{"id":"https://openalex.org/W2884039401","doi":"https://doi.org/10.1007/s00454-018-0019-8","title":"( $$\\delta ,{\\varepsilon }$$ \u03b4 , \u03b5 )-Ball Approximation of a Shape: Definition and Complexity","display_name":"( $$\\delta ,{\\varepsilon }$$ \u03b4 , \u03b5 )-Ball Approximation of a Shape: Definition and Complexity","publication_year":2018,"publication_date":"2018-07-20","ids":{"openalex":"https://openalex.org/W2884039401","doi":"https://doi.org/10.1007/s00454-018-0019-8","mag":"2884039401"},"language":"en","primary_location":{"id":"doi:10.1007/s00454-018-0019-8","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00454-018-0019-8","pdf_url":null,"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 & Computational Geometry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.science/hal-01798844","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5021546111","display_name":"Dominique Attali","orcid":null},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I899635006","display_name":"Universit\u00e9 Grenoble Alpes","ror":"https://ror.org/02rx3b187","country_code":"FR","type":"education","lineage":["https://openalex.org/I899635006"]},{"id":"https://openalex.org/I4210124956","display_name":"Grenoble Images Parole Signal Automatique","ror":"https://ror.org/02wrme198","country_code":"FR","type":"facility","lineage":["https://openalex.org/I106785703","https://openalex.org/I1294671590","https://openalex.org/I4210124956","https://openalex.org/I899635006","https://openalex.org/I899635006"]},{"id":"https://openalex.org/I106785703","display_name":"Institut polytechnique de Grenoble","ror":"https://ror.org/05sbt2524","country_code":"FR","type":"education","lineage":["https://openalex.org/I106785703","https://openalex.org/I899635006"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Dominique Attali","raw_affiliation_strings":["Universit\u00e9 Grenoble Alpes, CNRS, Grenoble INP, GIPSA-Lab, 38000, Grenoble, France","GIPSA-AGPIG - GIPSA - Architecture, G\u00e9om\u00e9trie, Perception, Images, Gestes (GIPSA-lab, 11 rue des Math\u00e9matiques, Grenoble Campus BP46, F-38402 SAINT MARTIN D'HERES CEDEX - France)"],"affiliations":[{"raw_affiliation_string":"Universit\u00e9 Grenoble Alpes, CNRS, Grenoble INP, GIPSA-Lab, 38000, Grenoble, France","institution_ids":["https://openalex.org/I4210124956","https://openalex.org/I1294671590","https://openalex.org/I899635006","https://openalex.org/I106785703"]},{"raw_affiliation_string":"GIPSA-AGPIG - GIPSA - Architecture, G\u00e9om\u00e9trie, Perception, Images, Gestes (GIPSA-lab, 11 rue des Math\u00e9matiques, Grenoble Campus BP46, F-38402 SAINT MARTIN D'HERES CEDEX - France)","institution_ids":["https://openalex.org/I4210124956"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001361540","display_name":"Tuong-Bach Nguyen","orcid":null},"institutions":[{"id":"https://openalex.org/I899635006","display_name":"Universit\u00e9 Grenoble Alpes","ror":"https://ror.org/02rx3b187","country_code":"FR","type":"education","lineage":["https://openalex.org/I899635006"]},{"id":"https://openalex.org/I106785703","display_name":"Institut polytechnique de Grenoble","ror":"https://ror.org/05sbt2524","country_code":"FR","type":"education","lineage":["https://openalex.org/I106785703","https://openalex.org/I899635006"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210124956","display_name":"Grenoble Images Parole Signal Automatique","ror":"https://ror.org/02wrme198","country_code":"FR","type":"facility","lineage":["https://openalex.org/I106785703","https://openalex.org/I1294671590","https://openalex.org/I4210124956","https://openalex.org/I899635006","https://openalex.org/I899635006"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Tuong-Bach Nguyen","raw_affiliation_strings":["Universit\u00e9 Grenoble Alpes, CNRS, Grenoble INP, GIPSA-Lab, 38000, Grenoble, France","GIPSA-AGPIG - GIPSA - Architecture, G\u00e9om\u00e9trie, Perception, Images, Gestes (GIPSA-lab, 11 rue des Math\u00e9matiques, Grenoble Campus BP46, F-38402 SAINT MARTIN D'HERES CEDEX - France)"],"affiliations":[{"raw_affiliation_string":"Universit\u00e9 Grenoble Alpes, CNRS, Grenoble INP, GIPSA-Lab, 38000, Grenoble, France","institution_ids":["https://openalex.org/I4210124956","https://openalex.org/I1294671590","https://openalex.org/I899635006","https://openalex.org/I106785703"]},{"raw_affiliation_string":"GIPSA-AGPIG - GIPSA - Architecture, G\u00e9om\u00e9trie, Perception, Images, Gestes (GIPSA-lab, 11 rue des Math\u00e9matiques, Grenoble Campus BP46, F-38402 SAINT MARTIN D'HERES CEDEX - France)","institution_ids":["https://openalex.org/I4210124956"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5026546650","display_name":"Isabelle Sivignon","orcid":null},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I899635006","display_name":"Universit\u00e9 Grenoble Alpes","ror":"https://ror.org/02rx3b187","country_code":"FR","type":"education","lineage":["https://openalex.org/I899635006"]},{"id":"https://openalex.org/I106785703","display_name":"Institut polytechnique de Grenoble","ror":"https://ror.org/05sbt2524","country_code":"FR","type":"education","lineage":["https://openalex.org/I106785703","https://openalex.org/I899635006"]},{"id":"https://openalex.org/I4210124956","display_name":"Grenoble Images Parole Signal Automatique","ror":"https://ror.org/02wrme198","country_code":"FR","type":"facility","lineage":["https://openalex.org/I106785703","https://openalex.org/I1294671590","https://openalex.org/I4210124956","https://openalex.org/I899635006","https://openalex.org/I899635006"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Isabelle Sivignon","raw_affiliation_strings":["Universit\u00e9 Grenoble Alpes, CNRS, Grenoble INP, GIPSA-Lab, 38000, Grenoble, France","GIPSA-AGPIG - GIPSA - Architecture, G\u00e9om\u00e9trie, Perception, Images, Gestes (GIPSA-lab, 11 rue des Math\u00e9matiques, Grenoble Campus BP46, F-38402 SAINT MARTIN D'HERES CEDEX - France)"],"affiliations":[{"raw_affiliation_string":"Universit\u00e9 Grenoble Alpes, CNRS, Grenoble INP, GIPSA-Lab, 38000, Grenoble, France","institution_ids":["https://openalex.org/I4210124956","https://openalex.org/I1294671590","https://openalex.org/I899635006","https://openalex.org/I106785703"]},{"raw_affiliation_string":"GIPSA-AGPIG - GIPSA - Architecture, G\u00e9om\u00e9trie, Perception, Images, Gestes (GIPSA-lab, 11 rue des Math\u00e9matiques, Grenoble Campus BP46, F-38402 SAINT MARTIN D'HERES CEDEX - France)","institution_ids":["https://openalex.org/I4210124956"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5021546111"],"corresponding_institution_ids":["https://openalex.org/I106785703","https://openalex.org/I1294671590","https://openalex.org/I4210124956","https://openalex.org/I899635006"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.11259398,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"61","issue":"3","first_page":"595","last_page":"625"},"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/T12923","display_name":"Digital Image Processing Techniques","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9993000030517578,"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/ball","display_name":"Ball (mathematics)","score":0.8581722974777222},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7353850603103638},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6756141185760498},{"id":"https://openalex.org/keywords/cardinality","display_name":"Cardinality (data modeling)","score":0.4799787700176239},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.47948843240737915},{"id":"https://openalex.org/keywords/unit-sphere","display_name":"Unit sphere","score":0.46748465299606323},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.0918084979057312}],"concepts":[{"id":"https://openalex.org/C122041747","wikidata":"https://www.wikidata.org/wiki/Q838611","display_name":"Ball (mathematics)","level":2,"score":0.8581722974777222},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7353850603103638},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6756141185760498},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.4799787700176239},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.47948843240737915},{"id":"https://openalex.org/C191948623","wikidata":"https://www.wikidata.org/wiki/Q1307800","display_name":"Unit sphere","level":2,"score":0.46748465299606323},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0918084979057312},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s00454-018-0019-8","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00454-018-0019-8","pdf_url":null,"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 & Computational Geometry","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-01798844v1","is_oa":true,"landing_page_url":"https://hal.science/hal-01798844","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"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":"https://link.springer.com/article/10.1007%2Fs00454-018-0019-8","raw_type":"Journal articles"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-01798844v1","is_oa":true,"landing_page_url":"https://hal.science/hal-01798844","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"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":"https://link.springer.com/article/10.1007%2Fs00454-018-0019-8","raw_type":"Journal articles"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":39,"referenced_works":["https://openalex.org/W200511831","https://openalex.org/W209708957","https://openalex.org/W596522316","https://openalex.org/W1496569514","https://openalex.org/W1503452772","https://openalex.org/W1601492549","https://openalex.org/W1859099443","https://openalex.org/W1977333786","https://openalex.org/W1989696335","https://openalex.org/W2004644355","https://openalex.org/W2020112047","https://openalex.org/W2022671649","https://openalex.org/W2037162618","https://openalex.org/W2040924621","https://openalex.org/W2051997380","https://openalex.org/W2053212688","https://openalex.org/W2069476964","https://openalex.org/W2080751646","https://openalex.org/W2115920764","https://openalex.org/W2126641170","https://openalex.org/W2139230981","https://openalex.org/W2140209577","https://openalex.org/W2142495952","https://openalex.org/W2156759998","https://openalex.org/W2157054705","https://openalex.org/W2164741953","https://openalex.org/W2168204810","https://openalex.org/W2168507359","https://openalex.org/W2249672461","https://openalex.org/W2333442752","https://openalex.org/W2604792949","https://openalex.org/W2732012689","https://openalex.org/W2946608300","https://openalex.org/W3021771031","https://openalex.org/W4213171111","https://openalex.org/W4230982142","https://openalex.org/W4298135281","https://openalex.org/W6620967127","https://openalex.org/W6630253416"],"related_works":["https://openalex.org/W2002177687","https://openalex.org/W2058438338","https://openalex.org/W2019471580","https://openalex.org/W2941284322","https://openalex.org/W4224920876","https://openalex.org/W2168299207","https://openalex.org/W1654151311","https://openalex.org/W2387072865","https://openalex.org/W2804455714","https://openalex.org/W1530081058"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}