{"id":"https://openalex.org/W2167583556","doi":"https://doi.org/10.1145/1137856.1137885","title":"On realistic terrains","display_name":"On realistic terrains","publication_year":2006,"publication_date":"2006-06-05","ids":{"openalex":"https://openalex.org/W2167583556","doi":"https://doi.org/10.1145/1137856.1137885","mag":"2167583556"},"language":"en","primary_location":{"id":"doi:10.1145/1137856.1137885","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1137856.1137885","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the twenty-second annual symposium on Computational geometry","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://dspace.library.uu.nl/handle/1874/24653","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5046375175","display_name":"Esther Moet","orcid":null},"institutions":[{"id":"https://openalex.org/I193662353","display_name":"Utrecht University","ror":"https://ror.org/04pp8hn57","country_code":"NL","type":"education","lineage":["https://openalex.org/I193662353"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Esther Moet","raw_affiliation_strings":["Universiteit Utrecht, Utrecht, The Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universiteit Utrecht, Utrecht, The Netherlands","institution_ids":["https://openalex.org/I193662353"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5053874521","display_name":"Marc van Kreveld","orcid":"https://orcid.org/0000-0001-8208-3468"},"institutions":[{"id":"https://openalex.org/I193662353","display_name":"Utrecht University","ror":"https://ror.org/04pp8hn57","country_code":"NL","type":"education","lineage":["https://openalex.org/I193662353"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Marc van Kreveld","raw_affiliation_strings":["Universiteit Utrecht, Utrecht, The Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universiteit Utrecht, Utrecht, The Netherlands","institution_ids":["https://openalex.org/I193662353"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5044860343","display_name":"A. Frank van der Stappen","orcid":"https://orcid.org/0000-0001-7965-2818"},"institutions":[{"id":"https://openalex.org/I193662353","display_name":"Utrecht University","ror":"https://ror.org/04pp8hn57","country_code":"NL","type":"education","lineage":["https://openalex.org/I193662353"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"A. Frank van der Stappen","raw_affiliation_strings":["Universiteit Utrecht, Utrecht, The Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universiteit Utrecht, Utrecht, The Netherlands","institution_ids":["https://openalex.org/I193662353"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.812,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.94821674,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"177","last_page":"186"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9997000098228455,"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":0.9997000098228455,"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/T11106","display_name":"Data Management and Algorithms","score":0.9954000115394592,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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":0.9553999900817871,"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/terrain","display_name":"Terrain","score":0.8720178604125977},{"id":"https://openalex.org/keywords/voronoi-diagram","display_name":"Voronoi diagram","score":0.783319890499115},{"id":"https://openalex.org/keywords/visibility","display_name":"Visibility","score":0.6860256195068359},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.6208230257034302},{"id":"https://openalex.org/keywords/computational-geometry","display_name":"Computational geometry","score":0.5275418758392334},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5250102281570435},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.5190870761871338},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.49188923835754395},{"id":"https://openalex.org/keywords/shortest-path-problem","display_name":"Shortest path problem","score":0.4756602644920349},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.47546714544296265},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.47158706188201904},{"id":"https://openalex.org/keywords/enhanced-data-rates-for-gsm-evolution","display_name":"Enhanced Data Rates for GSM Evolution","score":0.4219074249267578},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.41166025400161743},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.34709155559539795},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.3287501633167267},{"id":"https://openalex.org/keywords/computer-vision","display_name":"Computer vision","score":0.23467287421226501},{"id":"https://openalex.org/keywords/geography","display_name":"Geography","score":0.12736466526985168},{"id":"https://openalex.org/keywords/cartography","display_name":"Cartography","score":0.0739361047744751},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.06860658526420593}],"concepts":[{"id":"https://openalex.org/C161840515","wikidata":"https://www.wikidata.org/wiki/Q186131","display_name":"Terrain","level":2,"score":0.8720178604125977},{"id":"https://openalex.org/C24881265","wikidata":"https://www.wikidata.org/wiki/Q757267","display_name":"Voronoi diagram","level":2,"score":0.783319890499115},{"id":"https://openalex.org/C123403432","wikidata":"https://www.wikidata.org/wiki/Q654068","display_name":"Visibility","level":2,"score":0.6860256195068359},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.6208230257034302},{"id":"https://openalex.org/C29123130","wikidata":"https://www.wikidata.org/wiki/Q874709","display_name":"Computational geometry","level":2,"score":0.5275418758392334},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5250102281570435},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.5190870761871338},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.49188923835754395},{"id":"https://openalex.org/C22590252","wikidata":"https://www.wikidata.org/wiki/Q1058754","display_name":"Shortest path problem","level":3,"score":0.4756602644920349},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.47546714544296265},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.47158706188201904},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.4219074249267578},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.41166025400161743},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.34709155559539795},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3287501633167267},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.23467287421226501},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.12736466526985168},{"id":"https://openalex.org/C58640448","wikidata":"https://www.wikidata.org/wiki/Q42515","display_name":"Cartography","level":1,"score":0.0739361047744751},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.06860658526420593},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.0},{"id":"https://openalex.org/C153294291","wikidata":"https://www.wikidata.org/wiki/Q25261","display_name":"Meteorology","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":4,"locations":[{"id":"doi:10.1145/1137856.1137885","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1137856.1137885","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the twenty-second annual symposium on Computational geometry","raw_type":"proceedings-article"},{"id":"pmh:uu:oai:dspace.library.uu.nl:1874/24653","is_oa":true,"landing_page_url":"https://dspace.library.uu.nl/handle/1874/24653","pdf_url":"https://dspace.library.uu.nl/handle/1874/24653","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":"","raw_type":"info:eu-repo/semantics/other"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.105.1088","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.105.1088","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://delaunay.tem.uoc.gr/~mkaravel/ewcg06/papers/41.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.80.1829","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.80.1829","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.uu.nl/research/techreps/repo/CS-2006/2006-029.pdf","raw_type":"text"}],"best_oa_location":{"id":"pmh:uu:oai:dspace.library.uu.nl:1874/24653","is_oa":true,"landing_page_url":"https://dspace.library.uu.nl/handle/1874/24653","pdf_url":"https://dspace.library.uu.nl/handle/1874/24653","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":"","raw_type":"info:eu-repo/semantics/other"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities","score":0.6100000143051147}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2167583556.pdf"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W240977677","https://openalex.org/W1979838628","https://openalex.org/W1988367079","https://openalex.org/W2003072917","https://openalex.org/W2006517136","https://openalex.org/W2027190503","https://openalex.org/W2032596233","https://openalex.org/W2041935575","https://openalex.org/W2042746037","https://openalex.org/W2077120703","https://openalex.org/W2078013630","https://openalex.org/W2087027878","https://openalex.org/W2093778840","https://openalex.org/W2099698406","https://openalex.org/W2108567935","https://openalex.org/W2120039945","https://openalex.org/W2141110561","https://openalex.org/W2153204081","https://openalex.org/W2156803238","https://openalex.org/W2159549579","https://openalex.org/W2164377846","https://openalex.org/W2196955596","https://openalex.org/W4210283320","https://openalex.org/W4237372798","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2908074373","https://openalex.org/W4250008887","https://openalex.org/W2962789953","https://openalex.org/W2042426695","https://openalex.org/W2189603398","https://openalex.org/W4299527166","https://openalex.org/W2084691280","https://openalex.org/W889844791","https://openalex.org/W2351580801","https://openalex.org/W1492333335"],"abstract_inverted_index":{"We":[0,24,43,76],"study":[1],"worst-case":[2],"complexities":[3],"of":[4,21,30,105],"visibility":[5,28],"and":[6,18,54,64,70,97,117],"distance":[7],"structures":[8,130],"on":[9,14,56,90,108,131],"terrains":[10],"under":[11],"realistic":[12,35,58,92,110,132],"assumptions":[13],"edge":[15],"length":[16],"ratios":[17],"the":[19,22,27,47,66,83,99,128],"angles":[20],"triangles.":[23],"show":[25,81],"that":[26,46,65,82,98],"map":[29,86],"a":[31,34,57,91,109],"point":[32,89],"for":[33,87,102,126],"terrain":[36,59,93,111],"with":[37],"n":[38],"triangles":[39],"has":[40,72,94,112],"complexity":[41,73,95,113],"\u0398(n\u221an).":[42],"also":[44],"prove":[45],"shortest":[48,84],"path":[49,85],"between":[50,68],"two":[51],"points":[52,107],"p":[53,69],"q":[55,71],"passes":[60],"through":[61],"\u0398(\u221an)":[62],"triangles,":[63],"bisector":[67],"O(n":[74],"\u221an).":[75],"use":[77],"these":[78],"results":[79,120],"to":[80],"any":[88,103],"\u0398(n\u221an),":[96],"Voronoi":[100],"diagram":[101],"set":[104],"m":[106],"\u03a9(n":[114],"+":[115],"m\u221an)":[116],"O((n+m)\u221an).":[118],"Our":[119],"immediately":[121],"imply":[122],"more":[123],"efficient":[124],"algorithms":[125],"computing":[127],"various":[129],"terrains.":[133]},"counts_by_year":[{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}