{"id":"https://openalex.org/W1528872935","doi":"https://doi.org/10.1007/3-540-18170-9_173","title":"Numerical stability of simple geometric algorithms in the plane","display_name":"Numerical stability of simple geometric algorithms in the plane","publication_year":1987,"publication_date":"1987-01-01","ids":{"openalex":"https://openalex.org/W1528872935","doi":"https://doi.org/10.1007/3-540-18170-9_173","mag":"1528872935"},"language":"en","primary_location":{"id":"doi:10.1007/3-540-18170-9_173","is_oa":false,"landing_page_url":"https://doi.org/10.1007/3-540-18170-9_173","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","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/A5113581859","display_name":"Thomas Ottmann","orcid":null},"institutions":[{"id":"https://openalex.org/I102335020","display_name":"Karlsruhe Institute of Technology","ror":"https://ror.org/04t3en479","country_code":"DE","type":"education","lineage":["https://openalex.org/I102335020","https://openalex.org/I1305996414"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Thomas Ottmann","raw_affiliation_strings":["Institut f\u00fcr Angewandte Informatik und Formale Beschreibungsverfahren, Universit\u00e4t Karlsruhe, D-7500, Karlsruhe, West Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Angewandte Informatik und Formale Beschreibungsverfahren, Universit\u00e4t Karlsruhe, D-7500, Karlsruhe, West Germany","institution_ids":["https://openalex.org/I102335020"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090685057","display_name":"Gerald Thiemt","orcid":null},"institutions":[{"id":"https://openalex.org/I102335020","display_name":"Karlsruhe Institute of Technology","ror":"https://ror.org/04t3en479","country_code":"DE","type":"education","lineage":["https://openalex.org/I102335020","https://openalex.org/I1305996414"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Gerald Thiemt","raw_affiliation_strings":["Institut f\u00fcr Angewandte Informatik und Formale Beschreibungsverfahren, Universit\u00e4t Karlsruhe, D-7500, Karlsruhe, West Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Angewandte Informatik und Formale Beschreibungsverfahren, Universit\u00e4t Karlsruhe, D-7500, Karlsruhe, West Germany","institution_ids":["https://openalex.org/I102335020"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5113457868","display_name":"Christian Ullrich","orcid":null},"institutions":[{"id":"https://openalex.org/I102335020","display_name":"Karlsruhe Institute of Technology","ror":"https://ror.org/04t3en479","country_code":"DE","type":"education","lineage":["https://openalex.org/I102335020","https://openalex.org/I1305996414"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Christian Ullrich","raw_affiliation_strings":["Institut f\u00fcr Angewandte Mathematik, Universit\u00e4t Karlsruhe, D-7500, Karlsruhe, West Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Angewandte Mathematik, Universit\u00e4t Karlsruhe, D-7500, Karlsruhe, West Germany","institution_ids":["https://openalex.org/I102335020"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I102335020"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":1.204,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.71666667,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"277","last_page":"293"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9995999932289124,"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":0.9995999932289124,"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/T12698","display_name":"3D Modeling in Geospatial Applications","score":0.9965999722480774,"subfield":{"id":"https://openalex.org/subfields/2215","display_name":"Building and Construction"},"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9959999918937683,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/geometric-primitive","display_name":"Geometric primitive","score":0.7387169599533081},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6938024759292603},{"id":"https://openalex.org/keywords/geometric-design","display_name":"Geometric design","score":0.6565481424331665},{"id":"https://openalex.org/keywords/geometric-data-analysis","display_name":"Geometric data analysis","score":0.610863208770752},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5717282891273499},{"id":"https://openalex.org/keywords/geometric-modeling","display_name":"Geometric modeling","score":0.505251944065094},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.4912061095237732},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.4785607159137726},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.4662401080131531},{"id":"https://openalex.org/keywords/computational-geometry","display_name":"Computational geometry","score":0.4646678864955902},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.45899537205696106},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.45074915885925293},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.43299782276153564},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.43041759729385376},{"id":"https://openalex.org/keywords/geometric-shape","display_name":"Geometric shape","score":0.4281320571899414},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.28045356273651123},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.16483816504478455},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.16207152605056763}],"concepts":[{"id":"https://openalex.org/C181095308","wikidata":"https://www.wikidata.org/wiki/Q1541599","display_name":"Geometric primitive","level":2,"score":0.7387169599533081},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6938024759292603},{"id":"https://openalex.org/C40319758","wikidata":"https://www.wikidata.org/wiki/Q5535477","display_name":"Geometric design","level":2,"score":0.6565481424331665},{"id":"https://openalex.org/C136520226","wikidata":"https://www.wikidata.org/wiki/Q302814","display_name":"Geometric data analysis","level":2,"score":0.610863208770752},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5717282891273499},{"id":"https://openalex.org/C104065381","wikidata":"https://www.wikidata.org/wiki/Q1002535","display_name":"Geometric modeling","level":2,"score":0.505251944065094},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.4912061095237732},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.4785607159137726},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.4662401080131531},{"id":"https://openalex.org/C29123130","wikidata":"https://www.wikidata.org/wiki/Q874709","display_name":"Computational geometry","level":2,"score":0.4646678864955902},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.45899537205696106},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.45074915885925293},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.43299782276153564},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.43041759729385376},{"id":"https://openalex.org/C7305733","wikidata":"https://www.wikidata.org/wiki/Q207961","display_name":"Geometric shape","level":2,"score":0.4281320571899414},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.28045356273651123},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.16483816504478455},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.16207152605056763},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","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/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/3-540-18170-9_173","is_oa":false,"landing_page_url":"https://doi.org/10.1007/3-540-18170-9_173","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W17415252","https://openalex.org/W155342555","https://openalex.org/W1570345685","https://openalex.org/W1570927704","https://openalex.org/W1571045421","https://openalex.org/W1588000771","https://openalex.org/W1594991445","https://openalex.org/W1874694348","https://openalex.org/W1981233261","https://openalex.org/W2052165970","https://openalex.org/W2060924166","https://openalex.org/W2495937958","https://openalex.org/W2499612848","https://openalex.org/W2911302472","https://openalex.org/W3183121460"],"related_works":["https://openalex.org/W1978436383","https://openalex.org/W1528872935","https://openalex.org/W2332420753","https://openalex.org/W3113701594","https://openalex.org/W2331908441","https://openalex.org/W4306726750","https://openalex.org/W3188279632","https://openalex.org/W2125543379","https://openalex.org/W3494255","https://openalex.org/W2501882358"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-06-26T08:34:08.712188","created_date":"2025-10-10T00:00:00"}