{"id":"https://openalex.org/W1904718371","doi":"https://doi.org/10.37236/78","title":"Hyperbolization of Euclidean Ornaments","display_name":"Hyperbolization of Euclidean Ornaments","publication_year":2009,"publication_date":"2009-05-22","ids":{"openalex":"https://openalex.org/W1904718371","doi":"https://doi.org/10.37236/78","mag":"1904718371"},"language":"en","primary_location":{"id":"doi:10.37236/78","is_oa":true,"landing_page_url":"https://doi.org/10.37236/78","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v16i2r12/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v16i2r12/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5017143930","display_name":"Martin von Gagern","orcid":null},"institutions":[{"id":"https://openalex.org/I4210166048","display_name":"Gesellschaft Fur Mathematik Und Datenverarbeitung","ror":"https://ror.org/02g6d4t03","country_code":"DE","type":"facility","lineage":["https://openalex.org/I4210166048"]},{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Martin von Gagern","raw_affiliation_strings":["Lehrstuhl fr Geometrie und Visualisierung Zentrum Mathematik, Technische Universitt Mnchen, Germany","Lehrstuhl f\u00fcr Geometrie und Visualisierung Zentrum Mathematik, Technische Universit\u00e4t M\u00fcnchen, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Lehrstuhl fr Geometrie und Visualisierung Zentrum Mathematik, Technische Universitt Mnchen, Germany","institution_ids":["https://openalex.org/I4210166048"]},{"raw_affiliation_string":"Lehrstuhl f\u00fcr Geometrie und Visualisierung Zentrum Mathematik, Technische Universit\u00e4t M\u00fcnchen, Germany","institution_ids":["https://openalex.org/I62916508"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5070071334","display_name":"J\u00fcrgen Richter-Gebert","orcid":null},"institutions":[{"id":"https://openalex.org/I4210166048","display_name":"Gesellschaft Fur Mathematik Und Datenverarbeitung","ror":"https://ror.org/02g6d4t03","country_code":"DE","type":"facility","lineage":["https://openalex.org/I4210166048"]},{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"J\u00fcrgen Richter-Gebert","raw_affiliation_strings":["Lehrstuhl fr Geometrie und Visualisierung Zentrum Mathematik, Technische Universitt Mnchen, Germany","Lehrstuhl f\u00fcr Geometrie und Visualisierung Zentrum Mathematik, Technische Universit\u00e4t M\u00fcnchen, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Lehrstuhl fr Geometrie und Visualisierung Zentrum Mathematik, Technische Universitt Mnchen, Germany","institution_ids":["https://openalex.org/I4210166048"]},{"raw_affiliation_string":"Lehrstuhl f\u00fcr Geometrie und Visualisierung Zentrum Mathematik, Technische Universit\u00e4t M\u00fcnchen, Germany","institution_ids":["https://openalex.org/I62916508"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":20.1577,"has_fulltext":true,"cited_by_count":30,"citation_normalized_percentile":{"value":0.9911468,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"16","issue":"2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13518","display_name":"Architecture and Computational Design","score":0.9384999871253967,"subfield":{"id":"https://openalex.org/subfields/2216","display_name":"Architecture"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T13518","display_name":"Architecture and Computational Design","score":0.9384999871253967,"subfield":{"id":"https://openalex.org/subfields/2216","display_name":"Architecture"},"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/T12923","display_name":"Digital Image Processing Techniques","score":0.9035999774932861,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/hyperbolic-geometry","display_name":"Hyperbolic geometry","score":0.7599931955337524},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7386000156402588},{"id":"https://openalex.org/keywords/hyperbolic-triangle","display_name":"Hyperbolic triangle","score":0.7286033034324646},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.676612377166748},{"id":"https://openalex.org/keywords/hyperbolic-space","display_name":"Hyperbolic space","score":0.5898372530937195},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.5357574224472046},{"id":"https://openalex.org/keywords/conformal-map","display_name":"Conformal map","score":0.5035886168479919},{"id":"https://openalex.org/keywords/tessellation","display_name":"Tessellation (computer graphics)","score":0.4519115388393402},{"id":"https://openalex.org/keywords/plane-symmetry","display_name":"Plane symmetry","score":0.43115121126174927},{"id":"https://openalex.org/keywords/deformation","display_name":"Deformation (meteorology)","score":0.4286876320838928},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.41799238324165344},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.393818199634552},{"id":"https://openalex.org/keywords/differential-geometry","display_name":"Differential geometry","score":0.35391783714294434},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3260478079319}],"concepts":[{"id":"https://openalex.org/C206352148","wikidata":"https://www.wikidata.org/wiki/Q209306","display_name":"Hyperbolic geometry","level":3,"score":0.7599931955337524},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7386000156402588},{"id":"https://openalex.org/C82673646","wikidata":"https://www.wikidata.org/wiki/Q2246553","display_name":"Hyperbolic triangle","level":4,"score":0.7286033034324646},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.676612377166748},{"id":"https://openalex.org/C83677898","wikidata":"https://www.wikidata.org/wiki/Q1878538","display_name":"Hyperbolic space","level":2,"score":0.5898372530937195},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.5357574224472046},{"id":"https://openalex.org/C98214594","wikidata":"https://www.wikidata.org/wiki/Q850275","display_name":"Conformal map","level":2,"score":0.5035886168479919},{"id":"https://openalex.org/C43817857","wikidata":"https://www.wikidata.org/wiki/Q9357547","display_name":"Tessellation (computer graphics)","level":2,"score":0.4519115388393402},{"id":"https://openalex.org/C40425006","wikidata":"https://www.wikidata.org/wiki/Q7201020","display_name":"Plane symmetry","level":2,"score":0.43115121126174927},{"id":"https://openalex.org/C204366326","wikidata":"https://www.wikidata.org/wiki/Q3027650","display_name":"Deformation (meteorology)","level":2,"score":0.4286876320838928},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.41799238324165344},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.393818199634552},{"id":"https://openalex.org/C192939610","wikidata":"https://www.wikidata.org/wiki/Q188444","display_name":"Differential geometry","level":2,"score":0.35391783714294434},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3260478079319},{"id":"https://openalex.org/C153294291","wikidata":"https://www.wikidata.org/wiki/Q25261","display_name":"Meteorology","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/78","is_oa":true,"landing_page_url":"https://doi.org/10.37236/78","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v16i2r12/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.37236/78","is_oa":true,"landing_page_url":"https://doi.org/10.37236/78","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v16i2r12/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1904718371.pdf","grobid_xml":"https://content.openalex.org/works/W1904718371.grobid-xml"},"referenced_works_count":10,"referenced_works":["https://openalex.org/W28217284","https://openalex.org/W567060304","https://openalex.org/W2046979742","https://openalex.org/W2066842680","https://openalex.org/W2132754100","https://openalex.org/W3111561938","https://openalex.org/W4241284727","https://openalex.org/W4246001026","https://openalex.org/W6600424091","https://openalex.org/W6647655026"],"related_works":["https://openalex.org/W2094418681","https://openalex.org/W609517099","https://openalex.org/W2273260600","https://openalex.org/W2052639453","https://openalex.org/W4376654484","https://openalex.org/W54177252","https://openalex.org/W4365934646","https://openalex.org/W4293323153","https://openalex.org/W2596357324","https://openalex.org/W2091141226"],"abstract_inverted_index":{"In":[0,62],"this":[1,45,60],"article":[2],"we":[3],"outline":[4],"a":[5,14,27,34,109],"method":[6],"that":[7,56],"automatically":[8],"transforms":[9],"an":[10],"Euclidean":[11,28,75],"ornament":[12],"into":[13],"hyperbolic":[15,35,42,68,119],"one.":[16],"The":[17],"necessary":[18],"steps":[19,50],"are":[20,57,71],"pattern":[21],"recognition,":[22],"symmetry":[23,69],"detection,":[24],"extraction":[25],"of":[26,40,48,74,87,100],"fundamental":[29,36,102],"region,":[30],"conformal":[31,98],"deformation":[32,99],"to":[33,95,117],"region":[37],"and":[38],"tessellation":[39],"the":[41,97,101],"plane":[43],"with":[44,121],"patch.":[46],"Each":[47],"these":[49],"has":[51],"its":[52],"own":[53],"mathematical":[54],"subtleties":[55],"discussed":[58,66],"in":[59,93],"article.":[61],"particular,":[63],"it":[64,79,105],"is":[65,80,106],"which":[67],"groups":[70],"suitable":[72],"generalizations":[73],"wallpaper":[76],"groups.":[77],"Furthermore":[78],"shown":[81],"how":[82,108],"one":[83],"can":[84,114],"take":[85],"advantage":[86],"methods":[88],"from":[89],"discrete":[90],"differential":[91],"geometry":[92],"order":[94],"perform":[96],"region.":[103],"Finally":[104],"demonstrated":[107],"reverse":[110],"pixel":[111],"lookup":[112],"strategy":[113],"be":[115],"used":[116],"obtain":[118],"images":[120],"optimal":[122],"resolution.":[123]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
