{"id":"https://openalex.org/W2048215675","doi":"https://doi.org/10.1137/060672261","title":"Vertical Ray Shooting and Computing Depth Orders for Fat Objects","display_name":"Vertical Ray Shooting and Computing Depth Orders for Fat Objects","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W2048215675","doi":"https://doi.org/10.1137/060672261","mag":"2048215675"},"language":"en","primary_location":{"id":"doi:10.1137/060672261","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060672261","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://research.tue.nl/en/publications/4e9bb785-5361-4e83-b89e-d2a20594a344","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5028410825","display_name":"Mark de Berg","orcid":"https://orcid.org/0000-0001-5770-3784"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mark de Berg","raw_affiliation_strings":["mdberg@win.tue.nl and cgray@win.tue.nl#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"mdberg@win.tue.nl and cgray@win.tue.nl#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109898694","display_name":"Chris Gray","orcid":null},"institutions":[{"id":"https://openalex.org/I83019370","display_name":"Eindhoven University of Technology","ror":"https://ror.org/02c2kyt77","country_code":"NL","type":"education","lineage":["https://openalex.org/I83019370"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"Chris Gray","raw_affiliation_strings":["Department of Computing Science, TU Eindhoven, P.O. Box 513, 5600 MB Eindhoven, The Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computing Science, TU Eindhoven, P.O. Box 513, 5600 MB Eindhoven, The Netherlands","institution_ids":["https://openalex.org/I83019370"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5109898694"],"corresponding_institution_ids":["https://openalex.org/I83019370"],"apc_list":null,"apc_paid":null,"fwci":4.023,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.93489254,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"38","issue":"1","first_page":"257","last_page":"275"},"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/T11164","display_name":"Remote Sensing and LiDAR Applications","score":0.9894000291824341,"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"}},{"id":"https://openalex.org/T12923","display_name":"Digital Image Processing Techniques","score":0.9876999855041504,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.702547550201416},{"id":"https://openalex.org/keywords/polyhedron","display_name":"Polyhedron","score":0.6850491166114807},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.6409225463867188},{"id":"https://openalex.org/keywords/binary-logarithm","display_name":"Binary logarithm","score":0.6185421943664551},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5690246820449829},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5614994168281555},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.5499094724655151},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.5091869235038757},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.47577038407325745},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4753113389015198},{"id":"https://openalex.org/keywords/computational-geometry","display_name":"Computational geometry","score":0.45179271697998047},{"id":"https://openalex.org/keywords/running-time","display_name":"Running time","score":0.4230136275291443},{"id":"https://openalex.org/keywords/data-structure","display_name":"Data structure","score":0.41987186670303345},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3204745948314667},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.287822961807251},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.19746029376983643},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.11663061380386353}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.702547550201416},{"id":"https://openalex.org/C54829058","wikidata":"https://www.wikidata.org/wiki/Q172937","display_name":"Polyhedron","level":2,"score":0.6850491166114807},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.6409225463867188},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.6185421943664551},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5690246820449829},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5614994168281555},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.5499094724655151},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.5091869235038757},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.47577038407325745},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4753113389015198},{"id":"https://openalex.org/C29123130","wikidata":"https://www.wikidata.org/wiki/Q874709","display_name":"Computational geometry","level":2,"score":0.45179271697998047},{"id":"https://openalex.org/C3017489831","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Running time","level":2,"score":0.4230136275291443},{"id":"https://openalex.org/C162319229","wikidata":"https://www.wikidata.org/wiki/Q175263","display_name":"Data structure","level":2,"score":0.41987186670303345},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3204745948314667},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.287822961807251},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.19746029376983643},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11663061380386353},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/060672261","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060672261","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"},{"id":"pmh:oai:pure.tue.nl:openaire/4e9bb785-5361-4e83-b89e-d2a20594a344","is_oa":true,"landing_page_url":"https://research.tue.nl/en/publications/4e9bb785-5361-4e83-b89e-d2a20594a344","pdf_url":null,"source":{"id":"https://openalex.org/S4406922641","display_name":"TU/e Research Portal","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Berg, de, M & Gray, C M 2008, 'Vertical ray shooting and computing depth orders of fat objects', SIAM Journal on Computing, vol. 38, no. 1, pp. 257-275. https://doi.org/10.1137/060672261","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:tue:oai:pure.tue.nl:publications/4e9bb785-5361-4e83-b89e-d2a20594a344","is_oa":true,"landing_page_url":"https://research.tue.nl/nl/publications/4e9bb785-5361-4e83-b89e-d2a20594a344","pdf_url":null,"source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Computing, 38(1), 257 - 275. Society for Industrial and Applied Mathematics (SIAM)","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:pure.tue.nl:openaire/4e9bb785-5361-4e83-b89e-d2a20594a344","is_oa":true,"landing_page_url":"https://research.tue.nl/en/publications/4e9bb785-5361-4e83-b89e-d2a20594a344","pdf_url":null,"source":{"id":"https://openalex.org/S4406922641","display_name":"TU/e Research Portal","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Berg, de, M & Gray, C M 2008, 'Vertical ray shooting and computing depth orders of fat objects', SIAM Journal on Computing, vol. 38, no. 1, pp. 257-275. https://doi.org/10.1137/060672261","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1979838628","https://openalex.org/W2026200800","https://openalex.org/W2029814178","https://openalex.org/W2032605149","https://openalex.org/W2090847304","https://openalex.org/W2123702669","https://openalex.org/W2123869145","https://openalex.org/W2134898774","https://openalex.org/W2136863760","https://openalex.org/W2141110561","https://openalex.org/W2142728440","https://openalex.org/W2196955596","https://openalex.org/W2568603896"],"related_works":["https://openalex.org/W1990773291","https://openalex.org/W2113270940","https://openalex.org/W2004283824","https://openalex.org/W1976803949","https://openalex.org/W1581210843","https://openalex.org/W4230281099","https://openalex.org/W1992104669","https://openalex.org/W1982530285","https://openalex.org/W2521054645","https://openalex.org/W1998702677"],"abstract_inverted_index":{"We":[0,21,44,63],"present":[1],"new":[2],"results":[3,86],"for":[4,26],"three":[5,85],"problems":[6],"dealing":[7],"with":[8],"a":[9,23,54,74,80],"set":[10],"$\\mathcal{P}$":[11,31,58,78],"of":[12],"n":[13],"convex":[14],"constant-complexity":[15],"fat":[16],"polyhedra":[17],"in":[18,30,50,69],"3-space.":[19],"(i)":[20],"describe":[22],"data":[24],"structure":[25],"vertical":[27],"ray":[28],"shooting":[29],"that":[32],"has":[33],"$O(\\log^2":[34],"n)$":[35,41,52,71],"query":[36],"time":[37,53,72],"and":[38],"uses":[39],"$O(n\\log^2":[40],"storage.":[42],"(ii)":[43],"give":[45,64],"an":[46,65],"algorithm":[47,66],"to":[48,67],"compute":[49],"$O(n\\log^3":[51,70],"depth":[55,82],"order":[56,76],"on":[57,77,88],"if":[59],"it":[60],"exists.":[61],"(iii)":[62],"verify":[68],"whether":[73],"given":[75],"is":[79],"valid":[81],"order.":[83],"All":[84],"improve":[87],"previous":[89],"results.":[90]},"counts_by_year":[{"year":2019,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2016-06-24T00:00:00"}