{"id":"https://openalex.org/W6926137885","doi":"https://doi.org/10.2312/compaesth/compaesth12/107-114","title":"Surface Covering Curves","display_name":"Surface Covering Curves","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W6926137885","doi":"https://doi.org/10.2312/compaesth/compaesth12/107-114"},"language":"en","primary_location":{"id":"doi:10.2312/compaesth/compaesth12/107-114","is_oa":true,"landing_page_url":"https://doi.org/10.2312/compaesth/compaesth12/107-114","pdf_url":null,"source":{"id":"https://openalex.org/S7407052899","display_name":"Eurographics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null},"type":"other","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.2312/compaesth/compaesth12/107-114","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Xing, Q.","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xing, Q.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Akleman, Ergun","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Akleman, Ergun","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Taubin, Gabriel","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Taubin, Gabriel","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Chen, J.","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chen, J.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":true,"primary_topic":{"id":"https://openalex.org/T13370","display_name":"Diverse Scientific and Economic Studies","score":0.06599999964237213,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T13370","display_name":"Diverse Scientific and Economic Studies","score":0.06599999964237213,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T13354","display_name":"Genetics and Physical Performance","score":0.028599999845027924,"subfield":{"id":"https://openalex.org/subfields/1311","display_name":"Genetics"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T11674","display_name":"Sports Analytics and Performance","score":0.020899999886751175,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/surface","display_name":"Surface (topology)","score":0.763700008392334},{"id":"https://openalex.org/keywords/subdivision-surface","display_name":"Subdivision surface","score":0.654699981212616},{"id":"https://openalex.org/keywords/cover","display_name":"Cover (algebra)","score":0.593500018119812},{"id":"https://openalex.org/keywords/square","display_name":"Square (algebra)","score":0.46560001373291016},{"id":"https://openalex.org/keywords/triangulation","display_name":"Triangulation","score":0.44279998540878296},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.43479999899864197},{"id":"https://openalex.org/keywords/fractal","display_name":"Fractal","score":0.42480000853538513}],"concepts":[{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.763700008392334},{"id":"https://openalex.org/C199686383","wikidata":"https://www.wikidata.org/wiki/Q1529124","display_name":"Subdivision surface","level":3,"score":0.654699981212616},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.6428999900817871},{"id":"https://openalex.org/C2780428219","wikidata":"https://www.wikidata.org/wiki/Q16952335","display_name":"Cover (algebra)","level":2,"score":0.593500018119812},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.47850000858306885},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.46560001373291016},{"id":"https://openalex.org/C135981907","wikidata":"https://www.wikidata.org/wiki/Q188056","display_name":"Triangulation","level":2,"score":0.44279998540878296},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.43479999899864197},{"id":"https://openalex.org/C40636538","wikidata":"https://www.wikidata.org/wiki/Q81392","display_name":"Fractal","level":2,"score":0.42480000853538513},{"id":"https://openalex.org/C143392562","wikidata":"https://www.wikidata.org/wiki/Q449111","display_name":"Subdivision","level":2,"score":0.41749998927116394},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.3472999930381775},{"id":"https://openalex.org/C162329640","wikidata":"https://www.wikidata.org/wiki/Q332648","display_name":"Covering space","level":2,"score":0.3465999960899353},{"id":"https://openalex.org/C42058472","wikidata":"https://www.wikidata.org/wiki/Q810214","display_name":"Base (topology)","level":2,"score":0.28189998865127563},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.27709999680519104},{"id":"https://openalex.org/C2776542497","wikidata":"https://www.wikidata.org/wiki/Q5266672","display_name":"Development (topology)","level":2,"score":0.2700999975204468},{"id":"https://openalex.org/C3018391215","wikidata":"https://www.wikidata.org/wiki/Q2449377","display_name":"Flat surface","level":2,"score":0.2621999979019165},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.25529998540878296}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.2312/compaesth/compaesth12/107-114","is_oa":true,"landing_page_url":"https://doi.org/10.2312/compaesth/compaesth12/107-114","pdf_url":null,"source":{"id":"https://openalex.org/S7407052899","display_name":"Eurographics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":null}],"best_oa_location":{"id":"doi:10.2312/compaesth/compaesth12/107-114","is_oa":true,"landing_page_url":"https://doi.org/10.2312/compaesth/compaesth12/107-114","pdf_url":null,"source":{"id":"https://openalex.org/S7407052899","display_name":"Eurographics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities","score":0.5797095894813538}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"In":[0],"this":[1,135],"work,":[2],"we":[3,176],"present":[4],"the":[5,39,42,58,62,65,95,110],"concept":[6],"of":[7,41,64,101],"surface":[8,20,27,131],"covering":[9,180,183],"curves":[10,125,151,161,170,184,194],"that":[11,24,37,91,145,152,195],"can":[12,28,92,114,126],"be":[13,29,115],"used":[14,116],"to":[15,31,50,117,148],"construct":[16,51],"wire":[17],"sculptures":[18],"or":[19,166],"textures.":[21],"We":[22,45],"show":[23],"any":[25,102],"mesh":[26,43,59,96,130],"converted":[30],"a":[32,107,119,129,139,164,167,172],"single":[33],"closed":[34],"3D":[35,53],"curve":[36],"follows":[38],"shape":[40],"surface.":[44,97],"have":[46],"developed":[47],"two":[48],"methods":[49],"corresponding":[52],"ribbons":[54,73,82],"and":[55,61,121,174,192],"yarns":[56,87],"from":[57],"structure":[60],"connectivity":[63],"curve.":[66,123],"The":[67,78],"first":[68],"method":[69,80],"constructs":[70],"equal":[71,75],"thickness":[72,85],"(or":[74,86],"diameter":[76],"yarns).":[77],"second":[79],"creates":[81],"with":[83,88,138],"changing":[84,89],"diameter)":[90],"densely":[93,127],"cover":[94,128,171],"Since":[98],"each":[99],"iteration":[100],"subdivision":[103,140],"scheme":[104,141],"results":[105,144],"in":[106,132],"denser":[108,120,122],"mesh,":[109],"procedure":[111],"outlined":[112],"above":[113],"obtain":[118],"These":[124],"limit.":[133],"Therefore,":[134],"approach":[136],"along":[137],"provides":[142],"visual":[143],"are":[146,153,196],"similar":[147],"space":[149,159],"filling":[150,160],"created":[154],"by":[155],"fractal":[156],"algorithms.":[157],"Unlike":[158],"which":[162],"fills":[163],"square":[165],"cube,":[168],"our":[169],"surface,":[173],"henceforth,":[175],"called":[177],"them":[178],"\"surface":[179],"curves\".":[181],"Space":[182],"also":[185],"resemble":[186],"TSP":[187],"(traveling":[188],"salesmen":[189],"problem)":[190],"art":[191],"Truchet-like":[193],"embedded":[197],"on":[198],"surfaces.":[199]},"counts_by_year":[{"year":2012,"cited_by_count":1}],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2025-10-10T00:00:00"}
