{"id":"https://openalex.org/W4396692695","doi":"https://doi.org/10.1007/s00454-024-00653-x","title":"Representing Infinite Periodic Hyperbolic Delaunay Triangulations Using Finitely Many Dirichlet Domains","display_name":"Representing Infinite Periodic Hyperbolic Delaunay Triangulations Using Finitely Many Dirichlet Domains","publication_year":2024,"publication_date":"2024-05-07","ids":{"openalex":"https://openalex.org/W4396692695","doi":"https://doi.org/10.1007/s00454-024-00653-x"},"language":"en","primary_location":{"id":"doi:10.1007/s00454-024-00653-x","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s00454-024-00653-x","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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":"hybrid","oa_url":"http://dx.doi.org/10.1007/s00454-024-00653-x","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5064248690","display_name":"Vincent Despr\u00e9","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":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210121838","display_name":"Laboratoire Lorrain de Recherche en Informatique et ses Applications","ror":"https://ror.org/02vnf0c38","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I277688954","https://openalex.org/I4210107720","https://openalex.org/I4210121838","https://openalex.org/I4210159245","https://openalex.org/I90183372"]},{"id":"https://openalex.org/I90183372","display_name":"Universit\u00e9 de Lorraine","ror":"https://ror.org/04vfs2w97","country_code":"FR","type":"education","lineage":["https://openalex.org/I90183372"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Vincent Despr\u00e9","raw_affiliation_strings":["Inria, Universit\u00e9 de Lorraine, CNRS, LORIA, 54000, Nancy, France","Inria, Universit\u00e9 de Lorraine, CNRS, LORIA, Nancy, France","GAMBLE - Geometric Algorithms and Models Beyond the Linear and Euclidean realm (615 rue du Jardin Botanique 54600 Villers-l\u00e8s-Nancy - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Inria, Universit\u00e9 de Lorraine, CNRS, LORIA, 54000, Nancy, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I4210121838","https://openalex.org/I90183372"]},{"raw_affiliation_string":"Inria, Universit\u00e9 de Lorraine, CNRS, LORIA, Nancy, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I4210121838","https://openalex.org/I90183372"]},{"raw_affiliation_string":"GAMBLE - Geometric Algorithms and Models Beyond the Linear and Euclidean realm (615 rue du Jardin Botanique 54600 Villers-l\u00e8s-Nancy - France)","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001011989","display_name":"Benedikt Kolbe","orcid":"https://orcid.org/0009-0005-0440-4912"},"institutions":[{"id":"https://openalex.org/I135140700","display_name":"University of Bonn","ror":"https://ror.org/041nas322","country_code":"DE","type":"education","lineage":["https://openalex.org/I135140700"]},{"id":"https://openalex.org/I4391767997","display_name":"Hausdorff Center for Mathematics","ror":"https://ror.org/032n1tr36","country_code":"DE","type":"facility","lineage":["https://openalex.org/I135140700","https://openalex.org/I4391767997"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Benedikt Kolbe","raw_affiliation_strings":["Hausdorff Center for Mathematics, University of Bonn, Bonn, Germany","Hausdorff Center for Mathematics, University of Bonn, Friedrich-Hirzebruch-Allee 5, 53115, Bonn, Germany","GAMBLE - Geometric Algorithms and Models Beyond the Linear and Euclidean realm (615 rue du Jardin Botanique 54600 Villers-l\u00e8s-Nancy - France)","HCM - Hausdorff Center for Mathematics (Hausdorff Center for Mathematics Villa Maria Endenicher Allee 62 D-53115 Bonn Germany - Germany)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Hausdorff Center for Mathematics, University of Bonn, Bonn, Germany","institution_ids":["https://openalex.org/I135140700"]},{"raw_affiliation_string":"Hausdorff Center for Mathematics, University of Bonn, Friedrich-Hirzebruch-Allee 5, 53115, Bonn, Germany","institution_ids":["https://openalex.org/I135140700"]},{"raw_affiliation_string":"GAMBLE - Geometric Algorithms and Models Beyond the Linear and Euclidean realm (615 rue du Jardin Botanique 54600 Villers-l\u00e8s-Nancy - France)","institution_ids":[]},{"raw_affiliation_string":"HCM - Hausdorff Center for Mathematics (Hausdorff Center for Mathematics Villa Maria Endenicher Allee 62 D-53115 Bonn Germany - Germany)","institution_ids":["https://openalex.org/I4391767997"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5033226902","display_name":"Monique Teillaud","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":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210121838","display_name":"Laboratoire Lorrain de Recherche en Informatique et ses Applications","ror":"https://ror.org/02vnf0c38","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I277688954","https://openalex.org/I4210107720","https://openalex.org/I4210121838","https://openalex.org/I4210159245","https://openalex.org/I90183372"]},{"id":"https://openalex.org/I90183372","display_name":"Universit\u00e9 de Lorraine","ror":"https://ror.org/04vfs2w97","country_code":"FR","type":"education","lineage":["https://openalex.org/I90183372"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Monique Teillaud","raw_affiliation_strings":["Inria, Universit\u00e9 de Lorraine, CNRS, LORIA, 54000, Nancy, France","Inria, Universit\u00e9 de Lorraine, CNRS, LORIA, Nancy, France","GAMBLE - Geometric Algorithms and Models Beyond the Linear and Euclidean realm (615 rue du Jardin Botanique 54600 Villers-l\u00e8s-Nancy - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Inria, Universit\u00e9 de Lorraine, CNRS, LORIA, 54000, Nancy, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I4210121838","https://openalex.org/I90183372"]},{"raw_affiliation_string":"Inria, Universit\u00e9 de Lorraine, CNRS, LORIA, Nancy, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I4210121838","https://openalex.org/I90183372"]},{"raw_affiliation_string":"GAMBLE - Geometric Algorithms and Models Beyond the Linear and Euclidean realm (615 rue du Jardin Botanique 54600 Villers-l\u00e8s-Nancy - France)","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5001011989","https://openalex.org/A5033226902","https://openalex.org/A5064248690"],"corresponding_institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I135140700","https://openalex.org/I4210121838","https://openalex.org/I4391767997","https://openalex.org/I90183372"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":{"value":2990,"currency":"USD","value_usd":2990},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.12068376,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"72","issue":"1","first_page":"1","last_page":"28"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9987999796867371,"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":0.9987999796867371,"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/T10481","display_name":"Computer Graphics and Visualization Techniques","score":0.9739999771118164,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9648000001907349,"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/delaunay-triangulation","display_name":"Delaunay triangulation","score":0.9345924854278564},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6678009033203125},{"id":"https://openalex.org/keywords/constrained-delaunay-triangulation","display_name":"Constrained Delaunay triangulation","score":0.6443604230880737},{"id":"https://openalex.org/keywords/pitteway-triangulation","display_name":"Pitteway triangulation","score":0.5463235974311829},{"id":"https://openalex.org/keywords/bowyer\u2013watson-algorithm","display_name":"Bowyer\u2013Watson algorithm","score":0.5206934213638306},{"id":"https://openalex.org/keywords/triangulation","display_name":"Triangulation","score":0.4596954882144928},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.40979963541030884},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.39631661772727966},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.31768935918807983}],"concepts":[{"id":"https://openalex.org/C68010082","wikidata":"https://www.wikidata.org/wiki/Q192445","display_name":"Delaunay triangulation","level":2,"score":0.9345924854278564},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6678009033203125},{"id":"https://openalex.org/C128321387","wikidata":"https://www.wikidata.org/wiki/Q5164356","display_name":"Constrained Delaunay triangulation","level":3,"score":0.6443604230880737},{"id":"https://openalex.org/C178609930","wikidata":"https://www.wikidata.org/wiki/Q3538712","display_name":"Pitteway triangulation","level":3,"score":0.5463235974311829},{"id":"https://openalex.org/C121198538","wikidata":"https://www.wikidata.org/wiki/Q4951461","display_name":"Bowyer\u2013Watson algorithm","level":3,"score":0.5206934213638306},{"id":"https://openalex.org/C135981907","wikidata":"https://www.wikidata.org/wiki/Q188056","display_name":"Triangulation","level":2,"score":0.4596954882144928},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.40979963541030884},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.39631661772727966},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.31768935918807983}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s00454-024-00653-x","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s00454-024-00653-x","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete &amp; Computational Geometry","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-04577851v1","is_oa":true,"landing_page_url":"https://hal.science/hal-04577851","pdf_url":"https://hal.science/hal-04577851/document","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Discrete and Computational Geometry, 2024, &#x27E8;10.1007/s00454-024-00653-x&#x27E9;","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1007/s00454-024-00653-x","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s00454-024-00653-x","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete &amp; Computational Geometry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G678048077","display_name":"Structures on Surfaces","funder_award_id":"ANR-17-CE40-0033","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W1535866048","https://openalex.org/W1542085343","https://openalex.org/W1818932794","https://openalex.org/W1890795085","https://openalex.org/W1981450485","https://openalex.org/W1981691044","https://openalex.org/W1982286959","https://openalex.org/W1986513910","https://openalex.org/W2009795122","https://openalex.org/W2021014459","https://openalex.org/W2033198202","https://openalex.org/W2049804492","https://openalex.org/W2064258865","https://openalex.org/W2089192676","https://openalex.org/W2134090618","https://openalex.org/W2170128749","https://openalex.org/W2280143692","https://openalex.org/W2296706642","https://openalex.org/W2318980250","https://openalex.org/W2573028792","https://openalex.org/W2727943323","https://openalex.org/W2885390903","https://openalex.org/W2887687912","https://openalex.org/W2963274266","https://openalex.org/W2993723681","https://openalex.org/W3039948875","https://openalex.org/W3082227903","https://openalex.org/W3100439197","https://openalex.org/W3101235540","https://openalex.org/W3104277769","https://openalex.org/W4240028494","https://openalex.org/W4249845637","https://openalex.org/W4251591047","https://openalex.org/W4285126230","https://openalex.org/W4293217885","https://openalex.org/W6602828855","https://openalex.org/W6607175793","https://openalex.org/W6891711529"],"related_works":["https://openalex.org/W1883162576","https://openalex.org/W2001351033","https://openalex.org/W109258179","https://openalex.org/W2347819474","https://openalex.org/W1979362696","https://openalex.org/W2026181493","https://openalex.org/W2381889232","https://openalex.org/W1529719486","https://openalex.org/W2509795980","https://openalex.org/W2385297469"],"abstract_inverted_index":{"Abstract":[0],"The":[1,155],"Delaunay":[2,19,44,76,134,148,182],"triangulation":[3,20,77,149],"of":[4,7,17,21,27,62,74,109,116,122,142,146,151,166,176],"a":[5,11,54,59,75,79,99,147,152],"set":[6,23,61],"points":[8,29,63],"P":[9,25,36],"on":[10,133,163],"hyperbolic":[12,32,174],"surface":[13],"is":[14,38],"the":[15,18,22,31,40,47,66,87,114,120,144,164,167,177],"projection":[16],"$$\\widetilde{P}$$":[24,35],"~":[26,37],"lifted":[28],"in":[30,46,86,119,158,184],"plane.":[33],"Since":[34],"infinite,":[39],"algorithms":[41,178],"to":[42,98,129,179],"compute":[43,180],"triangulations":[45,135,183],"plane":[48],"do":[49],"not":[50],"generalize":[51],"naturally.":[52],"Using":[53],"Dirichlet":[55,100,153],"domain,":[56],"we":[57,84,105],"exhibit":[58,137],"finite":[60],"that":[64,71,112],"captures":[65],"full":[67],"triangulation.":[68],"We":[69,125],"prove":[70],"an":[72],"edge":[73],"has":[78],"combinatorial":[80],"length":[81],"(a":[82],"notion":[83],"define":[85],"paper)":[88],"smaller":[89],"than":[90],"$$12g-6$$":[91],"12":[92],"g":[93],"-":[94],"6":[95],"with":[96],"respect":[97],"domain.":[101,154],"To":[102],"achieve":[103],"this,":[104],"introduce":[106],"new":[107],"tools,":[108],"intrinsic":[110],"interest,":[111],"capture":[113],"properties":[115,141],"length-minimizing":[117],"curves":[118],"context":[121],"closed":[123],"curves.":[124],"then":[126],"use":[127],"these":[128],"derive":[130],"structural":[131],"results":[132],"and":[136,150],"certain":[138],"distance":[139],"minimizing":[140],"both":[143],"edges":[145],"bounds":[156],"produced":[157],"this":[159],"paper":[160],"depend":[161],"only":[162],"topology":[165],"surface.":[168],"They":[169],"provide":[170],"mathematical":[171],"foundations":[172],"for":[173],"analogs":[175],"periodic":[181],"Euclidean":[185],"space.":[186]},"counts_by_year":[],"updated_date":"2026-08-28T12:50:07.497085","created_date":"2025-10-10T00:00:00"}
