{"id":"https://openalex.org/W2048026042","doi":"https://doi.org/10.1007/s00454-010-9270-3","title":"Lines, Circles, Planes and Spheres","display_name":"Lines, Circles, Planes and Spheres","publication_year":2010,"publication_date":"2010-06-03","ids":{"openalex":"https://openalex.org/W2048026042","doi":"https://doi.org/10.1007/s00454-010-9270-3","mag":"2048026042"},"language":"en","primary_location":{"id":"doi:10.1007/s00454-010-9270-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-010-9270-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-010-9270-3.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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://link.springer.com/content/pdf/10.1007/s00454-010-9270-3.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"George B. Purdy","orcid":null},"institutions":[{"id":"https://openalex.org/I63135867","display_name":"University of Cincinnati","ror":"https://ror.org/01e3m7079","country_code":"US","type":"education","lineage":["https://openalex.org/I63135867"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"George B. Purdy","raw_affiliation_strings":["Department of Computer Science, University of Cincinnati, 814 Rhodes Hall, OH, 45221, Cincinnati, USA","Department of Computer Science, University of Cincinnati, Cincinnati, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Cincinnati, 814 Rhodes Hall, OH, 45221, Cincinnati, USA","institution_ids":["https://openalex.org/I63135867"]},{"raw_affiliation_string":"Department of Computer Science, University of Cincinnati, Cincinnati, USA","institution_ids":["https://openalex.org/I63135867"]}]},{"author_position":"last","author":{"id":null,"display_name":"Justin W. Smith","orcid":null},"institutions":[{"id":"https://openalex.org/I63135867","display_name":"University of Cincinnati","ror":"https://ror.org/01e3m7079","country_code":"US","type":"education","lineage":["https://openalex.org/I63135867"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Justin W. Smith","raw_affiliation_strings":["Department of Computer Science, University of Cincinnati, 814 Rhodes Hall, OH, 45221, Cincinnati, USA","Department of Computer Science, University of Cincinnati, Cincinnati, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Cincinnati, 814 Rhodes Hall, OH, 45221, Cincinnati, USA","institution_ids":["https://openalex.org/I63135867"]},{"raw_affiliation_string":"Department of Computer Science, University of Cincinnati, Cincinnati, USA","institution_ids":["https://openalex.org/I63135867"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I63135867"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.12747103,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"44","issue":"4","first_page":"860","last_page":"882"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.37619999051094055,"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":0.37619999051094055,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.3452000021934509,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11830","display_name":"Point processes and geometric inequalities","score":0.10029999911785126,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/spheres","display_name":"SPHERES","score":0.8460999727249146},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5116000175476074},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4672999978065491},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.3885999917984009},{"id":"https://openalex.org/keywords/general-position","display_name":"General position","score":0.3718000054359436},{"id":"https://openalex.org/keywords/position","display_name":"Position (finance)","score":0.36890000104904175}],"concepts":[{"id":"https://openalex.org/C72422203","wikidata":"https://www.wikidata.org/wiki/Q7392545","display_name":"SPHERES","level":2,"score":0.8460999727249146},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6288999915122986},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6150000095367432},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5116000175476074},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4672999978065491},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.44859999418258667},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.3885999917984009},{"id":"https://openalex.org/C150397156","wikidata":"https://www.wikidata.org/wiki/Q591310","display_name":"General position","level":2,"score":0.3718000054359436},{"id":"https://openalex.org/C198082294","wikidata":"https://www.wikidata.org/wiki/Q3399648","display_name":"Position (finance)","level":2,"score":0.36890000104904175},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.36070001125335693},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.357699990272522},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3537999987602234},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.34310001134872437},{"id":"https://openalex.org/C182124507","wikidata":"https://www.wikidata.org/wiki/Q166154","display_name":"Line segment","level":2,"score":0.29330000281333923},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.2906999886035919}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s00454-010-9270-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-010-9270-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-010-9270-3.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"},{"id":"pmh:oai:arXiv.org:0907.0724","is_oa":true,"landing_page_url":"http://arxiv.org/abs/0907.0724","pdf_url":"https://arxiv.org/pdf/0907.0724","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"doi:10.1007/s00454-010-9270-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-010-9270-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-010-9270-3.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":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2048026042.pdf","grobid_xml":"https://content.openalex.org/works/W2048026042.grobid-xml"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W89122021","https://openalex.org/W1493720529","https://openalex.org/W1974480997","https://openalex.org/W2000845118","https://openalex.org/W2005740603","https://openalex.org/W2009038699","https://openalex.org/W2023360066","https://openalex.org/W2046939500","https://openalex.org/W2061788258","https://openalex.org/W2078079767","https://openalex.org/W2081260663","https://openalex.org/W2319518804","https://openalex.org/W2535355524","https://openalex.org/W4235401965","https://openalex.org/W4243235810"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2026-06-19T15:47:20.252518","created_date":"2016-06-24T00:00:00"}
