{"id":"https://openalex.org/W2089715871","doi":"https://doi.org/10.1137/s0097539793244368","title":"Ray Shooting Amidst Convex Polyhedra and Polyhedral Terrains in Three Dimensions","display_name":"Ray Shooting Amidst Convex Polyhedra and Polyhedral Terrains in Three Dimensions","publication_year":1996,"publication_date":"1996-02-01","ids":{"openalex":"https://openalex.org/W2089715871","doi":"https://doi.org/10.1137/s0097539793244368","mag":"2089715871"},"language":"en","primary_location":{"id":"doi:10.1137/s0097539793244368","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0097539793244368","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5058649592","display_name":"Pankaj K. Agarwal","orcid":"https://orcid.org/0000-0002-9439-181X"},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]},{"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"]}],"countries":["IL","US"],"is_corresponding":true,"raw_author_name":"Pankaj K. Agarwal","raw_affiliation_strings":["New York University, New York, NY 10012","Department of Computer Science, P.O. Box 90129, Duke University, Durham, NC 27708-0129","tSchool of Mathematics, Tel Aviv University, Tel Aviv 69978, Israel, and Courant Institute of Mathematical Sciences,"],"affiliations":[{"raw_affiliation_string":"New York University, New York, NY 10012","institution_ids":["https://openalex.org/I57206974"]},{"raw_affiliation_string":"Department of Computer Science, P.O. Box 90129, Duke University, Durham, NC 27708-0129","institution_ids":[]},{"raw_affiliation_string":"tSchool of Mathematics, Tel Aviv University, Tel Aviv 69978, Israel, and Courant Institute of Mathematical Sciences,","institution_ids":["https://openalex.org/I16391192"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5055296785","display_name":"Micha Sharir","orcid":"https://orcid.org/0000-0002-2541-3763"},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]},{"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"]}],"countries":["IL","US"],"is_corresponding":false,"raw_author_name":"Micha Sharir","raw_affiliation_strings":["Department of Computer Science, P.O. Box 90129, Duke University, Durham, NC 27708-0129","New York University, New York, NY 10012","tSchool of Mathematics, Tel Aviv University, Tel Aviv 69978, Israel, and Courant Institute of Mathematical Sciences,"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, P.O. Box 90129, Duke University, Durham, NC 27708-0129","institution_ids":[]},{"raw_affiliation_string":"New York University, New York, NY 10012","institution_ids":["https://openalex.org/I57206974"]},{"raw_affiliation_string":"tSchool of Mathematics, Tel Aviv University, Tel Aviv 69978, Israel, and Courant Institute of Mathematical Sciences,","institution_ids":["https://openalex.org/I16391192"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5058649592"],"corresponding_institution_ids":["https://openalex.org/I16391192","https://openalex.org/I57206974"],"apc_list":null,"apc_paid":null,"fwci":1.7377,"has_fulltext":false,"cited_by_count":26,"citation_normalized_percentile":{"value":0.86666667,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"25","issue":"1","first_page":"100","last_page":"116"},"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":0.9973999857902527,"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/T10191","display_name":"Robotics and Sensor-Based Localization","score":0.9958999752998352,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/polyhedron","display_name":"Polyhedron","score":0.9208786487579346},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.735850989818573},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.6847654581069946},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.6380370259284973},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4864318370819092},{"id":"https://openalex.org/keywords/data-structure","display_name":"Data structure","score":0.4817473888397217},{"id":"https://openalex.org/keywords/preprocessor","display_name":"Preprocessor","score":0.4698198139667511},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.4493355453014374},{"id":"https://openalex.org/keywords/convex-polytope","display_name":"Convex polytope","score":0.44431424140930176},{"id":"https://openalex.org/keywords/binary-logarithm","display_name":"Binary logarithm","score":0.43832775950431824},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.41542887687683105},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.36986103653907776},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3234986662864685},{"id":"https://openalex.org/keywords/convex-set","display_name":"Convex set","score":0.24070942401885986},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.1885928213596344},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.12318554520606995},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.10289424657821655}],"concepts":[{"id":"https://openalex.org/C54829058","wikidata":"https://www.wikidata.org/wiki/Q172937","display_name":"Polyhedron","level":2,"score":0.9208786487579346},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.735850989818573},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.6847654581069946},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.6380370259284973},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4864318370819092},{"id":"https://openalex.org/C162319229","wikidata":"https://www.wikidata.org/wiki/Q175263","display_name":"Data structure","level":2,"score":0.4817473888397217},{"id":"https://openalex.org/C34736171","wikidata":"https://www.wikidata.org/wiki/Q918333","display_name":"Preprocessor","level":2,"score":0.4698198139667511},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.4493355453014374},{"id":"https://openalex.org/C110943637","wikidata":"https://www.wikidata.org/wiki/Q4129097","display_name":"Convex polytope","level":5,"score":0.44431424140930176},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.43832775950431824},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.41542887687683105},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36986103653907776},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3234986662864685},{"id":"https://openalex.org/C49870271","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex set","level":4,"score":0.24070942401885986},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.1885928213596344},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.12318554520606995},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.10289424657821655},{"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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"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/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/s0097539793244368","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0097539793244368","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:CiteSeerX.psu:10.1.1.294.9661","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.294.9661","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.duke.edu/~pankaj/publications/papers/ray-polytope.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.38.120","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.38.120","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ftp://ftp.cs.duke.edu/pub/dist/techreport/1993/1993-05.ps.gz","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320320947","display_name":"German-Israeli Foundation for Scientific Research and Development","ror":"https://ror.org/00tntzp09"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W155342555","https://openalex.org/W1545831398","https://openalex.org/W1763430070","https://openalex.org/W2010014170","https://openalex.org/W2015425624","https://openalex.org/W2015696135","https://openalex.org/W2016400774","https://openalex.org/W2021895827","https://openalex.org/W2027387410","https://openalex.org/W2030152280","https://openalex.org/W2050459520","https://openalex.org/W2052333483","https://openalex.org/W2054927768","https://openalex.org/W2057537033","https://openalex.org/W2059155916","https://openalex.org/W2061845601","https://openalex.org/W2067695105","https://openalex.org/W2078939351","https://openalex.org/W2080052061","https://openalex.org/W2088617781","https://openalex.org/W2090847304","https://openalex.org/W2101502605","https://openalex.org/W2103893986","https://openalex.org/W2568603896","https://openalex.org/W2609210027","https://openalex.org/W2911302472","https://openalex.org/W4210817330","https://openalex.org/W4232425010","https://openalex.org/W4235042979"],"related_works":["https://openalex.org/W4248823117","https://openalex.org/W2004058166","https://openalex.org/W2030718493","https://openalex.org/W2103429114","https://openalex.org/W2018708907","https://openalex.org/W2005538657","https://openalex.org/W1584292662","https://openalex.org/W2088151573","https://openalex.org/W2004897847","https://openalex.org/W4385474329"],"abstract_inverted_index":{"We":[0,55],"consider":[1],"the":[2,39,48,109,119],"problem":[3],"of":[4,12,24,43,118],"ray":[5,46],"shooting":[6],"in":[7,75,111,134],"a":[8,22,34,44,57,82,116,147],"three-dimensional":[9],"scene":[10],"consisting":[11],"m":[13,100],"(possibly":[14],"intersecting)":[15],"convex":[16],"polyhedra":[17,50],"or":[18],"polyhedral":[19],"terrains":[20],"with":[21],"total":[23],"n":[25],"faces,":[26],"i.e.,":[27],"we":[28,114],"want":[29],"to":[30],"preprocess":[31],"them":[32],"into":[33],"data":[35],"structure,":[36],"so":[37],"that":[38,59,121],"first":[40],"intersection":[41],"point":[42],"query":[45],"and":[47,68,70,97,129,131],"given":[49],"can":[51,71],"be":[52],"determined":[53],"quickly.":[54],"present":[56,115],"technique":[58,120],"requires":[60,122],"$O((mn)^{2":[61],"+":[62,92,124,142],"\\varepsilon":[63,93,125,143],"}":[64,144],")$":[65],"preprocessing":[66],"time":[67,135],"storage,":[69],"answer":[72],"ray-shooting":[73],"queries":[74,133],"$O(\\log":[76],"^2":[77],"n)$":[78],"time.":[79],"This":[80],"is":[81,101,107],"significant":[83,148],"improvement":[84,149],"over":[85,150],"previously":[86],"known":[87],"techniques":[88,152],"(which":[89],"require":[90],"$O(n^{4":[91],"})":[94,126],"$":[95,127],"space":[96,128],"preprocessing)":[98],"if":[99],"much":[102],"smaller":[103],"than":[104],"n,":[105],"which":[106],"often":[108],"case":[110],"practice.":[112],"Next,":[113],"variant":[117],"$O(n^{1":[123],"preprocessing,":[130],"answers":[132],"$O(m^{{1":[136],"/":[137,140],"4}}":[138],"n^{{1":[139],"2}":[141],")$,":[145],"again":[146],"previous":[151],"when":[153],"$m":[154],"\\ll":[155],"n$.":[156]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}