{"id":"https://openalex.org/W4386601594","doi":"https://doi.org/10.3390/sym15091738","title":"Adaptive Approximate Implicitization of Planar Parametric Curves via Asymmetric Gradient Constraints","display_name":"Adaptive Approximate Implicitization of Planar Parametric Curves via Asymmetric Gradient Constraints","publication_year":2023,"publication_date":"2023-09-11","ids":{"openalex":"https://openalex.org/W4386601594","doi":"https://doi.org/10.3390/sym15091738"},"language":"en","primary_location":{"id":"doi:10.3390/sym15091738","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15091738","pdf_url":"https://www.mdpi.com/2073-8994/15/9/1738/pdf?version=1694431811","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/15/9/1738/pdf?version=1694431811","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5018791285","display_name":"Minghao Guo","orcid":"https://orcid.org/0000-0003-3408-4997"},"institutions":[{"id":"https://openalex.org/I4385474403","display_name":"Changchun University of Technology","ror":"https://ror.org/052pakb34","country_code":"CN","type":"education","lineage":["https://openalex.org/I4385474403"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Minghao Guo","raw_affiliation_strings":["School of Mathematics and Statistics, Changchun University of Technology, Changchun 130000, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Changchun University of Technology, Changchun 130000, China","institution_ids":["https://openalex.org/I4385474403"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100462451","display_name":"Yan Gao","orcid":"https://orcid.org/0000-0002-3295-5755"},"institutions":[{"id":"https://openalex.org/I184983240","display_name":"Northeast Normal University","ror":"https://ror.org/02rkvz144","country_code":"CN","type":"education","lineage":["https://openalex.org/I184983240"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yan Gao","raw_affiliation_strings":["Beihu Mingda Experimental School, Northeast Normal University, Changchun 130000, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Beihu Mingda Experimental School, Northeast Normal University, Changchun 130000, China","institution_ids":["https://openalex.org/I184983240"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5018791285"],"corresponding_institution_ids":["https://openalex.org/I4385474403"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":0.1623,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.38187227,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"15","issue":"9","first_page":"1738","last_page":"1738"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9998999834060669,"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"}},{"id":"https://openalex.org/T10719","display_name":"3D Shape Modeling and Analysis","score":0.9950000047683716,"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"}},{"id":"https://openalex.org/T10531","display_name":"Advanced Vision and Imaging","score":0.9940999746322632,"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/mathematics","display_name":"Mathematics","score":0.6703596115112305},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.6418184041976929},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.6332117915153503},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.6132426261901855},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.587721049785614},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.5327430367469788},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.45992618799209595},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.4578072726726532},{"id":"https://openalex.org/keywords/parametric-equation","display_name":"Parametric equation","score":0.43850433826446533},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.39827823638916016},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.33276107907295227},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2822529971599579},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1605915129184723},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.147813618183136},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.10333949327468872}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6703596115112305},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.6418184041976929},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.6332117915153503},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.6132426261901855},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.587721049785614},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.5327430367469788},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45992618799209595},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.4578072726726532},{"id":"https://openalex.org/C99636146","wikidata":"https://www.wikidata.org/wiki/Q35889","display_name":"Parametric equation","level":2,"score":0.43850433826446533},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.39827823638916016},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.33276107907295227},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2822529971599579},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1605915129184723},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.147813618183136},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.10333949327468872},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","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},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/sym15091738","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15091738","pdf_url":"https://www.mdpi.com/2073-8994/15/9/1738/pdf?version=1694431811","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:31107467ec0b4696ab0a767b9dce04a6","is_oa":false,"landing_page_url":"https://doaj.org/article/31107467ec0b4696ab0a767b9dce04a6","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 15, Iss 9, p 1738 (2023)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/sym15091738","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15091738","pdf_url":"https://www.mdpi.com/2073-8994/15/9/1738/pdf?version=1694431811","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4386601594.pdf"},"referenced_works_count":21,"referenced_works":["https://openalex.org/W1583349148","https://openalex.org/W1622880316","https://openalex.org/W1980921235","https://openalex.org/W1994576922","https://openalex.org/W2050873481","https://openalex.org/W2093473068","https://openalex.org/W2616292232","https://openalex.org/W2896333478","https://openalex.org/W2923467384","https://openalex.org/W2945220839","https://openalex.org/W3025270217","https://openalex.org/W3101303322","https://openalex.org/W3121699086","https://openalex.org/W3130397378","https://openalex.org/W3132285960","https://openalex.org/W3146255791","https://openalex.org/W4321499015","https://openalex.org/W6623724720","https://openalex.org/W6758864021","https://openalex.org/W6804465012","https://openalex.org/W6941474586"],"related_works":["https://openalex.org/W4206327962","https://openalex.org/W2010009304","https://openalex.org/W1996851061","https://openalex.org/W3021694725","https://openalex.org/W2025195393","https://openalex.org/W2940695648","https://openalex.org/W1973684381","https://openalex.org/W2096304864","https://openalex.org/W1987955278","https://openalex.org/W2274305706"],"abstract_inverted_index":{"Converting":[0],"a":[1,15,40,53],"parametric":[2],"curve":[3],"into":[4],"the":[5,32,58,89,95,98,104,109,119,124,130],"implicit":[6,42,91,110],"form,":[7],"which":[8,68,87],"is":[9,106,114],"called":[10],"implicitization,":[11],"has":[12,47],"always":[13],"been":[14],"popular":[16],"but":[17],"challenging":[18],"problem":[19],"in":[20,118],"geometric":[21,36],"modeling":[22],"and":[23,38,65,83,132],"related":[24],"applications.":[25],"However,":[26],"existing":[27],"methods":[28],"mostly":[29],"suffer":[30],"from":[31],"problems":[33],"of":[34,78,97,123,135],"maintaining":[35],"features":[37],"choosing":[39],"reasonable":[41],"degree.":[43],"The":[44],"present":[45],"paper":[46],"two":[48,75],"contributions.":[49],"We":[50,72],"first":[51],"introduce":[52],"new":[54],"regularization":[55],"constraint":[56],"(called":[57],"asymmetric":[59,99,120],"gradient":[60,100,121],"constraint)":[61],"for":[62,81],"both":[63],"polynomial":[64,82],"non-polynomial":[66,84],"curves,":[67],"efficiently":[69],"possesses":[70],"shape-preserving.":[71],"then":[73],"propose":[74],"adaptive":[76],"algorithms":[77],"approximate":[79],"implicitization":[80],"curves":[85],"respectively,":[86],"find":[88],"\u201coptimal\u201d":[90],"degree":[92],"based":[93],"on":[94],"behavior":[96],"constraint.":[101],"More":[102],"precisely,":[103],"idea":[105],"gradually":[107],"increasing":[108],"degree,":[111],"until":[112],"there":[113],"no":[115],"obvious":[116],"improvement":[117],"loss":[122],"outputs.":[125],"Experimental":[126],"results":[127],"have":[128],"shown":[129],"effectiveness":[131],"high":[133],"quality":[134],"our":[136],"proposed":[137],"methods.":[138]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}