{"id":"https://openalex.org/W2025087491","doi":"https://doi.org/10.1080/10867651.2004.10504896","title":"Ray Bilinear Patch Intersections","display_name":"Ray Bilinear Patch Intersections","publication_year":2004,"publication_date":"2004-01-01","ids":{"openalex":"https://openalex.org/W2025087491","doi":"https://doi.org/10.1080/10867651.2004.10504896","mag":"2025087491"},"language":"en","primary_location":{"id":"doi:10.1080/10867651.2004.10504896","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10867651.2004.10504896","pdf_url":null,"source":{"id":"https://openalex.org/S4210240212","display_name":"Journal of Graphics Tools","issn_l":"1086-7651","issn":["1086-7651","2165-347X","2165-3488"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Graphics Tools","raw_type":"journal-article"},"type":"article","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/A5043929880","display_name":"Shaun D. Ramsey","orcid":null},"institutions":[{"id":"https://openalex.org/I223532165","display_name":"University of Utah","ror":"https://ror.org/03r0ha626","country_code":"US","type":"education","lineage":["https://openalex.org/I223532165"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Shaun D. Ramsey","raw_affiliation_strings":["\n School of Computing, University of Utah, 50. S. Central Campus Drive, 3190 MEB, Salt Lake City, UT, 84112 E-mail: ramsey@cs.utah.edu","School of Computing, University of Utah , 50. S. Central Campus Drive, 3190 MEB, Salt Lake City , UT , 84112 E-mail: ramsey@cs.utah.edu"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"\n School of Computing, University of Utah, 50. S. Central Campus Drive, 3190 MEB, Salt Lake City, UT, 84112 E-mail: ramsey@cs.utah.edu","institution_ids":["https://openalex.org/I223532165"]},{"raw_affiliation_string":"School of Computing, University of Utah , 50. S. Central Campus Drive, 3190 MEB, Salt Lake City , UT , 84112 E-mail: ramsey@cs.utah.edu","institution_ids":["https://openalex.org/I223532165"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003684910","display_name":"Kristin Potter","orcid":"https://orcid.org/0000-0003-1959-1691"},"institutions":[{"id":"https://openalex.org/I223532165","display_name":"University of Utah","ror":"https://ror.org/03r0ha626","country_code":"US","type":"education","lineage":["https://openalex.org/I223532165"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Kristin Potter","raw_affiliation_strings":["\n School of Computing, University of Utah, 50. S. Central Campus Drive, 3190 MEB, Salt Lake City, UT, 84112 E-mail: kpotter@cs.utah.edu","School of Computing, University of Utah , 50. S. Central Campus Drive, 3190 MEB, Salt Lake City , UT , 84112 E-mail: kpotter@cs.utah.edu"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"\n School of Computing, University of Utah, 50. S. Central Campus Drive, 3190 MEB, Salt Lake City, UT, 84112 E-mail: kpotter@cs.utah.edu","institution_ids":["https://openalex.org/I223532165"]},{"raw_affiliation_string":"School of Computing, University of Utah , 50. S. Central Campus Drive, 3190 MEB, Salt Lake City , UT , 84112 E-mail: kpotter@cs.utah.edu","institution_ids":["https://openalex.org/I223532165"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5065645994","display_name":"Charles Hansen","orcid":"https://orcid.org/0000-0002-8480-2152"},"institutions":[{"id":"https://openalex.org/I223532165","display_name":"University of Utah","ror":"https://ror.org/03r0ha626","country_code":"US","type":"education","lineage":["https://openalex.org/I223532165"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Charles Hansen","raw_affiliation_strings":["\n School of Computing, University of Utah, 50. S. Central Campus Drive, 3190 MEB, Salt Lake City, UT, 84112 E-mail: hansen@cs.utah.edu","School of Computing, University of Utah , 50. S. Central Campus Drive, 3190 MEB, Salt Lake City , UT , 84112 E-mail: hansen@cs.utah.edu"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"\n School of Computing, University of Utah, 50. S. Central Campus Drive, 3190 MEB, Salt Lake City, UT, 84112 E-mail: hansen@cs.utah.edu","institution_ids":["https://openalex.org/I223532165"]},{"raw_affiliation_string":"School of Computing, University of Utah , 50. S. Central Campus Drive, 3190 MEB, Salt Lake City , UT , 84112 E-mail: hansen@cs.utah.edu","institution_ids":["https://openalex.org/I223532165"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I223532165"],"apc_list":null,"apc_paid":null,"fwci":2.6721,"has_fulltext":false,"cited_by_count":44,"citation_normalized_percentile":{"value":0.88433958,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"9","issue":"3","first_page":"41","last_page":"47"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9998000264167786,"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":0.9998000264167786,"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/T10481","display_name":"Computer Graphics and Visualization Techniques","score":0.9997000098228455,"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":0.9991000294685364,"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/bilinear-interpolation","display_name":"Bilinear interpolation","score":0.8509348630905151},{"id":"https://openalex.org/keywords/parametric-surface","display_name":"Parametric surface","score":0.754802942276001},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.6012405753135681},{"id":"https://openalex.org/keywords/polygon","display_name":"Polygon (computer graphics)","score":0.5986754298210144},{"id":"https://openalex.org/keywords/surface","display_name":"Surface (topology)","score":0.5775719285011292},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.5469735264778137},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.48787522315979004},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.4845225214958191},{"id":"https://openalex.org/keywords/ray-tracing","display_name":"Ray tracing (physics)","score":0.4482661187648773},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4417172372341156},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.42350414395332336},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3940752446651459},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2482251226902008},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1405564844608307},{"id":"https://openalex.org/keywords/computer-vision","display_name":"Computer vision","score":0.1336190402507782},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11790403723716736},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.06240034103393555},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.06092843413352966}],"concepts":[{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.8509348630905151},{"id":"https://openalex.org/C2187777","wikidata":"https://www.wikidata.org/wiki/Q1071743","display_name":"Parametric surface","level":3,"score":0.754802942276001},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.6012405753135681},{"id":"https://openalex.org/C190694206","wikidata":"https://www.wikidata.org/wiki/Q3276654","display_name":"Polygon (computer graphics)","level":3,"score":0.5986754298210144},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.5775719285011292},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.5469735264778137},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.48787522315979004},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.4845225214958191},{"id":"https://openalex.org/C121483023","wikidata":"https://www.wikidata.org/wiki/Q7298343","display_name":"Ray tracing (physics)","level":2,"score":0.4482661187648773},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4417172372341156},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.42350414395332336},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3940752446651459},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2482251226902008},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1405564844608307},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.1336190402507782},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11790403723716736},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.06240034103393555},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.06092843413352966},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C126042441","wikidata":"https://www.wikidata.org/wiki/Q1324888","display_name":"Frame (networking)","level":2,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/10867651.2004.10504896","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10867651.2004.10504896","pdf_url":null,"source":{"id":"https://openalex.org/S4210240212","display_name":"Journal of Graphics Tools","issn_l":"1086-7651","issn":["1086-7651","2165-347X","2165-3488"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Graphics Tools","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":5,"referenced_works":["https://openalex.org/W1487859867","https://openalex.org/W1530695720","https://openalex.org/W1588714915","https://openalex.org/W2170120409","https://openalex.org/W2593976925"],"related_works":["https://openalex.org/W3729366","https://openalex.org/W2350142587","https://openalex.org/W2349816436","https://openalex.org/W2033912262","https://openalex.org/W2086189052","https://openalex.org/W2374939192","https://openalex.org/W2095627444","https://openalex.org/W2560064799","https://openalex.org/W157961242","https://openalex.org/W2353901727"],"abstract_inverted_index":{"Abstract":[0],"Ray":[1],"tracing":[2],"and":[3,17,48,75],"other":[4,57],"techniques":[5],"employ":[6],"algorithms":[7],"which":[8],"require":[9],"the":[10,49,53,60],"intersection":[11,63],"between":[12,46],"a":[13,29,71],"three-dimensional":[14],"parametric":[15,51],"ray":[16],"an":[18],"object":[19,24],"to":[20,25,78],"be":[21],"computed.":[22],"The":[23],"intersect":[26],"is":[27,86],"typically":[28],"sphere,":[30],"triangle,":[31],"or":[32],"polygon":[33],"but":[34],"many":[35],"surface":[36],"types":[37],"are":[38],"possible.":[39],"In":[40],"this":[41],"work":[42],"we":[43],"consider":[44],"intersections":[45,82],"rays":[47],"simplest":[50],"surface,":[52],"bilinear":[54],"patch.":[55],"Unlike":[56],"surfaces,":[58],"solving":[59],"ray-bilinear":[61,80],"patch":[62,81],"with":[64],"simple":[65],"algebraic":[66],"manipulations":[67],"fails.":[68],"We":[69],"present":[70],"complete,":[72],"efficient,":[73],"robust,":[74],"graceful":[76],"formulation":[77],"solve":[79],"quickly.":[83],"Source":[84],"code":[85],"available":[87],"online.":[88]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
