{"id":"https://openalex.org/W4389374958","doi":"https://doi.org/10.1145/3610538.3614620","title":"Discrete Laplacians for General Polygonal and Polyhedral Meshes","display_name":"Discrete Laplacians for General Polygonal and Polyhedral Meshes","publication_year":2023,"publication_date":"2023-12-06","ids":{"openalex":"https://openalex.org/W4389374958","doi":"https://doi.org/10.1145/3610538.3614620"},"language":"en","primary_location":{"id":"doi:10.1145/3610538.3614620","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3610538.3614620","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIGGRAPH Asia 2023 Courses","raw_type":"proceedings-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/A5059155303","display_name":"A. Bunge","orcid":"https://orcid.org/0000-0003-0295-5727"},"institutions":[{"id":"https://openalex.org/I200332995","display_name":"TU Dortmund University","ror":"https://ror.org/01k97gp34","country_code":"DE","type":"education","lineage":["https://openalex.org/I200332995"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Astrid Bunge","raw_affiliation_strings":["TU Dortmund University, Germany"],"affiliations":[{"raw_affiliation_string":"TU Dortmund University, Germany","institution_ids":["https://openalex.org/I200332995"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072827199","display_name":"Marc Alexa","orcid":"https://orcid.org/0000-0002-9854-8466"},"institutions":[{"id":"https://openalex.org/I4577782","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40","country_code":"DE","type":"education","lineage":["https://openalex.org/I4577782"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Marc Alexa","raw_affiliation_strings":["TU Berlin, Germany"],"affiliations":[{"raw_affiliation_string":"TU Berlin, Germany","institution_ids":["https://openalex.org/I4577782"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5033450578","display_name":"Mario Botsch","orcid":"https://orcid.org/0000-0001-9954-120X"},"institutions":[{"id":"https://openalex.org/I200332995","display_name":"TU Dortmund University","ror":"https://ror.org/01k97gp34","country_code":"DE","type":"education","lineage":["https://openalex.org/I200332995"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Mario Botsch","raw_affiliation_strings":["TU Dortmund University, Germany"],"affiliations":[{"raw_affiliation_string":"TU Dortmund University, Germany","institution_ids":["https://openalex.org/I200332995"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5059155303"],"corresponding_institution_ids":["https://openalex.org/I200332995"],"apc_list":null,"apc_paid":null,"fwci":0.2165,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.49632353,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"49"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10719","display_name":"3D Shape Modeling and Analysis","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/T10719","display_name":"3D Shape Modeling and Analysis","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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9998000264167786,"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/T10481","display_name":"Computer Graphics and Visualization Techniques","score":0.9997000098228455,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/polygon-mesh","display_name":"Polygon mesh","score":0.8363048434257507},{"id":"https://openalex.org/keywords/polyhedron","display_name":"Polyhedron","score":0.6643442511558533},{"id":"https://openalex.org/keywords/computer-graphics","display_name":"Computer graphics","score":0.6477457284927368},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5513104796409607},{"id":"https://openalex.org/keywords/geometry-processing","display_name":"Geometry processing","score":0.5367587208747864},{"id":"https://openalex.org/keywords/tessellation","display_name":"Tessellation (computer graphics)","score":0.5357104539871216},{"id":"https://openalex.org/keywords/volume-mesh","display_name":"Volume mesh","score":0.5115159749984741},{"id":"https://openalex.org/keywords/convex-geometry","display_name":"Convex geometry","score":0.49668508768081665},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.4804232120513916},{"id":"https://openalex.org/keywords/laplace-operator","display_name":"Laplace operator","score":0.46185338497161865},{"id":"https://openalex.org/keywords/computer-graphics","display_name":"Computer graphics (images)","score":0.46060970425605774},{"id":"https://openalex.org/keywords/surface","display_name":"Surface (topology)","score":0.4391050934791565},{"id":"https://openalex.org/keywords/graphics","display_name":"Graphics","score":0.4265369176864624},{"id":"https://openalex.org/keywords/computational-geometry","display_name":"Computational geometry","score":0.4262021780014038},{"id":"https://openalex.org/keywords/hexahedron","display_name":"Hexahedron","score":0.42374980449676514},{"id":"https://openalex.org/keywords/quadrilateral","display_name":"Quadrilateral","score":0.41214099526405334},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.40890681743621826},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.33328956365585327},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2633906602859497},{"id":"https://openalex.org/keywords/mesh-generation","display_name":"Mesh generation","score":0.2630329430103302},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.26176580786705017},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.15814068913459778},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1540164053440094},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.12557893991470337},{"id":"https://openalex.org/keywords/convex-analysis","display_name":"Convex analysis","score":0.1035890281200409}],"concepts":[{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.8363048434257507},{"id":"https://openalex.org/C54829058","wikidata":"https://www.wikidata.org/wiki/Q172937","display_name":"Polyhedron","level":2,"score":0.6643442511558533},{"id":"https://openalex.org/C77660652","wikidata":"https://www.wikidata.org/wiki/Q150971","display_name":"Computer graphics","level":2,"score":0.6477457284927368},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5513104796409607},{"id":"https://openalex.org/C2779521785","wikidata":"https://www.wikidata.org/wiki/Q5535529","display_name":"Geometry processing","level":3,"score":0.5367587208747864},{"id":"https://openalex.org/C43817857","wikidata":"https://www.wikidata.org/wiki/Q9357547","display_name":"Tessellation (computer graphics)","level":2,"score":0.5357104539871216},{"id":"https://openalex.org/C170589453","wikidata":"https://www.wikidata.org/wiki/Q7940896","display_name":"Volume mesh","level":4,"score":0.5115159749984741},{"id":"https://openalex.org/C110202963","wikidata":"https://www.wikidata.org/wiki/Q1783542","display_name":"Convex geometry","level":5,"score":0.49668508768081665},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.4804232120513916},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.46185338497161865},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.46060970425605774},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.4391050934791565},{"id":"https://openalex.org/C21442007","wikidata":"https://www.wikidata.org/wiki/Q1027879","display_name":"Graphics","level":2,"score":0.4265369176864624},{"id":"https://openalex.org/C29123130","wikidata":"https://www.wikidata.org/wiki/Q874709","display_name":"Computational geometry","level":2,"score":0.4262021780014038},{"id":"https://openalex.org/C22411076","wikidata":"https://www.wikidata.org/wiki/Q668113","display_name":"Hexahedron","level":3,"score":0.42374980449676514},{"id":"https://openalex.org/C151756577","wikidata":"https://www.wikidata.org/wiki/Q36810","display_name":"Quadrilateral","level":3,"score":0.41214099526405334},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.40890681743621826},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.33328956365585327},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2633906602859497},{"id":"https://openalex.org/C181145010","wikidata":"https://www.wikidata.org/wiki/Q4418033","display_name":"Mesh generation","level":3,"score":0.2630329430103302},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.26176580786705017},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.15814068913459778},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1540164053440094},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.12557893991470337},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.1035890281200409},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3610538.3614620","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3610538.3614620","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIGGRAPH Asia 2023 Courses","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","score":0.75,"display_name":"Sustainable cities and communities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":55,"referenced_works":["https://openalex.org/W41827812","https://openalex.org/W50490584","https://openalex.org/W69932122","https://openalex.org/W614105475","https://openalex.org/W1522382323","https://openalex.org/W1577039718","https://openalex.org/W1594387031","https://openalex.org/W1626653188","https://openalex.org/W1763606621","https://openalex.org/W1863866458","https://openalex.org/W1949248870","https://openalex.org/W1965816824","https://openalex.org/W1968754888","https://openalex.org/W1974739208","https://openalex.org/W1974956622","https://openalex.org/W1980460750","https://openalex.org/W1983124639","https://openalex.org/W1992923859","https://openalex.org/W2002757536","https://openalex.org/W2008531655","https://openalex.org/W2013149166","https://openalex.org/W2029853988","https://openalex.org/W2045686441","https://openalex.org/W2083509580","https://openalex.org/W2083561088","https://openalex.org/W2089024363","https://openalex.org/W2099534371","https://openalex.org/W2101501899","https://openalex.org/W2107576752","https://openalex.org/W2122519246","https://openalex.org/W2125537373","https://openalex.org/W2138486270","https://openalex.org/W2148729533","https://openalex.org/W2160692760","https://openalex.org/W2167745263","https://openalex.org/W2328294984","https://openalex.org/W2346992053","https://openalex.org/W2465633026","https://openalex.org/W2587288333","https://openalex.org/W2591803957","https://openalex.org/W2796985792","https://openalex.org/W2890742232","https://openalex.org/W2903195470","https://openalex.org/W2914576553","https://openalex.org/W2961356875","https://openalex.org/W3023742359","https://openalex.org/W3048965342","https://openalex.org/W3125178117","https://openalex.org/W3136375062","https://openalex.org/W3138464846","https://openalex.org/W3196144308","https://openalex.org/W4220743987","https://openalex.org/W4286611178","https://openalex.org/W4378083639","https://openalex.org/W4394666970"],"related_works":["https://openalex.org/W33112622","https://openalex.org/W2171421712","https://openalex.org/W2476914220","https://openalex.org/W2008571824","https://openalex.org/W4236665358","https://openalex.org/W2381018316","https://openalex.org/W2069605750","https://openalex.org/W2048163432","https://openalex.org/W2121691276","https://openalex.org/W2109819805"],"abstract_inverted_index":{"The":[0],"Laplace-Beltrami":[1],"operator":[2],"is":[3,28],"one":[4],"of":[5,55,94,121],"the":[6,53,56,68,109,118],"essential":[7],"tools":[8],"in":[9,33,59,102,139],"geometric":[10],"processing.":[11],"It":[12],"allows":[13,84],"us":[14],"to":[15,43,66,79,88],"solve":[16],"numerous":[17],"partial":[18],"differential":[19,125],"equations":[20],"on":[21,127],"discrete":[22],"surface":[23],"and":[24,71,76,86,100,114,130,132,137],"volume":[25],"meshes,":[26],"which":[27,50,96,107],"a":[29,91],"fundamental":[30],"building":[31],"block":[32],"many":[34],"computer":[35,141],"graphics":[36,142],"applications.":[37,143],"Discrete":[38],"Laplacians":[39],"are":[40,97],"typically":[41],"limited":[42],"standard":[44],"elements":[45,95],"like":[46],"triangles":[47],"or":[48],"quadrilaterals,":[49],"severely":[51],"constrains":[52],"tessellation":[54],"mesh.":[57],"But":[58],"recent":[60],"years,":[61],"several":[62],"approaches":[63],"were":[64],"able":[65],"generalize":[67],"Laplace":[69],"Beltrami":[70],"its":[72],"closely":[73],"related":[74],"gradient":[75],"divergence":[77],"operators":[78,126],"more":[80],"general":[81],"meshes.":[82],"This":[83,105],"artists":[85],"engineers":[87],"work":[89],"with":[90],"wider":[92],"range":[93],"sometimes":[98],"required":[99],"beneficial":[101],"their":[103,134],"field.":[104],"course,":[106],"extends":[108],"state-of-the-art":[110],"report":[111],"by":[112],"Bunge":[113],"Botsch":[115],"[2023],":[116],"discusses":[117],"different":[119],"constructions":[120],"these":[122],"three":[123],"ubiquitous":[124],"arbitrary":[128],"polygons":[129],"polyhedra":[131],"analyzes":[133],"individual":[135],"advantages":[136],"properties":[138],"common":[140]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}