{"id":"https://openalex.org/W4280506625","doi":"https://doi.org/10.1007/s41095-021-0257-1","title":"Constructing self-supporting surfaces with planar quadrilateral elements","display_name":"Constructing self-supporting surfaces with planar quadrilateral elements","publication_year":2022,"publication_date":"2022-05-11","ids":{"openalex":"https://openalex.org/W4280506625","doi":"https://doi.org/10.1007/s41095-021-0257-1"},"language":"en","primary_location":{"id":"doi:10.1007/s41095-021-0257-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s41095-021-0257-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s41095-021-0257-1.pdf","source":{"id":"https://openalex.org/S2487656537","display_name":"Computational Visual Media","issn_l":"2096-0433","issn":["2096-0433","2096-0662"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["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":"Computational Visual Media","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://link.springer.com/content/pdf/10.1007/s41095-021-0257-1.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100462127","display_name":"Long Ma","orcid":"https://orcid.org/0000-0002-3656-8576"},"institutions":[{"id":"https://openalex.org/I154099455","display_name":"Shandong University","ror":"https://ror.org/0207yh398","country_code":"CN","type":"education","lineage":["https://openalex.org/I154099455"]},{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]}],"countries":["CN","SG"],"is_corresponding":false,"raw_author_name":"Long Ma","raw_affiliation_strings":["School of Software, Shandong University, Jinan 250101, China; School of Computer Science and Engineering, Nanyang Technological University, Singapore 639798, Singapore","School of Computer Science and Engineering, Nanyang Technological University, Singapore, Singapore","School of Software, Shandong University, Jinan, China"],"affiliations":[{"raw_affiliation_string":"School of Software, Shandong University, Jinan 250101, China; School of Computer Science and Engineering, Nanyang Technological University, Singapore 639798, Singapore","institution_ids":["https://openalex.org/I172675005"]},{"raw_affiliation_string":"School of Computer Science and Engineering, Nanyang Technological University, Singapore, Singapore","institution_ids":["https://openalex.org/I172675005"]},{"raw_affiliation_string":"School of Software, Shandong University, Jinan, China","institution_ids":["https://openalex.org/I154099455"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5031142026","display_name":"Sidan Yao","orcid":"https://orcid.org/0000-0002-4911-9972"},"institutions":[{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Sidan Yao","raw_affiliation_strings":["School of Computer Science and Engineering, Nanyang Technological University, Singapore 639798, Singapore","School of Computer Science and Engineering, Nanyang Technological University, Singapore, Singapore"],"affiliations":[{"raw_affiliation_string":"School of Computer Science and Engineering, Nanyang Technological University, Singapore 639798, Singapore","institution_ids":["https://openalex.org/I172675005"]},{"raw_affiliation_string":"School of Computer Science and Engineering, Nanyang Technological University, Singapore, Singapore","institution_ids":["https://openalex.org/I172675005"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039953512","display_name":"Jianmin Zheng","orcid":"https://orcid.org/0000-0002-5062-6226"},"institutions":[{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Jianmin Zheng","raw_affiliation_strings":["School of Computer Science and Engineering, Nanyang Technological University, Singapore 639798, Singapore","School of Computer Science and Engineering, Nanyang Technological University, Singapore, Singapore"],"affiliations":[{"raw_affiliation_string":"School of Computer Science and Engineering, Nanyang Technological University, Singapore 639798, Singapore","institution_ids":["https://openalex.org/I172675005"]},{"raw_affiliation_string":"School of Computer Science and Engineering, Nanyang Technological University, Singapore, Singapore","institution_ids":["https://openalex.org/I172675005"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063685742","display_name":"Yang Liu","orcid":"https://orcid.org/0000-0002-3768-6654"},"institutions":[{"id":"https://openalex.org/I4210113369","display_name":"Microsoft Research Asia (China)","ror":"https://ror.org/0300m5276","country_code":"CN","type":"company","lineage":["https://openalex.org/I1290206253","https://openalex.org/I4210113369"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yang Liu","raw_affiliation_strings":["Internet Graphics Group, Microsoft Research Asia, Beijing 100080, China","Internet Graphics Group, Microsoft Research Asia, Beijing, China"],"affiliations":[{"raw_affiliation_string":"Internet Graphics Group, Microsoft Research Asia, Beijing 100080, China","institution_ids":["https://openalex.org/I4210113369"]},{"raw_affiliation_string":"Internet Graphics Group, Microsoft Research Asia, Beijing, China","institution_ids":["https://openalex.org/I4210113369"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038088018","display_name":"Yuanfeng Zhou","orcid":"https://orcid.org/0000-0001-6950-3261"},"institutions":[{"id":"https://openalex.org/I154099455","display_name":"Shandong University","ror":"https://ror.org/0207yh398","country_code":"CN","type":"education","lineage":["https://openalex.org/I154099455"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yuanfeng Zhou","raw_affiliation_strings":["School of Software, Shandong University, Jinan 250101, China","School of Software, Shandong University, Jinan, China"],"affiliations":[{"raw_affiliation_string":"School of Software, Shandong University, Jinan 250101, China","institution_ids":["https://openalex.org/I154099455"]},{"raw_affiliation_string":"School of Software, Shandong University, Jinan, China","institution_ids":["https://openalex.org/I154099455"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062030077","display_name":"Shiqing Xin","orcid":"https://orcid.org/0000-0001-8452-8723"},"institutions":[{"id":"https://openalex.org/I80143920","display_name":"Shandong University of Science and Technology","ror":"https://ror.org/04gtjhw98","country_code":"CN","type":"education","lineage":["https://openalex.org/I80143920"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shi-Qing Xin","raw_affiliation_strings":["School of Computer Science and Technology, Shandong University, Qingdao 266237, China","School of Computer Science and Technology, Shandong University, Qingdao, China"],"affiliations":[{"raw_affiliation_string":"School of Computer Science and Technology, Shandong University, Qingdao 266237, China","institution_ids":["https://openalex.org/I80143920"]},{"raw_affiliation_string":"School of Computer Science and Technology, Shandong University, Qingdao, China","institution_ids":["https://openalex.org/I80143920"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100389169","display_name":"Ying He","orcid":"https://orcid.org/0000-0002-6749-4485"},"institutions":[{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]}],"countries":["SG"],"is_corresponding":true,"raw_author_name":"Ying He","raw_affiliation_strings":["School of Computer Science and Engineering, Nanyang Technological University, Singapore 639798, Singapore","School of Computer Science and Engineering, Nanyang Technological University, Singapore, Singapore"],"affiliations":[{"raw_affiliation_string":"School of Computer Science and Engineering, Nanyang Technological University, Singapore 639798, Singapore","institution_ids":["https://openalex.org/I172675005"]},{"raw_affiliation_string":"School of Computer Science and Engineering, Nanyang Technological University, Singapore, Singapore","institution_ids":["https://openalex.org/I172675005"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":7,"corresponding_author_ids":["https://openalex.org/A5100389169"],"corresponding_institution_ids":["https://openalex.org/I172675005"],"apc_list":null,"apc_paid":null,"fwci":1.4682,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.87067723,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"8","issue":"4","first_page":"571","last_page":"583"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9993000030517578,"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":0.9993000030517578,"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/T11737","display_name":"Advanced Materials and Mechanics","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical 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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9962000250816345,"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/quadrilateral","display_name":"Quadrilateral","score":0.765945553779602},{"id":"https://openalex.org/keywords/principal-curvature","display_name":"Principal curvature","score":0.7454978823661804},{"id":"https://openalex.org/keywords/curvature","display_name":"Curvature","score":0.59477698802948},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5881071090698242},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.5701202750205994},{"id":"https://openalex.org/keywords/polygon-mesh","display_name":"Polygon mesh","score":0.500042200088501},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.486970990896225},{"id":"https://openalex.org/keywords/gravitational-singularity","display_name":"Gravitational singularity","score":0.4670749008655548},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.46191146969795227},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.4541094899177551},{"id":"https://openalex.org/keywords/surface","display_name":"Surface (topology)","score":0.4180074632167816},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.30424028635025024},{"id":"https://openalex.org/keywords/mean-curvature","display_name":"Mean curvature","score":0.24792572855949402},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2463381588459015},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.24002975225448608},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.13740426301956177},{"id":"https://openalex.org/keywords/computer-graphics","display_name":"Computer graphics (images)","score":0.12236684560775757},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07581698894500732}],"concepts":[{"id":"https://openalex.org/C151756577","wikidata":"https://www.wikidata.org/wiki/Q36810","display_name":"Quadrilateral","level":3,"score":0.765945553779602},{"id":"https://openalex.org/C16977076","wikidata":"https://www.wikidata.org/wiki/Q1589551","display_name":"Principal curvature","level":4,"score":0.7454978823661804},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.59477698802948},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5881071090698242},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.5701202750205994},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.500042200088501},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.486970990896225},{"id":"https://openalex.org/C12843","wikidata":"https://www.wikidata.org/wiki/Q201721","display_name":"Gravitational singularity","level":2,"score":0.4670749008655548},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.46191146969795227},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.4541094899177551},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.4180074632167816},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.30424028635025024},{"id":"https://openalex.org/C175017881","wikidata":"https://www.wikidata.org/wiki/Q1318998","display_name":"Mean curvature","level":3,"score":0.24792572855949402},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2463381588459015},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.24002975225448608},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.13740426301956177},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.12236684560775757},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07581698894500732},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s41095-021-0257-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s41095-021-0257-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s41095-021-0257-1.pdf","source":{"id":"https://openalex.org/S2487656537","display_name":"Computational Visual Media","issn_l":"2096-0433","issn":["2096-0433","2096-0662"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["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":"Computational Visual Media","raw_type":"journal-article"},{"id":"pmh:oai:dr.ntu.edu.sg:10356/160723","is_oa":true,"landing_page_url":"https://hdl.handle.net/10356/160723","pdf_url":null,"source":{"id":"https://openalex.org/S4306402609","display_name":"DR-NTU (Nanyang Technological University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I172675005","host_organization_name":"Nanyang Technological University","host_organization_lineage":["https://openalex.org/I172675005"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Journal Article"}],"best_oa_location":{"id":"doi:10.1007/s41095-021-0257-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s41095-021-0257-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s41095-021-0257-1.pdf","source":{"id":"https://openalex.org/S2487656537","display_name":"Computational Visual Media","issn_l":"2096-0433","issn":["2096-0433","2096-0662"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["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":"Computational Visual Media","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.7200000286102295,"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11"}],"awards":[{"id":"https://openalex.org/G1650911592","display_name":null,"funder_award_id":"62172257","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3317480652","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G36522386","display_name":null,"funder_award_id":"61802228","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G391238517","display_name":null,"funder_award_id":", and","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5475301337","display_name":null,"funder_award_id":"18022","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5760752404","display_name":null,"funder_award_id":"Projects","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5994120800","display_name":null,"funder_award_id":"Natural","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4280506625.pdf","grobid_xml":"https://content.openalex.org/works/W4280506625.grobid-xml"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W1485970454","https://openalex.org/W1626653188","https://openalex.org/W2010328065","https://openalex.org/W2015774454","https://openalex.org/W2016352584","https://openalex.org/W2018964608","https://openalex.org/W2036687457","https://openalex.org/W2051434435","https://openalex.org/W2052099027","https://openalex.org/W2055410695","https://openalex.org/W2091632568","https://openalex.org/W2125955829","https://openalex.org/W2981850640","https://openalex.org/W3003161728","https://openalex.org/W4211099560","https://openalex.org/W4232115556","https://openalex.org/W4234663939","https://openalex.org/W4237754737","https://openalex.org/W4300866069"],"related_works":["https://openalex.org/W2050042766","https://openalex.org/W2051741413","https://openalex.org/W2888009230","https://openalex.org/W2579280880","https://openalex.org/W3182680370","https://openalex.org/W278698820","https://openalex.org/W2093793201","https://openalex.org/W2149051171","https://openalex.org/W3215472701","https://openalex.org/W4223615835"],"abstract_inverted_index":{"We":[0],"present":[1],"a":[2,19,23,39,88,97,116,130],"simple":[3],"yet":[4],"effective":[5],"method":[6,139],"for":[7],"constructing":[8],"3D":[9],"self-supporting":[10,24,161],"surfaces":[11,157],"with":[12,18,82],"planar":[13,131],"quadrilateral":[14,132],"(PQ)":[15],"elements.":[16],"Starting":[17],"triangular":[20,36,105],"discretization":[21],"of":[22,34,63,75,99,154],"surface,":[25],"we":[26,53,66,86,107,128],"first":[27],"compute":[28,87],"the":[29,55,61,93,103,121,152,155],"principal":[30,56,76,94,112,123],"curvatures":[31],"and":[32,124,143,158],"directions":[33,95],"each":[35,80],"face":[37,81],"using":[38],"new":[40],"discrete":[41],"differential":[42],"geometry":[43,153],"approach,":[44],"yielding":[45],"more":[46],"accurate":[47],"results":[48,135],"than":[49],"existing":[50],"methods.":[51],"Then,":[52],"smooth":[54],"direction":[57,126],"field":[58],"to":[59,120],"reduce":[60],"number":[62],"singularities.":[64],"Next,":[65],"partition":[67],"all":[68],"faces":[69],"into":[70,96],"two":[71],"groups":[72],"in":[73],"terms":[74],"curvature":[77,84],"difference.":[78],"For":[79,102],"small":[83],"difference,":[85],"stretch":[89],"matrix":[90],"that":[91,137,149],"turns":[92],"pair":[98],"conjugate":[100,125],"directions.":[101,113],"remaining":[104],"faces,":[106],"simply":[108],"keep":[109],"their":[110,160],"smoothed":[111],"Finally,":[114],"applying":[115],"mixed-integer":[117],"programming":[118],"solver":[119],"mixed":[122],"field,":[127],"obtain":[129],"mesh.":[133],"Experimental":[134],"show":[136],"our":[138],"is":[140],"computationally":[141],"efficient":[142],"can":[144],"yield":[145],"high-quality":[146],"PQ":[147],"meshes":[148],"well":[150],"approximate":[151],"input":[156],"maintain":[159],"properties.":[162]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":2}],"updated_date":"2026-04-16T08:26:57.006410","created_date":"2025-10-10T00:00:00"}
