{"id":"https://openalex.org/W2008055107","doi":"https://doi.org/10.1080/10867651.1997.10487471","title":"Sampling with Hammersley and Halton Points","display_name":"Sampling with Hammersley and Halton Points","publication_year":1997,"publication_date":"1997-01-01","ids":{"openalex":"https://openalex.org/W2008055107","doi":"https://doi.org/10.1080/10867651.1997.10487471","mag":"2008055107"},"language":"en","primary_location":{"id":"doi:10.1080/10867651.1997.10487471","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10867651.1997.10487471","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/A5017857966","display_name":"Tien\u2010Tsin Wong","orcid":"https://orcid.org/0000-0002-7792-9307"},"institutions":[{"id":"https://openalex.org/I177725633","display_name":"Chinese University of Hong Kong","ror":"https://ror.org/00t33hh48","country_code":"HK","type":"education","lineage":["https://openalex.org/I177725633"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Tien-Tsin Wong","raw_affiliation_strings":["Department of Computer Science and Engineering , The Chinese University of Hong Kong , Shatin , Hong Kong E-mail: ttwong@acm.org"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Engineering , The Chinese University of Hong Kong , Shatin , Hong Kong E-mail: ttwong@acm.org","institution_ids":["https://openalex.org/I177725633"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109302065","display_name":"Wai-Shing Luk","orcid":"https://orcid.org/0009-0006-8322-8079"},"institutions":[{"id":"https://openalex.org/I99464096","display_name":"KU Leuven","ror":"https://ror.org/05f950310","country_code":"BE","type":"education","lineage":["https://openalex.org/I99464096"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Wai-Shing Luk","raw_affiliation_strings":["Departement Computerwetenschappen , Katholieke Universiteit Leuven , Celestijnenlaan 200A, B-3001 Heverlee, Belgium E-mail: Wai-Shing.Luk@cs.kuleuven.ac.be"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departement Computerwetenschappen , Katholieke Universiteit Leuven , Celestijnenlaan 200A, B-3001 Heverlee, Belgium E-mail: Wai-Shing.Luk@cs.kuleuven.ac.be","institution_ids":["https://openalex.org/I99464096"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5032708386","display_name":"Pheng\u2010Ann Heng","orcid":"https://orcid.org/0000-0003-3055-5034"},"institutions":[{"id":"https://openalex.org/I177725633","display_name":"Chinese University of Hong Kong","ror":"https://ror.org/00t33hh48","country_code":"HK","type":"education","lineage":["https://openalex.org/I177725633"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Pheng-Ann Heng","raw_affiliation_strings":["Department of Computer Science and Engineering , The Chinese University of Hong Kong , Shatin , Hong Kong E-mail: pheng@cse.cuhk.edu.hk"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Engineering , The Chinese University of Hong Kong , Shatin , Hong Kong E-mail: pheng@cse.cuhk.edu.hk","institution_ids":["https://openalex.org/I177725633"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":249,"citation_normalized_percentile":{"value":0.13484741,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"2","issue":"2","first_page":"9","last_page":"24"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10481","display_name":"Computer Graphics and Visualization Techniques","score":0.9922999739646912,"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":0.9922999739646912,"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":0.9886999726295471,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9830999970436096,"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/sampling","display_name":"Sampling (signal processing)","score":0.7837778329849243},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.5855446457862854},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.577301025390625},{"id":"https://openalex.org/keywords/tracing","display_name":"Tracing","score":0.5673983097076416},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.5621227622032166},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5428375005722046},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5416408777236938},{"id":"https://openalex.org/keywords/sampling-scheme","display_name":"Sampling scheme","score":0.5053170323371887},{"id":"https://openalex.org/keywords/importance-sampling","display_name":"Importance sampling","score":0.4386729598045349},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.32435494661331177},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.24434837698936462},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07463502883911133}],"concepts":[{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.7837778329849243},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.5855446457862854},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.577301025390625},{"id":"https://openalex.org/C138673069","wikidata":"https://www.wikidata.org/wiki/Q322229","display_name":"Tracing","level":2,"score":0.5673983097076416},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.5621227622032166},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5428375005722046},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5416408777236938},{"id":"https://openalex.org/C2985139394","wikidata":"https://www.wikidata.org/wiki/Q49908","display_name":"Sampling scheme","level":3,"score":0.5053170323371887},{"id":"https://openalex.org/C52740198","wikidata":"https://www.wikidata.org/wiki/Q1539564","display_name":"Importance sampling","level":3,"score":0.4386729598045349},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.32435494661331177},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.24434837698936462},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07463502883911133},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.0},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1080/10867651.1997.10487471","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10867651.1997.10487471","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.552.864","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.552.864","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cse.cuhk.edu.hk/~ttwong/papers/udpoint/udpoint.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320698","display_name":"National University of Singapore","ror":"https://ror.org/01tgyzw49"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W16072666","https://openalex.org/W31470552","https://openalex.org/W115130976","https://openalex.org/W128482236","https://openalex.org/W163039385","https://openalex.org/W1523557403","https://openalex.org/W1543768340","https://openalex.org/W1565148419","https://openalex.org/W1588580784","https://openalex.org/W1978361715","https://openalex.org/W2000261957","https://openalex.org/W2043419861","https://openalex.org/W2045422729","https://openalex.org/W2077220042","https://openalex.org/W2146261346","https://openalex.org/W2173197174","https://openalex.org/W2173672816","https://openalex.org/W2476762106","https://openalex.org/W2596964193","https://openalex.org/W3021902634","https://openalex.org/W3135037104","https://openalex.org/W4214574008","https://openalex.org/W4285719527","https://openalex.org/W4300580367","https://openalex.org/W6704339621"],"related_works":["https://openalex.org/W2742914308","https://openalex.org/W2370474211","https://openalex.org/W2510070654","https://openalex.org/W2330004501","https://openalex.org/W2017089693","https://openalex.org/W2299309501","https://openalex.org/W2703295919","https://openalex.org/W2793935943","https://openalex.org/W2616810199","https://openalex.org/W1984126792"],"abstract_inverted_index":{"Abstract":[0],"The":[1,37,78],"Hammersley":[2],"and":[3,29,55],"Halton":[4,38],"point":[5,39,64],"sets,":[6,65],"two":[7],"well-known,":[8],"low":[9,34],"discrepancy":[10],"sequences,":[11],"have":[12],"been":[13],"used":[14],"for":[15,44,62],"quasi-Monte":[16],"Carlo":[17],"integration":[18],"in":[19,91],"previous":[20],"research.":[21],"A":[22],"deterministic":[23],"formula":[24],"generates":[25],"a":[26,75,88],"uniformly":[27],"distributed":[28],"stochasticlooking":[30],"sampling":[31,79,95],"pattern":[32],"at":[33],"computational":[35],"cost.":[36],"set":[40],"is":[41,81],"also":[42,73,82],"useful":[43],"incremental":[45],"sampling.":[46],"In":[47],"this":[48],"paper,":[49],"we":[50],"discuss":[51],"detailed":[52],"implementation":[53],"issues":[54],"our":[56],"experience":[57],"of":[58],"choosing":[59],"suitable":[60],"bases":[61],"the":[63,69],"not":[66],"just":[67],"on":[68,74],"two-dimensional":[70],"plane":[71],"but":[72],"spherical":[76],"surface.":[77],"scheme":[80],"applied":[83],"to":[84],"ray":[85],"tracing,":[86],"with":[87],"significant":[89],"improvement":[90],"error":[92],"over":[93],"standard":[94],"techniques.":[96]},"counts_by_year":[{"year":2026,"cited_by_count":8},{"year":2025,"cited_by_count":16},{"year":2024,"cited_by_count":13},{"year":2023,"cited_by_count":18},{"year":2022,"cited_by_count":8},{"year":2021,"cited_by_count":19},{"year":2020,"cited_by_count":15},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":20},{"year":2017,"cited_by_count":17},{"year":2016,"cited_by_count":20},{"year":2015,"cited_by_count":9},{"year":2014,"cited_by_count":15},{"year":2013,"cited_by_count":11},{"year":2012,"cited_by_count":7}],"updated_date":"2026-07-16T13:24:37.021932","created_date":"2025-10-10T00:00:00"}