1991777702","https://openalex.org/W1999250663","https://openalex.org/W2002509771","https://openalex.org/W2009139756","https://openalex.org/W2053212688","https://openalex.org/W2057600146","https://openalex.org/W2060864182","https://openalex.org/W2064941560","https://openalex.org/W2071516467","https://openalex.org/W2085623174","https://openalex.org/W2123703543","https://openalex.org/W2126539456","https://openalex.org/W2157492339","https://openalex.org/W2160793724","https://openalex.org/W3113042792","https://openalex.org/W4231055238","https://openalex.org/W6601599188","https://openalex.org/W6610229207","https://openalex.org/W6644434169"],"related_works":["https://openalex.org/W2171909355","https://openalex.org/W50150243","https://openalex.org/W3036286480","https://openalex.org/W2387360586","https://openalex.org/W2096746646","https://openalex.org/W4237171675","https://openalex.org/W2964938419","https://openalex.org/W4287728368","https://openalex.org/W2349685851","https://openalex.org/W3163786145"],"abstract_inverted_index":{"Bounding":[0],"volumes":[1,85,122],"are":[2],"crucial":[3],"for":[4,17,28,50,123],"culling":[5],"in":[6,61,71],"interactive":[7],"graphics":[8],"applications.":[9],"For":[10],"dynamic":[11,33,124],"shapes,":[12],"computing":[13,120],"a":[14,29,64,72],"bounding":[15,84,121],"volume":[16],"each":[18,62],"frame":[19],"could":[20],"be":[21,55,128],"very":[22],"expensive.":[23],"We":[24,95],"analyze":[25],"the":[26,39,51,79,87,92,100,113,131,138],"situation":[27],"particular":[30,65],"class":[31],"of":[32,42,48,78,140],"geometry,":[34],"namely,":[35],"shapes":[36,125],"resulting":[37],"from":[38,86,105],"linear":[40,52],"interpolation":[41],"several":[43],"base":[44,141],"shapes.":[45,142],"The":[46],"space":[47,81],"weights":[49,106],"combination":[53],"can":[54],"decomposed":[56],"into":[57],"cells":[58],"so":[59],"that":[60],"cell":[63,76,101],"vertex":[66],"is":[67,134],"maximal":[68],"(resp.":[69],"minimal)":[70],"given":[73],"direction.":[74],"This":[75,117],"decomposition":[77],"weight":[80,88],"allows":[82],"deriving":[83],"vectors":[89],"rather":[90],"than":[91],"generated":[93],"geometry.":[94],"present":[96],"algorithms":[97],"to":[98,103,107,110,119,127,137],"generate":[99],"decomposition,":[102],"map":[104],"cells,":[108],"and":[109],"efficiently":[111],"compute":[112],"necessary":[114],"data":[115],"structures.":[116],"approach":[118],"proves":[126],"beneficial":[129],"if":[130],"geometry":[132],"representation":[133],"large":[135],"compared":[136],"number":[139]},"counts_by_year":[],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}