{"id":"https://openalex.org/W2467639534","doi":"https://doi.org/10.1145/2949035.2949050","title":"Pl\u00fccker Coordinates and Extended Cross Product for Robust and Fast Intersection Computation","display_name":"Pl\u00fccker Coordinates and Extended Cross Product for Robust and Fast Intersection Computation","publication_year":2016,"publication_date":"2016-06-27","ids":{"openalex":"https://openalex.org/W2467639534","doi":"https://doi.org/10.1145/2949035.2949050","mag":"2467639534"},"language":"en","primary_location":{"id":"doi:10.1145/2949035.2949050","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2949035.2949050","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 33rd Computer Graphics International","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/A5035524167","display_name":"V\u00e1clav Skala","orcid":"https://orcid.org/0000-0001-8886-4281"},"institutions":[{"id":"https://openalex.org/I92715842","display_name":"University of West Bohemia in Pilsen","ror":"https://ror.org/040t43x18","country_code":"CZ","type":"education","lineage":["https://openalex.org/I92715842"]}],"countries":["CZ"],"is_corresponding":true,"raw_author_name":"Vaclav Skala","raw_affiliation_strings":["Department of Computer Science and Engineering, University of West Bohemia, Czech Republic"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Engineering, University of West Bohemia, Czech Republic","institution_ids":["https://openalex.org/I92715842"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5035524167"],"corresponding_institution_ids":["https://openalex.org/I92715842"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"57","last_page":"60"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9919999837875366,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9919999837875366,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9918000102043152,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.989799976348877,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/homogeneous-coordinates","display_name":"Homogeneous coordinates","score":0.7999491691589355},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.6745384931564331},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5827792882919312},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.5238927602767944},{"id":"https://openalex.org/keywords/euclidean-space","display_name":"Euclidean space","score":0.5223451852798462},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4322742521762848},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4282161295413971},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.36434632539749146},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2461622655391693},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.21164491772651672}],"concepts":[{"id":"https://openalex.org/C106402246","wikidata":"https://www.wikidata.org/wiki/Q528525","display_name":"Homogeneous coordinates","level":2,"score":0.7999491691589355},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.6745384931564331},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5827792882919312},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.5238927602767944},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.5223451852798462},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4322742521762848},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4282161295413971},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.36434632539749146},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2461622655391693},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.21164491772651672},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/2949035.2949050","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2949035.2949050","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 33rd Computer Graphics International","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5765677804","display_name":null,"funder_award_id":"LH12181","funder_id":"https://openalex.org/F4320321842","funder_display_name":"Ministry of Education, Youth and Science"}],"funders":[{"id":"https://openalex.org/F4320310981","display_name":"Z\u00e1pado\u010desk\u00e1 Univerzita v Plzni","ror":"https://ror.org/040t43x18"},{"id":"https://openalex.org/F4320321842","display_name":"Ministry of Education, Youth and Science","ror":"https://ror.org/053pcb396"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W2050174852","https://openalex.org/W2051895014","https://openalex.org/W2105980191","https://openalex.org/W2116021467","https://openalex.org/W2123009205","https://openalex.org/W2129457743","https://openalex.org/W2162394290","https://openalex.org/W2273574509","https://openalex.org/W2481578392","https://openalex.org/W2488122590","https://openalex.org/W2970291528","https://openalex.org/W3026407818"],"related_works":["https://openalex.org/W2126504275","https://openalex.org/W2348909947","https://openalex.org/W4292672442","https://openalex.org/W2362101859","https://openalex.org/W2791431590","https://openalex.org/W2941610985","https://openalex.org/W4235810826","https://openalex.org/W2350688482","https://openalex.org/W2122135111","https://openalex.org/W2352688386"],"abstract_inverted_index":{"Many":[0],"geometrically":[1],"oriented":[2],"problems":[3,170],"lead":[4],"to":[5,9,20,50,53,67,74,149],"intersection":[6,21,29,59,154],"computation":[7,22,60,155],"or":[8,95],"its":[10],"dual":[11],"problems.":[12],"In":[13,102],"many":[14],"cases":[15,36],"the":[16,43,54,62,99,110,115,133,162,165],"problem":[17],"is":[18,49,81,122,143,172],"reduced":[19],"of":[23,30,70,77,84,156,164],"two":[24,31,157],"planes":[25,158],"in":[26,34,42,61,92,98,140],"E3,":[27],"e.g.":[28],"triangles.":[32],"However":[33],"several":[35],"triangles":[37],"are":[38,88],"given":[39],"by":[40],"vertices":[41],"homogeneous":[44],"coordinates.":[45,117],"The":[46,118,145],"usual":[47],"approach":[48,80,147],"convert":[51],"coordinates":[52,86],"Euclidean":[55,63],"space":[56,142],"and":[57,73,114,152,182],"make":[58],"space.":[64,101],"This":[65],"leads":[66,148],"extensive":[68],"use":[69],"division":[71,184],"operations":[72],"decreased":[75],"precision":[76],"computation.":[78],"Another":[79],"an":[82],"application":[83],"Pl\u00fccker":[85,116],"which":[87],"not":[89],"commonly":[90],"recognized":[91],"computer":[93],"graphics":[94],"direct":[96],"computing":[97],"projective":[100,166],"this":[103],"paper":[104],"we":[105],"present":[106],"a":[107,129],"relation":[108],"between":[109],"extended":[111,119,134],"cross":[112,120,135],"product":[113,121,136],"especially":[123],"convenient":[124],"for":[125,132,168],"GPU":[126],"application.":[127],"Also":[128,161],"new":[130],"formulation":[131],"using":[137],"matrix":[138],"notation":[139],"n-dimensional":[141],"introduced.":[144],"presented":[146,173],"simple,":[150],"robust":[151],"fast":[153],"on":[159],"GPU.":[160],"advantage":[163],"representation":[167],"geometrical":[169],"solution":[171],"as":[174],"it":[175],"actually":[176],"offers":[177],"\"doubled\"":[178],"mantissa":[179],"length":[180],"naturally":[181],"saves":[183],"operations.":[185]},"counts_by_year":[{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}