{"id":"https://openalex.org/W2953632108","doi":"https://doi.org/10.1109/msp.2019.2907375","title":"The Mystery Curve-Part 2: Local Symmetry and Frieze Groups [Lecture Notes]","display_name":"The Mystery Curve-Part 2: Local Symmetry and Frieze Groups [Lecture Notes]","publication_year":2019,"publication_date":"2019-06-26","ids":{"openalex":"https://openalex.org/W2953632108","doi":"https://doi.org/10.1109/msp.2019.2907375","mag":"2953632108"},"language":"en","primary_location":{"id":"doi:10.1109/msp.2019.2907375","is_oa":false,"landing_page_url":"https://doi.org/10.1109/msp.2019.2907375","pdf_url":null,"source":{"id":"https://openalex.org/S120977877","display_name":"IEEE Signal Processing Magazine","issn_l":"1053-5888","issn":["1053-5888","1558-0792"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Signal Processing Magazine","raw_type":"journal-article"},"type":"article","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/A5085279585","display_name":"Soo\u2010Chang Pei","orcid":"https://orcid.org/0000-0003-2448-4196"},"institutions":[{"id":"https://openalex.org/I16733864","display_name":"National Taiwan University","ror":"https://ror.org/05bqach95","country_code":"TW","type":"education","lineage":["https://openalex.org/I16733864"]}],"countries":["TW"],"is_corresponding":true,"raw_author_name":"Soo-Chang Pei","raw_affiliation_strings":["National Taiwan University, Taipei"],"affiliations":[{"raw_affiliation_string":"National Taiwan University, Taipei","institution_ids":["https://openalex.org/I16733864"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5054825387","display_name":"Kuo-Wei Chang","orcid":"https://orcid.org/0000-0002-5987-6862"},"institutions":[{"id":"https://openalex.org/I16733864","display_name":"National Taiwan University","ror":"https://ror.org/05bqach95","country_code":"TW","type":"education","lineage":["https://openalex.org/I16733864"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Kuo-Wei Chang","raw_affiliation_strings":["National Taiwan University, Taipei"],"affiliations":[{"raw_affiliation_string":"National Taiwan University, Taipei","institution_ids":["https://openalex.org/I16733864"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5085279585"],"corresponding_institution_ids":["https://openalex.org/I16733864"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.05741523,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"36","issue":"4","first_page":"161","last_page":"167"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12740","display_name":"Gait Recognition and Analysis","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"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/T12740","display_name":"Gait Recognition and Analysis","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"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/T12417","display_name":"Morphological variations and asymmetry","score":0.9675999879837036,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10812","display_name":"Human Pose and Action Recognition","score":0.965399980545044,"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/trigonometry","display_name":"Trigonometry","score":0.7090801000595093},{"id":"https://openalex.org/keywords/frieze","display_name":"Frieze","score":0.5935475826263428},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.5353202223777771},{"id":"https://openalex.org/keywords/rotation","display_name":"Rotation (mathematics)","score":0.4778701663017273},{"id":"https://openalex.org/keywords/focus","display_name":"Focus (optics)","score":0.46712571382522583},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.46676725149154663},{"id":"https://openalex.org/keywords/reflection-symmetry","display_name":"Reflection symmetry","score":0.4269610345363617},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3451656401157379},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3208630681037903},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2743373513221741},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.19965294003486633},{"id":"https://openalex.org/keywords/art","display_name":"Art","score":0.12173309922218323},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.10647720098495483},{"id":"https://openalex.org/keywords/art-history","display_name":"Art history","score":0.09271740913391113}],"concepts":[{"id":"https://openalex.org/C29001434","wikidata":"https://www.wikidata.org/wiki/Q8084","display_name":"Trigonometry","level":2,"score":0.7090801000595093},{"id":"https://openalex.org/C170383800","wikidata":"https://www.wikidata.org/wiki/Q183272","display_name":"Frieze","level":2,"score":0.5935475826263428},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.5353202223777771},{"id":"https://openalex.org/C74050887","wikidata":"https://www.wikidata.org/wiki/Q848368","display_name":"Rotation (mathematics)","level":2,"score":0.4778701663017273},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.46712571382522583},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.46676725149154663},{"id":"https://openalex.org/C133978748","wikidata":"https://www.wikidata.org/wiki/Q15955882","display_name":"Reflection symmetry","level":2,"score":0.4269610345363617},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3451656401157379},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3208630681037903},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2743373513221741},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.19965294003486633},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.12173309922218323},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.10647720098495483},{"id":"https://openalex.org/C52119013","wikidata":"https://www.wikidata.org/wiki/Q50637","display_name":"Art history","level":1,"score":0.09271740913391113}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/msp.2019.2907375","is_oa":false,"landing_page_url":"https://doi.org/10.1109/msp.2019.2907375","pdf_url":null,"source":{"id":"https://openalex.org/S120977877","display_name":"IEEE Signal Processing Magazine","issn_l":"1053-5888","issn":["1053-5888","1558-0792"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Signal Processing Magazine","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.6700000166893005,"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W123426918","https://openalex.org/W885276044","https://openalex.org/W1575198668","https://openalex.org/W1767325994","https://openalex.org/W2077071081","https://openalex.org/W2141710021","https://openalex.org/W2171671031","https://openalex.org/W2478884216","https://openalex.org/W2767223377"],"related_works":["https://openalex.org/W2105860741","https://openalex.org/W649143900","https://openalex.org/W4287206313","https://openalex.org/W3163798933","https://openalex.org/W2545569975","https://openalex.org/W4220988720","https://openalex.org/W3168648756","https://openalex.org/W2128654298","https://openalex.org/W2012018667","https://openalex.org/W2142080577"],"abstract_inverted_index":{"In":[0,49],"this":[1,24,84],"article,":[2],"we":[3,51],"continue":[4],"to":[5,75,86],"study":[6],"the":[7,20,87],"mystery":[8,34],"curve,":[9],"which":[10],"was":[11],"originally":[12],"named":[13],"by":[14],"Farris":[15],"[1]":[16],"and":[17,60,82],"discussed":[18],"in":[19,27,46],"first":[21],"part":[22],"of":[23,65],"two-part":[25],"article":[26],"<i>IEEE":[28],"Signal":[29],"Processing":[30],"Magazine</i>":[31],"[2].":[32],"The":[33],"curve":[35],"has":[36],"an":[37],"<i>N</i>-fold":[38],"property":[39],"with":[40,79],"additional":[41],"local":[42],"symmetry":[43],"as":[44],"shown":[45],"Figure":[47],"1.":[48],"particular,":[50],"focus":[52],"on":[53],"symmetric":[54],"patterns,":[55],"including":[56],"translation,":[57],"reflection,":[58],"rotation,":[59],"glide":[61],"reflection.":[62],"This":[63],"class":[64],"patterns":[66],"is":[67],"called":[68],"a":[69],"<i>frieze":[70],"group</i>.":[71],"We":[72],"show":[73],"how":[74],"construct":[76],"frieze":[77],"groups":[78],"trigonometric":[80],"functions":[81],"extend":[83],"method":[85],"mystery-curve":[88],"design.":[89]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
