{"id":"https://openalex.org/W2073288660","doi":"https://doi.org/10.1111/1467-8659.1330127","title":"Chebyshev Polynomials for Boxing and Intersections of Parametric Curves and Surfaces","display_name":"Chebyshev Polynomials for Boxing and Intersections of Parametric Curves and Surfaces","publication_year":1994,"publication_date":"1994-08-01","ids":{"openalex":"https://openalex.org/W2073288660","doi":"https://doi.org/10.1111/1467-8659.1330127","mag":"2073288660"},"language":"en","primary_location":{"id":"doi:10.1111/1467-8659.1330127","is_oa":false,"landing_page_url":"https://doi.org/10.1111/1467-8659.1330127","pdf_url":null,"source":{"id":"https://openalex.org/S67831204","display_name":"Computer Graphics Forum","issn_l":"0167-7055","issn":["0167-7055","1467-8659"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computer Graphics Forum","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/A5111426544","display_name":"Alain Fournier","orcid":null},"institutions":[{"id":"https://openalex.org/I141945490","display_name":"University of British Columbia","ror":"https://ror.org/03rmrcq20","country_code":"CA","type":"education","lineage":["https://openalex.org/I141945490"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Alain Fournier","raw_affiliation_strings":["Department of Computer Science, University of British Columbia, Vancouver, British Columbia V6T 1Z4, [email protected], [email protected]","Department of Computer Science, University of British Columbia, Vancouver, British Columbia V6T 1Z4, fournier@cs.ubc.ca, juancho@cs.ubc.ca"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of British Columbia, Vancouver, British Columbia V6T 1Z4, [email protected], [email protected]","institution_ids":["https://openalex.org/I141945490"]},{"raw_affiliation_string":"Department of Computer Science, University of British Columbia, Vancouver, British Columbia V6T 1Z4, fournier@cs.ubc.ca, juancho@cs.ubc.ca","institution_ids":["https://openalex.org/I141945490"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109223295","display_name":"John Buchanan","orcid":null},"institutions":[{"id":"https://openalex.org/I141945490","display_name":"University of British Columbia","ror":"https://ror.org/03rmrcq20","country_code":"CA","type":"education","lineage":["https://openalex.org/I141945490"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"John Buchanan","raw_affiliation_strings":["Department of Computer Science, University of British Columbia, Vancouver, British Columbia V6T 1Z4, [email protected], [email protected]","Department of Computer Science, University of British Columbia, Vancouver, British Columbia V6T 1Z4, fournier@cs.ubc.ca, juancho@cs.ubc.ca"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of British Columbia, Vancouver, British Columbia V6T 1Z4, [email protected], [email protected]","institution_ids":["https://openalex.org/I141945490"]},{"raw_affiliation_string":"Department of Computer Science, University of British Columbia, Vancouver, British Columbia V6T 1Z4, fournier@cs.ubc.ca, juancho@cs.ubc.ca","institution_ids":["https://openalex.org/I141945490"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5109223295"],"corresponding_institution_ids":["https://openalex.org/I141945490"],"apc_list":{"value":3710,"currency":"USD","value_usd":3710},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":25,"citation_normalized_percentile":{"value":0.19066074,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"13","issue":"3","first_page":"127","last_page":"142"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9995999932289124,"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":0.9995999932289124,"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":0.9915000200271606,"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":0.9842000007629395,"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/parametric-surface","display_name":"Parametric surface","score":0.6700679063796997},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6594449877738953},{"id":"https://openalex.org/keywords/rendering","display_name":"Rendering (computer graphics)","score":0.6420435309410095},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.6343594789505005},{"id":"https://openalex.org/keywords/chebyshev-polynomials","display_name":"Chebyshev polynomials","score":0.631301760673523},{"id":"https://openalex.org/keywords/parametric-equation","display_name":"Parametric equation","score":0.5706093907356262},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5364789366722107},{"id":"https://openalex.org/keywords/chebyshev-filter","display_name":"Chebyshev filter","score":0.49140965938568115},{"id":"https://openalex.org/keywords/geometric-design","display_name":"Geometric design","score":0.4725368022918701},{"id":"https://openalex.org/keywords/bilinear-interpolation","display_name":"Bilinear interpolation","score":0.4389806091785431},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4369143843650818},{"id":"https://openalex.org/keywords/computer-graphics","display_name":"Computer graphics","score":0.4304545521736145},{"id":"https://openalex.org/keywords/basis-function","display_name":"Basis function","score":0.42498287558555603},{"id":"https://openalex.org/keywords/computer-graphics","display_name":"Computer graphics (images)","score":0.41182103753089905},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.33525118231773376},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.24215155839920044},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1852608621120453},{"id":"https://openalex.org/keywords/computer-vision","display_name":"Computer vision","score":0.1256304681301117}],"concepts":[{"id":"https://openalex.org/C2187777","wikidata":"https://www.wikidata.org/wiki/Q1071743","display_name":"Parametric surface","level":3,"score":0.6700679063796997},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6594449877738953},{"id":"https://openalex.org/C205711294","wikidata":"https://www.wikidata.org/wiki/Q176953","display_name":"Rendering (computer graphics)","level":2,"score":0.6420435309410095},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.6343594789505005},{"id":"https://openalex.org/C129785596","wikidata":"https://www.wikidata.org/wiki/Q619511","display_name":"Chebyshev polynomials","level":2,"score":0.631301760673523},{"id":"https://openalex.org/C99636146","wikidata":"https://www.wikidata.org/wiki/Q35889","display_name":"Parametric equation","level":2,"score":0.5706093907356262},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5364789366722107},{"id":"https://openalex.org/C21424316","wikidata":"https://www.wikidata.org/wiki/Q718621","display_name":"Chebyshev filter","level":2,"score":0.49140965938568115},{"id":"https://openalex.org/C40319758","wikidata":"https://www.wikidata.org/wiki/Q5535477","display_name":"Geometric design","level":2,"score":0.4725368022918701},{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.4389806091785431},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4369143843650818},{"id":"https://openalex.org/C77660652","wikidata":"https://www.wikidata.org/wiki/Q150971","display_name":"Computer graphics","level":2,"score":0.4304545521736145},{"id":"https://openalex.org/C5917680","wikidata":"https://www.wikidata.org/wiki/Q2621825","display_name":"Basis function","level":2,"score":0.42498287558555603},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.41182103753089905},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.33525118231773376},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.24215155839920044},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1852608621120453},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.1256304681301117},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1111/1467-8659.1330127","is_oa":false,"landing_page_url":"https://doi.org/10.1111/1467-8659.1330127","pdf_url":null,"source":{"id":"https://openalex.org/S67831204","display_name":"Computer Graphics Forum","issn_l":"0167-7055","issn":["0167-7055","1467-8659"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computer Graphics Forum","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.73.3884","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.73.3884","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.ubc.ca/nest/imager/contributions/healey/imager-tr/ps/fournier.eurograph.94.ps.gz","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320323180","display_name":"University of British Columbia","ror":"https://ror.org/03rmrcq20"},{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W1533783383","https://openalex.org/W1967555766","https://openalex.org/W1991277745","https://openalex.org/W1991651582","https://openalex.org/W2004471745","https://openalex.org/W2038233234","https://openalex.org/W2055491898","https://openalex.org/W2057600146","https://openalex.org/W2071585055","https://openalex.org/W2152481451"],"related_works":["https://openalex.org/W2382532955","https://openalex.org/W2106962382","https://openalex.org/W4213342932","https://openalex.org/W2056379897","https://openalex.org/W2074316639","https://openalex.org/W2541927208","https://openalex.org/W3149156552","https://openalex.org/W2062803001","https://openalex.org/W1985426375","https://openalex.org/W2375011831"],"abstract_inverted_index":{"Abstract":[0],"Parametric":[1],"curves":[2,44,69],"and":[3,7,14,22,36,42,45,49,67,83,102,166,172],"surfaces":[4,88,108,148],"are":[5],"powerful":[6],"popular":[8,23],"modelling":[9],"tools":[10],"in":[11,32,78,161,164],"Computer":[12,15],"Graphics":[13],"Aided":[16],"Design.":[17],"Ray\u2010tracing":[18],"is":[19,27],"a":[20,29,91,139],"versatile":[21],"rendering":[24],"technique.":[25],"There":[26],"therefore":[28],"strong":[30],"incentive":[31],"developing":[33],"fast,":[34],"accurate":[35],"reliable":[37],"algorithms":[38],"to":[39,57,95],"intersect":[40],"rays":[41,66],"parametric":[43,68],"surfaces.":[46,71],"We":[47,136],"propose":[48],"demonstrate":[50],"the":[51,60,63,79,98,104,110,113,120,125,129,132,143,159],"use":[52,105],"of":[53,62,74,81,100,106,112,119,128,131,142,145,149,158],"Chebyshev":[54,75,133],"basis":[55,134],"functions":[56],"speed":[58,165],"up":[59],"computation":[61,80,111],"intersections":[64],"between":[65],"or":[70],"The":[72,117],"properties":[73],"polynomials":[76],"result":[77,156],"better":[82,92],"tighter":[84],"enclosing":[85],"boxes.":[86],"For":[87],"they":[89],"provide":[90],"termination":[93],"criterion":[94],"decide":[96],"on":[97,124],"limits":[99],"subdivision,":[101],"allow":[103],"bilinear":[107],"for":[109],"intersection":[114],"when":[115],"needed.":[116],"efficiency":[118],"techniques":[121,154],"used":[122],"depends":[123],"relative":[126],"magnitude":[127],"coefficients":[130],"functions.":[135],"show":[137],"from":[138],"statistical":[140],"analysis":[141],"characteristics":[144],"several":[146],"thousands":[147],"different":[150],"origin":[151],"that":[152],"these":[153],"will":[155],"most":[157],"time":[160],"significant":[162],"improvement":[163],"accuracy":[167],"over":[168],"other":[169,170],"boxing":[171],"subdivision":[173],"techniques.":[174]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}