{"id":"https://openalex.org/W2055884227","doi":"https://doi.org/10.1007/pl00009327","title":"Primal Dividing and Dual Pruning: Output-Sensitive Construction of Four-Dimensional Polytopes and Three-Dimensional Voronoi Diagrams","display_name":"Primal Dividing and Dual Pruning: Output-Sensitive Construction of Four-Dimensional Polytopes and Three-Dimensional Voronoi Diagrams","publication_year":1997,"publication_date":"1997-12-01","ids":{"openalex":"https://openalex.org/W2055884227","doi":"https://doi.org/10.1007/pl00009327","mag":"2055884227"},"language":"en","primary_location":{"id":"doi:10.1007/pl00009327","is_oa":true,"landing_page_url":"https://doi.org/10.1007/pl00009327","pdf_url":"https://link.springer.com/content/pdf/10.1007/PL00009327.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete &amp; Computational Geometry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://link.springer.com/content/pdf/10.1007/PL00009327.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102958684","display_name":"T M Chan","orcid":"https://orcid.org/0000-0002-5350-0290"},"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"]},{"id":"https://openalex.org/I145608581","display_name":"University of Miami","ror":"https://ror.org/02dgjyy92","country_code":"US","type":"education","lineage":["https://openalex.org/I145608581"]}],"countries":["CA","US"],"is_corresponding":true,"raw_author_name":"T. M. Chan","raw_affiliation_strings":["Department of Computer Science,  University of British Columbia,  Vancouver, BC, Canada V6T 1Z4, , , , , , CA","University of Miami","University of British Columbia"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science,  University of British Columbia,  Vancouver, BC, Canada V6T 1Z4, , , , , , CA","institution_ids":["https://openalex.org/I141945490"]},{"raw_affiliation_string":"University of Miami","institution_ids":["https://openalex.org/I145608581"]},{"raw_affiliation_string":"University of British Columbia","institution_ids":["https://openalex.org/I141945490"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074061303","display_name":"Jack Snoeyink","orcid":"https://orcid.org/0000-0002-3887-4008"},"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":"J. Snoeyink","raw_affiliation_strings":["Department of Computer Science,  University of British Columbia,  Vancouver, BC, Canada V6T 1Z4, , , , , , CA","Department of Computer Science,  University of British Columbia,  Vancouver, BC, Canada V6T 1Z4, , CA"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science,  University of British Columbia,  Vancouver, BC, Canada V6T 1Z4, , , , , , CA","institution_ids":["https://openalex.org/I141945490"]},{"raw_affiliation_string":"Department of Computer Science,  University of British Columbia,  Vancouver, BC, Canada V6T 1Z4, , CA","institution_ids":["https://openalex.org/I141945490"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5111579019","display_name":"Chee-Keng Yap","orcid":null},"institutions":[{"id":"https://openalex.org/I57206974","display_name":"New York University","ror":"https://ror.org/0190ak572","country_code":"US","type":"education","lineage":["https://openalex.org/I57206974"]},{"id":"https://openalex.org/I36672615","display_name":"Courant Institute of Mathematical Sciences","ror":"https://ror.org/037tm7f56","country_code":"US","type":"education","lineage":["https://openalex.org/I36672615","https://openalex.org/I57206974"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Chee-Keng Yap","raw_affiliation_strings":["Courant Institute of Mathematical Sciences,  New York University,  New York, NY 10012, USA, , , , , , US","Courant Institute of Mathematical Sciences,  New York University,  New York, NY 10012, USA, , US"],"affiliations":[{"raw_affiliation_string":"Courant Institute of Mathematical Sciences,  New York University,  New York, NY 10012, USA, , , , , , US","institution_ids":["https://openalex.org/I36672615","https://openalex.org/I57206974"]},{"raw_affiliation_string":"Courant Institute of Mathematical Sciences,  New York University,  New York, NY 10012, USA, , US","institution_ids":["https://openalex.org/I36672615"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5102958684"],"corresponding_institution_ids":["https://openalex.org/I141945490","https://openalex.org/I145608581"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":1.5445,"has_fulltext":true,"cited_by_count":52,"citation_normalized_percentile":{"value":0.82539683,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"18","issue":"4","first_page":"433","last_page":"454"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9998999834060669,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9998999834060669,"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/T10191","display_name":"Robotics and Sensor-Based Localization","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"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/T11164","display_name":"Remote Sensing and LiDAR Applications","score":0.9886000156402588,"subfield":{"id":"https://openalex.org/subfields/2305","display_name":"Environmental Engineering"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/voronoi-diagram","display_name":"Voronoi diagram","score":0.8808168172836304},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8261374831199646},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7968790531158447},{"id":"https://openalex.org/keywords/convex-hull","display_name":"Convex hull","score":0.7881699800491333},{"id":"https://openalex.org/keywords/delaunay-triangulation","display_name":"Delaunay triangulation","score":0.7386922836303711},{"id":"https://openalex.org/keywords/polytope","display_name":"Polytope","score":0.7053424119949341},{"id":"https://openalex.org/keywords/output-sensitive-algorithm","display_name":"Output-sensitive algorithm","score":0.6793858408927917},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5437783002853394},{"id":"https://openalex.org/keywords/bowyer\u2013watson-algorithm","display_name":"Bowyer\u2013Watson algorithm","score":0.5340403914451599},{"id":"https://openalex.org/keywords/pitteway-triangulation","display_name":"Pitteway triangulation","score":0.5207992792129517},{"id":"https://openalex.org/keywords/computational-geometry","display_name":"Computational geometry","score":0.4618918001651764},{"id":"https://openalex.org/keywords/power-diagram","display_name":"Power diagram","score":0.44032353162765503},{"id":"https://openalex.org/keywords/diagram","display_name":"Diagram","score":0.4386553466320038},{"id":"https://openalex.org/keywords/triangulation","display_name":"Triangulation","score":0.4187626242637634},{"id":"https://openalex.org/keywords/convex-polytope","display_name":"Convex polytope","score":0.41257938742637634},{"id":"https://openalex.org/keywords/convex-set","display_name":"Convex set","score":0.3836054503917694},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3286830186843872},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.21255767345428467},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.164883553981781}],"concepts":[{"id":"https://openalex.org/C24881265","wikidata":"https://www.wikidata.org/wiki/Q757267","display_name":"Voronoi diagram","level":2,"score":0.8808168172836304},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8261374831199646},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7968790531158447},{"id":"https://openalex.org/C206194317","wikidata":"https://www.wikidata.org/wiki/Q1138624","display_name":"Convex hull","level":3,"score":0.7881699800491333},{"id":"https://openalex.org/C68010082","wikidata":"https://www.wikidata.org/wiki/Q192445","display_name":"Delaunay triangulation","level":2,"score":0.7386922836303711},{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.7053424119949341},{"id":"https://openalex.org/C39132409","wikidata":"https://www.wikidata.org/wiki/Q7112860","display_name":"Output-sensitive algorithm","level":5,"score":0.6793858408927917},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5437783002853394},{"id":"https://openalex.org/C121198538","wikidata":"https://www.wikidata.org/wiki/Q4951461","display_name":"Bowyer\u2013Watson algorithm","level":3,"score":0.5340403914451599},{"id":"https://openalex.org/C178609930","wikidata":"https://www.wikidata.org/wiki/Q3538712","display_name":"Pitteway triangulation","level":3,"score":0.5207992792129517},{"id":"https://openalex.org/C29123130","wikidata":"https://www.wikidata.org/wiki/Q874709","display_name":"Computational geometry","level":2,"score":0.4618918001651764},{"id":"https://openalex.org/C20573064","wikidata":"https://www.wikidata.org/wiki/Q13410436","display_name":"Power diagram","level":3,"score":0.44032353162765503},{"id":"https://openalex.org/C186399060","wikidata":"https://www.wikidata.org/wiki/Q959962","display_name":"Diagram","level":2,"score":0.4386553466320038},{"id":"https://openalex.org/C135981907","wikidata":"https://www.wikidata.org/wiki/Q188056","display_name":"Triangulation","level":2,"score":0.4187626242637634},{"id":"https://openalex.org/C110943637","wikidata":"https://www.wikidata.org/wiki/Q4129097","display_name":"Convex polytope","level":5,"score":0.41257938742637634},{"id":"https://openalex.org/C49870271","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex set","level":4,"score":0.3836054503917694},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3286830186843872},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.21255767345428467},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.164883553981781},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/pl00009327","is_oa":true,"landing_page_url":"https://doi.org/10.1007/pl00009327","pdf_url":"https://link.springer.com/content/pdf/10.1007/PL00009327.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete &amp; Computational Geometry","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/pl00009327","is_oa":true,"landing_page_url":"https://doi.org/10.1007/pl00009327","pdf_url":"https://link.springer.com/content/pdf/10.1007/PL00009327.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete &amp; Computational Geometry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4952545190","display_name":null,"funder_award_id":"Fellowship","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G6894402473","display_name":null,"funder_award_id":"Fellowship","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320322337","display_name":"Killam Trusts","ror":"https://ror.org/021cbtn85"},{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2055884227.pdf","grobid_xml":"https://content.openalex.org/works/W2055884227.grobid-xml"},"referenced_works_count":42,"referenced_works":["https://openalex.org/W1579678295","https://openalex.org/W1593563200","https://openalex.org/W1958385715","https://openalex.org/W1964691748","https://openalex.org/W1974726020","https://openalex.org/W1976915153","https://openalex.org/W1984182033","https://openalex.org/W1987576325","https://openalex.org/W1993058867","https://openalex.org/W2000358470","https://openalex.org/W2001211700","https://openalex.org/W2005314985","https://openalex.org/W2005411543","https://openalex.org/W2006889851","https://openalex.org/W2011297770","https://openalex.org/W2022266599","https://openalex.org/W2035774625","https://openalex.org/W2041551783","https://openalex.org/W2049074379","https://openalex.org/W2050356354","https://openalex.org/W2050459520","https://openalex.org/W2052948190","https://openalex.org/W2058127000","https://openalex.org/W2058432138","https://openalex.org/W2059155916","https://openalex.org/W2061344951","https://openalex.org/W2065697367","https://openalex.org/W2078908612","https://openalex.org/W2079789648","https://openalex.org/W2091135431","https://openalex.org/W2097944783","https://openalex.org/W2103893986","https://openalex.org/W2106704696","https://openalex.org/W2118587873","https://openalex.org/W2132026455","https://openalex.org/W2142278387","https://openalex.org/W2147495235","https://openalex.org/W2168352426","https://openalex.org/W3190573802","https://openalex.org/W4210817330","https://openalex.org/W4235042979","https://openalex.org/W4300640952"],"related_works":["https://openalex.org/W2129618641","https://openalex.org/W2358109229","https://openalex.org/W2371448287","https://openalex.org/W2369399365","https://openalex.org/W2353535928","https://openalex.org/W2384419600","https://openalex.org/W1967060523","https://openalex.org/W2279660530","https://openalex.org/W2084525439","https://openalex.org/W4294492445"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":3}],"updated_date":"2026-03-15T09:29:46.208133","created_date":"2025-10-10T00:00:00"}
