{"id":"https://openalex.org/W2138620492","doi":"https://doi.org/10.1007/s00454-005-1160-8","title":"The Envelope of Lines Meeting a Fixed Line and Tangent to Two Spheres","display_name":"The Envelope of Lines Meeting a Fixed Line and Tangent to Two Spheres","publication_year":2005,"publication_date":"2005-03-28","ids":{"openalex":"https://openalex.org/W2138620492","doi":"https://doi.org/10.1007/s00454-005-1160-8","mag":"2138620492"},"language":"en","primary_location":{"id":"doi:10.1007/s00454-005-1160-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-005-1160-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-005-1160-8.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/s00454-005-1160-8.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5113506790","display_name":"G. Megyesi","orcid":null},"institutions":[{"id":"https://openalex.org/I28407311","display_name":"University of Manchester","ror":"https://ror.org/027m9bs27","country_code":"GB","type":"education","lineage":["https://openalex.org/I28407311"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"G\ufffdbor Megyesi","raw_affiliation_strings":["Department of Mathematics, UMIST, P.O. Box 88, Manchester, M60 1QD, England","Department of Mathematics, UMIST, #N#  P.O. Box 88, Manchester, M60 1QD, England"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, UMIST, P.O. Box 88, Manchester, M60 1QD, England","institution_ids":["https://openalex.org/I28407311"]},{"raw_affiliation_string":"Department of Mathematics, UMIST, #N#  P.O. Box 88, Manchester, M60 1QD, England","institution_ids":["https://openalex.org/I28407311"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5078229263","display_name":"Frank Sottile","orcid":"https://orcid.org/0000-0003-0087-7120"},"institutions":[{"id":"https://openalex.org/I91045830","display_name":"Texas A&M University","ror":"https://ror.org/01f5ytq51","country_code":"US","type":"education","lineage":["https://openalex.org/I91045830"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Frank Sottile","raw_affiliation_strings":["Department of Mathematics, Texas A&M University, College Station, TX 77843, USA","Department of Mathematics,#N#Texas A&M University,#N#College Station, TX 77843, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Texas A&M University, College Station, TX 77843, USA","institution_ids":["https://openalex.org/I91045830"]},{"raw_affiliation_string":"Department of Mathematics,#N#Texas A&M University,#N#College Station, TX 77843, USA","institution_ids":["https://openalex.org/I91045830"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":2.1049,"has_fulltext":true,"cited_by_count":12,"citation_normalized_percentile":{"value":0.86903729,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"33","issue":"4","first_page":"617","last_page":"644"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9980000257492065,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/spheres","display_name":"SPHERES","score":0.7288973927497864},{"id":"https://openalex.org/keywords/tangent","display_name":"Tangent","score":0.7275897860527039},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.634904146194458},{"id":"https://openalex.org/keywords/line","display_name":"Line (geometry)","score":0.5742660760879517},{"id":"https://openalex.org/keywords/tangent-vector","display_name":"Tangent vector","score":0.49346745014190674},{"id":"https://openalex.org/keywords/tangent-space","display_name":"Tangent space","score":0.4695499539375305},{"id":"https://openalex.org/keywords/projective-space","display_name":"Projective space","score":0.4492529332637787},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.42832261323928833},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.42807090282440186},{"id":"https://openalex.org/keywords/suspension","display_name":"Suspension (topology)","score":0.4185776114463806},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.34272295236587524},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3414725065231323},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.14515668153762817},{"id":"https://openalex.org/keywords/homotopy","display_name":"Homotopy","score":0.1248333752155304},{"id":"https://openalex.org/keywords/projective-test","display_name":"Projective test","score":0.09833729267120361},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.09001657366752625}],"concepts":[{"id":"https://openalex.org/C72422203","wikidata":"https://www.wikidata.org/wiki/Q7392545","display_name":"SPHERES","level":2,"score":0.7288973927497864},{"id":"https://openalex.org/C138187205","wikidata":"https://www.wikidata.org/wiki/Q131251","display_name":"Tangent","level":2,"score":0.7275897860527039},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.634904146194458},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.5742660760879517},{"id":"https://openalex.org/C47890412","wikidata":"https://www.wikidata.org/wiki/Q1179296","display_name":"Tangent vector","level":3,"score":0.49346745014190674},{"id":"https://openalex.org/C157157409","wikidata":"https://www.wikidata.org/wiki/Q909601","display_name":"Tangent space","level":2,"score":0.4695499539375305},{"id":"https://openalex.org/C75280867","wikidata":"https://www.wikidata.org/wiki/Q877775","display_name":"Projective space","level":3,"score":0.4492529332637787},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.42832261323928833},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.42807090282440186},{"id":"https://openalex.org/C105341887","wikidata":"https://www.wikidata.org/wiki/Q1307987","display_name":"Suspension (topology)","level":3,"score":0.4185776114463806},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.34272295236587524},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3414725065231323},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.14515668153762817},{"id":"https://openalex.org/C5961521","wikidata":"https://www.wikidata.org/wiki/Q746083","display_name":"Homotopy","level":2,"score":0.1248333752155304},{"id":"https://openalex.org/C177846678","wikidata":"https://www.wikidata.org/wiki/Q1501864","display_name":"Projective test","level":2,"score":0.09833729267120361},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.09001657366752625},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0}],"mesh":[],"locations_count":8,"locations":[{"id":"doi:10.1007/s00454-005-1160-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-005-1160-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-005-1160-8.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:pure.atira.dk:openaire_cris_publications/e3f0d68e-6983-4f7b-8f69-39f8279eaa13","is_oa":false,"landing_page_url":"https://research.manchester.ac.uk/en/publications/e3f0d68e-6983-4f7b-8f69-39f8279eaa13","pdf_url":null,"source":{"id":"https://openalex.org/S4306400662","display_name":"Research Explorer (The University of Manchester)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I28407311","host_organization_name":"University of Manchester","host_organization_lineage":["https://openalex.org/I28407311"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Megyesi, G & Sottile, F 2005, 'The envelope of lines meeting a fixed line and tangent to two spheres', Discrete & Computational Geometry , vol. 33, no. 4, pp. 617-644. https://doi.org/10.1007/s00454-005-1160-8","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:543","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400452","display_name":"MIMS EPrints (University of Southampton)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I43439940","host_organization_name":"University of Southampton","host_organization_lineage":["https://openalex.org/I43439940"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.235.8922","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.235.8922","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/math/0304346v1.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.237.9356","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.237.9356","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/math/0304346v2.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.7.4966","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.7.4966","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.umass.edu/~sottile/ps/3Spheres.ps.gz","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.86.7945","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.86.7945","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.tamu.edu/~sottile/subject/pdf/3Spheres.pdf","raw_type":"text"},{"id":"pmh:oai:pure.atira.dk:publications/e3f0d68e-6983-4f7b-8f69-39f8279eaa13","is_oa":false,"landing_page_url":"https://www.research.manchester.ac.uk/portal/en/publications/the-envelope-of-lines-meeting-a-fixed-line-and-tangent-to-two-spheres(e3f0d68e-6983-4f7b-8f69-39f8279eaa13).html","pdf_url":null,"source":{"id":"https://openalex.org/S4306400662","display_name":"Research Explorer (The University of Manchester)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I28407311","host_organization_name":"University of Manchester","host_organization_lineage":["https://openalex.org/I28407311"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Megyesi, G & Sottile, F 2005, 'The envelope of lines meeting a fixed line and tangent to two spheres', Discrete & Computational Geometry , vol. 33, no. 4, pp. 617-644. https://doi.org/10.1007/s00454-005-1160-8","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":{"id":"doi:10.1007/s00454-005-1160-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-005-1160-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-005-1160-8.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":[{"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11","score":0.7200000286102295}],"awards":[{"id":"https://openalex.org/G5412631906","display_name":"CAREER:   Computation, Combinatorics, and Reality in Algebraic Geometry, with Applications","funder_award_id":"0134860","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/F4320308125","display_name":"Texas AgriLife Research","ror":"https://ror.org/01f5ytq51"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2138620492.pdf","grobid_xml":"https://content.openalex.org/works/W2138620492.grobid-xml"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W17351244","https://openalex.org/W1515192744","https://openalex.org/W1518341038","https://openalex.org/W1564550597","https://openalex.org/W1567722298","https://openalex.org/W1601864594","https://openalex.org/W1642096418","https://openalex.org/W1718023260","https://openalex.org/W1975523543","https://openalex.org/W1980261256","https://openalex.org/W1995847341","https://openalex.org/W2019524783","https://openalex.org/W2036174934","https://openalex.org/W4285719527","https://openalex.org/W6811179486"],"related_works":["https://openalex.org/W2361271799","https://openalex.org/W4249328994","https://openalex.org/W2391887161","https://openalex.org/W2577818139","https://openalex.org/W2096561270","https://openalex.org/W2381565014","https://openalex.org/W2098859420","https://openalex.org/W2390580168","https://openalex.org/W2353074735","https://openalex.org/W2358302317"],"abstract_inverted_index":null,"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2015,"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"}
